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14024823 | Methylenetetrahydrofolate—tRNA-(uracil-5-)-methyltransferase | In enzymology, a methylenetetrahydrofolate-tRNA-(uracil-5-)-methyltransferase (EC 2.1.1.74) is an enzyme that catalyzes the chemical reaction
5,10-methylenetetrahydrofolate + tRNA containing uridine at position 54 + FADH2 formula_0 tetrahydrofolate + tRNA containing ribothymidine at position 54 + FAD
The 3 substrates of this enzyme are 5,10-methylenetetrahydrofolate, tRNA containing uridine at position 54, and FADH2, whereas its 3 products are tetrahydrofolate, tRNA containing ribothymidine at position 54, and FAD.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is 5,10-methylenetetrahydrofolate:tRNA (uracil-5-)-methyl-transferase. Other names in common use include (FADH2-oxidizing), folate-dependent ribothymidyl synthase, methylenetetrahydrofolate-transfer ribonucleate uracil, 5-methyltransferase, 5,10-methylenetetrahydrofolate:tRNA-UPsiC, and (uracil-5-)-methyl-transferase.
References.
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| https://en.wikipedia.org/wiki?curid=14024823 |
14024837 | Methylquercetagetin 6-O-methyltransferase | In enzymology, a methylquercetagetin 6-O-methyltransferase (EC 2.1.1.84) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + 5,6,3',4'-tetrahydroxy-3,7-dimethoxyflavone formula_0 S-adenosyl-L-homocysteine + 5,3',4'-trihydroxy-3,6,7-trimethoxyflavone
Thus, the two substrates of this enzyme are S-adenosyl methionine and 5,6,3',4'-tetrahydroxy-3,7-dimethoxyflavone, whereas its two products are S-adenosylhomocysteine and 5,3',4'-trihydroxy-3,6,7-trimethoxyflavone.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:3',4',5,6-tetrahydroxy-3,7-dimethoxyflavone 6-O-methyltransferase. Other names in common use include flavonol 6-O-methyltransferase, flavonol 6-methyltransferase, 6-OMT, S-adenosyl-L-methionine:3',4',5,6-tetrahydroxy-3,7-dimethoxyflavone, and 6-O-methyltransferase.
References.
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| https://en.wikipedia.org/wiki?curid=14024837 |
14024846 | MRNA (2'-O-methyladenosine-N6-)-methyltransferase | Enzyme
In enzymology, a mRNA (2'-"O"-methyladenosine-"N"6-)-methyltransferase (EC 2.1.1.62) is an enzyme that catalyzes the chemical reaction
"S"-adenosyl-L-methionine + m7G(5')pppAm formula_0 "S"-adenosyl-L-homocysteine + m7G(5')pppm6Am (mRNA containing an "N"6,2'-"O"-dimethyladenosine cap)
Thus, the two substrates of this enzyme are "S"-adenosyl methionine and m7G(5')pppAm, whereas its two products are "S"-adenosylhomocysteine and m7G(5')pppm6Am (mRNA containing an "N"6,2'-"O"-dimethyladenosine cap).
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is "S"-adenosyl-L-methionine:mRNA (2'-"O"-methyladenosine-"N"6-)-methyltransferase. Other names in common use include messenger ribonucleate 2'-O-methyladenosine NG-methyltransferase, S-adenosyl-L-methionine:mRNA, and (2'-O-methyladenosine-6-N-)-methyltransferase.
References.
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| https://en.wikipedia.org/wiki?curid=14024846 |
14024861 | MRNA (guanine-N7-)-methyltransferase | Enzyme
In enzymology, a mRNA (guanine-N7-)-methyltransferase also known as mRNA cap guanine-N7 methyltransferase is an enzyme that catalyzes the chemical reaction
"S"-adenosyl--methionine + G(5')pppR-RNA formula_0 "S"-adenosyl--homocysteine + m7G(5')pppR-RNA (mRNA containing an N7-methylguanine cap)
Thus, the two substrates of this enzyme are S-adenosyl methionine and G(5')pppR-RNA, whereas its two products are S-adenosylhomocysteine and m7G(5')pppR-RNA. This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases.
In humans, mRNA cap guanine-N7 methyltransferase is encoded by the "RNMT" gene.
Nomenclature.
The systematic name of this enzyme class is S-adenosyl-L-methionine:mRNA (guanine-N7-)-methyltransferase. Other names in common use include:
References.
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Further reading.
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14024877 | MRNA (nucleoside-2'-O-)-methyltransferase | Enzyme
In enzymology, a mRNA (nucleoside-2'-O-)-methyltransferase (EC 2.1.1.57) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + m7G(5')pppR-RNA formula_0 S-adenosyl-L-homocysteine + m7G(5')pppRm-RNA (mRNA containing a 2'-O-methylpurine cap)
Thus, the two substrates of this enzyme are S-adenosyl methionine and m7G(5')pppR-RNA, whereas its two products are S-adenosylhomocysteine and m7G(5')pppRm-RNA (mRNA containing a 2'-O-methylpurine cap).
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:mRNA (nucleoside-2'-O-)-methyltransferase. Other names in common use include messenger ribonucleate nucleoside 2'-methyltransferase, and messenger RNA (nucleoside-2'-)-methyltransferase.
Structural studies.
As of late 2007, two structures have been solved for this class of enzymes, with PDB accession codes 2GA9 and 2GAF.
References.
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| https://en.wikipedia.org/wiki?curid=14024877 |
14024894 | (Myelin basic protein)-arginine N-methyltransferase | Class of enzymes
In enzymology, a [myelin basic protein]-arginine N-methyltransferase (EC 2.1.1.126) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + [myelin basic protein]-arginine formula_0 S-adenosyl-L-homocysteine + [myelin basic protein]-Nomega-methyl-arginine
Thus, the two substrates of this enzyme are S-adenosyl methionine and myelin basic protein-arginine, whereas its two products are S-adenosylhomocysteine and myelin basic protein-Nomega-methyl-arginine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:[myelin-basic-protein]-arginine Nomega-methyltransferase. Other names in common use include myelin basic protein methylase I, protein methylase I, S-adenosyl-L-methionine:[myelin-basic-protein]-arginine, and omega-N-methyltransferase.
References.
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| https://en.wikipedia.org/wiki?curid=14024894 |
14024914 | Myricetin O-methyltransferase | In enzymology, a myricetin O-methyltransferase (EC 2.1.1.149) is an enzyme that catalyzes the chemical reaction
2 S-adenosyl-L-methionine + myricetin formula_0 2 S-adenosyl-L-homocysteine + syringetin
Thus, the two substrates of this enzyme are S-adenosyl methionine and myricetin, whereas its two products are S-adenosylhomocysteine and syringetin.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:myricetin O-methyltransferase.
References.
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14024932 | N-benzoyl-4-hydroxyanthranilate 4-O-methyltransferase | In enzymology, a N-benzoyl-4-hydroxyanthranilate 4-O-methyltransferase (EC 2.1.1.105) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + N-benzoyl-4-hydroxyanthranilate formula_0 S-adenosyl-L-homocysteine + N-benzoyl-4-methoxyanthranilate
Thus, the two substrates of this enzyme are S-adenosyl methionine and N-benzoyl-4-hydroxyanthranilate, whereas its two products are S-adenosylhomocysteine and N-benzoyl-4-methoxyanthranilate.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:N-benzoyl-4-O-hydroxyanthranilate 4-O-methyltransferase. Other names in common use include N-benzoyl-4-hydroxyanthranilate 4-methyltransferase, and benzoyl-CoA:anthranilate N-benzoyltransferase.
References.
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14024957 | Nicotinamide N-methyltransferase | In enzymology, a nicotinamide N-methyltransferase (NNMT) (EC 2.1.1.1) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + nicotinamide formula_0 S-adenosyl-L-homocysteine + 1-methylnicotinamide.
Thus, the two substrates of this enzyme are S-adenosyl methionine and nicotinamide, whereas its two products are S-adenosylhomocysteine and 1-methylnicotinamide.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:nicotinamide N-methyltransferase. This enzyme is also called nicotinamide methyltransferase.
Function.
This enzyme participates in nicotinate and nicotinamide metabolism.
NNMT affects a biochemical mechanism known as a futile cycle, which plays a role in metabolic regulation. NNMT is found in human fat cells and the liver. NNMT processes vitamin B3 and has been linked with certain types of cancer. Silencing the gene that codes for NNMT reduces its presence and increases the presence of sugar transporter GLUT4.
Mice that produced large amounts of GLUT4 were insulin sensitive and protected against diabetes, while mice with no GLUT4 were insulin resistant and at risk. High levels of NNMT are often found in the fat cells of animals that are insulin resistant. When the researchers silenced the NNMT gene in mice on high-fat diets, the mice gained less weight than those in whom the NNMT gene was functioning normally. (The mice did not change their eating or exercise habits).
Antisense oligonucleotide (ASO) technology can be used to silence the expression of the NNMT gene only in fat and liver cells. ASOs are short strings of DNA that can be designed to prevent the synthesis of specific proteins. ASOs have been approved for use by the U.S. Food and Drug Administration for the treatment of conditions with other genetic causes—such as elevated cholesterol and hyperlipidemia.
Structural studies.
As of late 2007, two structures have been solved for this class of enzymes, with PDB accession codes 2I62 and 2IIP.
References.
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| https://en.wikipedia.org/wiki?curid=14024957 |
14024969 | Nicotinate N-methyltransferase | In enzymology, a nicotinate N-methyltransferase (EC 2.1.1.7) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + nicotinate formula_0 S-adenosyl-L-homocysteine + N-methylnicotinate
Thus, the two substrates of this enzyme are S-adenosyl methionine and nicotinate, whereas its two products are S-adenosylhomocysteine and N-methylnicotinate.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:nicotinate N-methyltransferase. Other names in common use include furanocoumarin 8-methyltransferase, and furanocoumarin 8-O-methyltransferase. This enzyme participates in nicotinate and nicotinamide metabolism.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 5MHT.
References.
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| https://en.wikipedia.org/wiki?curid=14024969 |
14024990 | O-demethylpuromycin O-methyltransferase | In enzymology, an O-demethylpuromycin O-methyltransferase (EC 2.1.1.38) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + O-demethylpuromycin formula_0 S-adenosyl-L-homocysteine + puromycin
Thus, the two substrates of this enzyme are S-adenosyl methionine and O-demethylpuromycin, whereas its two products are S-adenosylhomocysteine and puromycin.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:O-demethylpuromycin O-methyltransferase. This enzyme is also called O-demethylpuromycin methyltransferase. This enzyme participates in puromycin biosynthesis.
References.
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| https://en.wikipedia.org/wiki?curid=14024990 |
14025006 | Phenol O-methyltransferase | Class of enzymes
In enzymology, a phenol O-methyltransferase (EC 2.1.1.25) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + phenol formula_0 S-adenosyl-L-homocysteine + anisole
Thus, the two substrates of this enzyme are S-adenosyl methionine and phenol, whereas its two products are S-adenosylhomocysteine and anisole.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:phenol O-methyltransferase. This enzyme is also called PMT. This enzyme participates in tyrosine metabolism.
References.
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| https://en.wikipedia.org/wiki?curid=14025006 |
14025048 | Phosphatidyl-N-methylethanolamine N-methyltransferase | In enzymology, a phosphatidyl-N-methylethanolamine N-methyltransferase (EC 2.1.1.71) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + phosphatidyl-N-methylethanolamine formula_0 S-adenosyl-L-homocysteine + phosphatidyl-N-dimethylethanolamine
Thus, the two substrates of this enzyme are S-adenosyl methionine and phosphatidyl-N-methylethanolamine, whereas its two products are S-adenosylhomocysteine and phosphatidyl-N-dimethylethanolamine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:phosphatidyl-N-methylethanolamine N-methyltransferase. Other names in common use include phosphatidylmonomethylethanolamine methyltransferase, methyltransferase II, phospholipid methyltransferase, PLMT, phosphatidyl-N-methylethanolamine methyltransferase, phosphatidyl-N-monomethylethanolamine methyltransferase, phosphatidylethanolamine methyltransferase I, and phosphatidylmonomethylethanolamine methyltransferase. This enzyme participates in glycine, serine and threonine metabolism and glycerophospholipid metabolism.
References.
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14025063 | Phosphoethanolamine N-methyltransferase | In enzymology, a phosphoethanolamine N-methyltransferase (EC 2.1.1.103) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + ethanolamine phosphate formula_0 S-adenosyl-L-homocysteine + N-methylethanolamine phosphate
Thus, the two substrates of this enzyme are S-adenosyl methionine and ethanolamine phosphate, whereas its two products are S-adenosylhomocysteine and N-methylethanolamine phosphate.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:ethanolamine-phosphate N-methyltransferase. This enzyme is also called phosphoethanolamine methyltransferase. This enzyme participates in glycerophospholipid metabolism.
References.
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| https://en.wikipedia.org/wiki?curid=14025063 |
14025077 | Polysaccharide O-methyltransferase | Enzyme
In enzymology, a polysaccharide O-methyltransferase (EC 2.1.1.18) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + 1,4-alpha-D-glucooligosaccharide formula_0 S-adenosyl-L-homocysteine + oligosaccharide containing 6-methyl-D-glucose units
Thus, the two substrates of this enzyme are S-adenosyl methionine and 1,4-alpha-D-glucooligosaccharide, whereas its two products are S-adenosylhomocysteine and oligosaccharide containing 6-methyl-D-glucose units.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:1,4-alpha-D-glucan 6-O-methyltransferase. Other names in common use include polysaccharide methyltransferase, and acylpolysacharide 6-methyltransferase.
References.
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14025092 | Precorrin-2 C20-methyltransferase | In enzymology, a precorrin-2 C20-methyltransferase (EC 2.1.1.130) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + precorrin-2 formula_0 S-adenosyl-L-homocysteine + precorrin-3A
The two substrates of this enzyme are S-adenosyl methionine and precorrin 2 and its two products are S-adenosylhomocysteine and precorrin 3A.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:precorrin-4 C20-methyltransferase and another names in common use is CobI. The enzyme is part of the biosynthetic pathway to cobalamin (vitamin B12) in aerobic bacteria.
Structural studies.
As of late 2007, two structures have been solved for this class of enzymes, with PDB accession codes 2E0K and 2E0N.
References.
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| https://en.wikipedia.org/wiki?curid=14025092 |
14025103 | Precorrin-3B C17-methyltransferase | In enzymology, precorrin-3B C17-methyltransferase (EC 2.1.1.131) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + precorrin-3B formula_0 S-adenosyl-L-homocysteine + precorrin-4
The two substrates of this enzyme are S-adenosyl methionine and precorrin 3B, and its two products are S-adenosylhomocysteine and precorrin 4.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:precorrin-3B C17-methyltransferase. Other names in common use include precorrin-3 methyltransferase, and CobJ. This enzyme is part of the biosynthetic pathway to cobalamin (vitamin B12) in aerobic bacteria and during this step the macrocycle ring-contracts so that the corrin core of the vitamin is formed.
References.
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| https://en.wikipedia.org/wiki?curid=14025103 |
14025119 | Precorrin-4 C11-methyltransferase | In enzymology, a precorrin-4 C11-methyltransferase (EC 2.1.1.133) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + precorrin-4 formula_0 S-adenosyl-L-homocysteine + precorrin-5
The two substrates of this enzyme are S-adenosyl methionine and precorrin 4; its two products are S-adenosylhomocysteine and precorrin 5.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:precorrin-4 C11 methyltransferase. Other names in common use include precorrin-3 methylase, and CobM. It is part of the biosynthetic pathway to cobalamin (vitamin B12) in aerobic bacteria.
Structural studies.
As of late 2007, two structures have been solved for this class of enzymes, with PDB accession codes 1CBF and 2CBF.
References.
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| https://en.wikipedia.org/wiki?curid=14025119 |
14025140 | Precorrin-6A synthase (deacetylating) | In enzymology, precorrin-6A synthase (deacetylating) (EC 2.1.1.152) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + precorrin-5 + H2O formula_0 S-adenosyl-L-homocysteine + precorrin-6A + acetate
The 3 substrates of this enzyme are S-adenosyl methionine, precorrin 5, and H2O. Its 3 products are S-adenosylhomocysteine, precorrin 6A, and acetate.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:precorrin-5 C1-methyltransferase (deacetylating). Other names in common use include precorrin-6X synthase (deacetylating), and CobF. This enzyme is part of the biosynthetic pathway to cobalamin (vitamin B12) in aerobic bacteria.
References.
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| https://en.wikipedia.org/wiki?curid=14025140 |
14025152 | Precorrin-6Y C5,15-methyltransferase (decarboxylating) | In enzymology, a precorrin-6Y C5,15-methyltransferase (decarboxylating) (EC 2.1.1.132) is an enzyme that catalyzes the chemical reaction
2 S-adenosyl-L-methionine + precorrin-6Y formula_0 2 S-adenosyl-L-homocysteine + precorrin-8X + CO2
The two substrates of this enzyme are S-adenosyl methionine and precorrin 6Y; its three products are S-adenosylhomocysteine, precorrin 8X, and CO2.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:1-precorrin-6Y C5,15-methyltransferase (C-12-decarboxylating). Other names in common use include precorrin-6 methyltransferase, precorrin-6Y methylase and CobL. This enzyme is part of the biosynthetic pathway to cobalamin (vitamin B12) in aerobic bacteria.
References.
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| https://en.wikipedia.org/wiki?curid=14025152 |
14025168 | Protein-glutamate O-methyltransferase | In enzymology, a protein-glutamate O-methyltransferase (EC 2.1.1.80) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + protein L-glutamate formula_0 S-adenosyl-L-homocysteine + protein L-glutamate methyl ester
Thus, the two substrates of this enzyme are S-adenosyl methionine and protein L-glutamic acid, whereas its two products are S-adenosylhomocysteine and protein L-glutamate methyl ester.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:protein-L-glutamate O-methyltransferase. Other names in common use include methyl-accepting chemotaxis protein O-methyltransferase, S-adenosylmethionine-glutamyl methyltransferase, methyl-accepting chemotaxis protein methyltransferase II, S-adenosylmethionine:protein-carboxyl O-methyltransferase, protein methylase II, MCP methyltransferase I, MCP methyltransferase II, protein O-methyltransferase, protein(aspartate)methyltransferase, protein(carboxyl)methyltransferase, protein carboxyl-methylase, protein carboxyl-O-methyltransferase, protein carboxylmethyltransferase II, protein carboxymethylase, protein carboxymethyltransferase, and protein methyltransferase II. This enzyme participates in bacterial chemotaxis - general and bacterial chemotaxis - organism-specific.
CheR proteins are part of the chemotaxis signaling mechanism which methylates the chemotaxis receptor at specific glutamate residues. Methyl transfer from the ubiquitous S-adenosyl-L-methionine (AdoMet/SAM) to either nitrogen, oxygen or carbon atoms is frequently employed in diverse organisms ranging from bacteria to plants and mammals. The reaction is catalysed by methyltransferases (Mtases) and modifies DNA, RNA, proteins and small molecules, such as catechol for regulatory purposes. The various aspects of the role of DNA methylation in prokaryotic restriction-modification systems and in a number of cellular processes in eukaryotes including gene regulation and differentiation is well documented.
Flagellated bacteria swim towards favourable chemicals and away from deleterious ones. Sensing of chemoeffector gradients involves chemotaxis receptors, transmembrane (TM) proteins that detect stimuli through their periplasmic domains and transduce the signals via their cytoplasmic domains . Signalling outputs from these receptors are influenced both by the binding of the chemoeffector ligand to their periplasmic domains and by methylation of specific glutamate residues on their cytoplasmic domains. Methylation is catalysed by CheR, an S-adenosylmethionine-dependent methyltransferase, which reversibly methylates specific glutamate residues within a coiled coil region, to form gamma-glutamyl methyl ester residues. The structure of the "Salmonella typhimurium" chemotaxis receptor methyltransferase CheR, bound to S-adenosylhomocysteine, has been determined to a resolution of 2.0 Angstrom. The structure reveals CheR to be a two-domain protein, with a smaller N-terminal helical domain linked via a single polypeptide connection to a larger C-terminal alpha/beta domain. The C-terminal domain has the characteristics of a nucleotide-binding fold, with an insertion of a small anti-parallel beta-sheet subdomain. The S-adenosylhomocysteine-binding site is formed mainly by the large domain, with contributions from residues within the N-terminal domain and the linker region.
Structural studies.
As of late 2007, two structures have been solved for this class of enzymes, with PDB accession codes 1AF7 and 1BC5.
References.
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| https://en.wikipedia.org/wiki?curid=14025168 |
14025183 | Protein-histidine N-methyltransferase | In enzymology, a protein-histidine N-methyltransferase (EC 2.1.1.85) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + protein L-histidine formula_0 S-adenosyl-L-homocysteine + protein Ntau-methyl-L-histidine
Thus, the two substrates of this enzyme are S-adenosyl methionine and protein L-histidine, whereas its two products are S-adenosylhomocysteine and protein Ntau-methyl-L-histidine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:protein-L-histidine N-tele-methyltransferase. Other names in common use include protein methylase IV, protein (histidine) methyltransferase, actin-specific histidine methyltransferase, and S-adenosyl methionine:protein-histidine N-methyltransferase.
References.
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| https://en.wikipedia.org/wiki?curid=14025183 |
14025208 | Protein-S-isoprenylcysteine O-methyltransferase | The isoprenylcysteine o-methyltransferase (EC 2.1.1.100) carries out carboxyl methylation of cleaved eukaryotic proteins that terminate in a CaaX motif. In "Saccharomyces cerevisiae" (Baker's yeast) this methylation is carried out by Ste14p, an integral endoplasmic reticulum membrane protein. Ste14p is the founding member of the isoprenylcysteine carboxyl methyltransferase (ICMT) family, whose members share significant sequence homology.
The enzyme catalyzes the chemical reaction
S-adenosyl-L-methionine + protein C-terminal S-farnesyl-L-cysteine formula_0 S-adenosyl-L-homocysteine + protein C-terminal S-farnesyl-L-cysteine methyl ester
Thus, the two substrates of this enzyme are S-adenosyl methionine and protein C-terminal S-farnesyl-L-cysteine, whereas its two products are S-adenosylhomocysteine and protein C-terminal S-farnesyl-L-cysteine methyl ester.
References.
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| https://en.wikipedia.org/wiki?curid=14025208 |
14025225 | Putrescine N-methyltransferase | Enzyme
In enzymology, a putrescine N-methyltransferase (EC 2.1.1.53) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + putrescine formula_0 S-adenosyl-L-homocysteine + N-methylputrescine
Thus, the two substrates of this enzyme are S-adenosyl methionine and putrescine, whereas its two products are S-adenosylhomocysteine and N-methylputrescine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:putrescine N-methyltransferase. This enzyme is also called putrescine methyltransferase. This enzyme participates in alkaloid biosynthesis ii.
This enzyme is important in the synthesis of many plant alkaloids. It evolved from spermidine synthase.
References.
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| https://en.wikipedia.org/wiki?curid=14025225 |
14025246 | Pyridine N-methyltransferase | In enzymology, a pyridine N-methyltransferase (EC 2.1.1.87) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + pyridine formula_0 S-adenosyl-L-homocysteine + N-methylpyridinium
Thus, the two substrates of this enzyme are S-adenosyl methionine and pyridine, whereas its two products are S-adenosylhomocysteine and N-methylpyridinium.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:pyridine N-methyltransferase. This enzyme is also called pyridine methyltransferase.
References.
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| https://en.wikipedia.org/wiki?curid=14025246 |
14025256 | Quercetin 3-O-methyltransferase | In enzymology, a quercetin 3-O-methyltransferase (EC 2.1.1.76) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + 3,5,7,3',4'-pentahydroxyflavone formula_0 S-adenosyl-L-homocysteine + 3-methoxy-5,7,3',4'-tetrahydroxyflavone
Thus, the two substrates of this enzyme are S-adenosyl methionine and 3,5,7,3',4'-pentahydroxyflavone, whereas its two products are S-adenosylhomocysteine and 3-methoxy-5,7,3',4'-tetrahydroxyflavone.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:3,5,7,3',4'-pentahydroxyflavone 3-O-methyltransferase. Other names in common use include flavonol 3-O-methyltransferase, and flavonoid 3-methyltransferase. This enzyme participates in flavonoid biosynthesis.
References.
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{
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| https://en.wikipedia.org/wiki?curid=14025256 |
14025265 | (Ribulose-bisphosphate carboxylase)-lysine N-methyltransferase | Class of enzymes
In enzymology, a [ribulose-bisphosphate carboxylase]-lysine N-methyltransferase (EC 2.1.1.127) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + [ribulose-1,5-bisphosphate carboxylase]-lysine formula_0 S-adenosyl-L-homocysteine + [ribulose-1,5-bisphosphate carboxylase]-N6-methyl-L-lysine
Thus, the two substrates of this enzyme are S-adenosyl methionine and ribulose-1,5-bisphosphate carboxylase-lysine, whereas its two products are S-adenosylhomocysteine and ribulose-1,5-bisphosphate carboxylase-N6-methyl-L-lysine.
Transferase Family.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases.
The systematic name of this enzyme class is S-adenosyl-L-methionine:[3-phospho-D-glycerate-carboxy-lyase (dimerizing)]-lysine N6-methyltransferase.
Other names in common use include rubisco methyltransferase, ribulose-bisphosphate-carboxylase/oxygenase N-methyltransferase, ribulose-1,5-bisphosphate carboxylase/oxygenase large subunit, epsilonN-methyltransferase, S-adenosyl-L-methionine:[3-phospho-D-glycerate-carboxy-lyase, and (dimerizing)]-lysine 6-N-methyltransferase.
Structural studies.
As of late 2007, 7 structures have been solved for this class of enzymes, with PDB accession codes 1MLV, 1OZV, 1P0Y, 2H21, 2H23, 2H2E, and 2H2J. | [
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| https://en.wikipedia.org/wiki?curid=14025265 |
14025278 | RRNA (adenine-N6-)-methyltransferase | In enzymology, a rRNA (adenine-N6-)-methyltransferase (EC 2.1.1.48) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + rRNA formula_0 S-adenosyl-L-homocysteine + rRNA containing N6-methyladenine
Thus, the two substrates of this enzyme are S-adenosyl methionine and rRNA, whereas its two products are S-adenosylhomocysteine and rRNA containing N6-methyladenine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:rRNA (adenine-N6-)-methyltransferase. Other names in common use include ribosomal ribonucleate adenine 6-methyltransferase, gene ksgA methyltransferase, ribonucleic acid-adenine (N6) methylase, ErmC 23S rRNA methyltransferase, and S-adenosyl-L-methionine:rRNA (adenine-6-N-)-methyltransferase.
Structural studies.
As of late 2007, 6 structures have been solved for this class of enzymes, with PDB accession codes 1QAM, 1QAN, 1QAO, 1QAQ, 1YUB, and 2ERC.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025278 |
14025308 | RRNA (guanine-N1-)-methyltransferase | In enzymology, a rRNA (guanine-N1-)-methyltransferase (EC 2.1.1.51) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + rRNA formula_0 S-adenosyl-L-homocysteine + rRNA containing N1-methylguanine
Thus, the two substrates of this enzyme are S-adenosyl methionine and rRNA, whereas its two products are S-adenosylhomocysteine and rRNA containing N1-methylguanine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:rRNA (guanine-N1-)-methyltransferase. Other names in common use include ribosomal ribonucleate guanine 1-methyltransferase, and S-adenosyl-L-methionine:rRNA (guanine-1-N-)-methyltransferase.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 1P91.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025308 |
14025319 | RRNA (guanine-N2-)-methyltransferase | In enzymology, a rRNA (guanine-N2-)-methyltransferase (EC 2.1.1.52) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + rRNA formula_0 S-adenosyl-L-homocysteine + rRNA containing N2-methylguanine
Thus, the two substrates of this enzyme are S-adenosyl methionine and rRNA, whereas its two products are S-adenosylhomocysteine and rRNA containing N2-methylguanine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:rRNA (guanine-N2-)-methyltransferase. Other names in common use include ribosomal ribonucleate guanine-2-methyltransferase, and S-adenosyl-L-methionine:rRNA (guanine-2-N-)-methyltransferase.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 2PJD.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025319 |
14025333 | (RS)-1-benzyl-1,2,3,4-tetrahydroisoquinoline N-methyltransferase | Class of enzymes
In enzymology, a (RS)-1-benzyl-1,2,3,4-tetrahydroisoquinoline N-methyltransferase is an enzyme that catalyzes the chemical reaction:
S-adenosyl-L-methionine + (RS)-1-benzyl-1,2,3,4-tetrahydroisoquinoline formula_0 S-adenosyl-L-homocysteine + N-methyl-(RS)-1-benzyl-1,2,3,4-tetrahydroisoquinoline
This enzyme participates in alkaloid biosynthesis.
Nomenclature.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:(RS)-1-benzyl-1,2,3,4-tetrahydroisoquinoline N-methyltransferase. This enzyme is also called norreticuline N-methyltransferase.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025333 |
14025349 | (RS)-norcoclaurine 6-O-methyltransferase | Class of enzymes
In enzymology, a (RS)-norcoclaurine 6-O-methyltransferase (EC 2.1.1.128) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + (RS)-norcoclaurine formula_0 S-adenosyl-L-homocysteine + (RS)-coclaurine
Thus, the two substrates of this enzyme are S-adenosyl methionine and (R,S)-norcoclaurine, whereas its two products are S-adenosylhomocysteine and (R,S)-coclaurine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:(RS)-norcoclaurine 6-O-methyltransferase. This enzyme participates in alkaloid biosynthesis i.
References.
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| https://en.wikipedia.org/wiki?curid=14025349 |
14025365 | (S)-coclaurine-N-methyltransferase | Class of enzymes
In enzymology, a (S)-coclaurine-N-methyltransferase (EC 2.1.1.140) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + (S)-coclaurine formula_0 S-adenosyl-L-homocysteine + (S)-N-methylcoclaurine
Thus, the two substrates of this enzyme are S-adenosyl methionine and (S)-coclaurine, whereas its two products are S-adenosylhomocysteine and (S)-N-methylcoclaurine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:(S)-coclaurine-N-methyltransferase. This enzyme participates in alkaloid biosynthesis i.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025365 |
14025375 | (S)-scoulerine 9-O-methyltransferase | Class of enzymes
In enzymology, a (S)-scoulerine 9-O-methyltransferase (EC 2.1.1.117) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + (S)-scoulerine formula_0 S-adenosyl-L-homocysteine + (S)-tetrahydrocolumbamine
Thus, the two substrates of this enzyme are S-adenosyl methionine and (S)-scoulerine, whereas its two products are S-adenosylhomocysteine and (S)-tetrahydrocolumbamine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:(S)-scoulerine 9-O-methyltransferase. This enzyme participates in alkaloid biosynthesis i.
References.
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| https://en.wikipedia.org/wiki?curid=14025375 |
14025389 | Sterigmatocystin 8-O-methyltransferase | In enzymology, a sterigmatocystin 8-O-methyltransferase (EC 2.1.1.110) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + sterigmatocystin formula_0 S-adenosyl-L-homocysteine + 8-O-methylsterigmatocystin
Thus, the two substrates of this enzyme are S-adenosyl methionine and sterigmatocystin, whereas its two products are S-adenosylhomocysteine and 8-O-methylsterigmatocystin.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:sterigmatocystin 8-O-methyltransferase. Other names in common use include sterigmatocystin methyltransferase, O-methyltransferase II, sterigmatocystin 7-O-methyltransferase (incorrect), S-adenosyl-L-methionine:sterigmatocystin 7-O-methyltransferase, and (incorrect).
References.
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{
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| https://en.wikipedia.org/wiki?curid=14025389 |
14025411 | Sterol 24-C-methyltransferase | In enzymology, a sterol 24-C-methyltransferase (EC 2.1.1.41) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + 5alpha-cholesta-8,24-dien-3beta-ol formula_0 S-adenosyl-L-homocysteine + 24-methylene-5alpha-cholest-8-en-3beta-ol
Thus, the two substrates of this enzyme are S-adenosyl methionine and 5alpha-cholesta-8,24-dien-3beta-ol, whereas its two products are S-adenosylhomocysteine and 24-methylene-5alpha-cholest-8-en-3beta-ol.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:zymosterol 24-C-methyltransferase. Other names in common use include Delta24-methyltransferase, Delta24-sterol methyltransferase, zymosterol-24-methyltransferase, S-adenosyl-4-methionine:sterol Delta24-methyltransferase, SMT1, 24-sterol C-methyltransferase, S-adenosyl-L-methionine:Delta24(23)-sterol methyltransferase, and phytosterol methyltransferase. This enzyme participates in biosynthesis of steroids. It employs one cofactor, glutathione.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025411 |
14025423 | (S)-tetrahydroprotoberberine N-methyltransferase | Class of enzymes
In enzymology, a (S)-tetrahydroprotoberberine N-methyltransferase (EC 2.1.1.122) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + (S)-7,8,13,14-tetrahydroprotoberberine formula_0 S-adenosyl-L-homocysteine + cis-N-methyl-(S)-7,8,13,14-tetrahydroprotoberberine
Thus, the two substrates of this enzyme are S-adenosyl methionine and (S)-7,8,13,14-tetrahydroprotoberberine, whereas its two products are S-adenosylhomocysteine and cis-N-methyl-(S)-7,8,13,14-tetrahydroprotoberberine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:(S)-7,8,13,14-tetrahydroprotoberberine cis-N-methyltransferase. This enzyme is also called tetrahydroprotoberberine cis-N-methyltransferase. This enzyme participates in alkaloid biosynthesis i.
References.
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{
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| https://en.wikipedia.org/wiki?curid=14025423 |
14025443 | Tabersonine 16-O-methyltransferase | In enzymology, a tabersonine 16-O-methyltransferase (EC 2.1.1.94) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + 16-hydroxytabersonine formula_0 S-adenosyl-L-homocysteine + 16-methoxytabersonine
Thus, the two substrates of this enzyme are S-adenosyl methionine and 16-hydroxytabersonine, whereas its two products are S-adenosylhomocysteine and 16-methoxytabersonine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:16-hydroxytabersonine 16-O-methyltransferase. Other names in common use include 11-demethyl-17-deacetylvindoline 11-methyltransferase, 11-O-demethyl-17-O-deacetylvindoline O-methyltransferase, S-adenosyl-L-methionine:11-O-demethyl-17-O-deacetylvindoline, and 11-O-methyltransferase. This enzyme participates in terpene indole and ipecac alkaloid biosynthesis.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025443 |
14025456 | Tetrahydrocolumbamine 2-O-methyltransferase | In enzymology, a tetrahydrocolumbamine 2-O-methyltransferase (EC 2.1.1.89) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + 5,8,13,13a-tetrahydrocolumbamine formula_0 S-adenosyl-L-homocysteine + tetrahydropalmatine
Thus, the two substrates of this enzyme are S-adenosyl methionine and 5,8,13,13a-tetrahydrocolumbamine, whereas its two products are S-adenosylhomocysteine and tetrahydropalmatine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:5,8,13,13a-tetrahydrocolumbamine 2-O-methyltransferase. This enzyme is also called tetrahydrocolumbamine methyltransferase. This enzyme participates in alkaloid biosynthesis i.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025456 |
14025469 | Tetrahydromethanopterin S-methyltransferase | In enzymology, a tetrahydromethanopterin S-methyltransferase (EC 2.1.1.86) is an enzyme that catalyzes the chemical reaction
5-methyl-5,6,7,8-tetrahydromethanopterin + 2-mercaptoethanesulfonate formula_0 5,6,7,8-tetrahydromethanopterin + 2-(methylthio)ethanesulfonate
Thus, the two substrates of this enzyme are 5-methyl-5,6,7,8-tetrahydromethanopterin and 2-mercaptoethanesulfonate (coenzyme M), whereas its two products are 5,6,7,8-tetrahydromethanopterin and 2-(methylthio)ethanesulfonate.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is 5-methyl-5,6,7,8-tetrahydromethanopterin:2-mercaptoethanesulfonate 2-methyltransferase. This enzyme is also called tetrahydromethanopterin methyltransferase. This enzyme participates in folate biosynthesis.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025469 |
14025488 | Theobromine synthase | In enzymology, a theobromine synthase (EC 2.1.1.159) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + 7-methylxanthine formula_0 S-adenosyl-L-homocysteine + 3,7-dimethylxanthine
Thus, the two substrates of this enzyme are S-adenosyl methionine and 7-methylxanthine, whereas its two products are S-adenosylhomocysteine and 3,7-dimethylxanthine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:7-methylxanthine N3-methyltransferase. Other names in common use include monomethylxanthine methyltransferase, MXMT, CTS1, CTS2, and S-adenosyl-L-methionine:7-methylxanthine 3-N-methyltransferase.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025488 |
14025502 | Thetin-homocysteine S-methyltransferase | In enzymology, a thetin-homocysteine S-methyltransferase (EC 2.1.1.3) is an enzyme that catalyzes the chemical reaction
dimethylsulfonioacetate + L-homocysteine formula_0 S-methylthioglycolate + L-methionine
Thus, the two substrates of this enzyme are dimethylsulfonioacetic acid and L-homocysteine, whereas its two products are S-methylthioglycolic acid and L-methionine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is dimethylsulfonioacetic acid:L-homocysteine S-methyltransferase. Other names in common use include dimethylthetin-homocysteine methyltransferase, and thetin-homocysteine methylpherase.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025502 |
14025513 | Thioether S-methyltransferase | In enzymology, a thioether S-methyltransferase (EC 2.1.1.96) is an enzyme that catalyzes the chemical reaction.
S-adenosyl-L-methionine + dimethyl sulfide formula_0 S-adenosyl-L-homocysteine + trimethylsulfonium
Thus, the two substrates of this enzyme are S-adenosyl methionine and dimethyl sulfide, whereas its two products are S-adenosylhomocysteine and trimethylsulfonium.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:dimethyl-sulfide S-methyltransferase. Other names in common use include S-adenosyl-L-methionine:thioether S-methyltransferase, and thioether methyltransferase.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025513 |
14025530 | Thiol S-methyltransferase | In enzymology, a thiol S-methyltransferase (EC 2.1.1.9) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + a thiol formula_0 S-adenosyl-L-homocysteine + a thioether
Thus, the two substrates of this enzyme are S-adenosyl methionine and thiol, whereas its two products are S-adenosylhomocysteine and thioether.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:thiol S-methyltransferase. Other names in common use include S-methyltransferase, thiol methyltransferase, and TMT. This enzyme participates in selenoamino acid metabolism.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025530 |
14025543 | Thymidylate synthase (FAD) | In enzymology, a thymidylate synthase (FAD) (EC 2.1.1.148) is an enzyme that catalyzes the chemical reaction
5,10-methylenetetrahydrofolate + dUMP + FADH2 formula_0 dTMP + tetrahydrofolate + FAD
The 3 substrates of this enzyme are 5,10-methylenetetrahydrofolate, dUMP, and FADH2, whereas its 3 products are dTMP, tetrahydrofolate, and FAD.
This enzyme belongs to the family of transferases, to be specific those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is 5,10-methylenetetrahydrofolate,FADH2:dUMP C-methyltransferase. Other names in common use include Thy1, and ThyX. This enzyme participates in pyrimidine metabolism and one carbon pool by folate.
Most organisms, including humans, use the thyA- or TYMS-encoded classic thymidylate synthase whereas some bacteria use the similar flavin-dependent thymidylate synthase (FDTS) instead.
Structural studies.
As of late 2007, 3 structures have been solved for this class of enzymes, with PDB accession codes 2AF6, 2CFA, and 2GQ2.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025543 |
14025555 | Tocopherol O-methyltransferase | In enzymology, a tocopherol O-methyltransferase (EC 2.1.1.95) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + gamma-tocopherol formula_0 S-adenosyl-L-homocysteine + alpha-tocopherol
Thus, the two substrates of this enzyme are S-adenosyl methionine and gamma-tocopherol, whereas its two products are S-adenosylhomocysteine and alpha-tocopherol.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:gamma-tocopherol 5-O-methyltransferase. This enzyme is also called gamma-tocopherol methyltransferase. This enzyme participates in biosynthesis of steroids.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14025555 |
14025572 | Trans-aconitate 2-methyltransferase | In enzymology, a trans-aconitate 2-methyltransferase (EC 2.1.1.144) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + trans-aconitate formula_0 S-adenosyl-L-homocysteine + (E)-3-(methoxycarbonyl)pent-2-enedioate
Thus, the two substrates of this enzyme are S-adenosyl methionine and trans-aconitate, whereas its two products are S-adenosylhomocysteine and (E)-3-(methoxycarbonyl)pent-2-enedioate.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:(E)-prop-1-ene-1,2,3-tricarboxylate 2'-O-methyltransferase.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 2P35.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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"text": "\\rightleftharpoons"
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]
| https://en.wikipedia.org/wiki?curid=14025572 |
14025585 | Trans-aconitate 3-methyltransferase | In enzymology, a trans-aconitate 3-methyltransferase (EC 2.1.1.145) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + trans-aconitate formula_0 S-adenosyl-L-homocysteine + (E)-2-(methoxycarbonylmethyl)butenedioate
Thus, the two substrates of this enzyme are S-adenosyl methionine and trans-aconitate, whereas its two products are S-adenosylhomocysteine and (E)-2-(methoxycarbonylmethyl)butenedioate.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:(E)-prop-1-ene-1,2,3-tricarboxylate 3'-O-methyltransferase.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14025585 |
14025594 | Trimethylsulfonium—tetrahydrofolate N-methyltransferase | In enzymology, a trimethylsulfonium-tetrahydrofolate N-methyltransferase (EC 2.1.1.19) is an enzyme that catalyzes the chemical reaction
trimethylsulfonium + tetrahydrofolate formula_0 dimethylsulfide + 5-methyltetrahydrofolate
Thus, the two substrates of this enzyme are trimethylsulfonium and tetrahydrofolate, whereas its two products are dimethyl sulfide and 5-methyltetrahydrofolate.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is trimethylsulfonium:tetrahydrofolate N-methyltransferase. This enzyme is also called trimethylsulfonium-tetrahydrofolate methyltransferase. This enzyme participates in one carbon pool by folate.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14025594 |
14025604 | TRNA (5-methylaminomethyl-2-thiouridylate)-methyltransferase | In enzymology, a tRNA (5-methylaminomethyl-2-thiouridylate)-methyltransferase (EC 2.1.1.61) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + tRNA formula_0 S-adenosyl-L-homocysteine + tRNA containing 5-methylaminomethyl-2-thiouridylate
Thus, the two substrates of this enzyme are S-adenosyl methionine and tRNA, whereas its two products are S-adenosylhomocysteine and tRNA containing 5-methylaminomethyl-2-thiouridylic acid.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:tRNA (5-methylaminomethyl-2-thio-uridylate)-methyltransferase. Other names in common use include transfer ribonucleate 5-methylaminomethyl-2-thiouridylate, 5-methyltransferase, and tRNA 5-methylaminomethyl-2-thiouridylate 5'-methyltransferase.
Structural studies.
As of late 2007, 4 structures have been solved for this class of enzymes, with PDB accession codes 2DER, 2DET, 2DEU, and 2HMA.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14025604 |
14025620 | TRNA (adenine-N1-)-methyltransferase | In enzymology, a tRNA (adenine-N1-)-methyltransferase (EC 2.1.1.36) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + tRNA formula_0 S-adenosyl-L-homocysteine + tRNA containing N1-methyladenine
Thus, the two substrates of this enzyme are S-adenosyl methionine and tRNA, whereas its two products are S-adenosylhomocysteine and tRNA containing N1-methyladenine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:tRNA (adenine-N1-)-methyltransferase. Other names in common use include transfer ribonucleate adenine 1-methyltransferase, transfer RNA (adenine-1) methyltransferase, 1-methyladenine transfer RNA methyltransferase, adenine-1-methylase, and S-adenosyl-L-methionine:tRNA (adenine-1-N-)-methyltransferase.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14025620 |
14025633 | Bipolar transistor biasing | Process necessary for BJT amplifiers to work correctly
Bipolar transistors must be properly biased to operate correctly. In circuits made with individual devices (discrete circuits), biasing networks consisting of resistors are commonly employed. Much more elaborate biasing arrangements are used in integrated circuits, for example, bandgap voltage references and current mirrors. The voltage divider configuration achieves the correct voltages by the use of resistors in certain patterns. By selecting the proper resistor values, stable current levels can be achieved that vary only little over temperature and with transistor properties such as β.
The operating point of a device, also known as "bias point", "quiescent point", or "Q-point", is the point on the output characteristics that shows the DC collector–emitter voltage ("V"ce) and the collector current ("I"c) with no input signal applied.
Bias circuit requirements.
A bias network is selected to stabilize the operating point of the transistor, by reducing the following effects of device variability, temperature, and voltage changes:
A bias circuit may be composed of only resistors, or may include elements such as temperature-dependent resistors, diodes, or additional voltage sources, depending on the range of operating conditions expected.
Signal requirements.
For analog operation of a class-A amplifier, the Q-point is placed so the transistor stays in active mode (does not shift to operation in the saturation region or cut-off region) across the input signal's range. Often, the Q-point is established near the center of the active region of a transistor characteristic to allow similar signal swings in positive and negative directions.
For digital operation, the Q-point is instead chosen so the transistor switches from the "on" (saturation) to the "off" (cutoff) state.
Thermal considerations.
At constant current, the voltage across the emitter–base junction "V"BE of a bipolar transistor "decreases" by 2 mV (silicon) and 1.8 mV (germanium) for each 1 °C rise in temperature (reference being 25 °C). By the Ebers–Moll model, if the base–emitter voltage "V"BE is held constant and the temperature rises, the current through the base–emitter junction "I"B will increase, and thus the collector current "I"C will also increase. Depending on the bias point, the power dissipated in the transistor may also increase, which will further increase its temperature and exacerbate the problem. This deleterious positive feedback results in thermal runaway. There are several approaches to mitigate bipolar transistor thermal runaway. For example,
Types of bias circuit for class-A amplifiers.
The following discussion treats five common biasing circuits used with class-A bipolar transistor amplifiers:
Fixed bias (base bias).
This form of biasing is also called "base bias or fixed resistance biasing".
In the given fixed bias circuit,formula_0For a given transistor, Vbe doesn't vary significantly during use. And since Rb and the DC voltage source Vcc are constant, the base current Ib also doesn't vary significantly. Thus this type of biasing is called "fixed bias".
The common-emitter current gain of a transistor (specified as a range on its data sheet as "h"FE or "β"), allows us to obtain formula_1 as well:formula_2Now Vce can be determined:formula_3Thus an operating point formula_4 for a transistor can be set using Rb and Rc.
Advantages:
Disadvantages:
Usage:
Due to the above inherent drawbacks, fixed bias is rarely used in linear circuits (i.e., those circuits which use the transistor as a current source). Instead, it is often used in circuits where the transistor is used as a switch. However, one application of fixed bias is to achieve crude automatic gain control in the transistor by feeding the base resistor from a DC signal derived from the AC output of a later stage.
Collector feedback bias.
This configuration employs negative feedback to prevent thermal runaway and stabilize the operating point. In this form of biasing, the base resistor formula_5 is connected to the collector instead of connecting it to formula_6. So any thermal runaway will induce a voltage drop across the formula_7 resistor that will throttle the transistor's base current.
From Kirchhoff's voltage law, the voltage formula_8 across the base resistor formula_5 is
formula_9
By the Ebers–Moll model, formula_10, and so
formula_11
From Ohm's law, the base current formula_12, and so
formula_13
Hence, the base current formula_14 is
formula_15
If formula_16 is held constant and temperature increases, then the collector current formula_17 increases. However, a larger formula_17 causes the voltage drop across resistor formula_7 to increase, which in turn reduces the voltage formula_8 across the base resistor formula_5. A lower base-resistor voltage drop reduces the base current formula_14, which results in less collector current formula_17. Because an increase in collector current with temperature is opposed, the operating point is kept stable.
Advantages:
Disadvantages:
Usage:
In this configuration, which is known as "voltage-shunt feedback', the output voltage is sensed and the feedback signal (a current) is applied in shunt (i.e., in parallel with the input). This means that the input impedance "looking into the base" is actually reduced. This can easily be verified by application of Miller's Theorem. This situation is similar to that of an inverting op-amp circuit where the input impedance of the amplifier at the virtual earth is near zero and the overall input impedance is determined by the external series resistor. Due to the gain reduction from feedback, this biasing form is used only when the trade-off for stability is warranted. Adding an emitter resistor to this circuit will increase the input impedance
Fixed bias with emitter resistor.
The fixed bias circuit is modified by attaching an external resistor to the emitter. This resistor introduces negative feedback that stabilizes the Q-point. From Kirchhoff's voltage law, the voltage across the base resistor isformula_21From Ohm's law, the base current isformula_22The way feedback controls the bias point is as follows. If Vbe is held constant and temperature increases, emitter current increases. However, a larger Ie increases the emitter voltage Ve = IeRe, which in turn reduces the voltage VRb across the base resistor. A lower base-resistor voltage drop reduces the base current, which results in less collector current because Ic = β Ib. Collector current and emitter current are related by Ic = α Ie with α ≈ 1, so the increase in emitter current with temperature is opposed, and the operating point is kept stable.
Similarly, if the transistor is replaced by another, there may be a change in Ic (corresponding to change in β-value, for example). By similar process as above, the change is negated and operating point kept stable.
For the given circuit,formula_23Advantages:
The circuit has the tendency to stabilize operating point against changes in temperature and β-value.
Disadvantages:
Usage:
The feedback also increases the input impedance of the amplifier when seen from the base, which can be advantageous. Due to the above disadvantages, this type of biasing circuit is used only with careful consideration of the trade-offs involved.
Collector-Stabilized Biasing.
Voltage divider biasing or emitter Resistor Stabilizer bias.
"The voltage divider is formed using external resistors" R1 and R2. The voltage across R2 forward biases the emitter junction. By proper selection of resistors R1 and R2, the operating point of the transistor can be made independent of β. In this circuit, the voltage divider holds the base voltage fixed (independent of base current), provided the divider current is large compared to the base current. However, even with a fixed base voltage, collector current varies with temperature (for example) so an emitter resistor is added to stabilize the Q-point, similar to the above circuits with emitter resistor. The voltage divider configuration achieves the correct voltages by the use of resistors in certain patterns. By manipulating the resistors in certain ways you can achieve more stable current levels without having β value affect it too much.
In this circuit the base voltage, formula_26, across formula_27is given byformula_28provided formula_29.
It is also known thatformula_30For the given circuit,formula_31Advantages:
Disadvantages:
Usage:
The circuit's stability and merits as above make it widely used for linear circuits.
Voltage divider with AC bypass capacitor.
The standard voltage divider circuit discussed above faces a drawback – AC feedback caused by resistor Re reduces the gain. This can be avoided by placing a capacitor (Ce) in parallel with Re, as shown in circuit diagram.
Advantages:
Disadvantages:
Emitter bias.
When a split supply (dual power supply) is available, this biasing circuit is the most effective. It provides zero bias voltage at the emitter or collector for load. The negative supply Vee is used to forward-bias the emitter junction through Re. The positive supply Vcc is used to reverse-bias the collector junction.
If Rb is small enough, base voltage will be approximately zero. Therefore, emitter current is,formula_35Advantages:
Disadvantages:
Class-B and AB amplifiers.
Signal requirements.
Class B and AB amplifiers employ 2 active devices to cover the complete 360 deg of input signal flow. Each transistor is therefore biased to perform over approximately 180 deg of the input signal. Class B bias is when the collector current Ic with no signal is just conducting (about 1% of maximum possible value). Class-AB bias is when the collector current Ic is about <templatestyles src="Fraction/styles.css" />1⁄4 of maximum possible value. The class-AB push–pull output amplifier circuit below could be the basis for a moderate-power audio amplifier.
Q3 is a common emitter stage that provides amplification of the signal and the DC bias current through D1 and D2 to generate a bias voltage for the output devices. The output pair are arranged in class-AB push–pull, also called a complementary pair. The diodes D1 and D2 provide a small amount of constant voltage bias for the output pair, just biasing them into the conducting state so that crossover distortion is minimized. That is, the diodes push the output stage into class-AB mode (assuming that the base-emitter drop of the output transistors is reduced by heat dissipation).
This design automatically stabilizes its operating point, since overall feedback internally operates from DC up through the audio range and beyond. The use of fixed diode bias requires the diodes to be both electrically and thermally matched to the output transistors. If the output transistors conduct too much, they can easily overheat and destroy themselves, as the full current from the power supply is not limited at this stage.
A common solution to help stabilize the output device operating point is to include some emitter resistors, typically an ohm or so. Calculating the values of the circuit's resistors and capacitors is done based on the components employed and the intended use of the amplifier.
References.
<templatestyles src="Reflist/styles.css" />
Further reading.
<templatestyles src="Refbegin/styles.css" /> | [
{
"math_id": 0,
"text": "I_{\\text{b}} = \\frac{V_{\\text{cc}} - V_{\\text{be}}}{{R_{\\text{b}}}} \\,."
},
{
"math_id": 1,
"text": " I_\\text{c} "
},
{
"math_id": 2,
"text": "I_{\\text{c}} = \\beta I_{\\text{b}} \\,."
},
{
"math_id": 3,
"text": "V_{\\text{ce}} = V_{\\text{cc}} - {I_{\\text{c}} R_{\\text{c}}} \\,."
},
{
"math_id": 4,
"text": " ( V_{\\text{ce}}, \\ I_{\\text{c}} ) "
},
{
"math_id": 5,
"text": "R_{\\text{b}}"
},
{
"math_id": 6,
"text": "V_{\\text{cc}}"
},
{
"math_id": 7,
"text": "R_{\\text{c}}"
},
{
"math_id": 8,
"text": "V_{\\text{R}_{\\text{b}}}"
},
{
"math_id": 9,
"text": "V_{\\text{R}_{\\text{b}}} = V_{\\text{cc}} \\, - \\, \\mathord{\\overbrace{(I_{\\text{c}} + I_{\\text{b}}) R_{\\text{c}}}^{\\text{Voltage drop across } R_{\\text{c}}}} \\, - \\, \\mathord{\\overbrace{V_{\\text{be}}}^{\\text{Voltage at base}}}."
},
{
"math_id": 10,
"text": "I_{\\text{c}} = \\beta I_{\\text{b}}"
},
{
"math_id": 11,
"text": "V_{\\text{R}_{\\text{b}}} = V_{\\text{cc}} - (\\overbrace{\\beta I_{\\text{b}}}^{I_{\\text{c}}} + I_{\\text{b}}) R_{\\text{c}} - V_{\\text{be}} = V_{\\text{cc}} - I_{\\text{b}} (\\beta + 1) R_{\\text{c}} - V_{\\text{be}}."
},
{
"math_id": 12,
"text": "I_{\\text{b}} = V_{\\text{R}_{\\text{b}}} / R_{\\text{b}}"
},
{
"math_id": 13,
"text": "\\overbrace{I_{\\text{b}} R_{\\text{b}}}^{V_{\\text{R}_{\\text{b}}}} = V_{\\text{cc}} - I_{\\text{b}} (\\beta + 1) R_{\\text{c}} - V_{\\text{be}}."
},
{
"math_id": 14,
"text": "I_{\\text{b}}"
},
{
"math_id": 15,
"text": "I_{\\text{b}} = \\frac{ V_{\\text{cc}} - V_{\\text{be}} }{ R_{\\text{b}} + ( \\beta + 1 ) R_{\\text{c}} }"
},
{
"math_id": 16,
"text": "V_{\\text{be}}"
},
{
"math_id": 17,
"text": "I_{\\text{c}}"
},
{
"math_id": 18,
"text": "\\beta"
},
{
"math_id": 19,
"text": "I_{\\text{c}} = \\beta I_{\\text{b}} = \\frac { \\beta (V_{\\text{cc}} - V_{\\text{be}})}{R_{\\text{b}} + R_{\\text{c}} + \\beta R_{\\text{c}}} \\approx \\frac{(V_{\\text{cc}} - V_{\\text{be}})}{R_{\\text{c}}}"
},
{
"math_id": 20,
"text": "\\beta R_{\\text{c}} \\gg R_{\\text{b}}."
},
{
"math_id": 21,
"text": " V_{R_{\\text{b}}} = V_{\\text{cc}} - I_{\\text{e}} R_{\\text{e}} - V_{\\text{be}} "
},
{
"math_id": 22,
"text": "I_{\\text{b}} = \\frac {V_{R_{\\text{b}}}}{R_\\text{b}} "
},
{
"math_id": 23,
"text": "I_{\\text{b}} = \\frac { V_\\text{cc} - V_\\text{be} } { R_\\text{b} + ( \\beta+1) R_\\text{e} }"
},
{
"math_id": 24,
"text": "I_\\text{c} = \\beta I_\\text{b} = \\frac { \\beta (V_\\text{cc} - V_\\text{be})}{R_\\text{b} + ( \\beta+1) R_\\text{e}} \\approx \\frac {(V_\\text{cc} - V_\\text{be})}{R_\\text{e}}"
},
{
"math_id": 25,
"text": "(\\beta + 1)R_\\text{e} \\gg R_\\text{b}. "
},
{
"math_id": 26,
"text": "V_{\\text{b}} "
},
{
"math_id": 27,
"text": "R_2 \\ "
},
{
"math_id": 28,
"text": "V_\\text{b} = \nV_\\text{cc} \\frac{R_2}{(R_1+R_2)} - I_\\text{b} \\frac{R_1 R_2}{(R_1+R_2)}\n\\approx V_\\text{cc} \\frac{R_2}{(R_1+R_2)}"
},
{
"math_id": 29,
"text": "I_\\text{b} << I_1 = V_\\text{b} / R_1 "
},
{
"math_id": 30,
"text": "V_\\text{b} = V_\\text{be} + V_\\text{e} = V_\\text{be} + I_\\text{e} R_\\text{e} . "
},
{
"math_id": 31,
"text": " I_\\text{b} =\\frac \n{\n \\frac \n{V_\\text{cc}}{1+R_1/R_2}\n - V_\\text{be}\n}\n{( \\beta + 1)R_\\text{e} + R_1 \\parallel R_2 }"
},
{
"math_id": 32,
"text": "I_\\text{c} = \\beta I_\\text{b} = \\beta \\frac \n{ \n \\frac \n{V_\\text{cc}}{1+R_1/R_2}\n - V_\\text{be}\n}\n{( \\beta + 1)R_\\text{e} + R_1 \\parallel R_2 } \\approx \\frac \n{ \\frac {V_\\text{cc}}{1+R_1/R_2}- V_\\text{be}}\n{R_\\text{e}} , "
},
{
"math_id": 33,
"text": "( \\beta + 1 ) R_\\text{e} >> R_1 \\parallel R_2"
},
{
"math_id": 34,
"text": "R_{\\text{c}}/R_{\\text{e}}"
},
{
"math_id": 35,
"text": " I_\\text{e} = {\\frac {V_\\text{ee} - V_\\text{be}} {R_\\text{e}}} "
},
{
"math_id": 36,
"text": " \\beta "
},
{
"math_id": 37,
"text": " R_\\text{e} \\gg R_\\text{b} / \\beta "
}
]
| https://en.wikipedia.org/wiki?curid=14025633 |
14025635 | TRNA (adenine-N6-)-methyltransferase | In enzymology, a tRNA (adenine-N6-)-methyltransferase (EC 2.1.1.55) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + tRNA formula_0 S-adenosyl-L-homocysteine + tRNA containing N6-methyladenine
Thus, the two substrates of this enzyme are S-adenosyl methionine and tRNA, whereas its two products are S-adenosylhomocysteine and tRNA containing N6-methyladenine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:tRNA (adenine-N6-)-methyltransferase. This enzyme is also called S-adenosyl-L-methionine:tRNA (adenine-6-N-)-methyltransferase.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14025635 |
14025648 | TRNA (cytosine-5-)-methyltransferase | In enzymology, a tRNA (cytosine-5-)-methyltransferase (EC 2.1.1.29) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + tRNA formula_0 S-adenosyl-L-homocysteine + tRNA containing 5-methylcytosine
Thus, the two substrates of this enzyme are S-adenosyl methionine and tRNA, whereas its two products are S-adenosylhomocysteine and tRNA containing 5-methylcytosine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:tRNA (cytosine-5-)-methyltransferase. Other names in common use include transfer ribonucleate cytosine 5-methyltransferase, and transfer RNA cytosine 5-methyltransferase.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14025648 |
14025662 | TRNA (guanine-N1-)-methyltransferase | In enzymology, a tRNA (guanine-N1-)-methyltransferase (EC 2.1.1.31) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + tRNA formula_0 S-adenosyl-L-homocysteine + tRNA containing N1-methylguanine
Thus, the two substrates of this enzyme are S-adenosyl methionine and tRNA, whereas its two products are S-adenosylhomocysteine and tRNA containing N1-methylguanine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:tRNA (guanine-N1-)-methyltransferase. Other names in common use include transfer ribonucleate guanine 1-methyltransferase, tRNA guanine 1-methyltransferase, and S-adenosyl-L-methionine:tRNA (guanine-1-N-)-methyltransferase.
Structural studies.
As of late 2007, 6 structures have been solved for this class of enzymes, with PDB accession codes 1OY5, 1P9P, 1UAJ, 1UAK, 1UAL, and 1UAM.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14025662 |
14025678 | TRNA (guanine-N2-)-methyltransferase | In enzymology, a tRNA (guanine-N2-)-methyltransferase (EC 2.1.1.32) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + tRNA formula_0 S-adenosyl-L-homocysteine + tRNA containing N2-methylguanine
Thus, the two substrates of this enzyme are S-adenosyl methionine and tRNA, whereas its two products are S-adenosylhomocysteine and tRNA containing N2-Methylguanine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:tRNA (guanine-N2-)-methyltransferase. Other names in common use include transfer ribonucleate guanine 2-methyltransferase, transfer ribonucleate guanine N2-methyltransferase, transfer RNA guanine 2-methyltransferase, guanine-N2-methylase, and S-adenosyl-L-methionine:tRNA (guanine-2-N-)-methyltransferase.
Structural studies.
As of late 2007, 3 structures have been solved for this class of enzymes, with PDB accession codes 2DUL, 2EJT, and 2EJU.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14025678 |
14025700 | TRNA (guanine-N7-)-methyltransferase | In enzymology, a tRNA (guanine-N7-)-methyltransferase (EC 2.1.1.33) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + tRNA formula_0 S-adenosyl-L-homocysteine + tRNA containing N7-methylguanine
Thus, the two substrates of this enzyme are S-adenosyl methionine and tRNA, whereas its two products are S-adenosylhomocysteine and tRNA containing N7-methylguanine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:tRNA (guanine-N7-)-methyltransferase. Other names in common use include transfer ribonucleate guanine 7-methyltransferase, 7-methylguanine transfer ribonucleate methylase, tRNA guanine 7-methyltransferase, N7-methylguanine methylase, and S-adenosyl-L-methionine:tRNA (guanine-7-N-)-methyltransferase.
Structural studies.
As of late 2007, two structures have been solved for this class of enzymes, with PDB accession codes 1YZH and 2FCA.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14025700 |
14025713 | TRNA guanosine-2'-O-methyltransferase | In enzymology, a tRNA guanosine-2'-O-methyltransferase (EC 2.1.1.34) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + tRNA formula_0 S-adenosyl-L-homocysteine + tRNA containing 2'-O-methylguanosine
Thus, the two substrates of this enzyme are S-adenosyl methionine and tRNA, whereas its two products are S-adenosylhomocysteine and tRNA containing 2'-O-methylguanosine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:tRNA guanosine-2'-O-methyltransferase. Other names in common use include transfer ribonucleate guanosine 2'-methyltransferase, tRNA guanosine 2'-methyltransferase, tRNA (guanosine 2')-methyltransferase, tRNA (Gm18) 2'-O-methyltransferase, tRNA (Gm18) methyltransferase, tRNA (guanosine-2'-O-)-methyltransferase, and S-adenosyl-L-methionine:tRNA (guanosine-2'-O-)-methyltransferase.
Structural studies.
As of late 2007, two structures have been solved for this class of enzymes, with PDB accession codes 1V2X and 1ZJR.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14025713 |
14025727 | TRNA (uracil-5-)-methyltransferase | In enzymology, a tRNA (uracil-5-)-methyltransferase (EC 2.1.1.35) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + tRNA containing uridine at position 54 formula_0 S-adenosyl-L-homocysteine + tRNA containing ribothymidine at position 54
Thus, the two substrates of this enzyme are S-adenosyl methionine and tRNA containing uridine at position 54, whereas its two products are S-adenosylhomocysteine and tRNA containing ribothymidine at position 54.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:tRNA (uracil-5-)-methyltransferase. Other names in common use include ribothymidyl synthase, transfer RNA uracil 5-methyltransferase, transfer RNA uracil methylase, tRNA uracil 5-methyltransferase, m5U-methyltransferase, tRNA:m5U54-methyltransferase, and RUMT.
References.
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14025738 | Tryptophan 2-C-methyltransferase | In enzymology, a tryptophan 2-C-methyltransferase (EC 2.1.1.106) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + L-tryptophan formula_0 S-adenosyl-L-homocysteine + L-2-methyltryptophan
Thus, the two substrates of this enzyme are S-adenosyl methionine and L-tryptophan, whereas its two products are S-adenosylhomocysteine and L-2-methyltryptophan.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:L-tryptophan 2-C-methyltransferase. Other names in common use include tryptophan 2-methyltransferase, and S-adenosylmethionine:tryptophan 2-methyltransferase.
References.
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14025753 | Tyramine N-methyltransferase | In enzymology, a tyramine N-methyltransferase (EC 2.1.1.27) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + tyramine formula_0 S-adenosyl-L-homocysteine + N-methyltyramine
Thus, the two substrates of this enzyme are S-adenosyl methionine and tyramine, whereas its two products are S-adenosylhomocysteine and N-methyltyramine.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:tyramine N-methyltransferase. Other names in common use include DIB O-methyltransferase (3,5-diiodo-4-hydroxy-benzoic acid), S-adenosyl-methionine:tyramine N-methyltransferase, and tyramine methylpherase. This enzyme participates in tyrosine metabolism.
References.
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14025766 | Vitexin 2"-O-rhamnoside 7-O-methyltransferase | In enzymology, a vitexin 2"-O-rhamnoside 7-O-methyltransferase (EC 2.1.1.153) is an enzyme that catalyzes the chemical reaction
S-adenosyl-L-methionine + vitexin 2"-O-beta-L-rhamnoside formula_0 S-adenosyl-L-homocysteine + 7-O-methylvitexin 2"-O-beta-L-rhamnoside
Thus, the two substrates of this enzyme are S-adenosyl methionine and vitexin 2"-O-beta-L-rhamnoside, whereas its two products are S-adenosylhomocysteine and 7-O-methylvitexin 2"-O-beta-L-rhamnoside.
This enzyme belongs to the family of transferases, specifically those transferring one-carbon group methyltransferases. The systematic name of this enzyme class is S-adenosyl-L-methionine:vitexin-2"-O-beta-L-rhamnoside 7-O-methyltransferase.
References.
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14026380 | S-matrix theory | Precursor physical model to string theory and quantum chromodynamics
"S"-matrix theory was a proposal for replacing local quantum field theory as the basic principle of elementary particle physics.
It avoided the notion of space and time by replacing it with abstract mathematical properties of the "S"-matrix. In "S"-matrix theory, the "S"-matrix relates the infinite past to the infinite future in one step, without being decomposable into intermediate steps corresponding to time-slices.
This program was very influential in the 1960s, because it was a plausible substitute for quantum field theory, which was plagued with the zero interaction phenomenon at strong coupling. Applied to the strong interaction, it led to the development of string theory.
"S"-matrix theory was largely abandoned by physicists in the 1970s, as quantum chromodynamics was recognized to solve the problems of strong interactions within the framework of field theory. But in the guise of string theory, "S"-matrix theory is still a popular approach to the problem of quantum gravity.
The "S"-matrix theory is related to the holographic principle and the AdS/CFT correspondence by a flat space limit. The analog of the "S"-matrix relations in AdS space is the boundary conformal theory.
The most lasting legacy of the theory is string theory. Other notable achievements are the Froissart bound, and the prediction of the pomeron.
History.
"S"-matrix theory was proposed as a principle of particle interactions by Werner Heisenberg in 1943, following John Archibald Wheeler's 1937 introduction of the "S"-matrix.
It was developed heavily by Geoffrey Chew, Steven Frautschi, Stanley Mandelstam, Vladimir Gribov, and Tullio Regge. Some aspects of the theory were promoted by Lev Landau in the Soviet Union, and by Murray Gell-Mann in the United States.
Basic principles.
The basic principles are:
The basic analyticity principles were also called "analyticity of the first kind", and they were never fully enumerated, but they include
These principles were to replace the notion of microscopic causality in field theory, the idea that field operators exist at each spacetime point, and that spacelike separated operators commute with one another.
Bootstrap models.
The basic principles were too general to apply directly, because they are satisfied automatically by any field theory. So to apply to the real world, additional principles were added.
The phenomenological way in which this was done was by taking experimental data and using the dispersion relations to compute new limits. This led to the discovery of some particles, and to successful parameterizations of the interactions of pions and nucleons.
This path was mostly abandoned because the resulting equations, devoid of any space-time interpretation, were very difficult to understand and solve.
Regge theory.
The principle behind the Regge theory hypothesis (also called "analyticity of the second kind" or the "bootstrap principle") is that all strongly interacting particles lie on Regge trajectories. This was considered the definitive sign that all the hadrons are composite particles, but within "S"-matrix theory, they are not thought of as being made up of elementary constituents.
The Regge theory hypothesis allowed for the construction of string theories, based on bootstrap principles. The additional assumption was the narrow resonance approximation, which started with stable particles on Regge trajectories, and added interaction loop by loop in a perturbation series.
String theory was given a Feynman path-integral interpretation a little while later. The path integral in this case is the analog of a sum over particle paths, not of a sum over field configurations. Feynman's original path integral formulation of field theory also had little need for local fields, since Feynman derived the propagators and interaction rules largely using Lorentz invariance and unitarity. | [
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140271 | Kardashev scale | Measure of a civilization's evolution
The Kardashev scale () is a method of measuring a civilization's level of technological advancement based on the amount of energy it is capable of harnessing and using. The measure was proposed by Soviet astronomer Nikolai Kardashev (1932–2019) in 1964 and was named after him.
Kardashev first outlined his scale in a paper presented at the 1964 conference that communicated findings on BS-29-76, Byurakan conference in Armenia, a scientific meeting that reviewed the Soviet radio astronomy space listening program. The paper was titled "" ("Transmission of Information by Extraterrestrial Civilizations"). Starting from a functional definition of civilization, based on the immutability of physical laws and using human civilization as a model of extrapolation, Kardashev's initial model was developed. He proposed a classification of civilizations into three types, based on the axiom of exponential growth:
Under this scale, the sum of human civilization does not reach Type I status (though it continues to approach it). Various extensions of the scale have since been proposed, including a wider range of power levels (Types 0, IV, and V) and the use of metrics other than pure power (e.g., computational growth or food consumption).
In a second article, entitled "Strategies of Searching for Extraterrestrial Intelligence", published in 1980, Kardashev wonders about the ability of a civilization, which he defines by its ability to access energy, to sustain itself, and to integrate information from its environment. Two more articles followed: "On the Inevitability and the Possible Structure of Super Civilizations" and "Cosmology and Civilizations", published in 1985 and 1997, respectively; the Soviet astronomer proposed ways to detect super civilizations and to direct the SETI (Search for Extra Terrestrial Intelligence) programs.
A number of scientists have conducted searches for possible civilizations, but with no conclusive results. However, in part thanks to such searches, unusual objects, now known to be either pulsars or quasars, were identified.
Origin of the classification.
First publication (1964).
Kardashev presented for the first time a classification of civilizations according to their level of energy consumption in an article entitled "Transmission of Information by Extraterrestrial Civilizations", published in 1964 first in Russian in the March–April issue of the Astronomicheskii Zhurnal, then in English in the September–October 1964 issue of the Soviet Astronomical Journal. In this article, the scientist presents a calculation of the evolution of the energy needs of humanity, and calculates that the energy consumption of the latter will be equal to that emitted by the Sun, evaluated at 4 × 1026 watts (W), in about 3,200 years, then will be equal to that emitted by 1011 stars similar to ours (which corresponds to the estimated number of stars in the Milky Way) in 5,800 years. Based on this observation, and considering that there is no reason to assume that the evolution of humanity's energy consumption can decrease, Kardashev comes to propose a classification of technological civilizations into three types.
A civilization known as "Type I" is able to collect and use all the available energy on its planet, that is, the theoretical equivalent of 1016 watts. According to Kardashev, it is the type of civilization that Earth was closest to achieving in 1964. A civilization known as "Type II" would surpass the first by a factor of 10 billion, reaching a consumption of 1026 watts, this time using all the power emitted by its star. Finally, a civilization known as "Type III" would be able to collect and consume all the energy emitted by its galaxy, which is equivalent to 1037 watts.
Assuming the development of radio, Kardashev predicted that in the following two decades (i.e. in the 1980s) it would be possible to build antennas of 100,000 m2 capable of detecting Type II and III civilizations. A Type I civilization like that of earth would be able to receive the extraordinary energetic emissions of the other types of civilizations, which would supposedly be able to emit continuously.
Kardashev then examined the characteristics of a transmission from an artificial source. He mentioned the two cosmic radio sources discovered in 1963 by the California Institute of Technology, CTA-21 and CTA-102 in particular, which would have characteristics close to those of a presumed artificial source. The most suitable region of the galaxy for observing Type II and III civilizations would then be the Galactic Center, due to the high density of the stellar population it harbors. He then recommended that the search programs for such artificial sources should focus on other nearby galaxies, such as the Andromeda Galaxy, the Magellanic Clouds, M87, or Centaurus A. Kardashev concluded his paper by noting that the possible discovery of even the simplest organisms on Mars would increase the likelihood that Type II civilizations exist in the galaxy.
Second publication (1980).
Towards an energetic definition of civilization.
In 1980, Nikolai Kardashev published a second article entitled "Strategies of Searching for Extraterrestrial Intelligence: A Fundamental Approach to the Basic Problem," in which he stated that:<templatestyles src="Template:Blockquote/styles.css" />Detection and studies of extraterrestrial civilizations constitute a problem of immense significance for the progress of humanity and for its culture and philosophy. The discovery of intelligent life in the Universe would provide a guideline to the possible development of our civilization over astronomical time spans.
According to the Soviet astronomer, our civilization would be too young to be able to contact another civilization that would certainly be more advanced than us; the solar system is too young with its five billion years, and the first ancestors of today's man appeared only 6 million years ago at the earliest; the oldest celestial objects are between 10 and 14 billion years old; it is clear that the other civilizations are incomparably older than the human civilization. Therefore, the knowledge of these civilizations must be greater than ours, and, he reasoned, they must surely be aware of what we are doing.
Kardashev believed it is probable that the present state of our civilization is only one of the stages through which civilizations pass during their evolution. It is thus possible to define civilization on the basis of this universal characteristic, which allowed Aleksandr Lyapunov to define life as "a highly stable state of matter, which uses information encoded by the states of individual molecules to produce maintaining reactions", which Kardashev calls the "functional definition of civilization". He therefore suggests thinking of civilization as a "highly stable state of matter capable of acquiring, making abstract analysis of, and utilizing information to obtain qualitatively new information about its environment and about itself, to improve its capabilities of gathering new information for producing sustaining reactions." Civilization is therefore characterized by the quality of the information acquired by its operating program, and by the energy required to implement these functions. By "information about its environment and about itself", Kardashev specified that it is data about organic or inorganic nature, science, technology, economy, culture, arts, etc. From this definition, he proposed a diagram representing the interactions between a civilization and its environment, and enumerated a number of scientific problems arising from these interactions with the information available in the Universe.
From this definition, Kardashev drew three conclusions. The first postulated that because of the vast and unlimited set of activities required by scientific problems, the period during which civilizations must transmit and communicate is necessarily long, even unlimited. On the other hand, since our present development covers only a negligible fraction of this communication phase, Kardashev hypothesized the high improbability that we will meet "brothers in intelligence" who are at the same stage of evolution as are we. After all, highly advanced civilizations know and use the laws of physics to a degree that we have yet to suspect. Kardashev asserted that "this last point should be taken into account in the research programs of extraterrestrial civilizations" and concluded that it is very likely that our present state is only one of the stages through which every civilization passes during its evolution.
Two strategies for searching for intelligent signals.
Kardashev then analyzed various models and hypotheses of the evolution of civilization. Answering the question of the Russian astronomer Iosif Shklovsky, who in an article published in 1977 and titled "Possibility of the Intelligent Life in the Universe Being Unique" found it strange that the "shock wave of intelligence" of a supercivilization had not yet reached the limits of the whole Universe, Kardashev put forward two explanatory hypotheses. In the first, he postulated that it would not be useful for a supercivilization to expand the space it occupies in order to maintain its activity, and in the second, it is possible that a civilization, instead of dispersing itself in space, would rather continue its activities of information analysis in order to discover new fundamental laws (such as the exploration of the microcosm, or black holes for example).
However, such civilization activities require the use of abundant energy. According to the laws of thermodynamics, an important part of this consumed energy must be converted into radiation of a bolometric magnitude approximately equal to that of the radiation background surrounding the source. The spectral distribution of this intensity must be close to that of a black body. This would be a possible way to search for extraterrestrial civilizations. Such energy consumption would also require a large amount of solid matter for stellar engineering activities, which Kardashev called "cosmic miracles". In short, information about the possible existence of an extraterrestrial civilization would come in the form of electromagnetic radiation.
With regard to the fate of civilizations, Kardashev saw two concepts, from which two strategies for the search for extraterrestrial civilizations can be derived. The first, which he called "terrestrial chauvinism", is based on the principle that civilizations can only stabilize or perish at a level of development close to ours currently reached. The second, which he called the "evolutionary concept", holds that civilizations are capable of reaching higher levels of development than that of contemporary humanity. In the first case, the best search strategy using astronomical detection means (e.g., the SETI program) would be to observe the most powerful (and often the most distant) sources of radiation in space. The observer will then be able to determine if they are natural emission sources, and only then can the search focus on objects with weaker radiation. In the second case, he recommended to search for new and powerful sources of radiation, especially in the poorly known regions of the electromagnetic spectrum. These sources could be significant or periodic monochromatic signals from the galactic center, from other galaxies or from quasars and other exotic cosmic objects. Kardashev believed that the search should focus on the millimeter wavelength spectrum, close to the maximum intensity of the cosmic microwave background, rather than in the 21-centimeter band (which is the domain of investigation of the SETI program). According to Kardashev, in order to capture the significant radiation of an advanced civilization emitted by a megastructure (such as a Dyson sphere), a radio telescope with a diameter larger than the diameter of the Earth would have to be placed in orbital space.
Kardashev concluded by predicting that the search for extraterrestrial civilizations would lead to positive results in the [then] next decade, giving humanity access to a vast amount of information about the Universe and its evolution over a period of several billion years.
Third publication (1985).
Discovering supercivilizations.
In the article "On the Inevitability and the Possible Structure of Supercivilizations" published in 1985, Kardashev evokes the possible scenarios and the means of investigation available to humanity for the detection of hypothetical extraterrestrial supercivilizations. The Soviet astronomer reminds us that we search for these supercivilizations on the basis of our own development criteria, and that predictions are possible only for extraterrestrial worlds close to our technological level, the others being beyond our intellectual representation. Nevertheless, it seems useful to him to conceive models of supercivilizations based at the same time on imagination and on our present scientific knowledge. Since the laws of physics are immutable, even if new laws are discovered in the future, they will not abolish those already known.
According to Kardashev, theoretical models of supercivilizations must meet two basic assumptions. The first is that the range of supercivilization activities that obey the laws of physics is limited only by natural and scientific constraints, while the second is that the evolution of supercivilization activities cannot be interrupted or limited by intrinsic, inherent contingencies, such as large-scale social conflicts. For Kardashev, unlike other scientists, supercivilizations cannot self-destruct or retrogress. According to these principles, there must exist in space megastructures of great size, emitting a lot of energy and information, and existing for billions of years, while being compact enough to rapidly exchange large amounts of data between them. A supercivilization would thus create a technological structure of cosmic dimensions. As an example, Kardashev cites Freeman Dyson's megastructure, in the form of a sphere of several astronomical units in diameter. Other phenomena may indicate highly technological activities, such as artificially exploding stars or the changing of stellar orbits to store mass and energy. Giant molecular clouds also hold great potential for astroengineering. Kardashev even raises the possibility of a supercivilization reshaping the entire galaxy.
Then he evokes the theoretical and mathematical possibility of the existence of a megastructure in the form of a disk rotating on itself at a constant angular velocity. According to him, the search for intelligent signals should be directed to the detection of such megastructures at the characteristic radiation (20 μm). Quasars or galactic centers can be excellent candidates to testify to the existence of a supercivilization since they emit strong infrared radiation, which indicates a solid structure. The astronomer advises to look for these objects in a wavelength range from a few microns to a few millimeters. Large intelligent structures can also be detected by the fact that they screen or reflect the surrounding radiation.
Possible scenarios for the evolution of supercivilizations.
Kardashev believes that it is very likely that a supercivilization has already detected and observed humanity through cosmic-sized telescopes. He discusses this in a 1997 article on the subject, entitled "Radioastron – a Radio Telescope Much Greater than the Earth". For this supercivilization, the science of "cosmic ethnography" must be highly developed. However, the fact that no contact has been made so far could be explained by ethical considerations of these civilizations. Based on this principle, Kardashev sees only two possible evolutionary scenarios for a supercivilization: natural evolution and evolution after contact with other extraterrestrial civilizations. He considers more likely the scenario based on contact between two civilizations highly developed technologically and culturally advanced civilizations; this scenario, which he calls the "Urbanization Hypothesis", would result in the regrouping and unification of several civilizations within a few compact regions of the Universe.
Kardashev lists, in the form of investigative tools, six possible scenarios (summarized in a table at the end of his 1997 article) that explain the evolution of a civilization. Each of the scenarios corresponds to a probability, one or more objects to be observed, an adapted procedure, and, finally the possible consequences for our civilization:
Fourth publication (1997).
In the article "Cosmology and Civilizations" published in 1997, Kardashev reiterates the need to carefully observe astronomical objects with strong radiation in order to detect supercivilizations. However, the discovery of a civilization at a stage of development similar to ours is unlikely. The existence of such supercivilizations is made possible by the fact that life on Earth is recent compared to the age of the Universe (8 × 109 years before the formation of the Solar System). He then examines the conditions for the appearance of life on cosmological time scales. Assuming the rate of evolution of life on Earth and considering the age of the Universe, it is reasonable to assume that a civilization could have reached our level of technological development in 6 × 109 years. Such civilizations can be observed in nearby regions, since the farther away we observe, the younger the objects are. Recent discoveries of sources of intense radiation deadly to life show that life could have flourished under cover for the time necessary for its appearance and maintenance. Another argument for the possibility of a very old supercivilization is that most of the objects that could be megastructures have not yet been discovered and mapped. In addition, 95% of the matter remains invisible or can only be inferred by the gravitational influence it produces.
According to Kardashev, it is essential to focus our search tools on new objects radiating at a wavelength of a few microns to a few millimeters, and at a temperature of 3 to 300 K, which is characteristic of large structures of solid matter. It would then be possible to detect structures belonging to Type II in our galaxy or in those nearby. Type III structures can also be observed at large cosmological distances. Kardashev recalls that a study was conducted on 3000 sources of the IRAS catalog from the four directions of the sky. Two temperature bands were targeted: from 110 to 120 K and from 280 to 290 K. The analysis showed that the 110–120 K sources are clustered in the Galactic plane and in its center. Kardashev explains that only more powerful observations in the infrared and submillimeter range can reveal possible artificial sources of radiation. He then refers to projects that he has proposed, in particular that of putting into orbit a cryogenic space telescope (the "Millimetron Project").
According to Kardashev, these results, combined with those of other research on the age of certain cosmic objects, suggest that civilizations dating from 6 to 8 billion years ago may exist in our galaxy. It is likely that they have long since discovered our own civilization, a hypothesis that could answer the question posed by Enrico Fermi when he formulated his paradox: "Where are they?". Without the discovery of artificial sources, however, Shklovsky's theory that civilizations self-destruct as a result of large-scale social conflicts would be proven. Kardashev mentions another hypothesis that, in his opinion, is capable of explaining the dynamics of the supercivilizations: the "feedback effect" (theorized by Sebastian von Hoerner in 1975), which is based on the hypothesis that at a high technological level, civilizations tend to converge rather than to isolate themselves. The distance between supercivilizations could then be determined by half the time of the technological evolution of the oldest civilization, which would be about 3 to 4 billion years. On the other hand, this supercivilization may not have been present in our galaxy for a long time. Kardashev concludes by saying that since the expansion of the Universe is infinite, the number and lifetime of such supercivilizations are also infinite.
Categories defined by Kardashev.
The hypothetical classification, known as the Kardashev scale, distinguishes three stages in the evolution of civilizations according to the dual criteria of access and energy consumption. The purpose of this classification is to guide the search for extraterrestrial civilizations, particularly within SETI, in which Kardashev participated, and this on the assumption that a fraction of the energy used by each type is intended for communication with other civilizations. To make this scale more understandable, Lemarchand compares the speed at which a volume of information equivalent to 100,000 average-sized books can be transmitted across the galaxy. A Type II civilization can send this data using a transmission beam that lasts for only 100 seconds. A similar amount of information can be sent across intergalactic distances of about ten million light years, with a transmission time of several weeks. A Type III civilization can send the same amount of data to the entire observable universe with a transmission time of 3 seconds.
Kardashev's classification is based on the assumption of a growth rate of 1% per year. Kardashev believed that it would take humanity 3,200 years to reach Type II, and 5,800 years to reach Type III. However, Dr. Michio Kaku believes that humanity must increase its energy consumption by 3% per year to reach Type I in 100–200 years. These types are thus separated from each other by a growth rate of several billion.
Type I.
A civilization "close to the level currently achieved on Earth, with an energy consumption of ≈4×1019 erg/sec" (4×1012 watts). A Type I civilization is usually defined as one that can harness all the energy that reaches its home planet from its parent star (for Earth, this value is about 2×1017 watts), which is about four orders of magnitude higher than the amount currently achieved on Earth, with an energy consumption of ≈2×1013 watts by 2020. The astronomer Guillermo A. Lemarchand defined Type I as a level close to today's terrestrial civilization, with an energy capacity equivalent to Earth's solar irradiance, between 1016 and 1017 watts.
Type II.
A civilization capable of harnessing the energy radiated by its own large star – for example, by successfully completing a Dyson sphere or Matrioshka brain – with an energy consumption of ≈4×1033 erg/sec. Lemarchand defined such civilizations as being able to harness and channel the entire radiation output of their star. The energy consumption would then be comparable to the luminosity of the Sun, about 4×1033 erg/sec (4×1026 watts).
Type III.
A civilization with energy on the scale of its own galaxy, with an energy consumption of ≈4×1044 erg/sec. Lemarchand defined civilizations of this type as having access to energy comparable to the luminosity of the entire Milky Way galaxy, about 4×1044 erg/sec (4×1037 watts).
In accordance with the data available at the time, Kardashev did not go beyond a Type III civilization. However, new types (0, IV, V, and VI) have been proposed.
Reassessments of the Kardashev scale.
Sagan's finer classification.
In 1973, Carl Sagan discovered Kardashev's work on the classification of civilizations. He found that the differences between the types Kardashev identified were so great that they did not allow for the best possible modeling of the evolution of civilizations. Consequently, Sagan proposes a more refined classification, still based on Kardashev's types, but integrating intermediate levels using the following logarithmic interpolation formula:
formula_0,
where "K" is the Kardashev type of a civilization and "W" is the amount of power it uses, in watts. Thus, a "Type 1.1" civilization would be defined by a power of 1017 watts, while a "Type 2.3" civilization would be able to harness 1029 watts.
Moreover, the above formula could be used to extrapolate beyond Kardashev's original types. For example, a Type 0 civilization, not defined by Kardashev, would control about 1 MW of power (equivalent to having around 100 campfires burning at any given time); on Earth, the emergence of Type 0 civilizations is roughly concurrent with the rise of civilization in a general sense.
Sagan estimated that, according to this revised scale, 1970s humanity would be Type 0.7 (about 10 terawatts), equivalent to 0.16% of the power available on Earth. This level is characterized, according to him, by the ability to self-destruct, which he calls "technological adolescence". In 2021, the total world energy consumption was 595.15 exajoules (165,319 TWh), equivalent to an average power consumption of 18.87 TW or a Kardashev rating of 0.73 (to 2 s.f.).
Sagan also suggests that, for completeness, an alphabetical scale should be added to indicate the level of social development, expressed in the amount of information available to the civilization. Thus, a Class A civilization would be based on 106 bits of information (less than any recorded human culture), a Class B on 107, a Class C on 108, and so on. Humanity in 1973 would belong to the "0.7 H" class. According to Sagan, the first civilization with which humanity would come into contact could be between "1.5 J" and "1.8 K"; a galactic supercivilization would be at the "3 Q" stage, while a federation of galaxies could be at the "4 Z" stage. The information and energy axes are not strictly interdependent, so even a level Z civilization would not have to be Kardashev Type III. Sagan believed that no civilization had yet reached level Z, speculating that so much unique information would exceed that of all the intelligent species in a galactic supercluster, and observing that the universe is not old enough to exchange information effectively over large distances.
In 2017, the total amount of information generated on the internet was 26 zettabytes (with an estimated 120 zettabytes in 2023), equivalent to 0.73 R/S on Sagan's combined scale.
Kaku and the knowledge economy.
In "Physics of the Future" (2011), American physicist Michio Kaku examines the conditions for humanity to converge on a Type I planetary civilization. This convergence is based primarily on the knowledge economy. Kaku uses the Kardashev scale, but develops it by adding an additional stage: a Type IV civilization would be able to draw the energy it needs from extragalactic radiation. By studying the evolution of technologies that have changed history (paper, the integrated circuit), Kaku believes that humanity is moving toward a civilization of planetary dimensions, the "starting point" of which is the Internet.
A Type I civilization consumes power on the order of thousands to millions of times our current planetary output, about 100 trillion trillion watts. It would have enough energy to manipulate the occurrence of certain natural phenomena, such as earthquakes or volcanoes, and could build cities on the oceans. We can see the beginnings of a Type I civilization in the fact that a global language is developing (English), a global communication system is emerging (the Internet), a global economic system is in the making (the establishment of the European Union), and even a globalized culture is standardizing humanity (mass media, television, rock music, and Hollywood movies). To achieve Type I, humanity must be able to communicate with the rest of the world and to focus on several areas: building infrastructure to facilitate communication and cooperation, education, research and development, and innovation, as well as building strong ties between diasporas and their countries of origin, and between migrants and non-migrants. If development fails, it is likely that the world will not be able to achieve Type II. If these areas do not develop, Kaku predicts that humanity will sink into the "abyss": an advanced civilization must grow faster than the frequency of occurrence of extinction-level cosmic catastrophes, such as comet or asteroid impacts. A Type I civilization should also be able to master space travel to deflect threatening objects. It would also have to anticipate the onset of ice ages and modify the climate long before they occur to avoid them.
In addition, in his books "Hyperspace" and "Parallel Worlds", Michio Kaku has discussed a Type IV civilization that could harness "extragalactic" energy sources such as dark energy.
Zubrin's planet mastery.
In "Entering Space: Creating a Spacefaring Civilization", Robert Zubrin suggests another form: his definition of a Type I civilization is described as one that has achieved full mastery of the resources of its planet (global), a Type II of its solar system (interplanetary), and a Type III would have unleashed the full potential of the galaxy (starfaring civilization). Metrics other than pure energy consumption have also been proposed.
He ponders the possibility of a Type IV civilization, one that would dominate the universe, noting that there are limits to how minds can connect and interact on a galactic or intergalactic basis. As an example, he mentions that communication from the center of our galaxy to its edge would take about 50,000 years (since nothing can travel faster than light, according to our understanding of physics).
Barrow's microdimensional mastering.
The astronomer John D. Barrow of the University of Sussex has hypothesized that there are other stages beyond Type III. These Type IV, V, or even VI civilizations would be able to manipulate cosmic structures (galaxies, galactic clusters, superclusters) and even escape the Big Crunch through holes in space.
Barrow also proposes an "anti-Kardashev scale": he observes that humans have found it more cost effective to extend their ability to manipulate their environment to smaller and smaller scales rather than to larger and larger ones. He, therefore, proposes a reverse classification, from Type I-minus to Type Omega-minus:
"In Impossibility: The Limits of Science and the Science of Limits" (1998), Barrow proposes a scale ranging from "BI" to "BVI", with an ultimate stage he calls "BΩ", the former characterized by the possibility of manipulating one's environment, while the latter allows for the modification of spacetime.
Galántai's miniaturization and resilience to catastrophes.
Zoltan Galántai recognizes the important role that Kardashev's classification has played in the SETI program, but he believes that another scale is possible, without using energy consumption, by resorting to miniaturization. The hypothesis of Donald Tarter, researcher at SETI, is that a civilization based on nanotechnology would not need an ever-increasing amount of energy. A Type I civilization that masters local space travel could colonize its planetary system and even the Oort cloud without needing an amount of energy that would make it Type II. This scale loses its meaning beyond Type II, since it is impossible to predict the evolution of civilizations over long distances in a galactic colonization process. Finally, the Kardashev scale is the product of an era of insufficient scientific knowledge, which considered the possibility of stellar object CTA-102 as an artificial Type III source, whereas today we know that it is a galactic nucleus.
In another article, Zoltan Galántai suggests considering another scale, no longer based on energy consumption, but on a civilization's ability to survive natural and cosmic disasters. Type I would describe a civilization capable of surviving a local natural disaster, like the Anasazi. A Type II civilization would have the means to withstand a regional or continental disaster, and finally Type III could face a global disaster such as an asteroid's impact, a supervolcano's eruption, or an ice age. Beyond the first three types are civilizations that have scattered throughout the galaxy. The Type IV civilization would still be vulnerable to some cosmic threats, while the Type V civilization would be technically immortal, as no cosmic catastrophe could reach it. The Kardashev scale can be a relevant tool for preventing catastrophes, whether human or natural, according to Richard Wilson, who relates this scale to the power of destruction, in TNT. A Type I civilization would use 25 megatons of equivalent TNT per second, a Type II civilization 4 × 109 times more (4 billion hydrogen bombs per second), while a Type III civilization would use 1011 times more.
Progression through the types.
Towards type I.
According to Carl Sagan, Type I should be reached around 2100.
Physicist and futurist Michio Kaku has suggested that, if humans increase their energy consumption at an average rate of 3 percent per year, they could reach Type I status in 100–200 years, Type II status in a few thousand years, and Type III status in 100,000 to a million years.
Physicist Freeman Dyson has calculated that Type I should be reached in about 200 years, while Richard Carrigan has estimated that the Earth is just four-tenths of the way to Type I on the Sagan scale. If Type I is reached soon (in the year 3000 for Richard Wilson), it would be accompanied by profound social upheavals, but also by a significant risk of self-destruction.
According to Per Calissendorff, energy consumption cannot be the main parameter to explain the transition from one type to another. Civilizations must have the means to maintain their growth rate despite climatic conditions and major natural disasters, even on the cosmic scale. A civilization moving towards Type II must have mastered space travel, interplanetary communication, stellar engineering, and climate. It must also have developed a planetary communication system, such as the Internet. For Michio Kaku, the only serious threat to a Type II civilization would be the explosion of a nearby supernova, while no known cosmic catastrophe would be capable of wiping out a Type III civilization.
According to Philip T. Metzger, humanity has reached Type I, but faces an energy challenge. In his 2011 paper "Nature's Way of Making Audacious Space Projects Viable", he states that the Earth's non-renewable energy sources are nearly exhausted; natural gas will be depleted by 2020–2030, coal by 2035, uranium by 2056, while oil production peaked in 2006–2008. Nuclear energy cannot fully meet the world's energy needs (it represented only 6% in 2011). In addition, renewable energy cannot meet the growing demand for energy. Most of the minerals used by humans are in danger of becoming scarce; 11 minerals are already classified as having passed their peak production. For Metzger, humanity must therefore undertake a "100-year project" aimed at building a spacecraft ("100 Year Starship") capable of accessing the vast energy resources of the Solar System. For Metzger, it is even probable that if extraterrestrials coveted the energy resources of our Solar System, they would not look for them on Earth, but on the various asteroids and planetoids. Robotics is the only way to access so many dispersed resources, and humanity should embark on a second long-term project, which Metzger calls the "robotsphere", that would begin with the energetic exploitation of the Moon (estimated at 2.3 × 1013 J/year). This first step would make it possible to reach Type II in 53 years. Then the robotsphere (self-replicating and self-learning automated probes) would extend to the rest of the Solar System. Current advances in artificial intelligence suggest that the foundations of a robotsphere could be reached early in the next century, beginning in 2100. Metzger sees eight benefits for humanity in building the 100 Year Starship, including zero launch costs because the spacecraft will be built in space by robots that can do so with little human assistance (drastically reducing manufacturing costs), the creation of a Solar System-wide economy, and the use of resources from celestial objects and possibly terraforming them.
Towards type II.
Viorel Badescu and Richard B. Cathcart have studied the possibility that a Type II civilization could use a 450 million kilometer device to direct solar radiation and thus be able to impart a kinetic motion to its star that deviates it from its usual trajectory by about 35 to 40 parsecs, allowing it, among other things, to capture its energy and navigate the galaxy.
For Claude Semay, "a Type II civilization could be detected at great distances (by what is called "astro-technical leakage"), provided that it is not located in a region of the galaxy that is too distant from us, or that it does not occupy a location that is obscured from us by clouds of gas or dust".
Towards type III.
A Type III civilization should be detectable because of the large amount of radiation captured on a galaxy-wide scale. Calissendorff suggests using 75% of the total light emitted by a galaxy to determine that a Type III civilization uses many Dyson spheres. If only three or four of these spheres occupy the galaxy, it does not necessarily mean that the civilization has reached Type III; it may still be in transition.
However, such civilizations may remain beyond the reach of our understanding and instruments. Sagan believes that the nearest Type III civilization is at an average distance of 10,000 light-years from us, but that it is not interested in classical radio transmissions, being of a different technological level. Only small, low-level civilizations could communicate with us.
However, "a Type III civilization should not be confused with what science fiction writers call a 'galactic empire'", Semay notes, knowing that it can only exist if interstellar travel is achieved. Semay argues that there is no evidence that this will ever be possible. Based on Dyson's calculations, Semay believes that such a journey would take three centuries, with an average distance between stars of about 7 light years. Overall, the speed of the colonization front, which ranges from 4 × 10−4 to 5 × 10−3 light-years per year, would result in humanity spreading throughout the galaxy in a period of 16 to 200 million years. "A Type III civilization, having thus "domesticated" its galaxy by building a large number of Dyson spheres, would be detectable over intergalactic distances of several million light-years."
A Type III civilization could theoretically live inside a supermassive black hole, in a stable periodic orbit, which would make it completely undetectable, according to V. I. Dokuchaev.
Towards type IV.
Zoltan Galántai notes that neither Kardashev nor Sagan thought to extend the scale and define a Type IV (which would use the energy of an entire Universe). They simply did not envision a civilization capable of manipulating its environment on the largest possible scale (about 14 billion parsecs). The concept of a Type IV supercivilization approaches divine possibilities, enabling the creation of, and travel through, alternate Universes of such a civilization's own design, although the latter possibility is reserved for a Type V civilization by Carrigan. The fraction of energy captured by a civilization capable of powering itself on a black hole could also be used to classify civilizations.
Possible scenarios.
According to Kardashev, the most important parameters to define the existence of a civilization are three: the presence of very powerful energy sources, the use of non-standard technologies, and the transmission of significant amounts of information of various kinds through space.
Energy sources.
Kardashev's classification is based on the hypothesis that an advanced civilization uses significant energy, which implies that it must be de facto detectable over long distances, as summarized by Zoltan Galántai. For Kardashev, the limit of a civilization's energy consumption is originally located in the region of the electromagnetic spectrum from 106 to 108 Hz, which allows two observations related to thermodynamics. First, all the energy consumed is inevitably converted into heat. Second, this energy can only be dissipated in the form of radiation scattered in space. These two findings are the pillars of Kardashev's theory that cosmic objects with strong radiation could be artificial sources. He also considered the possibility of detecting an artificial source by emphasizing the spectral line of hydrogen in its use for nuclear fusion.
Dutil and Dumas consider several physical limits to continuous energy production, such as photosynthesis (about 10 TW), climate (about 127 TW), and solar flux (174,000 TW). The only inexhaustible source of energy that can sustain a civilization for over several billion years, is deuterium (used in nuclear fusion). The sustainability of a civilization must therefore involve "strict control of the exploitation of available resources"; this difficulty in exceeding energy limits may explain the fact that the vast majority of civilizations fail to engage in a space colonization project.
Astrophysicist Makoto Inoue and economist Hiromitsu Yokoo have explored the possibility that a Type III civilization could extract energy from a supermassive black hole (SMBH). The captured energy could meet the extraordinary needs of a civilization that requires about 4 × 1044 erg/s. The energy would be captured in the form of radiation emitted by the matter rushing into the star, by means of collectors located within the accretion disk. These collectors are similar to Dyson spheres. The overflow, as well as the waste of the civilization, would be redirected towards the black hole. A fraction of this energy, directed as a high-powered beam, could be useful for space travel. A galactic club of civilizations could transmit the energy through networks within the galaxy. Within the various central power stations that make up the network, power transmission is periodically switched between transmitter and receiver, according to the galactic rotation. To be efficient, this network should be located at the center of the galaxy.
The technology.
This parameter is one of the most undetectable in the Universe due to the fact that solid matter structures are at low temperatures and emit weak radiation. Their luminosity, which is difficult to observe, also makes it impossible to observe them with telescopes. Likewise, we cannot detect them by their gravitational effects. On the other hand their existence can be detected by analyzing the wavelengths between 8 and 13 microns, corresponding to surface temperatures of 300 K. A hypothetical Dyson sphere could thus be detected, provided that the observation is made from space. Locally, the significant dip in luminosity that would result from a giant Dyson sphere (or "Fermi bubble") would allow the detection of a Type III civilization.
A megastructure like a Dyson sphere could be the result of a technology based on self-replicating probes, as those imagined by von Neumann. A Type III civilization would indeed have the means to disperse a significant number of these spheres throughout the galaxy, which would have the effect of attenuating the light emitted by the galaxy. Kaku also considers this to be the most efficient method of colonizing space. For example, a galaxy 100,000 light years in diameter would be explored in half a million years. Paul Davies has suggested that a civilization could colonize the galaxy by scattering miniature probes, no larger than the palm of a hand, using nanotechnology. This thesis is realistic, he explains, because it is obvious that the technology is becoming increasingly miniaturized and proportionally less expensive.
Type II megastructures would be easier to detect. This would be the case of a Dyson sphere used as a "stellar engine", as well as the contribution of heavy elements. Similarly, "Shkadov thrusters", which would produce a lateral thrust of 4.4 parsecs on their star by reflecting solar radiation through a structure made of mirrors, would be observable objects. This device would break the symmetry of solar radiation and counteract gravitational forces, allowing a Type II civilization to move its home solar system through space. Drake and Shklovski have also considered the possibility of "seeding" a star (Stellar salting) by artificially adding extremely rare elements such as technetium or promethium. Such an intervention in a star's composition would be detectable.
It is still possible that humanity could discover traces of lost Type I, II, or III civilizations. The search for material traces of such civilizations (e.g. Dyson spheres or stellar engines), an "interesting alternative" to the conventional SETI program, lays the foundation for a "cosmic archaeology" according to Richard A. Carrigan. Efforts to detect intelligence markers in the atmospheres of exoplanets (such as freon, oxygen, or even ozone, residues of biotic activity according to James Lovelock's research) are one of the most promising avenues. A civilization watching its star die (as a red giant, for example) could have tried to prolong its existence through megastructures that should be detectable. The possible traces could be nuclear remnants, to be sought within the spectral types going from A5 to F2 according to Whitmire and Wright. It could also be a change in the isotopic ratio, due to a stellar engine, or an unusual spectral modulation in the composition of the star.
The interstellar transmission of information.
According to Kardashev, the transmissions of an extraterrestrial civilization (what SERENDIP is looking for) can be divided into two types. On the one hand, there can be an exchange of information between highly developed civilizations or civilizations at similar stages of evolution. On the other hand, the transmission of information can be aimed at raising the level of other less developed civilizations. If supercivilizations do exist, the transmissions of the first type must remain inaccessible to our observation because they must be unidirectional and not be directed toward the Solar System. Conversely, those of the second type must be easily detectable by our listening devices. A signal of artificial origin should contain more than 10 and less than 100 bits. The latter would be of two types: transient and stable. Several criteria allow us to distinguish a signal of artificial origin from others. First, the optimal region of the spectrum to host artificial signals is the one where the temperature of the cosmic microwave background is the lowest. Second, artificial sources must have a minimum angular size. Finally, the presence of suspicious data in other regions of the spectrum (such as circular polarization, radio and optical frequencies, or X-ray emissions) can confirm that it is an intelligent transmission. Two sources among those studied have parameters close to those expected: 1934-63 and 3C 273B.
For L. M. Gindilis, there are two criteria for a signal to be called artificial: one related to the artificial nature of the source and the other related to a particular radiation, intentionally designed to ensure communication and facilitate detection. Only Type II or III civilizations can communicate using isotropic transmissions that allow omnidirectional reception. In a 1 MHz band (which requires about 1024 watts), detection of signals from a Type II civilization is possible up to 1,000 light-years away, while signals from a Type III civilization are detectable virtually throughout the observable Universe. However, building an omnidirectional transmitter powerful enough to transmit over a range of 1,000 light years would take several million years. According to V.S. Troitsky, the energy required and the limitations in its production would be two obstacles to completing this project in a reasonable time.
For Zoltan Galántai, we would not be able to distinguish between an intelligent extraterrestrial signal and a signal of natural origin. Therefore, he does not believe that Type II, III or even IV civilizations can be detected. Even if humanity reaches Type IV, it will not be able to detect another supercivilization of a similar level, and we will consider their changes in the universe to be the result of natural causes. Thus, there may be many Type IV civilizations in the universe, but none of them will be able to detect the others. Moreover, the dimensions of the universe make these supercivilizations like islands far from the others, which Dyson defines as a "Carroll Universe".
For Alexander L. Zaitsev, the radio transmission of interstellar messages (IRM) is the most likely method used by civilizations. Planetary radio telescopes and those installed on asteroids would make it possible to listen to the many messages that could be sent to us. In 2007, the SETI program analyzed the only television frequencies sent by a Type 0 civilization, notes Michio Kaku. Therefore, our galaxy may have communications from Type II and III civilizations, but our listening devices can only detect Type 0 messages.
Search and detection of civilizations.
The Byurakan Conference (1964).
From 1962, Kardashev was a member of a SETI research group at the Sternberg Astronomical Institute in Moscow. In 1964, he organized the first Soviet conference on the possibility of extraterrestrial civilizations, which was held at the Byurakan astrophysical observatory in Armenia. This national conference was held in response to the American seminar known as the "Green Bank conference" of 1961, which was held at the Green Bank observatory in the United States. It brought together radio astronomers with the aim of "finding rational technical and linguistic solutions to the problem of communication with an extraterrestrial civilization that is more advanced than the Earth's civilization". Kardashev presented his classification, while Troitskii announced that it was possible to detect signals from other galaxies.
For Kardashev, "in the next 5 to 10 years, all the sources of radiation with the largest observable flux, in all the regions of the electromagnetic spectrum, will have been discovered and studied", the sensitivity of the listening devices having indeed reached their technical limits. According to him, the entire electromagnetic spectrum will be known and, consequently, the list of the objects that could be artificial sources could thus be extended. The search for artificial signals will then have to concentrate on objects of maximum luminosity or radiation belonging to a certain region of the spectrum, but also on objects of significant mass, and on those that represent the essence of matter in the Universe. As early as 1971, Kardashev considered that this observation requires the preparation of a plan of listening and analysis, which will allow the success of the search for extraterrestrial civilizations. Humanity will then be able to solve the "main dilemma", as it was stated by Enrico Fermi. This dilemma is, according to the Soviet astronomer, is certainly connected with our lack of information and knowledge.
Kardashev believes that a research project like Ozma is incapable of detecting a Type I civilization (an idea also promoted by Kaplan in 1971), and that SETI should instead focus on searching for intense radio signals that could emanate from active Type II or III civilizations. To prove the effectiveness of this approach, Kardashev therefore turned his attention to two radio sources discovered by the California Institute of Technology, nicknamed CTA-21 and CTA-102. Subsequently, Gennadii Borisovich Sholomitskii then used the Russian astronomical research station to study the data from CTA-102. He found that this radio source is characterized by its variability. Kardashev then considered that this could be an indication of an artificial emission source, albeit of rather short life span.
Towards a "physical eschatology".
The knowledge of these hypothetical supercivilizations must fit into a wide range of physical laws that contain the entirety of our current knowledge, since the technical and scientific developments of mankind can be considered as an inevitable and necessary stage in the process of the evolution of a civilization. Based on this principle, Kardashev proposes to define several concepts applicable to extraterrestrial civilizations. The physical laws, which are universal, can be used as a common basis for understanding other civilizations and, in particular, allow us to develop an objective research program. Michio Kaku also believes that the evolution of civilizations obeys the "iron laws of physics" and in particular the laws of thermodynamics, those of stable matter (baryonic matter) and those of planetary evolution (probability of occurrence of natural or cosmic catastrophes). The anthropic principle also makes it possible to predict the sociological characteristics at the basis of any civilization.
However, these universal laws are not the only parameters to consider. Zoltan Galántai explains that "it is impossible to calculate the future of the Universe over long periods of time without including the effects of life and intelligence", a position close to that of Freeman Dyson. Taking into account these two phenomena, the universal physical laws and the intelligence resulting from life, defines a "physical eschatology", as Galántai puts it. This approach began in the 1970s with the work of Kardashev, and then physical eschatology gradually interested a number of scientists and thinkers, notes Dyson.
A functional definition of civilization.
Observation of the development of living organisms shows that they are characterized by the tendency to store a maximum amount of information, both about the environment and about themselves. This information then leads to an abstract analysis, which plays an important role in the development of life forms. Thus, Kardashev defines civilization from a functional perspective as "a state of very stable matter capable of acquiring, abstractly analyzing and applying information in order to extract data about the environment and itself, in order to develop survival reactions ". However, this functional definition of civilization implies that it cannot have a goal or end, since it is based on the principle of accumulating more and more information. Taking up von Hoerner's categories, Kardashev sees four possible scenarios for the development of civilizations:
However, he refuses to see these as inevitable ends. But the assumption that the only limit to the development of a civilization can be the existence of a finite amount of information, in all areas, is also false, since it is highly improbable that information in the Universe is infinite. Given these two hypotheses, Kardashev argues that there is no universal civilization (supercivilization) because highly developed civilizations lose interest in space exploration. In any case, and despite the problem of the end of civilizations, he concludes, in the light of his functional definition of the advanced civilization, that the latter must use mass and energy on fantastic scales. According to him, there is no reason to denounce the hypothesis that the expansion of the Universe would not be an effect of the intelligent activity of a supercivilization.
Human civilization: a model for extrapolation.
Kardashev poses the following question: "Is it possible to describe the development of a civilization in general terms over large cosmological periods?" Now many of the fundamental parameters that characterize the development of civilization on Earth are growing exponentially. In the field of energy, astronomer Don Goldsmith estimated that the Earth receives about one billionth of the Sun's energy, and that humans use about one millionth of it. So we consume about one millionth of a billionth of the Sun's total energy. Since human expansion is exponential, we can determine how long it will take for humanity to go from Type II to Type III according to Michio Kaku. Thus, the rate of development of our own world remains the only criterion for extrapolating the state of civilizations older than humanity. The same is true for social values and basic needs according to Ashkenazi. Therefore, the time to double technical knowledge is about ten years, and to double energy output, available reserves, and population is about 25 years. Two scenarios are then possible: spatial expansion or energy stagnation, the latter being possible only for 125 years, according to Kardashev, using the following relationship formula_1:
formula_2
where formula_3 is the number of years, formula_4 is a parameter that increases annually as a function of formula_5 and of formula_3 according to formula_6 and formula_7, a growth rate.
If formula_1, then humanity's energy consumption will exceed the incident solar power (1,742 × 1017 W) after 240 years, the total power of the Sun (3,826 × 1026 W) after 800 years, and that of the Galaxy (7,29 × 1036 W) after 1,500 years. Based on this calculation, Zuckerman estimates the number of civilizations that could exist in our galaxy at 10,000. Kardashev concludes that the current exponential growth is a transitional phase in the development of a civilization, and that it is inevitably limited by natural factors. In fact, he believes that the required mass and energy will continue to grow exponentially for another 1,000 years. Civilization is thus defined by an exponential rate of increase. Humanity as a model for thinking about the development of extraterrestrial civilizations has its limitations, which can be truly overcome by a multidisciplinary approach according to the work of Kathryn Denning.
Research conducted.
In 1963, Nikolai Kardashev and Gennady Borissovich Sholomitskii studied the CTA 102 radio source on the 920 MHz band from the "Crimea Deep Space Station", looking for signs of a Type III civilization. CTA 102 had been discovered by Sholomitskii a year earlier, and Kardashev quickly saw it as a possible artificial source to study in order to validate his classification. The observation lasted until February 1965, and on April 12, Sholomitskii announced to the press (via the Russian ITAR-TASS) that Soviet astronomers had discovered a signal that could be of extraterrestrial origin. On April 14, he gave a conference in Moscow where he repeated his announcement; but by November 1964, two American astronomers had identified CTA 102 as a quasar, and their publication definitively closed the "CTA 102 case". It was the study of this source that had led to the Byurakan conference in 1964.
In 1975 and 1976, the American astronomers Frank Drake and Carl Sagan searched at Arecibo for signs of Type II civilizations in four galaxies of the Local Group: M33, M49, Leo I and Leo II. The year before, the two men had sent mankind's first message to M13. The results were published as "The Search for Extraterrestrial Intelligence" in "Scientific American" in May 1975.
In 1976, Kardashev, Troitskii, and Gindilis used the RATAN-600 radio telescope in the North Caucasus to search for signals from Type II or III civilizations in the Milky Way and other nearby galaxies. The radio telescope was built in 1966 under the supervision of Gindilis to listen at centimeter wavelengths.
In 1987, Tarter, Kardashev, and Slysh used the VLA to detect possible infrared sources near the galactic center from the IRAS telescope catalog. All three were looking for evidence of hypothetical Dyson spheres. The objects turn out to be OH/IR type stars.
A small-scale search for possible Type III sources was conducted by James Annis in 1999 and published in the "Journal of the British Interplanetary Society" under the title "Placing a limit on star-fed Kardashev type III civilizations". An astrophysicist at Fermilab (US), Annis studied a sample of 31 galaxies, both spiral and elliptical, using the Tully-Fisher diagram, in which the absolute magnitude is a function of the galaxies' rotational speed. Annis suggested that 75% of the least luminous objects (i.e., those with a decrease in absolute magnitude of 1.5 compared to the diagram) could be considered as possible candidates. However, no object with this characteristic is observed in his survey. On the other hand, Annis uses the available astronomical data to estimate the probability that a Type III civilization could exist. He shows that the average time that could allow for the emergence of such a civilization is 300 billion years, so none can exist in our present Universe.
Per Calissendorff conducted a study on a sample of spiral galaxies from two databases: 4,861 from the "Spiral Field I-band" (SFI++ catalog compiled by Springob et al. in 2005) and 95 from that of Reyes et al. in 2011. The same procedure was followed as in Annis, but the sample of galaxies used is 80 times larger than that used in the Annis study. Some sources were classified as "lopsided": they appear asymmetric in shape, meaning that one side of the galactic disc is more massive and less luminous than the other. This characteristic, according to Calissendorff, could be an indication that the galaxy is home to a civilization that has placed Dyson spheres in its main part. This can be explained by the fact that the colonization starts from one side of the galactic disk, making it appear darker and leading a distant observer to believe that the core has moved to that same side. On the other hand, a galaxy hosting Dyson spheres should be characterized by a significant source of far-infrared radiation. The fact remains that a Type III civilization can consume energy through a Dyson sphere without surrounding a star. Indeed, such megastructures could also extract energy from a black hole, according to the study by Inoue and Yokoo (2011). However, such a structure would not reduce the luminosity of an observed galaxy. Calissendorff's study concludes that 11 of the sources analyzed (out of a catalog of 2,411 galaxies, or 0.46%) show possible evidence of a Type III civilization. Searching for objects that obscure 90% of the light leaves only one source remains that meets the criteria. These positive sources show a low redshift (so they are old, about 100 million years), which is consistent with possible Type III civilizations, that could have flourished only in the early past. To have a better chance of detecting Type III artificial sources, Calissendorff suggests taking several photographs in a row, fast enough to fix the movement of turbulence in the atmosphere, applying different photometric filters and looking for dark areas (the case of a Dyson sphere being assembled by a Type II civilization), or analyzing the infrared spectrum of galaxies. A much larger sample of objects should be studied.
Observational evidence.
In 2015, a study of galactic mid-infrared emissions concluded that "Kardashev Type III civilizations are either very rare or do not exist in the local Universe".
In 2016, Paul Gilster, author of the Centauri Dreams website, described a signal apparently coming from the star HD 164595 as requiring the power of a Type I or Type II civilization, if produced by extraterrestrial lifeforms. In August 2016, however, it was discovered that the origin of the signal was most likely a military satellite orbiting the Earth.
Possible listening criteria.
Kardashev's point of view.
According to Kardashev, our ignorance of the physical possibilities of communication through space is great. We know only a negligible fraction of the electromagnetic spectrum and, therefore, of the existing sources of information in the Universe. Thus, of the 89% of information that we lack, 42% concerns the range from 109 to 1014 Hz (centimetric, millimetric, submillimetric and infrared waves) and 25% concerns the range from 1015 to 1018 Hz (ultraviolet radiation and X-rays). Kardashev distinguishes two categories of listening areas: objects emitting in a broad frequency spectrum and objects emitting on the contrary in a narrow spectral line, the second category posing much more theoretical problems than the first, while being central, both for astrophysics and for the search for extraterrestrial civilizations. Despite advances in astrophysics, the available information is still insufficient to prove the absence of supercivilizations, based on the inability to observe signs of activity. However, because of the possibility that planetary systems are much older than our own, and considering that cosmic objects such as quasars could be products of supercivilization activity, a detailed program of listening and searching for intelligent signs remains valid. This program includes:
According to Kardashev, only a radio interferometer with a base, either of the order of or larger than the diameter of the Earth, placed in orbital space, would allow listening to centimetric and decimetric frequencies. Once a set of unusual sources has been selected, the next step is to look for significant content in the radiations from these objects. In 1998, Nikolai Kardashev, S. F. Likhachev, and V. I. Zhuravlev proposed two SETI space projects to detect artificial sources: the "Millimetron" project (an orbiting observatory with a 10-meter diameter mirror) and the "VLBI optical telescope" (for interferometric synthesis of ultraviolet, optical, and infrared images).
Other leads.
For Samuil Aronovich Kaplan, "the most reliable criterion" remains the small angular diameter of the radio source. The wavelength of 21 cm, privileged since 1959, according to the study of Cocconi and Morrison, is not the only listening region. Kaplan, in 1971, also mentioned the radio region of the spectrum, characterized by the hydroxyl radical (OH). For Livio, the means of detection should focus on globular clusters, the regions most likely to harbor planets similar to the Earth.
For Guillermo A. Lemarchand, extraterrestrial civilizations should not use an omnidirectional transmitter. Instead, they should look for signals of weak information, intermittent and unidirectional. They will certainly need to use interferometry to inspect solar systems where life might appear. From Earth, it would be possible to pick up such signals at distances of up to 35 + (t_f - 2000) / 2, where t_f is the observation date in years, knowing that t_f ≥ 2000. However, there are many techniques for transmitting an interstellar message, ranging from bosons to particles and even antiparticles.
An artificial source located in the accretion disk of a supermassive black hole would be undetectable by the beams used to transmit the collected energy. In fact, the probability of detecting a beam of one micron arc-second is less than 10−23. Moreover, the energy emitted by the black hole would not allow detection of the energy used by the Type III civilization. On the other hand, the specular reflection system of the radiation could be detected by the shadow it casts on the accretion disk.
A Type III civilization using a "Fermi bubble" would be detectable by the fact that it decreases the luminosity of a region of the galaxy. An infrared observation would make it possible to highlight it, especially in elliptical galaxies, Annis suggests.
Unusual objects.
The quasar 3C 9 is cited by Kardashev as early as 1971. The study of the quasar 3C 273 shows that it has a solid structure. Other quasars (3C 279, 3C 345, 3C 84) have properties close to those expected from an artificial source, especially since the emissions are powerful in the intermediate region of the spectrum (between radio and optical frequencies). Quasars are potential artificial sources, especially since their age corresponds to the technical possibilities of supercivilizations. Radio sources at the center of galaxies can also be artificial sources, according to Kardashev, even if in 2013 they were proven to be supermassive black holes. In 1971, Kardashev believed that the objects most likely to be artificial sources could be discovered in the [then] next few years.
The extraordinary periodicity of pulsar emissions was already considered an artificial source in 1968 by Antony Hewish, the discoverer of the first pulsar (CP 19019). The press of the time nicknamed this object "LGM-1" (for "little green men"), following the clumsiness of Hewish, who did not wait for the necessary verifications. Kaplan, in 1971, removed the pulsar from the list of objects that could be a source of artificial origin.
In 2011, James and Dominic Benford examined the possibilities that exist to distinguish pulsars from possible artificial sources emitting intelligent signals, such as: bandwidth (signals of about 100 MHz could be artificial), pulse length (to reduce costs, the pulse should be short) and frequency (about 10 GHz, also for economic reasons). The radio source PSR J1928+15 (observed in 2005 near the Galactic disk, at a frequency of 1.44 GHz, at Arecibo) could be of extraterrestrial origin. James and Dominic Benford consider three scenarios in which the cost factor is taken into account. If the source is cost-optimized, it belongs to a civilization of Type 0.35 (the Earth being of Type 0.73). If it is not cost-optimized and operates with a small antenna, the Type is 0.86. With a large antenna, it would be from a Type 0.66. Using this cost/efficiency method, it can be estimated that low-intensity sources may be the most prevalent, but also the most difficult to observe.
Criticisms of the classification.
Irrelevant assumptions.
William I. Newman and Carl Sagan believe that the growth of energy consumption alone cannot describe the evolution of civilizations; it is also necessary to consider population growth, and in particular the fact that it can be limited by the transport capacity of interplanetary means of travel. They conclude that there can be no ancient civilizations of galactic dimensions, nor galactic empires, although the possibility of networks of colonized worlds (of about 5 to 10 planets) is strong.
The scale theorized by Kardashev was born in the geopolitical context of the Cold War, in which energy had supreme value. According to Guillermo A. Lemarchand, a physicist at the University of Buenos Aires, there are four arguments against Kardashev's classification:
For the British meteorologist Lewis Fry Richardson, author of a statistical study on mortality (published in "Statistics of Deadly Quarrels", 1960), man's aggressiveness does not allow us to predict a life span that will allow humanity to reach more evolved stages. He estimates that man's violent impulses will destroy the social order over a period of 1000 years. Moreover, mankind will probably be destroyed with weapons of mass destruction within a few centuries at the most.
Transhumanists Paul Hughes and John Smart explain the absence of signals from a Type III civilization with two hypotheses: either it has self-destructed or it has not followed the trajectory described by Kardashev. The growth of energy consumption should lead to a climate crisis, which Yvan Dutil and Stéphane Dumas set at 1 W/m2 of the Earth or 127 TW for the entire planet. At a growth rate of 2% per year, an industrial civilization should stop growing quite early in its history (after a few centuries). In summary, the impossibility of sustainably securing energy resources may explain the absence of Type II and III civilizations.
For Zoltan Galántai, it is not possible to imagine a civilization project that spans centuries (like a Dyson sphere) or even millions of years, unless one imagines a thought and an ethic different from ours, within the reach of an ancestral civilization. He therefore proposes to classify civilizations according to their ability to carry out large-scale civilization projects over the long term.
Finally, for Freeman Dyson, communication and life can continue forever in an open Universe with a finite amount of energy; intelligence is therefore the only fundamental parameter for a civilization to survive in the very long term, and energy is then no longer what defines it, a thesis he develops in his article "Time Without End: Physics and Biology in an Open Universe".
Civilization implications.
There are many historical examples of human civilization undergoing large-scale transitions, such as the Industrial Revolution. The transitions between Kardashev scale levels could potentially represent similarly dramatic periods of social upheaval, as they involve exceeding the hard limits of the resources available within a civilization's existing territory. A common speculation is that the transition from Type 0 to Type I could carry a strong risk of self-destruction, since in some scenarios there would be no room for further expansion on the civilization's home planet, as in a Malthusian catastrophe.
For example, excessive energy consumption without adequate heat removal could plausibly render the planet of a Type I approaching civilization unsuitable for the biology of the dominant life forms and their food sources. Using Earth as an example, ocean temperatures above 95 °F (35 °C) would endanger marine life and make it difficult, if not impossible, for mammals to cool to temperatures suitable for their metabolism. Of course, these theoretical speculations may not become problems, possibly through the application of future engineering and technology. Also, by the time a civilization reaches Type I, it may have colonized other planets or established O'Neill-type colonies, so that waste heat could be distributed throughout the star system.
The limitations of biological life forms and the evolution of computer technology may lead to the transformation of the civilization through mind uploading and artificial general intelligence in general during the transition from Type I to Type II, leading to a digitized civilization.
See also.
<templatestyles src="Div col/styles.css"/>
Notes.
<templatestyles src="Reflist/styles.css" />
References.
<templatestyles src="Reflist/styles.css" />
Further reading.
<templatestyles src="Refbegin/styles.css" /> | [
{
"math_id": 0,
"text": "K = \\frac{\\log_{10}{W}-6} {10}"
},
{
"math_id": 1,
"text": "\\alpha = 1,04"
},
{
"math_id": 2,
"text": "t = \\frac{\\log \\left(P/P_o\\right)}{\\log \\alpha}"
},
{
"math_id": 3,
"text": "t"
},
{
"math_id": 4,
"text": "P"
},
{
"math_id": 5,
"text": "P_o"
},
{
"math_id": 6,
"text": "P = P_o \\alpha^t"
},
{
"math_id": 7,
"text": "\\alpha"
}
]
| https://en.wikipedia.org/wiki?curid=140271 |
1403024 | Corwin Hansch | American pharmacologist
Corwin Herman Hansch (October 6, 1918 – May 8, 2011) was a professor of chemistry at Pomona College in California. He became known as the 'father of computer-assisted molecule design.'
Education and career.
Hansch was born on October 6, 1918, in Kenmare, North Dakota. He earned a BS from the University of Illinois in 1940 and a PhD from New York University in 1944. He briefly worked as a postdoc at the University of Illinois Chicago.
Hansch worked on the Manhattan Project at the University of Chicago and as a group leader at DuPont Nemours in Richland, Washington. In February 1946 he received an academic position at Pomona College, where he taught until 1988. Hansch completed sabbaticals at ETH Zurich with Vladimir Prelog and at University of Munich with Rolf Huisgen.
Hansch taught Organic Chemistry for many years at Pomona College, and was known for giving complex lectures without using notes. His course in Physical Bio-Organic Medicinal Chemistry was ground-breaking at an undergraduate level.
Hansch may be best known as the father of the concept of quantitative structure-activity relationship (QSAR), the quantitative correlation of the physicochemical properties of molecules with their biological activities.
He is also noted for the Hansch equation, which is used in
Research Interests:
Organic Chemistry; Interaction of organic chemicals with living organisms, Quantitative Structure Activity Relationships (QSAR).
Death.
He died of pneumonia on May 8, 2011, in Claremont, California, at 92.
Notes.
His research group at Pomona College worked on QSAR studies and in building and expanding the database of chemical and physical data as C-QSAR and Bioloom. His postgraduate associates were Rajni Garg, Cynthia R. D. Selassie, Suresh Babu Mekapati, and Alka Kurup.
The Journal of Computer-Aided Molecular Design carried four obituaries (as found in a Pubmed personal subject [ps] search).
Among his students at Pomona was Jennifer Doudna, co-recipient of the 2020 Nobel Prize in Chemistry. Doudna has credited Hansch as an influence.
Bibliography.
A preliminary search in WorldCat and in PubMed, two among many relevant bibliographic and citation indexes, shows the following:
The Pomona College Archives holds reprints of Hansch's articles published between 1962 and 2009 in addition to other materials.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\pi"
}
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| https://en.wikipedia.org/wiki?curid=1403024 |
14031360 | Reprojection error | The reprojection error is a geometric error corresponding to the image distance between a projected point and a measured one. It is used to quantify how closely an estimate of a 3D point formula_0 recreates the point's true projection formula_1. More precisely, let formula_2 be the projection matrix of a camera and formula_3 be the image projection of formula_0, i.e. formula_4. The reprojection error of formula_0 is given by formula_5, where formula_5 denotes the Euclidean distance between the image points represented by vectors formula_1 and formula_3.
Minimizing the reprojection error can be used for estimating the error from point correspondences between two images. Suppose we are given 2D to 2D point imperfect correspondences formula_6. We wish to find a homography formula_7 and pairs of perfectly matched points formula_8 and formula_9, i.e. points that satisfy formula_10 that minimize the reprojection error function given by
formula_11
So the correspondences can be interpreted as imperfect images of a world point and the reprojection error quantifies their deviation from the true image projections formula_12 | [
{
"math_id": 0,
"text": "\\hat{\\mathbf{X}}"
},
{
"math_id": 1,
"text": "\\mathbf{x}"
},
{
"math_id": 2,
"text": "\\mathbf{P}"
},
{
"math_id": 3,
"text": "\\hat{\\mathbf{x}}"
},
{
"math_id": 4,
"text": "\\hat{\\mathbf{x}}=\\mathbf{P} \\, \\hat{\\mathbf{X}}"
},
{
"math_id": 5,
"text": "d(\\mathbf{x}, \\, \\hat{\\mathbf{x}})"
},
{
"math_id": 6,
"text": "\\{\\mathbf{x_i} \\leftrightarrow \\mathbf{x_i}'\\}"
},
{
"math_id": 7,
"text": "\\hat{\\mathbf{H}}"
},
{
"math_id": 8,
"text": "\\hat{\\mathbf{x_i}}"
},
{
"math_id": 9,
"text": "\\hat{\\mathbf{x}}_i'"
},
{
"math_id": 10,
"text": "\\hat{\\mathbf{x_i}}' = \\hat{H}\\mathbf{\\hat{x}_i}"
},
{
"math_id": 11,
"text": " \\sum_i d(\\mathbf{x_i}, \\hat{\\mathbf{x_i}})^2 + d(\\mathbf{x_i}', \\hat{\\mathbf{x_i}}')^2"
},
{
"math_id": 12,
"text": "\\hat{\\mathbf{x_i}}, \\hat{\\mathbf{x_i}}'"
}
]
| https://en.wikipedia.org/wiki?curid=14031360 |
14031635 | Rook polynomial | Generating polynomial of the number of ways to place non-attacking rooks on a chessboard
In combinatorial mathematics, a rook polynomial is a generating polynomial of the number of ways to place non-attacking rooks on a board that looks like a checkerboard; that is, no two rooks may be in the same row or column. The board is any subset of the squares of a rectangular board with "m" rows and "n" columns; we think of it as the squares in which one is allowed to put a rook. The board is the ordinary chessboard if all squares are allowed and "m" = "n" = 8 and a chessboard of any size if all squares are allowed and "m" = "n". The coefficient of "x" "k" in the rook polynomial "R""B"("x") is the number of ways "k" rooks, none of which attacks another, can be arranged in the squares of "B". The rooks are arranged in such a way that there is no pair of rooks in the same row or column. In this sense, an arrangement is the positioning of rooks on a static, immovable board; the arrangement will not be different if the board is rotated or reflected while keeping the squares stationary. The polynomial also remains the same if rows are interchanged or columns are interchanged.
The term "rook polynomial" was coined by John Riordan.
Despite the name's derivation from chess, the impetus for studying rook polynomials is their connection with counting permutations (or partial permutations) with restricted positions. A board "B" that is a subset of the "n" × "n" chessboard corresponds to permutations of "n" objects, which we may take to be the numbers 1, 2, ..., "n", such that the number "a""j" in the "j"-th position in the permutation must be the column number of an allowed square in row "j" of "B". Famous examples include the number of ways to place "n" non-attacking rooks on:
Interest in rook placements arises in pure and applied combinatorics, group theory, number theory, and statistical physics. The particular value of rook polynomials comes from the utility of the generating function approach, and also from the fact that the zeroes of the rook polynomial of a board provide valuable information about its coefficients, i.e., the number of non-attacking placements of "k" rooks.
Definition.
The rook polynomial "R""B"("x") of a board "B" is the generating function for the numbers of arrangements of non-attacking rooks:
formula_0
where formula_1 is the number of ways to place "k" non-attacking rooks on the board "B". There is a maximum number of non-attacking rooks the board can hold; indeed, there cannot be more rooks than the number of rows or number of columns in the board (hence the limit formula_2).
Complete boards.
For rectangular "m" × "n" boards "B""m","n", we write "Rm,n" := "R"B"m","n", and if "m"="n", "Rn" := "R""m","n".
The first few rook polynomials on square "n" × "n" boards are:
formula_3
In words, this means that on a 1 × 1 board, 1 rook can be arranged in 1 way, and zero rooks can also be arranged in 1 way (empty board); on a complete 2 × 2 board, 2 rooks can be arranged in 2 ways (on the diagonals), 1 rook can be arranged in 4 ways, and zero rooks can be arranged in 1 way; and so forth for larger boards.
The rook polynomial of a rectangular chessboard is closely related to the generalized Laguerre polynomial "L""n""α"("x") by the identity
formula_4
Matching polynomials.
A rook polynomial is a special case of one kind of matching polynomial, which is the generating function of the number of "k"-edge matchings in a graph.
The rook polynomial "R""m","n"("x") corresponds to the complete bipartite graph "K""m","n" . The rook polynomial of a general board "B" ⊆ "B""m","n" corresponds to the bipartite graph with left vertices "v"1, "v"2, ..., "v""m" and right vertices "w"1, "w"2, ..., "w""n" and an edge "v""i""w""j" whenever the square ("i", "j") is allowed, i.e., belongs to "B". Thus, the theory of rook polynomials is, in a sense, contained in that of matching polynomials.
We deduce an important fact about the coefficients "r""k", which we recall given the number of non-attacking placements of "k" rooks in "B": these numbers are unimodal, i.e., they increase to a maximum and then decrease. This follows (by a standard argument) from the theorem of Heilmann and Lieb about the zeroes of a matching polynomial (a different one from that which corresponds to a rook polynomial, but equivalent to it under a change of variables), which implies that all the zeroes of a rook polynomial are negative real numbers.
Connection to matrix permanents.
For incomplete square "n" × "n" boards, (i.e. rooks are not allowed to be played on some arbitrary subset of the board's squares) computing the number of ways to place "n" rooks on the board is equivalent to computing the permanent of a 0–1 matrix.
Complete rectangular boards.
Rooks problems.
A precursor to the rook polynomial is the classic "Eight rooks problem" by H. E. Dudeney in which he shows that the maximum number of non-attacking rooks on a chessboard is eight by placing them on one of the main diagonals (Fig. 1). The question asked is: "In how many ways can eight rooks be placed on an 8 × 8 chessboard so that neither of them attacks the other?" The answer is: "Obviously there must be a rook in every row and every column. Starting with the bottom row, it is clear that the first rook can be put on any one of eight different squares (Fig. 1). Wherever it is placed, there is the option of seven squares for the second rook in the second row. Then there are six squares from which to select the third row, five in the fourth, and so on. Therefore the number of different ways must be 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 40,320" (that is, 8!, where "!" is the factorial).
The same result can be obtained in a slightly different way. Let us endow each rook with a positional number, corresponding to the number of its rank, and assign it a name that corresponds to the name of its file. Thus, rook a1 has position 1 and name "a", rook b2 has position 2 and name "b", etc. Then let us order the rooks into an ordered list (sequence) by their positions. The diagram on Fig. 1 will then transform in the sequence (a,b,c,d,e,f,g,h). Placing any rook on another file would involve moving the rook that hitherto occupied the second file to the file, vacated by the first rook. For instance, if rook a1 is moved to "b" file, rook b2 must be moved to "a" file, and now they will become rook b1 and rook a2. The new sequence will become (b,a,c,d,e,f,g,h). In combinatorics, this operation is termed permutation, and the sequences, obtained as a result of the permutation, are permutations of the given sequence. The total number of permutations, containing 8 elements from a sequence of 8 elements is 8! (factorial of 8).
To assess the effect of the imposed limitation "rooks must not attack each other", consider the problem without such limitation. In how many ways can eight rooks be placed on an 8 × 8 chessboard? This will be the total number of combinations of 8 rooks on 64 squares:
formula_5
Thus, the limitation "rooks must not attack each other" reduces the total number of allowable positions from combinations to permutations which is a factor of about 109,776.
A number of problems from different spheres of human activity can be reduced to the rook problem by giving them a "rook formulation". As an example: A company must employ "n" workers on "n" different jobs and each job must be carried out only by one worker. In how many ways can this appointment be done?
Let us put the workers on the ranks of the "n" × "n" chessboard, and the jobs − on the files. If worker "i" is appointed to job "j", a rook is placed on the square where rank "i" crosses file "j". Since each job is carried out only by one worker and each worker is appointed to only one job, all files and ranks will contain only one rook as a result of the arrangement of "n" rooks on the board, that is, the rooks do not attack each other.
The rook polynomial as a generalization of the rooks problem.
The classical rooks problem immediately gives the value of "r"8, the coefficient in front of the highest order term of the rook polynomial. Indeed, its result is that 8 non-attacking rooks can be arranged on an 8 × 8 chessboard in "r"8 = 8! = 40320 ways.
Let us generalize this problem by considering an "m" × "n" board, that is, a board with "m" ranks (rows) and "n" files (columns). The problem becomes: In how many ways can one arrange "k" rooks on an "m" × "n" board in such a way that they do not attack each other?
It is clear that for the problem to be solvable, "k" must be less or equal to the smaller of the numbers "m" and "n"; otherwise one cannot avoid placing a pair of rooks on a rank or on a file. Let this condition be fulfilled. Then the arrangement of rooks can be carried out in two steps. First, choose the set of "k" ranks on which to place the rooks. Since the number of ranks is "m", of which "k" must be chosen, this choice can be done in formula_6 ways. Similarly, the set of "k" files on which to place the rooks can be chosen in formula_7 ways. Because the choice of files does not depend on the choice of ranks, according to the products rule there are formula_8 ways to choose the square on which to place the rook.
However, the task is not yet finished because "k" ranks and "k" files intersect in "k"2 squares. By deleting unused ranks and files and compacting the remaining ranks and files together, one obtains a new board of "k" ranks and "k" files. It was already shown that on such board "k" rooks can be arranged in "k"! ways (so that they do not attack each other). Therefore, the total number of possible non-attacking rooks arrangements is:
formula_9
For instance, 3 rooks can be placed on a conventional chessboard (8 × 8) in formula_10 ways. For "k" = "m" = "n", the above formula gives "rk" = "n"! that corresponds to the result obtained for the classical rooks problem.
The rook polynomial with explicit coefficients is now:
formula_11
If the limitation "rooks must not attack each other" is removed, one must choose any "k" squares from "m" × "n" squares. This can be done in:
formula_12 ways.
If the "k" rooks differ in some way from each other, e.g., they are labelled or numbered, all the results obtained so far must be multiplied by "k"!, the number of permutations of "k" rooks.
Symmetric arrangements.
As a further complication to the rooks problem, let us require that rooks not only be non-attacking but also symmetrically arranged on the board. Depending on the type of symmetry, this is equivalent to rotating or reflecting the board.
Symmetric arrangements lead to many problems, depending on the symmetry condition.
The simplest of those arrangements is when rooks are symmetric about the centre of the board. Let us designate with "Gn" the number of arrangements in which "n" rooks are placed on a board with "n" ranks and "n" files. Now let us make the board to contain 2"n" ranks and 2"n" files. A rook on the first file can be placed on any of the 2"n" squares of that file. According to the symmetry condition, placement of this rook defines the placement of the rook that stands on the last file − it must be arranged symmetrically to the first rook about the board centre. Let us remove the first and the last files and the ranks that are occupied by rooks (since the number of ranks is even, the removed rooks cannot stand on the same rank). This will give a board of 2"n" − 2 files and 2"n" − 2 ranks. It is clear that to each symmetric arrangement of rooks on the new board corresponds a symmetric arrangement of rooks on the original board. Therefore, "G"2"n" = 2"nG"2"n" − 2 (the factor 2"n" in this expression comes from the possibility for the first rook to occupy any of the 2"n" squares on the first file). By iterating the above formula one reaches to the case of a 2 × 2 board, on which there are 2 symmetric arrangements (on the diagonals). As a result of this iteration, the final expression is "G"2"n" = 2"n""n"! For the usual chessboard (8 × 8), "G"8 = 24 × 4! = 16 × 24 = 384 centrally symmetric arrangements of 8 rooks. One such arrangement is shown in Fig. 2.
For odd-sized boards (containing 2"n" + 1 ranks and 2"n" + 1 files) there is always a square that does not have its symmetric double − this is the central square of the board. There must always be a rook placed on this square. Removing the central file and rank, one obtains a symmetric arrangement of 2"n" rooks on a 2"n" × 2"n" board. Therefore, for such board, once again "G"2"n" + 1 = "G"2"n" = 2"n""n"!.
A little more complicated problem is to find the number of non-attacking arrangements that do not change upon 90° rotation of the board. Let the board have 4"n" files and 4"n" ranks, and the number of rooks is also 4"n". In this case, the rook that is on the first file can occupy any square on this file, except the corner squares (a rook cannot be on a corner square because after a 90° rotation there would 2 rooks that attack each other). There are another 3 rooks that correspond to that rook and they stand, respectively, on the last rank, the last file, and the first rank (they are obtained from the first rook by 90°, 180°, and 270° rotations). Removing the files and ranks of those rooks, one obtains the rook arrangements for a (4"n" − 4) × (4"n" − 4) board with the required symmetry. Thus, the following recurrence relation is obtained: "R"4"n" = (4"n" − 2)"R"4"n" − 4, where "Rn" is the number of arrangements for a "n" × "n" board. Iterating, it follows that "R"4"n" = 2"n"(2"n" − 1)(2"n" − 3)...1. The number of arrangements for a (4"n" + 1) × (4"n" + 1) board is the same as that for a 4"n" × 4"n" board; this is because on a (4"n" + 1) × (4"n" + 1) board, one rook must necessarily stand in the centre and thus the central rank and file can be removed. Therefore "R"4"n" + 1 = "R"4"n". For the traditional chessboard ("n" = 2), "R"8 = 4 × 3 × 1 = 12 possible arrangements with rotational symmetry.
For (4"n" + 2) × (4"n" + 2) and (4"n" + 3) × (4"n" + 3) boards, the number of solutions is zero. Two cases are possible for each rook: either it stands in the centre or it doesn't stand in the centre. In the second case, this rook is included in the rook quartet that exchanges squares on turning the board at 90°. Therefore, the total number of rooks must be either 4"n" (when there is no central square on the board) or 4"n" + 1. This proves that "R"4"n" + 2 = "R"4"n" + 3 = 0.
The number of arrangements of "n" non-attacking rooks symmetric to one of the diagonals (for determinacy, the diagonal corresponding to a1–h8 on the chessboard) on a "n" × "n" board is given by the telephone numbers defined by the recurrence "Q""n" = "Q""n" − 1 + ("n" − 1)"Q""n" − 2. This recurrence is derived in the following way. Note that the rook on the first file either stands on the bottom corner square or it stands on another square. In the first case, removal of the first file and the first rank leads to the symmetric arrangement "n" − 1 rooks on a ("n" − 1) × ("n" − 1) board. The number of such arrangements is "Q""n" − 1. In the second case, for the original rook there is another rook, symmetric to the first one about the chosen diagonal. Removing the files and ranks of those rooks leads to a symmetric arrangement "n" − 2 rooks on a ("n" − 2) × ("n" − 2) board. Since the number of such arrangements is "Q""n" − 2 and the rook can be put on the "n" − 1 square of the first file, there are ("n" − 1)"Q""n" − 2 ways for doing this, which immediately gives the above recurrence. The number of diagonal-symmetric arrangements is then given by the expression:
formula_13
This expression is derived by partitioning all rook arrangements in classes; in class "s" are those arrangements in which "s" pairs of rooks do not stand on the diagonal. In exactly the same way, it can be shown that the number of "n"-rook arrangements on a "n" × "n" board, such that they do not attack each other and are symmetric to both diagonals is given by the recurrence equations "B"2"n" = 2"B"2"n" − 2 + (2"n" − 2)"B"2"n" − 4 and "B"2"n" + 1 = "B"2"n".
Arrangements counted by symmetry classes.
A different type of generalization is that in which rook arrangements that are obtained from each other by symmetries of the board are counted as one. For instance, if rotating the board by 90 degrees is allowed as a symmetry, then any arrangement obtained by a rotation of 90, 180, or 270 degrees is considered to be "the same" as the original pattern, even though these arrangements are counted separately in the original problem where the board is fixed. For such problems, Dudeney observes: "How many ways there are if mere reversals and reflections are not counted as different has not yet been determined; it is a difficult problem." The problem reduces to that of counting symmetric arrangements via Burnside's lemma. | [
{
"math_id": 0,
"text": "R_B(x)= \\sum_{k=0}^{\\min{(m,n)}} r_k(B) x^k,"
},
{
"math_id": 1,
"text": "r_k(B)"
},
{
"math_id": 2,
"text": "\\min(m,n)"
},
{
"math_id": 3,
"text": "\\begin{align}\n R_1(x) & = x + 1 \\\\\n R_2(x) & = 2 x^2 + 4 x + 1 \\\\\n R_3(x) & = 6 x^3 + 18 x^2 + 9 x + 1 \\\\\n R_4(x) & = 24 x^4 + 96 x^3 + 72 x^2 + 16 x + 1.\n\\end{align}"
},
{
"math_id": 4,
"text": "R_{m,n}(x)= n! x^n L_n^{(m-n)}(-x^{-1})."
},
{
"math_id": 5,
"text": " {64 \\choose 8} = \\frac{64!}{8!(64-8)!} = 4,426,165,368."
},
{
"math_id": 6,
"text": "\\binom{m}{k}"
},
{
"math_id": 7,
"text": "\\binom{n}{k}"
},
{
"math_id": 8,
"text": "\\binom{m}{k}\\binom{n}{k}"
},
{
"math_id": 9,
"text": "r_k = \\binom{m}{k}\\binom{n}{k} k! = \\frac{n! m!}{k! (n-k)! (m-k)!}."
},
{
"math_id": 10,
"text": "\\textstyle{\\frac{8! 8!}{3!5!5!}} = 18,816"
},
{
"math_id": 11,
"text": "R_{m,n}(x) = \\sum_{k=0}^{\\min(m,n)} \\binom{m}{k} \\binom{n}{k} k! x^k = \\sum_{k=0}^{\\min(m,n)}\\frac{n! m!}{k! (n-k)! (m-k)!} x^k."
},
{
"math_id": 12,
"text": "\\binom{mn}{k} = \\frac{(mn)!}{k! (mn-k)!}"
},
{
"math_id": 13,
"text": "Q_n = 1 + \\binom{n}{2} + \\frac{1}{1 \\times 2}\\binom{n}{2}\\binom{n-2}{2} + \\frac{1}{1 \\times 2 \\times 3}\\binom{n}{2}\\binom{n-2}{2}\\binom{n-4}{2} + \\cdots."
}
]
| https://en.wikipedia.org/wiki?curid=14031635 |
1403190 | Law of identity | Logic statement
In logic, the law of identity states that each thing is identical with itself. It is the first of the historical three laws of thought, along with the law of noncontradiction, and the law of excluded middle. However, few systems of logic are built on just these laws.
History.
Ancient philosophy.
The earliest recorded use of the law appears in Plato's dialogue "Theaetetus" (185a), wherein Socrates attempts to establish that what we call "sounds" and "colours" are two different classes of thing:
<templatestyles src="Template:Blockquote/styles.css" />Socrates: With regard to sound and colour, in the first place, do you think this about both: that they both are? <br>Theaetetus: Yes.<br>Socrates: Then do you think that each differs to the other, and "the same as itself"?<br>Theaetetus: Certainly.<br>Socrates: And that both are two and each of them one?<br>Theaetetus: Yes, that too.
It is used explicitly only once in Aristotle, in a proof in the "Prior Analytics":
<templatestyles src="Template:Blockquote/styles.css" />When A belongs to the whole of B and to C and is affirmed of nothing else, and B also belongs to all C, it is necessary that A and B should be convertible: for since A is said of B and C only, and B is "affirmed both of itself" and of C, it is clear that B will be said of everything of which A is said, except A itself.
Medieval philosophy.
Aristotle believed the law of non-contradiction to be the most fundamental law. Both Thomas Aquinas ("Met." IV, lect. 6) and Duns Scotus ("Quaest. sup. Met." IV, Q. 3) follow Aristotle in this respect. Antonius Andreas, the Spanish disciple of Scotus (d. 1320), argues that the first place should belong to the law "Every Being is a Being" ("Omne Ens est Ens", Qq. in Met. IV, Q. 4), but the late scholastic writer Francisco Suárez ("Disp. Met." III, § 3) disagreed, also preferring to follow Aristotle.
Another possible allusion to the same principle may be found in the writings of Nicholas of Cusa (1431–1464) where he says: <templatestyles src="Template:Blockquote/styles.css" />... there cannot be several things exactly the same, for in that case there would not be several things, but the same thing itself. Therefore all things both agree with and differ from one another.
Modern philosophy.
Gottfried Wilhelm Leibniz claimed that the law of identity, which he expresses as "Everything is what it is", is the first primitive truth of reason which is affirmative, and the law of noncontradiction is the first negative truth ("Nouv. Ess." IV, 2, § i), arguing that "the statement that a thing is what it is, is prior to the statement that it is not another thing" ("Nouv. Ess." IV, 7, § 9). Wilhelm Wundt credits Gottfried Leibniz with the symbolic formulation, "A is A". Leibniz's Law is a similar principle, that if two objects have all the same properties, they are in fact one and the same: Fx and Fy iff x = y.
John Locke ("Essay Concerning Human Understanding" IV. vii. iv. ("Of Maxims") says:
<templatestyles src="Template:Blockquote/styles.css" />[...] whenever the mind with attention considers any proposition, so as to perceive the two ideas signified by the terms, and affirmed or denied one of the other to be the same or different; it is presently and infallibly certain of the truth of such a proposition; and this equally whether these propositions be in terms standing for more general ideas, or such as are less so: e.g., whether the general idea of Being be affirmed of itself, as in this proposition, "whatsoever is, is"; or a more particular idea be affirmed of itself, as "a man is a man"; or, "whatsoever is white is white" [...]
Afrikan Spir proclaims the law of identity as the fundamental law of knowledge, which is opposed to the changing appearance of the empirical reality.
George Boole, in the introduction to his treatise "The Laws of Thought" made the following observation with respect to the nature of language and those principles that must inhere naturally within them, if they are to be intelligible:
<templatestyles src="Template:Blockquote/styles.css" />There exist, indeed, certain general principles founded in the very nature of language, by which the use of symbols, which are but the elements of scientific language, is determined. To a certain extent these elements are arbitrary. Their interpretation is purely conventional: we are permitted to employ them in whatever sense we please. But this permission is limited by two indispensable conditions, first, that from the sense once conventionally established we never, in the same process of reasoning, depart; secondly, that the laws by which the process is conducted be founded exclusively upon the above fixed sense or meaning of the symbols employed.
Objectivism, the philosophy founded by novelist Ayn Rand, is grounded in three axioms, one of which is the law of identity, "A is A". In the Objectivism of Ayn Rand, the law of identity is used with the concept existence to deduce that that which exists is something. Logic in Objectivist epistemology is based on the three laws of logic.
Contemporary philosophy.
Analytic.
In the "Foundations of Arithmetic", Gottlob Frege associated the number one with the property of being self identical. Frege's paper "On Sense and Reference" begins with a discussion on equality and meaning. Frege wondered how a true statement of the form "a = a", a trivial instance of the law of identity, could be different from a true statement of the form "a = b", a genuine extension of knowledge, if the meaning of a term was its referent.
Bertrand Russell in "On Denoting" has this similar puzzle: "If a is identical with b, whatever is true of the one is true of the other, and either may be substituted for the other without altering the truth or falsehood of that proposition. Now George IV wished to know whether Scott was the author of "Waverley"; and in fact Scott was the author of "Waverley". Hence we may substitute “Scott” for “the author of "Waverley"” and thereby prove that George IV wished to know whether Scott was Scott. Yet an interest in the law of identity can hardly be attributed to the first gentleman of Europe.”
In his "Tractatus Logico-Philosophicus", Ludwig Wittgenstein writes that "roughly speaking: to say of two things that they are identical is nonsense, and to say of one thing that it is identical with itself is to say nothing".
In the formal logic of analytical philosophy, the law of identity is written ""a" = "a"" or "For all "x": "x" = "x"", where a or x refer to a term rather than a proposition, and thus the law of identity is not used in propositional logic. It is that which is expressed by the equals sign "=", the notion of identity or equality.
Continental.
Martin Heidegger gave a talk in 1957 entitled "Der Satz der Identität" (The Statement of Identity), where he linked the law of identity "A=A" to the Parmenides' fragment "to gar auto estin noien te kai einai" (...for the same thing can be thought and can exist). Heidegger thus understands identity starting from the relationship of Thinking and Being, and from the belonging-together of Thinking and Being.
Gilles Deleuze wrote that "Difference and Repetition" is prior to any concept of identity.
Modern logic.
In first-order logic, identity (or equality) is represented as a two-place predicate, or relation, =. Identity is a relation on individuals. It is not a relation between propositions, and is not concerned with the meaning of propositions, nor with equivocation. The law of identity can be expressed as formula_0, where x is a variable ranging over the domain of all individuals. In logic, there are various different ways identity can be handled. In first-order logic with identity, identity is treated as a logical constant and its axioms are part of the logic itself. Under this convention, the law of identity is a logical truth.
In first-order logic without identity, identity is treated as an interpretable predicate and its axioms are supplied by the theory. This allows a broader equivalence relation to be used that may allow "a = b" to be satisfied by distinct individuals "a" and "b". Under this convention, a model is said to be normal when no distinct individuals "a" and "b" satisfy "a = b".
One example of a logic that rejects or restricts the law of identity in this way is Schrödinger logic.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\forall x (x = x)"
}
]
| https://en.wikipedia.org/wiki?curid=1403190 |
14032611 | M/M/1 queue | Queue with Markov (Poisson) arrival process, exponential service time distribution and one server
In queueing theory, a discipline within the mathematical theory of probability, an M/M/1 queue represents the queue length in a system having a single server, where arrivals are determined by a Poisson process and job service times have an exponential distribution. The model name is written in Kendall's notation. The model is the most elementary of queueing models and an attractive object of study as closed-form expressions can be obtained for many metrics of interest in this model. An extension of this model with more than one server is the M/M/c queue.
Model definition.
An M/M/1 queue is a stochastic process whose state space is the set {0,1,2,3...} where the value corresponds to the number of customers in the system, including any currently in service.
The model can be described as a continuous time Markov chain with transition rate matrix
formula_0
on the state space {0,1,2,3...}. This is the same continuous time Markov chain as in a birth–death process. The state space diagram for this chain is as below.
Stationary analysis.
The model is considered stable only if λ < μ. If, on average, arrivals happen faster than service completions the queue will grow indefinitely long and the system will not have a stationary distribution. The stationary distribution is the limiting distribution for large values of "t".
Various performance measures can be computed explicitly for the M/M/1 queue. We write ρ = λ/μ for the utilization of the buffer and require ρ < 1 for the queue to be stable. ρ represents the average proportion of time which the server is occupied.
The probability that the stationary process is in state "i" (contains "i" customers, including those in service) is
formula_1
Average number of customers in the system.
We see that the number of customers in the system is geometrically distributed with parameter 1 − "ρ". Thus the average number of customers in the system is "ρ"/(1 − "ρ") and the variance of number of customers in the system is "ρ"/(1 − "ρ")2. This result holds for any work conserving service regime, such as processor sharing.
Busy period of server.
The busy period is the time period measured between the instant a customer arrives to an empty system until the instant a customer departs leaving behind an empty system. The busy period has probability density function
formula_2
where "I"1 is a modified Bessel function of the first kind, obtained by using Laplace transforms and inverting the solution.
The Laplace transform of the M/M/1 busy period is given by
formula_3
which gives the moments of the busy period, in particular the mean is 1/("μ" − "λ") and variance is given by
formula_4
Response time.
The average response time or sojourn time (total time a customer spends in the system) does not depend on scheduling discipline and can be computed using Little's law as 1/("μ" − "λ"). The average time spent waiting is 1/("μ" − "λ") − 1/"μ" = "ρ"/("μ" − "λ"). The distribution of response times experienced does depend on scheduling discipline.
First-come, first-served discipline.
For customers who arrive and find the queue as a stationary process, the response time they experience (the sum of both waiting time and service time) has Laplace transform
("μ" − "λ")/("s" + "μ" − "λ") and therefore probability density function
formula_5
Processor sharing discipline.
In an M/M/1-PS queue there is no waiting line and all jobs receive an equal proportion of the service capacity. Suppose the single server serves at rate 16 and there are 4 jobs in the system, each job will experience service at rate 4. The rate at which jobs receive service changes each time a job arrives at or departs from the system.
For customers who arrive to find the queue as a stationary process, the Laplace transform of the distribution of response times experienced by customers was published in 1970, for which an integral representation is known. The waiting time distribution (response time less service time) for a customer requiring "x" amount of service has transform
formula_6
where "r" is the smaller root of the equation
formula_7
The mean response time for a job arriving and requiring amount "x" of service can therefore be computed as "x μ"/("μ" − "λ"). An alternative approach computes the same results using a spectral expansion method.
Transient solution.
We can write a probability mass function dependent on "t" to describe the probability that the M/M/1 queue is in a particular state at a given time. We assume that the queue is initially in state "i" and write "p""k"("t") for the probability of being in state "k" at time "t". Then
formula_8
where formula_9 is the initial number of customers in the station at time formula_10,formula_11, formula_12 and formula_13 is the modified Bessel function of the first kind. Moments for the transient solution can be expressed as the sum of two monotone functions.
Diffusion approximation.
When the utilization "ρ" is close to 1 the process can be approximated by a reflected Brownian motion with drift parameter "λ" – "μ" and variance parameter "λ" + "μ". This heavy traffic limit was first introduced by John Kingman.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "Q=\\begin{pmatrix}\n-\\lambda & \\lambda \\\\\n\\mu & -(\\mu+\\lambda) & \\lambda \\\\\n&\\mu & -(\\mu+\\lambda) & \\lambda \\\\\n&&\\mu & -(\\mu+\\lambda) & \\lambda &\\\\\n&&&&\\ddots\n\\end{pmatrix}"
},
{
"math_id": 1,
"text": "\\pi_i=(1-\\rho)\\rho^i.\\,"
},
{
"math_id": 2,
"text": "f(t)=\\begin{cases}\n\\frac{1}{t\\sqrt{\\rho}}e^{-(\\lambda+\\mu)t}I_1(2t\\sqrt{\\lambda\\mu}) & t>0\\\\\n0 & \\text{otherwise}\\end{cases}"
},
{
"math_id": 3,
"text": "\\mathbb E( e^{-s F} )= \\frac{1}{2 \\lambda}(\\lambda + \\mu + s - \\sqrt{(\\lambda + \\mu + s)^2 - 4 \\lambda \\mu})"
},
{
"math_id": 4,
"text": "\\frac{1+\\frac{\\lambda}{\\mu}}{\\mu^2(1-\\frac{\\lambda}{\\mu})^3}."
},
{
"math_id": 5,
"text": "f(t)=\n\\begin{cases}\n(\\mu-\\lambda)e^{-(\\mu-\\lambda)t} & t>0\\\\\n0 & \\text{otherwise.}\n\\end{cases}"
},
{
"math_id": 6,
"text": "W^\\ast(s|x) = \\frac{(1-\\rho)(1-\\rho r^2)e^{-[\\lambda(1-r)+s]x}}{(1-\\rho r^2)-\\rho(1-r)^2e^{-(\\mu/r-\\lambda r)x}}"
},
{
"math_id": 7,
"text": "\\lambda r^2 - (\\lambda + \\mu + s)r + \\mu = 0."
},
{
"math_id": 8,
"text": "p_k(t)=e^{-(\\lambda+\\mu)t} \\left[ \\rho^{\\frac{k-i}{2}} I_{k-i}(at) + \\rho^{\\frac{k-i-1}{2}} I_{k+i+1}(at) + (1-\\rho) \\rho^{k} \\sum_{j=k+i+2}^{\\infty} \\rho^{-j/2}I_j(at) \\right]"
},
{
"math_id": 9,
"text": "i"
},
{
"math_id": 10,
"text": "t=0"
},
{
"math_id": 11,
"text": "\\rho=\\lambda/\\mu"
},
{
"math_id": 12,
"text": "a=2\\sqrt{\\lambda\\mu}"
},
{
"math_id": 13,
"text": "I_k"
}
]
| https://en.wikipedia.org/wiki?curid=14032611 |
14035775 | End correction | Whenever a wave forms through a medium/object (organ pipe) with a closed/open end, there is a chance of error in the formation of the wave, i.e. it may not actually start from the opening of the object but instead before the opening, thus resulting on an error when studying it theoretically. Hence an end correction is sometimes required to appropriately study its properties. The end correction depends on the radius of the object.
An acoustic pipe, such as an organ pipe, marimba, or flute resonates at a specific pitch or frequency. Longer pipes resonate at lower frequencies, producing lower-pitched sounds. The details of acoustic resonance are taught in many elementary physics classes. In an ideal tube, the wavelength of the sound produced is directly proportional to the length of the tube. A tube which is open at one end and closed at the other produces sound with a wavelength equal to four times the length of the tube. A tube which is open at both ends produces sound whose wavelength is just twice the length of the tube. Thus, when a Boomwhacker with two open ends is capped at one end, the pitch produced by the tube goes down by one octave.
The analysis above applies only to an ideal tube, of zero diameter. When designing an organ or Boomwhacker, the diameter of the tube must be taken into account. In acoustics, end correction is a short distance applied or added to the actual length of a resonance pipe, in order to calculate the precise resonant frequency of the pipe. The pitch of a real tube is lower than the pitch predicted by the simple theory. A finite diameter pipe appears to be acoustically somewhat longer than its physical length.
A theoretical basis for computation of the end correction is the radiation acoustic impedance of a circular piston. This impedance represents the ratio of acoustic pressure at the piston, divided by the flow rate induced by it. The air speed is typically assumed to be uniform across the tube end. This is a good approximation, but not exactly true in reality, since air viscosity reduces the flow rate in the boundary layer very close to the tube surface. Thus, the air column inside the tube is loaded by the external fluid due to sound energy radiation. This requires an additional length to be added to the regular length for calculating the natural frequency of the pipe system.
The end correction is denoted by formula_0 and sometimes by formula_1 . In organ pipes, a displacement antinode is not formed exactly at the open end. Rather, the antinode is formed a little
distance formula_0 away from the open end outside it.
This formula_0 is known as "end correction", which can be calculated as:
formula_2,
If you add this in total length calculated based on sound frequency the actual length will be longer. This equation will increase the flute length if flute diameter will be larger but in real sense it reduces the length as the diameter increases. It looks contradictory but in real sense this equation is not accurate for all bore / pipe diameter. For example this is correct for G bass flute for 20mm bore diameter but as diameter increases then this equation have negative effect means length will reduce. The pipe wall thickness correction also need to be added here for accuracy.
where formula_3 is the radius of the neck and formula_4 is the hydraulic diameter of the neck;
formula_5.
The exact number for the end correction depends on a number of factors relating to the geometry of the pipe. Lord Rayleigh was the first experimenter to publish a figure, in 1871: it was formula_6. Other experiments have yielded results such as formula_7 and formula_8. The end correction for ideal cylindrical tubes was calculated to be formula_9 by Levine and Schwinger.
Notes.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": " \\Delta L "
},
{
"math_id": 1,
"text": " e "
},
{
"math_id": 2,
"text": " \\Delta L = 0.6 \\cdot r = 0.3 \\cdot D "
},
{
"math_id": 3,
"text": "r"
},
{
"math_id": 4,
"text": "D"
},
{
"math_id": 5,
"text": " \\Delta L = 1.2 \\cdot r = 0.6 \\cdot D "
},
{
"math_id": 6,
"text": "0.3 \\cdot r "
},
{
"math_id": 7,
"text": " 0.576 \\cdot r "
},
{
"math_id": 8,
"text": " 0.66 \\cdot r "
},
{
"math_id": 9,
"text": " 0.6133 \\cdot r "
}
]
| https://en.wikipedia.org/wiki?curid=14035775 |
1403749 | Force density | <templatestyles src="Hlist/styles.css"/>
In fluid mechanics, the force density is the negative gradient of pressure. It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid. Force density is represented by the symbol f, and given by the following equation, where "p" is the pressure:
formula_0.
The net force on a differential volume element "dV" of the fluid is:
formula_1
Force density acts in different ways which is caused by the boundary conditions. There are stick-slip boundary conditions and stick boundary conditions which affect force density.
In a sphere placed in an arbitrary non-stationary flow field of viscous incompressible fluid for stick boundary conditions where the force density's calculations leads to show the generalisation of Faxen's theorem to force multipole moments of arbitrary order.
In a sphere moving in an incompressible fluid in a non-stationary flow with mixed stick-slip boundary condition where the force of density shows an expression of the Faxén type for the total force, but the total torque and the symmetric force-dipole moment.
The force density at a point in a fluid, divided by the density, is the acceleration of the fluid at that point.
The force density f is defined as the force per unit volume, so that the net force can be calculated by:
formula_2.
The force density in an electromagnetic field is given in CGS by:
formula_3,
where formula_4 is the charge density, E is the electric field, J is the current density, c is the speed of light, and B is the magnetic field. | [
{
"math_id": 0,
"text": "\\mathbf{f} = - \\nabla p "
},
{
"math_id": 1,
"text": "d\\mathbf{F} = \\mathbf{f}dV"
},
{
"math_id": 2,
"text": "\\mathbf{F}=\\int f(\\mathbf{r})d^3 \\mathbf{r} "
},
{
"math_id": 3,
"text": "\\mathbf{f}=\\rho \\mathbf{E}+ \\frac{\\mathbf{J}}{c} \\times \\mathbf{B} "
},
{
"math_id": 4,
"text": "\\rho "
}
]
| https://en.wikipedia.org/wiki?curid=1403749 |
1403783 | Bas van Fraassen | American philosopher (born 1941)
Bastiaan Cornelis van Fraassen (; born 5 April 1941) is a Dutch-American philosopher noted for his contributions to philosophy of science, epistemology and formal logic. He is a Distinguished Professor of Philosophy at San Francisco State University and the McCosh Professor of Philosophy Emeritus at Princeton University.
Biography and career.
Van Fraassen was born in the German-occupied Netherlands on 5 April 1941. His father, a steam fitter, was forced by the Nazis to work in a factory in Hamburg. After the war, the family reunited and, in 1956, emigrated to Edmonton, in western Canada.
Van Fraassen earned his B.A. (1963) from the University of Alberta and his M.A. (1964) and Ph.D. (1966, under the direction of Adolf Grünbaum) from the University of Pittsburgh. He previously taught at Yale University, the University of Southern California, the University of Toronto and, from 1982 to 2008, at Princeton University, where he is now emeritus. Since 2008, van Fraassen has taught at San Francisco State University, where he teaches courses in the philosophy of science, philosophical logic, and the role of modeling in scientific practice.
Van Fraassen is an adult convert to the Roman Catholic Church and is one of the founders of the Kira Institute. He is a fellow of the American Academy of Arts and Sciences; an overseas member of the Royal Netherlands Academy of Arts and Sciences since 1995; and a member of the International Academy of Philosophy of Science. In 1986, van Fraassen received the Lakatos Award for his contributions to the philosophy of science and, in 2012, the Philosophy of Science Association's inaugural Hempel Award for lifetime achievement in philosophy of science.
Among his many students are the philosophers Elisabeth Lloyd at Indiana University, Anja Jauernig at New York University, Jenann Ismael at Johns Hopkins University, Ned Hall at Harvard University, Alan Hajek at the Australian National University and Professor of Mathematics Jukka Keranen at UCLA.
Philosophical work.
Philosophy of science.
Van Fraassen coined the term "constructive empiricism" in his 1980 book "The Scientific Image", in which he argued for agnosticism about the reality of unobservable entities. That book was "widely credited with rehabilitating scientific anti-realism." According to the "Stanford Encyclopedia of Philosophy": <templatestyles src="Template:Blockquote/styles.css" />The constructive empiricist follows the logical positivists in rejecting metaphysical commitments in science, but parts with them regarding their endorsement of the verificationist criterion of meaning, as well as their endorsement of the suggestion that theory-laden discourse can and should be removed from science. Before van Fraassen's "The Scientific Image", some philosophers had viewed scientific anti-realism as dead, because logical positivism was dead. Van Fraassen showed that there were other ways to be an empiricist with respect to science, without following in the footsteps of the logical positivists.
Paul M. Churchland, one of van Fraassen's critics, contrasted van Fraassen's idea of unobservable phenomena with the idea of merely unobserved phenomena.
In his 1989 book "Laws and Symmetry", van Fraassen attempted to lay the ground-work for explaining physical phenomena without assuming that such phenomena are caused by rules or laws which can be said to cause or govern their behavior. Focusing on the problem of underdetermination, he argued for the possibility that theories could have empirical equivalence but differ in their ontological commitments. He rejects the notion that the aim of science is to produce an account of the physical world that is literally true and instead maintains that its aim is to produce theories that are empirically adequate. Van Fraassen has also studied the philosophy of quantum mechanics, philosophical logic, and Bayesian epistemology.
Philosophical logic.
Van Fraassen has been the editor of the "Journal of Philosophical Logic" and co-editor of the "Journal of Symbolic Logic".
In logic, Van Frassen is best known for his work on free logic and his introduction of the supervaluation semantics. In his paper "Singular Terms, Truth-value Gaps, and Free Logic", van Fraassen opens with a very brief introduction of the problem of non-referring names.
Instead of any unique formalization, though, he simply adjusts the axioms of a standard predicate logic such as that found in Willard Van Orman Quine's "Methods of Logic". Instead of an axiom like formula_0 he uses formula_1; this will naturally be true if the existential claim of the antecedent is false. If a name fails to refer, then an atomic sentence containing it, that is not an identity statement, can be assigned a truth value arbitrarily. Free logic is proved to be complete under this interpretation.
He indicates that, however, he sees no good reason to call statements which employ them either true or false. Some have attempted to solve this problem by means of many-valued logics; van Fraassen offers in their stead the use of supervaluations. Questions of completeness change when supervaluations are admitted, since they allow for valid arguments that do not correspond to logically true conditionals.
His paper "Facts and tautological entailment" (J Phil 1969) is now regarded as the beginning of truth-maker semantics.
Bayesian epistemology.
In Bayesian epistemology, van Fraassen proposed what is now known as van Fraassen's reflection principle: "to satisfy the principle, the agent's present subjective probability for proposition "A", on the supposition that his subjective probability for this proposition will equal "r" at some later time, must equal this same number "r"".
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\forall x\\,Px \\Rightarrow \\exists x\\,Px"
},
{
"math_id": 1,
"text": "( \\forall x\\,Px \\land \\exists x\\,(x = a)) \\Rightarrow \\exists x\\,Px"
}
]
| https://en.wikipedia.org/wiki?curid=1403783 |
1403889 | Ultraparallel theorem | Theorem in hyperbolic geometry
In hyperbolic geometry, two lines are said to be ultraparallel if they do not intersect and are not limiting parallel.
The ultraparallel theorem states that every pair of (distinct) ultraparallel lines has a unique common perpendicular (a hyperbolic line which is perpendicular to both lines).
Hilbert's construction.
Let r and s be two ultraparallel lines.
From any two distinct points A and C on s draw AB and CB' perpendicular to r with B and B' on r.
If it happens that AB = CB', then the desired common perpendicular joins the midpoints of AC and BB' (by the symmetry of the Saccheri quadrilateral ACB'B).
If not, we may suppose AB < CB' without loss of generality. Let E be a point on the line s on the opposite side of A from C. Take A' on CB' so that A'B' = AB. Through A' draw a line s' (A'E') on the side closer to E, so that the angle B'A'E' is the same as angle BAE. Then s' meets s in an ordinary point D'. Construct a point D on ray AE so that AD = A'D'.
Then D' ≠ D. They are the same distance from r and both lie on s. So the perpendicular bisector of D'D (a segment of s) is also perpendicular to r.
Proof in the Poincaré half-plane model.
Let
formula_0
be four distinct points on the abscissa of the Cartesian plane. Let formula_1 and formula_2 be semicircles above the abscissa with diameters formula_3 and formula_4 respectively. Then in the Poincaré half-plane model HP, formula_1 and formula_2 represent ultraparallel lines.
Compose the following two hyperbolic motions:
formula_5
formula_6
Then formula_7
Now continue with these two hyperbolic motions:
formula_8
formula_9
Then formula_10 stays at formula_11, formula_12, formula_13, formula_14 (say). The unique semicircle, with center at the origin, perpendicular to the one on formula_15 must have a radius tangent to the radius of the other. The right triangle formed by the abscissa and the perpendicular radii has hypotenuse of length formula_16. Since formula_17 is the radius of the semicircle on formula_15, the common perpendicular sought has radius-square
formula_18
The four hyperbolic motions that produced formula_19 above can each be inverted and applied in reverse order to the semicircle centered at the origin and of radius formula_20 to yield the unique hyperbolic line perpendicular to both ultraparallels formula_1 and formula_2.
Proof in the Beltrami-Klein model.
In the Beltrami-Klein model of the hyperbolic geometry:
If one of the chords happens to be a diameter, we do not have a pole, but in this case any chord perpendicular to the diameter it is also perpendicular in the Beltrami-Klein model, and so we draw a line through the pole of the other line intersecting the diameter at right angles to get the common perpendicular.
The proof is completed by showing this construction is always possible:
Alternatively, we can construct the common perpendicular of the ultraparallel lines as follows: the ultraparallel lines in Beltrami-Klein model are two non-intersecting chords. But they actually intersect outside the circle. The polar of the intersecting point is the desired common perpendicular.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "a < b < c < d"
},
{
"math_id": 1,
"text": "p"
},
{
"math_id": 2,
"text": "q"
},
{
"math_id": 3,
"text": "ab"
},
{
"math_id": 4,
"text": "cd"
},
{
"math_id": 5,
"text": "x \\to x-a"
},
{
"math_id": 6,
"text": "\\mbox{inversion in the unit semicircle.}"
},
{
"math_id": 7,
"text": "a \\to \\infty, \\quad b \\to (b-a)^{-1},\\quad c \\to (c-a)^{-1},\\quad d \\to (d-a)^{-1}."
},
{
"math_id": 8,
"text": "x \\to x-(b-a)^{-1}"
},
{
"math_id": 9,
"text": "x \\to \\left [ (c-a)^{-1} - (b-a)^{-1} \\right ]^{-1} x"
},
{
"math_id": 10,
"text": "a"
},
{
"math_id": 11,
"text": "\\infty"
},
{
"math_id": 12,
"text": "b \\to 0"
},
{
"math_id": 13,
"text": "c \\to 1"
},
{
"math_id": 14,
"text": "d \\to z"
},
{
"math_id": 15,
"text": "1z"
},
{
"math_id": 16,
"text": "\\begin{matrix} \\frac{1}{2} \\end{matrix} (z+1)"
},
{
"math_id": 17,
"text": "\\begin{matrix} \\frac{1}{2} \\end{matrix} (z-1)"
},
{
"math_id": 18,
"text": "\\frac{1}{4} \\left [ (z+1)^2 - (z-1)^2 \\right ] = z."
},
{
"math_id": 19,
"text": "z"
},
{
"math_id": 20,
"text": "\\sqrt{z}"
}
]
| https://en.wikipedia.org/wiki?curid=1403889 |
14039665 | Decene | Organic compound (C10H20)
<templatestyles src="Chembox/styles.css"/>
Chemical compound
Decene is an organic compound with the chemical formula . Decene contains a chain of ten carbon atoms with one double bond, making it an alkene. There are many isomers of decene depending on the position and geometry of the double bond. Dec-1-ene is the only isomer of industrial importance. As an alpha olefin, it is used as a comonomer in copolymers and is an intermediate in the production of epoxides, amines, oxo alcohols, synthetic lubricants, synthetic fatty acids and alkylated aromatics.
The industrial processes used in the production of dec-1-ene are oligomerization of ethylene by the Ziegler process or by the cracking of petrochemical waxes.
In ethenolysis, methyl oleate, the "methyl ester" of oleic acid, converts to 1-decene and methyl 9-decenoate:
formula_0
Dec-1-ene has been isolated from the leaves and rhizome of the plant "Farfugium japonicum" and has been detected as the initial product in the microbial degradation of "n"-decane.
References.
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{
"math_id": 0,
"text": "\\overset{\\text{methyl oleate}}{\\ce{CH3(CH2)7CH=CH(CH2)7CO2Me}} + {\\color{red}\\ce{CH2=CH2}} \\longrightarrow \\overset{\\text{1-decene}}{\\ce{CH3(CH2)7CH=}{\\color{red}\\ce{CH2}}} + \\overset{\\text{9-decenoate}}{\\ce{MeO2C(CH2)7CH=}{\\color{red}\\ce{CH2}}}"
}
]
| https://en.wikipedia.org/wiki?curid=14039665 |
14039775 | Oxidizable carbon ratio dating | Method of dating soil and sediment
Oxidizable carbon ratio dating is a method of dating in archaeology and earth science that can be used to derive or estimate the age of soil and sediment samples up to 35,000 years old. The method is experimental, and it is not as widely used in archaeology as other chronometric methods such as radiocarbon dating.
The methodology was introduced by Archaeology Consulting Team from Essex Junction in 1992.
Process.
This dating method works by measuring the ratio of oxidizable carbon to organic carbon. If the sample is freshly burned there will be no oxidizable carbon because it would have all been removed by the combustion process. Over time this will change and the amount of organic carbon will decrease to be replaced by oxidizable carbon. By measuring the ratio of oxidized carbon to organic carbon (the OCR) and applying it to the following equation the age of the sample can be determined with a very low standard error.
formula_0
Evaluations and applications of the method.
It is important to note that the OCR dating method is, like any scientific procedure, subject to testing, evaluation, and refinement.
The Oxidizable Carbon Ratio method was the subject of a Point–CounterPoint feature of the Society for American Archaeology Bulletin in 1999. In that article, Killick, Jull, and Burr suggest that the OCR method has (1) never been described in a peer-reviewed journal article, (2) that no "scientifically acceptable" demonstration of the accuracy and precision of OCR dating has been published, and (3) that the equation underlying the OCR method is questionable because of site-specific environmental factors. Frink's rejoinder to these comments points out that (1) the OCR method has indeed been described in a peer-reviewed journal article, (2) that the accuracy and precision of the method have been reported in multiple venues and that the concept of "scientifically acceptable" is context- and person-specific (and therefore a red herring), and that (3) the equation underlying the OCR method takes into account the seven factors of soil formation, and that these factors are routinely used in soil science applications without question. In the end, Frink concludes that the OCR method—like any scientific advance—warrants further study, and he points out that even the now venerable "scientifically acceptable" method of radiocarbon dating was much maligned when it was first introduced.
Frink and others have published multiple studies demonstrating that OCR dates can correlate well with radiocarbon dates (see list of published references provided below). Fullen's study of the Sarah Peralta site in Louisiana found that the OCR method served as an effective means of inferring time at the site in the absence of radiometrically dateable charcoal. He concludes that whereas debate remains concerning the OCR procedure, "the well-corroborated dates that the LSU Museum of Natural Science has had returned on material processed with OCR and conventional radiocarbon dating...the dates returned on material from Zone 3 will be considered accurate until such time that OCR dating is proven invalid." ("ibid". p. 65)
The OCR method has been used in a large number of archaeological and geomorphological studies, and an incomplete list of published references is provided below. It has been used to evaluate soil development in a range of temperature regimes including arid, semi-arid
, thermic, mesic, and frigic. It has also been applied to a variety of landforms including stratified fluvial deposits, desert pavements and vesicular soils, and glacial deposits. Analyses also include monumental earthworks and geoglyphs.
References.
<templatestyles src="Reflist/styles.css" />
https://en.wikipedia.org/wiki/Oxidizable_carbon_ratio_dating
Published references.
Abbott, James T., Raymond Mauldin, Patience E. Patterson, W. Nicholas Trierweiler, Robert J. Hard, Christopher R. Lintz, and Cynthia L. Tennis
1997 "Significance Standards for Prehistoric Archeological Sites at Fort Bliss: A Design for Further Research and the Management of Cultural Resources". TRC Mariah Associates Inc. Austin, Texas. pp 70–71.
Bradbury, Andrew P.
1995 "A National Register Evaluation of Twelve Sites in Adair, Cumberland and Metcalfe Counties, Kentucky". Contract Publication Series 95-69. Cultural Resource Analysts, Inc., Lexington, Kentucky.
Burkett, Kenneth
1999 Prehistoric Occupations at Fishbasket. "Pennsylvania Archaeologist" 69(1):1-100.
Cable, John S., Kenneth F. Styer, and Charles E. Cantley
n.d. "Data Recovery Excavations at the Maple Swamp (38HR309) and Big Jones (38HR315) Sites on the Conway Bypass. Horry County, South Carolina: Prehistoric Sequence and Settlement on the North Coastal Plain of South Carolina". New South Associates, Inc., Stone Mountain, Georgia. Submitted to the South Carolina Department of Transportation, Columbia, South Carolina.
Cantley, Charles E., Leslie E. Raymer, Johannes H. N. Loubser, and Mary Beth Reed
1997 "Phase III Data Recovery at Four Prehistoric Sites in the Horton Creek Reservoir Project Area, Fayette County, Georgia". New South Associates, Inc., Stone Mountain, Georgia. Submitted to Mallett & Associates, Inc., Smyrna, Georgia.
Cantley, Charles E., Lotta Danielsson-Murphy, Thad Murphy, Undine McEvoy, Leslie E. Raymer, John S. Cable, Robert Yallop, Cindy Rhodes, Mary Beth Reed, and Lawerence A. Abbott
1997 "Fort Polk, Louisiana: A Phase I Archaeological Survey of 14,622 Acres in Vernon Parish. New South Associates, Inc., Stone Mountain, Georgia". Submitted to the National Park Service, Atlanta, Georgia.
Childress, Mitchell R. and Guy G. Weaver
In Prep. (1998) "National Register Eligibility Assessment of Four Sites on Upper Roubidoux Creek (23PU483, 23PU458, 23PU354, 23PU264), Fort Leonard Wood, Missouri". Brockington and Associates, Inc., Memphis. Submitted to the United States Army Construction engineering Research Laboratories (USACERL), Champaign, Illinois.
Dorn, Ronald I., Edward Stasack, Diane Stasack, and Persis Clarkson
2001 Analyzing Petroglyphs and Geoglyphs with Four New Perspectives: Evaluating What's There and What's Not. "American Indian Rock Art" 27: 77-96.
Elliott, Rita F., Johannes H. N. Loubser, Leslie E. Raymer, Mary Beth Reed, and Charles E. Cantley
1995 "Archaeological Testing of Three Sites Along the SR 21, Effingham and Screven Counties, Georgia. New South Associates, Inc., Stone Mountain, Georgia". Submitted to the Georgia Department of Transportation, Atlanta, Georgia.
Frink, Douglas S. and Ronald I. Dorn
2001 Beyond Taphonomy: Pedogenic Transformations of the Archaeological Record in Monumental Earthworks. "Journal of the Arizona-Nevada Academy of Science" 33(3): 182-202.
Frink, Douglas S. and Timothy K. Perttula
2001 Analysis of the 39 Oxidizable Carbon Ratio Dates from Mound A, Mound B, and the Village Area at the Calvin Davis or Morse Mounds Site (41SY27). "North American Archaeologist" 22(2): 143-160.
Fullen, Steven R.
2005 "Temporal Trends in Tchula Period Pottery in Louisiana". Unpublished MA thesis, Department of Geography and Anthropology, Louisiana State University and Agricultural and Mechanical College.
Gunn, Joel D, Thomas G. Lilly, Cheryl Claassen, John Byrd, and Andrea Brewer Shea
1995 "Archaeological Data Recovery Investigations at Sites 38BU905 and 38BU921 Along the Hilton Head Cross Island Expressway, Beaufort County, South Carolina". Garrow & Associates, Inc., Raleigh, North Carolina.
Harrison, Rodney, and Frink, Douglas S.
2000 The OCR Carbon Dating Procedure in Australia: New Dates from Wilinyjibari Rockshelter, Southeast Kimberley, Western Australia. "Australian Archaeology" 51:6-15.
Hoffman, Curtiss, Maryanne MacLeod, and Alan Smith
1999 Symbols in Stone: Chiastolites in New England Archaeology. "Bulletin of the Massachusetts Archaeological Society" 60(1).
Johnson, Jay K., Gena M. Aleo, Rodney T. Stuart, and John Sullivan
1998 "The 1996 Excavations at the Batesville Mounds: A Woodland Period Platform Mound Complex in Northwest Mississippi". Submitted to the Panola County Industrial Authority.
Keith, Scot
1998 OCR Dating of Prehistoric Features at the Sandhill Site (22-WA-676), Southeast Mississippi. "Mississippi Archaeology". 33(2): 77-114
Killick, D.J., A.J.T. Jull, and G.S. Burr
1999 Point/Counterpoint: Failure to Discriminate: Querying Oxidizable Carbon Ratio (OCR) Dating. "SAA Bulletin" 17(5):32-36.
Response: Frink, Douglas S.
Kindall, Sheldon
1997 The Oxidizable Carbon Ratio (OCR) Technique: A New, Low-Cost Dating Method. "The Steward: Collected Papers on Texas Archeology" 4:91-94.
Messick, Denise P., Johannes Loubser, Theresa M. Hamby, Joe W. Joseph, Mary Beth Reed, and Leslie Raymer
n.d. "Prehistoric and Historic Excavations at Site 9Gw347, Annistown Road Improvement Project, Gwinnett County, Georgia". New South Associates, Inc., Stone Mountain Georgia. Submitted to the Gwinnett County Department of Transportation, Lawrenceville, Georgia and Moreland Altobelli Associates, Atlanta, Georgia.
Nami, Hugo, and Frink, Douglas S.
1999 Cronologia Obtenida por la Tasa del Carbono Organico Oxidable (OCR) en Markatch Aike 1 (Cuenca del Rio Chico, Santa Cruz). "Anales del Instituo de la Patagonia" 27:231-237
Patterson, Leland W.
1998 Oxidizable Carbon Ration Dating. "La Tierra: Journal of the Southern Texas Archaeological Association" 25(1):46-48.
n.d. "Dates for Formation of Huntington Mound, Fort Bend Co., Texas". Submitted to Houston Archeological Society Journal
Patterson, L.W., J.D. Hudgins, S.M. Kindall, W.L. McClure, and S.D. Pollan
1995 Excavations at Site 41WH24, Wharton Co., Texas. "Journal of the Houston Archeological Society" 113:11-21.
Patterson, L.W., J.D. Hudgins, W.L. McClure
1996 Additional Excavations at Marik Site, Wharton Co., Texas. "Journal of the Houston Archeological Society" 115:9-15.
Patterson, L.W., S.D. Hemming, and W.L. McClure
1997 "Investigations at Site 41FB245, Fort Bend County, Texas". Fort Bend Archeological Society 5.
Perttula, Timothy K., Douglas S. Frink
2001 Results of Recent Oxidizable Carbon Ratio Dating at Lake Naconiche Sites. "East Texas Archaeological Society Newsletter" 8(6):3-5
Perttula, Timothy K., Mike Turner, and Bo Nelson
1997 Radiocarbon and Oxidizable Carbon Ratio Dates from the Camp Joy Mound (41UR144) in Northeast Texas. "Caddoan Archeology" 7(4):10-16.
Perttula, Timothy K.
1997 A Compendium of Radiocarbon and Oxidizable Carbon Ratio Dates from Archaeological Sites in East Texas, with a Discussion of the Age and Dating of Select Components and Phases. "Radiocarbon" 39(3): 305-342.
Saunders, Joe W., Rolfe D. Mandel, Roger T. Saucier, E. Thurman Allen, C.T. Hallmark, Jay K. Johnson, Edwin H. Jackson, Charles M. Allen, Gary L. Stringer, Douglas S. Frink, James K. Feathers, Stephen Williams, Kristen J. Gremillion, Malcolm F. Vidrine, and Reca Jones
1997 A Mound Complex in Louisiana at 5400-5000 Years Before Present. "Science" 277:1796-1799
Steen, Carl, Chrostopher Judge, and James Legg.
1995 "An Archaeological Survey of the Nature Conservancy's Peachtree Rock Preserv"e. Diachronic Research Foundation, Columbia, S.C.
Tennis, Cynthia L. (Ed.), I. Waynne Cox, Jeffrey J. Durst, Donna D. Edmondson, Barbara A. Meissner, Steve A. Tomka, Douglas S. Frink, John G. Jones, and Rick C. Robinson
2001 "Archaeological Investigations at Four San Antonio Missions: Mission Trails Underground Conversion Project". Center for Archaeological Research, The University of Texas at San Antonio, Archaeological Survey Report 297.
Webb, Paul A., and David S. Leigh
1995 Geomorphological and Archaeological Investigations of a Buried Site on the Yadkin River Floodplain. "Southern Indian Studies" 44:1-36.
Wesler, Kit
1997 The Wickliffe Mounds Project: Implications for Late Mississippi Period Chronology, Settlement and Mortuary Patterns in Western Kentucky. "Proceedings of the Prehistoric Society" 63:261-283.
2001 "Excavations at Wickliffe Mounds". The University of Alabama Press, Tuscaloosa.
Worth, J.E.
1996 Upland Lamar, Vining, and Cartersville: An Interim Report from Raccoon Ridge. "Early Georgia" 24(1): 34-83. | [
{
"math_id": 0,
"text": "\\text{OCR}_\\text{DATE} = \\frac{\\text{OCR} \\times \\text{Depth} \\times \\text{Mean temperature} \\times \\text{Mean rainfall}}{\\text{Mean texture} \\times \\sqrt\\text{pH}\\times\\sqrt{\\%C}\\times 14.4888}"
}
]
| https://en.wikipedia.org/wiki?curid=14039775 |
14040060 | 1,2-dihydrovomilenine reductase | Class of enzymes
In enzymology, a 1,2-dihydrovomilenine reductase (EC 1.3.1.73) is an enzyme that catalyzes the chemical reaction
17-O-acetylnorajmaline + NADP+ formula_0 1,2-dihydrovomilenine + NADPH + H+
Thus, the two substrates of this enzyme are 17-O-acetylnorajmaline and NADP+, whereas its 3 products are 1,2-dihydrovomilenine, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 17-O-acetylnorajmaline:NADP+ oxidoreductase. This enzyme participates in indole and ipecac alkaloid biosynthesis.
References.
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{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14040060 |
14040086 | 1,2-dihydroxy-6-methylcyclohexa-3,5-dienecarboxylate dehydrogenase | Class of enzymes
In enzymology, a 1,2-dihydroxy-6-methylcyclohexa-3,5-dienecarboxylate dehydrogenase (EC 1.3.1.68) is an enzyme that catalyzes the chemical reaction
1,2-dihydroxy-6-methylcyclohexa-3,5-dienecarboxylate + NAD+ formula_0 3-methylcatechol + NADH + CO2
Thus, the two substrates of this enzyme are 1,2-dihydroxy-6-methylcyclohexa-3,5-dienecarboxylate and NAD+, whereas its 3 products are 3-methylcatechol, NADH, and CO2.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 1,2-dihydroxy-6-methylcyclohexa-3,5-dienecarboxylate:NAD+ oxidoreductase (decarboxylating). This enzyme participates in toluene and xylene degradation.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14040086 |
14040156 | 15-oxoprostaglandin 13-oxidase | Class of enzymes
In enzymology, a 15-oxoprostaglandin 13-oxidase (EC 1.3.1.48) is an enzyme that catalyzes the chemical reaction
(5Z)-(15S)-11alpha-hydroxy-9,15-dioxoprostanoate + NAD(P)+ formula_0 (5Z)-(15S)-11alpha-hydroxy-9,15-dioxoprosta-13-enoate + NAD(P)H + H+
The 3 substrates of this enzyme are (5Z)-(15S)-11alpha-hydroxy-9,15-dioxoprostanoate, NAD+, and NADP+, whereas its 4 products are (5Z)-(15S)-11alpha-hydroxy-9,15-dioxoprosta-13-enoate, NADH, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (5Z)-(15S)-11alpha-hydroxy-9,15-dioxoprostanoate:NAD(P)+ Delta13-oxidoreductase. Other names in common use include 15-oxo-Delta13-prostaglandin reductase, Delta13-15-ketoprostaglandin reductase, 15-ketoprostaglandin Delta13-reductase, prostaglandin Delta13-reductase, prostaglandin 13-reductase, and 15-ketoprostaglandin Delta13-reductase.
Structural studies.
As of late 2007, 4 structures have been solved for this class of enzymes, with PDB accession codes 1V3T, 1V3U, 1V3V, and 2DM6.
References.
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{
"math_id": 0,
"text": "\\rightleftharpoons"
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]
| https://en.wikipedia.org/wiki?curid=14040156 |
14040324 | 1,6-dihydroxycyclohexa-2,4-diene-1-carboxylate dehydrogenase | Class of enzymes
In enzymology, a 1,6-dihydroxycyclohexa-2,4-diene-1-carboxylate dehydrogenase (EC 1.3.1.25) is an enzyme that catalyzes the chemical reaction
(1R,6R)-1,6-dihydroxycyclohexa-2,4-diene-1-carboxylate + NAD+ formula_0 catechol + CO2 + NADH + H+
Thus, the two substrates of this enzyme are (1R,6R)-1,6-dihydroxycyclohexa-2,4-diene-1-carboxylate and NAD+, whereas its 4 products are catechol, CO2, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (1R,6R)-1,6-dihydroxycyclohexa-2,4-diene-1-carboxylate:NAD+ oxidoreductase (decarboxylating). Other names in common use include 3,5-cyclohexadiene-1,2-diol-1-carboxylate dehydrogenase, 3,5-cyclohexadiene-1,2-diol-1-carboxylic acid dehydrogenase, dihydrodihydroxybenzoate dehydrogenase, DHBDH, cis-1,2-dihydroxycyclohexa-3,5-diene-1-carboxylate dehydrogenase, 2-hydro-1,2-dihydroxybenzoate dehydrogenase, cis-1,2-dihydroxycyclohexa-3,5-diene-1-carboxylate:NAD+, oxidoreductase, and dihydrodihydroxybenzoate dehydrogenase. This enzyme participates in benzoate degradation via hydroxylation and benzoate degradation via coa ligation.
References.
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{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14040324 |
14040336 | 2,3-dihydro-2,3-dihydroxybenzoate dehydrogenase | InterPro Family
In enzymology, a 2,3-dihydro-2,3-dihydroxybenzoate dehydrogenase (EC 1.3.1.28) is an enzyme that catalyzes the chemical reaction
2,3-dihydro-2,3-dihydroxybenzoate + NAD+ formula_0 2,3-dihydroxybenzoate + NADH + H+
Thus, the two substrates of this enzyme are 2,3-dihydro-2,3-dihydroxybenzoate and NAD+, whereas its 3 products are 2,3-dihydroxybenzoate, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 2,3-dihydro-2,3-dihydroxybenzoate:NAD+ oxidoreductase. This enzyme is also called 2,3-diDHB dehydrogenase. This enzyme participates in biosynthesis of siderophore group nonribosomal.
Structure.
2,3-diDHB dehydrogenase is a tetramer protein with dimension 65x69x43 Å. It has a crystallographic 222 symmetry, which exhibited for other members of short-chain oxireductase (SCOR) family of enzymes. The length of each monomer is 248 residues and the weight of the protein is 24647 Da. Each monomer consists of 7 beta-pleated sheets and 6 alpha helices.
Although the structure of the binding protein is not clearly defined, it was proposed that the binding pocket is made out of Leu83, Met85, Arg138, Gly140, Met141, Ser176, Met181, Gln182 and Leu185. It was also speculated that Arg138 is a likely subunit that interacts with the carboxyl group of 2,3-diDHB. Since there was a strong indication of oxidation at C3 position, Ser176 and Gln182 interact with the C2-hydroxyl group in order for the stereo-selective reaction to occur.
Reaction mechanism.
In times of limited iron number in the environment, the EntA reaction is irreversible physiologically. The exact mechanism for the reaction is unknown; however, the proposed reaction scheme for the reaction is as following:
Rate of reaction.
The rate of the conversion reaction is determined by several factors. The regiochemical position of the carboxyl group and the 3-hydroxyl group plays one role in the reaction, in which the rate of reaction of 1,3-"cis"-substituted substrate gives about 40-fold higher kcat/Km value than the 1,3-trans-substituted substrate.
Roles in bacteria.
"E. coli".
2,3-diDHB dehydrogenase catalyzes the NAD+-dependent oxidation of 2,3-dihydro-2,3-dihydroxybenzoate to produce an aromatic compound 2,3-dihydroxybenzoic acid (2,3-DHB or simply DHB). In times of iron deficiency, iron uptake is controlled by three genes: "ent", "fep", and "fes" for synthesis, export, and uptake of ferric Enterobactin and its hydrolytic cleavage to release Fe3+ into the cell. This production of this compound is controlled by eight genes: entA-entF, entH, and entS. In E. coli, all of these genes are controlled by the Fur repressor, such that the genes are turned on when the concentration of iron in the environment is low. From these six genes, EntA, EntB, and EntC are responsible for the synthesis of DHB from chorismic acid and the gene EntA encodes the information of 2,3-diDHB dehydrogenase. Without entA, entB, and entC, the bacteria show almost an absolute requirement of DHB in order to survive.
"A. tumefaciens".
Production of siderophores also exhibited in some plant-infecting bacteria, such as "Agrobacterium tumefaciens". The enzyme is controlled by gene cluster agb and the production of 2,3-diDHB dehydrogenase is controlled by the gene agbA. The enzyme AgbA is homologous to the EntA enzyme in "E. coli", the same enzyme that produces 2,3-diDHB dehydrogenase.
References.
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{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=14040336 |
14040351 | 2,3-dihydroxy-2,3-dihydro-p-cumate dehydrogenase | Class of enzymes
In enzymology, a 2,3-dihydroxy-2,3-dihydro-p-cumate dehydrogenase (EC 1.3.1.58) is an enzyme that catalyzes the chemical reaction
cis-5,6-dihydroxy-4-isopropylcyclohexa-1,3-dienecarboxylate + NAD+ formula_0 2,3-dihydroxy-p-cumate + NADH + H+
Thus, the two substrates of this enzyme are cis-5,6-dihydroxy-4-isopropylcyclohexa-1,3-dienecarboxylate and NAD+, whereas its 3 products are 2,3-dihydroxy-p-cumate, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is cis-2,3-dihydroxy-2,3-dihydro-p-cumate:NAD+ oxidoreductase. This enzyme participates in biphenyl degradation.
References.
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{
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"text": "\\rightleftharpoons"
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| https://en.wikipedia.org/wiki?curid=14040351 |
14040362 | Arc routing | Category of routing problem minimizing total distance and time
Arc routing problems (ARP) are a category of general routing problems (GRP), which also includes node routing problems (NRP). The objective in ARPs and NRPs is to traverse the edges and nodes of a graph, respectively. The objective of arc routing problems involves minimizing the total distance and time, which often involves minimizing deadheading time, the time it takes to reach a destination. Arc routing problems can be applied to garbage collection, school bus route planning, package and newspaper delivery, deicing and snow removal with winter service vehicles that sprinkle salt on the road, mail delivery, network maintenance, street sweeping, police and security guard patrolling, and snow ploughing. Arc routings problems are NP hard, as opposed to route inspection problems that can be solved in polynomial-time.
For a real-world example of arc routing problem solving, Cristina R. Delgado Serna & Joaquín Pacheco Bonrostro applied approximation algorithms to find the best school bus routes in the Spanish province of Burgos secondary school system. The researchers minimized the number of routes that took longer than 60 minutes to traverse first. They also minimized the duration of the longest route with a fixed maximum number of vehicles.
There are generalizations of arc routing problems that introduce multiple mailmen, for example the k Chinese Postman Problem (KCPP).
Background.
The efficient scheduling and routing of vehicles can save industry and government millions of dollars every year. Arc routing problems have applications in school bus planning, garbage and waste and refuse collection in cities, mail and package delivery by mailmen and postal services, winter gritting and laying down salt to keep roads safe in the winter, snow plowing and removal, meter reading including remote radio frequency identification meter reading technology, street maintenance and sweeping, police patrol car route planning, and more.
Basis.
The basic routing problem is: given a set of nodes and/or arcs to be serviced by a fleet of vehicles, find routes for each vehicle starting and ending at a depot. A vehicle route is a sequence of points or nodes, which the vehicle must traverse in order, starting and ending at a depot.
Chinese postman problem.
The Chinese Postman Problem (CPP) is aimed at finding the minimum length cycle for a single postman. The CPP requires all edges be traversed once, the rural postman problem (RPP) requires a subset of the edges to be traversed with the minimum length cycle.
Vehicle routing problems/VRP.
Arc routing problems impact strategic, tactical, and operational planning decisions. The strategic role of where a depot is placed depends on the most efficient arc route available. The decision of the vehicle fleet size and vehicle types with varying specifications relate to the tactical aspect of arc routing problems in operations research. Routing and scheduling decisions are operational planning decisions in arc routing problems. The operational planning decisions also includes the time that the vehicles are used by workers with staff decisions. Vehicle routing decisions for the location of a depot depend on the cost of transporting materials over a geographical region. Bodin et. al applied vehicle routing to the dial a ride problem.
Rural postman problem.
In some situations, the set of edges that are required is different from the edges in the graph. This is modeled by the Rural Postman Problem (RPP), where the required edges are a subset of the system of edges.
Algorithms.
Finding an efficient solution with large amounts data to the Chinese Postman Problem (CPP), the Windy Postman Problem (WPP), the Rural Postman Problem (RPP), the "k"-Chinese postman problem (KCPP), the mixed Chinese postman problem (MCPP), the Directed Chinese Postman Problem (DCPP), the Downhill Plowing Problem (DPP), the Plowing with Precedence Problem (PPP), the Windy Rural Postman Problem (WRPP) and the Windy General Routing Problem (WGRP) requires using thoughtful mathematical concepts, including heuristic optimization methods, branch-and-bound methods, integer linear programming, and applications of traveling salesman problem algorithms such as the Held–Karp algorithm makes an improvement from formula_0 to formula_1. In addition to these algorithms, these classes of problems can also be solved with the cutting plane algorithm, convex optimization, convex hulls, Lagrange multipliers and other dynamic programming methods. In cases where it is not feasible to run the Held–Karp algorithm because of its high computational complexity, algorithms like this can be used to approximate the solution in a reasonable amount of time.
Eulerian circuits.
The earliest documented reference to the area of arc routing problems is the classic bridges of Königsberg challenge, which Euler proved to be impossible. The resident of Konigsberg, now part of Kaliningrad, wanted to find a way to cross all seven bridges over the river Pregel without backtracking or retracing their steps, that is crossing each bridge once and only once. In 1736, Euler reduced the problem to a question of nodes and edges and showed that the problem was impossible. In 1873, Hierholzer did more work on the question of closed circuits.
The work on the Eulerian circuits was popularized with Scientific American on July 1, 1953. This work was extended by Meigu Guan, also known as Kwan Mei-Ko at Shangtun Normal College. Meigu Guan was interested in a different question instead of determining a closed circuit. Guan worked to find out a minimum length walk that traversed every edge of the graph at least once. Guan described his goal in 1962: "A mailman has to cover his assigned segment before returning to the post office. The problem is to find the shortest walking distance for the mailman."
Problem types.
Arc routing problems (ARPs) differ in their goal and heuristics. However, all of them are known to be NP-hard.
Undirected rural postman problem.
This problem is named after the postman and his challenge to deliver mail in any order he may choose, but minimizing his costs such as time or travel distance. It is also sometimes called the "undirected chinese postman problem". The undirected rural postman problem (URPP) aims to minimize the total cost of a route that maps the entire network, or in more specific cases, a route that maps every edge that requires a service. If the whole network must be mapped, the route that maps the entire network is called a "covering tour". In the case where only certain edges need to be mapped, the problem aims to solve the route that optimizes the demands, crossing over into non-required routes a minimal number of times.
Undirected capacitated arc routing problem.
The undirected capacitated arc routing problem consists of demands placed on the edges, and each edge must meet the demand. An example is garbage collection, where each route might require both a garbage collection and a recyclable collection. Problems in real life applications might arise if there are timing issues, such as the case in which certain routes cannot be serviced due to timing or scheduling conflicts, or constraints, such as a limited period of time. The heuristics described in this article ignore any such problems that arise due to application constraints.
History.
The URPP was first introduced in 1974 and was proven to be an NP-hard problem by Lenstra and Kan. The UCARP can be derived from the URPP, and thus is NP-hard as well. In 1981, another pair of computer scientists, Golden and Wong, managed to prove that even deriving a .5 approximation to the URPP was NP-hard. In 2000, Dror published a book describing different arc routing problems.
Windy postman problem and variants.
The windy postman problem proposed by Minieka is a variant of the route inspection problem in which the input is an undirected graph, but where each edge may have a different cost for traversing it in one direction than for traversing it in the other direction. In contrast to the solutions for directed and undirected graphs, it is NP-complete. The cost of traveling in one direction is greater when the wind is blowing in your face than when the wind is at your back, and this is the origin of the name Windy Postman problem. The work that it takes to traverse the street in one direction is different than the work it takes to traverse the street in another direction on a windy day.
The windy postman problem is an arc routing problem (ARP) that contains the Mixed Chinese Postman Problem MCPP as a special case.
The problem can be defined in the following manner: "Given an undirected and connected graph G=(V,E) with two non-negative costs formula_2 and formula_3 associated with each edge formula_4 corresponding to the cost of traversing it from i to j and from j to i, respectively, the WPP is to find a minimum cost tour on G traversing each edge at least once." This problem was introduced by Minieka. The WPP is NP-complete in general and can be solved in polynomial time if G is Eulerian, if the cost of two opposite orientations of every cycle in G in same or if G is a series-parallel graph. The Windy Rural Postman Problem (WRPP) is a generalization of the WPP in which not all the edges in the graph have to be traversed but only those in a given subset of required edges. For example, some rural roads are not required for the postman to cross and some roads on steep hills take longer to go up than down.
The Windy Rural Postman Problem (WRPP) is a generalization of the WPP in which not all the edges in the graph have to be traversed but only those in a given subset of required edges. For example, some rural roads are not required for the postman to cross and some roads on steep hills take longer to go up than down. Consider an undirected graph formula_5 with two costs formula_6 and formula_7 associated with the cost to traverse the edge formula_8 starting from i and j, respectively. G is the windy graph and we are interested in the subset of edges, or in mathematical symbols, formula_9.
If the WRPP includes the additional constraint that a certain set of vertices must be visited—formula_10, the problem turns into the Windy General Routing Problem (WGRP). Benavent proposed an integer linear programming formulation and different heuristics and lower bounds for the WRPP.
Benavent et al published an evaluation of several heuristic methods used for solving the WRPP in a few seconds with a deviation no greater than 1% from the lower bound on medium sized graphs. They improved on this with a Scatter Search algorithm that reduced the difference to 0.5%. Scatter Search found solutions that deviated by less than 2% when implemented on networks with hundreds of nodes and thousands of edges.
In real world applications, there are multiple vehicles that can move, which leads to the generalization named the Min-Max K-vehicles Windy Rural Postman Problem (MM K-WRPP). The min–max K-vehicles Windy Rural Postman Problem (MM K-WRPP) is defined as follows: Given a windy graph formula_11, a distinguished vertex, formula_12, representing the depot, a subset of required edges formula_13, and a fixed number K of vehicles, the MM K-WRPP consists of finding a set of K tours for the vehicles in such a way that each tour starts and ends at the depot and each required edge is serviced by exactly one vehicle. The objective is to minimize the length of the longest tour in order to find a set of balanced routes for the vehicles. Some real-life applications of routing problems with min–max objectives are school bus routing (Delgado and Pacheco 2001), the delivery of newspapers to customers (Applegate et al. 2002) and waste collection (Lacomme et al. 2004).
The best MM K_WRPP algorithm was very close to the minimum solution with 2 and 3 vehicles, less than 0.4% on average. The gap increases to about 1.00% and 1.60% at 4 and 5 vehicles.
According to Dussault et al and Benavent et al, a metaheuristics multi-objective simulating annealing algorithm (MOSA) can solve the different contraints imposed on the WRPP. The WRPP is an important Arc Routing Problem which generalizes many of the single-vehicles Arc Routing problems. In real applications of math, a solution that minimizes the total costs of all vehicles route and the length of the longest tour is preferable. It's hard to be in a location where your package is always hours late. We should start with the assumption that several vehicles with a specific measurable capacity to serve customers is more realistic than one vehicle with unmeasurable infinite capacity. Rabbani et. al measured the performance of MOSA algorithms and models using a multi-objective development of Cuckoo search—developed by Yang et al, also referred to as Multi-objective Cuckoo Search and abbreviated by MOCS. They concluded that MOSA methods were more efficient than MOCS methods. In the future comparisons with other meta-heuristic methods could be researched, including Non-dominated Sorting Genetic Algorithm (NSGA- ), multi-objective particle swarm optimization algorithm (MOPSO) and multi-objective Imperialist Competitive Algorithm.
In the Windy Postman Problem (WPP) model, the cost of going in one direction is different than the cost it takes to go in the other direction. For example, if the wind is blowing down the street it takes more time and energy to go against the wind than with the wind. Another example of the WPP is the cost of plowing uphill is greater than the cost of plowing downhill. This is modeled by a variant studied by Dussault et al, the Downhill Plowing Problem (DPP).
A branch and cut algorithm was published by Angel Corberan for the windy postman problem. The algorithm is based on heuristic and exact methods for manipulating odd-cut inequality violations.
Applications.
Various combinatorial problems have been reduced to the Chinese Postman Problem, including finding a maximum cut in a planar graph and a minimum-mean length circuit in an undirected graph.
Snow plows.
In winter a common question is what set of routes has the smallest (minimum) maximum route length? Typically, this is assessed as an arc routing problem with a graph. The time it takes to travel a street, known as deadhead time, is faster than the time it takes to plow the snow from the streets (or deliver mail or drop off packages). Another aspect that must be considered when applying arc routing to snow plowing is the fact that on steep streets it is either difficult or impossible to plow uphill. The objective is a route that avoids plowing uphill on steep streets that completes the job faster by maximizing the deadhead time to get the location. This was modeled with a heuristic algorithm that approximates a lower bound by Dussault, Golden and Wasil. This is the Downhill Plow Problem (DPP). Snow teams prefer to plow downhill and deadhill uphill. This problem assumes that the conditions are severe enough that the streets are closed and there is no traffic.
The Downhill Plowing Problem ignores the Plowing with Precedence Problem (PPP), which is built on the reasonable assumption that if the snow is too deep the snow plow cannot deadhead an unplowed street. The DPP makes the assumption that the snow level is low enough that the streets that are not plowed can be deadheaded, but that the snow is deep enough that there is no traffic. If there is traffic on the roads, the assumption that it is impossible to plow uphill can no longer be held. The simulation for the DPP deadheaded unplowed street about 5% of the time, which is a topic for future graph theory and arc routing research.
Considering an undirected graph formula_14 where formula_15 is the set of vertices and nodes and formula_16 is the set of arcs. Each arc represented by formula_17 has four costs: formula_18, defined as the cost of plowing from formula_19 to formula_20, formula_21, the cost of plowing from formula_20 to formula_19, formula_22, the cost of deadheading from formula_19 to formula_20, and formula_23, the cost of deadheading from formula_20 to formula_19. The setup assumes that formula_20 has a higher elevation formula_19, which leads to the statement: formula_24. In practice, downhill plowing time is two times as efficient as uphill plowing and deadheading is twice as efficient as plowing. The algorithm finds formula_25 routes will each begin and end at the depot formula_26, plow the arc two times because the left side and right side of the street take two passes to plow.
The best solution will minimize the maximum route length. Dussault, Golden, and Wasil found an algorithm that did not exceed the lower bound by 5.5% in over 80 test runs. The deviation increased as the complexity of the model increased because there are more unoptimized approximations than optimized approximation as the model grows. An improvement on Dussault et. al's DPP algorithm might have penalties for making U-turns and left hand turns, or going straight across an intersection, which take additional time and pushes snow into the middle of the intersection, respectively. (see The Directed Rural Postman Problem with Turn Penalties problem, often referred to as the DRPP-TP below).
"k"-Chinese postman problem ("k"-CPP).
The "k"-Chinese Postman can be stated as follows: "given a connected edge-weighted graph "G" and integers "p" and "k", decide whether there are at least "k" closed walks such that every edge of "G" is contained in at least one of them and the total weight of the edges in the walks is at most "p"?" The process of obtaining the solution to the "k"-CPP is NP complete. Gutin, Muciaccia, and Yeo proved in 2013 that the "k"-CPP is fixed-parameter tractable. The authors prove the "k"-CPP admits a kernel with formula_27 vertices and the directed version of the "k"-CPP is NP complete.
Rural postman problem (RPP) and generalizations.
The rural postman problem (RPP) makes some routes mandatory and absolute but the person traversing the graph does not have to go in one particular direction. The RPP is NP hard and complete, in the same way that the kCPP, the DPP, the PPP, are NP hard. Benevant studied a generalization of this named Directed Rural Postman Problem with Turn Penalties (DRPP-TP). Benevant's algorithm approximated the solution by transforming the DRPP-TP into an asymmetrical traveling salesman problem (ATSP).
Heuristics and algorithms.
Most algorithms require a pre-processing of the graph, which simplifies the initial graph by removing all edges that are not in the shortest path between two required edges. Another simplification that the pre-processing adds is that it transforms the shortest path between 2 required edges into a single, non-required edge, regardless of the number of edges in the path, provided that there were no required edges in the path.
Once the pre-processing is done, the problem can be generalized into a convex hull problem, with the edges being the points of the hull. The convex hull problem can be solved through linear programming or through convex hull algorithms, but the process of finding the convex hull is an exponential problem.
Methods of solving the URPP after the pre-processing is done consist of the "cutting plane algorithm" and the "branch & cut methodology".
Complexity.
This is a list of computational complexities for different arc routing problems.
References.
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"text": "c_{ij}^+\\gg c_{ji}^+\\gg c_{ij}^- \\geq c_{ji}^-"
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"text": "O(k^2\\log(k))"
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| https://en.wikipedia.org/wiki?curid=14040362 |
14040367 | 2,4-dichlorobenzoyl-CoA reductase | Class of enzymes
In enzymology, a 2,4-dichlorobenzoyl-CoA reductase (EC 1.3.1.63) is an enzyme that catalyzes the chemical reaction
4-chlorobenzoyl-CoA + NADP+ + HCl formula_0 2,4-dichlorobenzoyl-CoA + NADPH + H+
The 3 substrates of this enzyme are 4-chlorobenzoyl-CoA, NADP+, and HCl, whereas its 3 products are 2,4-dichlorobenzoyl-CoA, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 4-chlorobenzoyl-CoA:NADP+ oxidoreductase (halogenating). This enzyme participates in 2,4-dichlorobenzoate degradation.
References.
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14040384 | 2-alkenal reductase | Class of enzymes
In enzymology, a 2-alkenal reductase (EC 1.3.1.74) is an enzyme that catalyzes the chemical reaction
n-alkanal + NAD(P)+ formula_0 alk-2-enal + NAD(P)H + H+
The 3 substrates of this enzyme are n-alkanal, NAD+, and NADP+, whereas its 4 products are alk-2-enal, NADH, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is n-alkanal:NAD(P)+ 2-oxidoreductase. Other names in common use include NAD(P)H-dependent alkenal/one oxidoreductase, and NADPH:2-alkenal alpha,beta-hydrogenase.
Structural studies.
As of late 2007, three structures have been solved for this class of enzymes, with PDB accession codes 2DM6, 2J3J, and 2J3K.
References.
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14040410 | 2-Coumarate reductase | Class of enzymes
In enzymology, a 2-coumarate reductase or melilotate dehydrogenase (EC 1.3.1.11) is an enzyme that catalyzes the chemical reaction
3-(2-hydroxyphenyl)propanoate + NAD+ formula_0 2-coumarate + NADH + H+
Thus, the two substrates of this enzyme are 3-(2-hydroxyphenyl)propanoate and NAD+, whereas its 3 products are 2-coumarate, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 3-(2-hydroxyphenyl)propanoate:NAD+ oxidoreductase. This enzyme participates in phenylalanine metabolism.
References.
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14040425 | 2-enoate reductase | Class of enzymes
In enzymology, a 2-enoate reductase (EC 1.3.1.31) is an enzyme that catalyzes the chemical reaction
butanoate + NAD+ formula_0 2-butenoate + NADH + H+
Thus, the two substrates of this enzyme are butanoate and NAD+, whereas its 3 products are 2-butenoate, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is butanoate:NAD+ Delta2-oxidoreductase. This enzyme is also called enoate reductase. This enzyme participates in phenylalanine metabolism. It has 4 cofactors: FAD, Iron, Sulfur, and Iron-sulfur.
References.
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14040658 | 2-furoyl-CoA dehydrogenase | Class of enzymes
In enzymology, a 2-furoyl-CoA dehydrogenase (EC 1.3.99.8) is an enzyme that catalyzes the chemical reaction
2-furoyl-CoA + H2O + acceptor formula_0 S-(5-hydroxy-2-furoyl)-CoA + reduced acceptor
The 3 substrates of this enzyme are 2-furoyl-CoA, H2O, and acceptor, whereas its two products are S-(5-hydroxy-2-furoyl)-CoA and reduced acceptor.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with other acceptors. The systematic name of this enzyme class is 2-furoyl-CoA:acceptor 5-oxidoreductase (hydroxylating). Other names in common use include furoyl-CoA hydroxylase, 2-furoyl coenzyme A hydroxylase, 2-furoyl coenzyme A dehydrogenase, and 2-furoyl-CoA:(acceptor) 5-oxidoreductase (hydroxylating). It employs one cofactor, copper.
References.
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14040670 | 2-hexadecenal reductase | Enzyme
In enzymology, a 2-hexadecenal reductase (EC 1.3.1.27) is an enzyme that catalyzes the chemical reaction
hexadecanal + NADP+ formula_0 2-trans-hexadecenal + NADPH + H+
Thus, the two substrates of this enzyme are hexadecanal and NADP+, whereas its 3 products are 2-trans-hexadecenal, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is hexadecanal:NADP+ Delta2-oxidoreductase. Other names in common use include 2-alkenal reductase, and hexadecanal: NADP+ oxidoreductase.
References.
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14040692 | 2-hydroxy-6-oxo-6-phenylhexa-2,4-dienoate reductase | Class of enzymes
In enzymology, a 2-hydroxy-6-oxo-6-phenylhexa-2,4-dienoate reductase (EC 1.3.1.40) is an enzyme that catalyzes the chemical reaction
2,6-dioxo-6-phenylhexanoate + NADP+ formula_0 2-hydroxy-6-oxo-6-phenylhexa-2,4-dienoate + NADPH + H+
Thus, the two substrates of this enzyme are 2,6-dioxo-6-phenylhexanoate and NADP+, whereas its 3 products are 2-hydroxy-6-oxo-6-phenylhexa-2,4-dienoate, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 2,6-dioxo-6-phenylhexanoate:NADP+ Delta2-oxidoreductase. Other names in common use include 2-hydroxy-6-oxo-phenylhexa-2,4-dienoate (reduced nicotinamide, and adenine dinucleotide phosphate) reductase.
References.
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14040708 | 2'-hydroxydaidzein reductase | Class of enzymes
In enzymology, a 2'-hydroxydaidzein reductase (EC 1.3.1.51) is an enzyme that catalyzes the chemical reaction
2'-hydroxy-2,3-dihydrodaidzein + NADP+ formula_0 2'-hydroxydaidzein + NADPH + H+
Thus, the two substrates of this enzyme are 2'-hydroxy-2,3-dihydrodaidzein and NADP+, whereas its 3 products are 2'-hydroxydaidzein, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 2'-hydroxy-2,3-dihydrodaidzein:NADP+ 2'-oxidoreductase. Other names in common use include NADPH:2'-hydroxydaidzein oxidoreductase, HDR, and 2'-hydroxydihydrodaidzein:NADP+ 2'-oxidoreductase. This enzyme participates in isoflavonoid biosynthesis.
References.
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14040725 | 2'-Hydroxyisoflavone reductase | Class of enzymes
In enzymology, a 2'-hydroxyisoflavone reductase (EC 1.3.1.45) is an enzyme that catalyzes the chemical reaction
vestitone + NADP+ formula_0 2'-hydroxyformononetin + NADPH + H+
Thus, the two substrates of this enzyme are vestitone and NADP+, whereas its 3 products are 2'-hydroxyformononetin, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is vestitone:NADP+ oxidoreductase. Other names in common use include NADPH:2'-hydroxyisoflavone oxidoreductase, isoflavone reductase, and 2',7-dihydroxy-4',5'-methylenedioxyisoflavone reductase.
References.
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| https://en.wikipedia.org/wiki?curid=14040725 |
14040742 | 2-methylacyl-CoA dehydrogenase | Class of enzymes
In enzymology, a 2-methylacyl-CoA dehydrogenase (EC 1.3.99.12) is an enzyme that catalyzes the chemical reaction
2-methylbutanoyl-CoA + acceptor formula_0 2-methylbut-2-enoyl-CoA + reduced acceptor
Thus, the two substrates of this enzyme are 2-methylbutanoyl-CoA and acceptor, whereas its two products are 2-methylbut-2-enoyl-CoA and reduced acceptor.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with other acceptors. The systematic name of this enzyme class is 2-methylbutanoyl-CoA:acceptor oxidoreductase. Other names in common use include branched-chain acyl-CoA dehydrogenase, 2-methyl branched chain acyl-CoA dehydrogenase, and 2-methylbutanoyl-CoA:(acceptor) oxidoreductase. This enzyme participates in valine, leucine and isoleucine degradation.
References.
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14040760 | 2-methyl-branched-chain-enoyl-CoA reductase | Class of enzymes
In enzymology, a 2-methyl-branched-chain-enoyl-CoA reductase (EC 1.3.8.5) is an enzyme that catalyzes the chemical reaction
2-methylbutanoyl-CoA + electron transfer flavoprotein formula_0 2-methylcrotonoyl-CoA + reduced electron transfer flavoprotein + H+
Thus, the two substrates of this enzyme are 2-methylbutanoyl-CoA and an electron transfer flavoprotein, whereas its 3 products are 2-methylcrotonoyl-CoA, reduced electron transfer flavoprotein, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donors with flavin as acceptor. The systematic name of this enzyme class is 2-methyl-branched-chain-acyl-CoA:electron-transfer flavoprotein 2-oxidoreductase . This enzyme participates in the degradation of isoleucine. It employs one cofactor, FAD.
References.
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}
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| https://en.wikipedia.org/wiki?curid=14040760 |
14040783 | 3-methyleneoxindole reductase | Class of enzymes
In enzymology, a 3-methyleneoxindole reductase (EC 1.3.1.17) is an enzyme that catalyzes the chemical reaction
3-methyl-1,3-dihydroindol-2-one + NADP+ formula_0 3-methylene-1,3-dihydro-2H-indol-2-one + NADPH + H+
Thus, the two substrates of this enzyme are 3-methyl-1,3-dihydroindol-2-one and NADP+, whereas its three products are 3-methylene-1,3-dihydro-2H-indol-2-one, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 3-methyl-1,3-dihydroindol-2-one:NADP+ oxidoreductase. This enzyme is also termed 3-methyloxindole:NADP+ oxidoreductase.
References.
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| https://en.wikipedia.org/wiki?curid=14040783 |
14040817 | 3-oxo-5beta-steroid 4-dehydrogenase | Class of enzymes
In enzymology, a 3-oxo-5beta-steroid 4-dehydrogenase (EC 1.3.99.6) is an enzyme that catalyzes the chemical reaction
a 3-oxo-5beta-steroid + acceptor formula_0 a 3-oxo-Delta4-steroid + reduced acceptor
Thus, the two substrates of this enzyme are 3-oxo-5beta-steroid and acceptor, whereas its two products are 3-oxo-Delta4-steroid and reduced acceptor.
This enzyme belongs to the family of oxidoreductases, to be specific, those acting on the CH-CH group of donor with other acceptors. The systematic name of this enzyme class is 3-oxo-5beta-steroid:acceptor Delta4-oxidoreductase. This enzyme is also called 3-oxo-5beta-steroid:(acceptor) Delta4-oxidoreductase. This enzyme participates in 3 metabolic pathways: bile acid biosynthesis, c21-steroid hormone metabolism, and androgen and estrogen metabolism.
References.
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| https://en.wikipedia.org/wiki?curid=14040817 |
14040841 | 3-oxosteroid 1-dehydrogenase | Class of enzymes
In enzymology, a 3-oxosteroid 1-dehydrogenase (EC 1.3.99.4) is an enzyme that catalyzes the chemical reaction
a 3-oxosteroid + acceptor formula_0 a 3-oxo-Delta1-steroid + reduced acceptor
Thus, the two substrates of this enzyme are 3-oxosteroid and acceptor, whereas its two products are 3-oxo-Delta1-steroid and reduced acceptor.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with other acceptors. The systematic name of this enzyme class is 3-oxosteroid:acceptor Delta1-oxidoreductase. Other names in common use include 3-oxosteroid Delta1-dehydrogenase, Delta1-dehydrogenase, 3-ketosteroid-1-en-dehydrogenase, 3-ketosteroid-Delta1-dehydrogenase, 1-ene-dehydrogenase, 3-oxosteroid:(2,6-dichlorphenolindophenol) Delta1-oxidoreductase, 4-en-3-oxosteroid:(acceptor)-1-en-oxido-reductase, Delta1-steroid reductase, and 3-oxosteroid:(acceptor) Delta1-oxidoreductase.
References.
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| https://en.wikipedia.org/wiki?curid=14040841 |
14040856 | (3S,4R)-3,4-dihydroxycyclohexa-1,5-diene-1,4-dicarboxylate dehydrogenase | Enzyme
In enzymology, a (3S,4R)-3,4-dihydroxycyclohexa-1,5-diene-1,4-dicarboxylate dehydrogenase (EC 1.3.1.53) is an enzyme that catalyzes the chemical reaction
(3S,4R)-3,4-dihydroxycyclohexa-1,5-diene-1,4-dicarboxylate + NAD+ formula_0 3,4-dihydroxybenzoate + CO2 + NADH
Thus, the two substrates of this enzyme are (3S,4R)-3,4-dihydroxycyclohexa-1,5-diene-1,4-dicarboxylate and NAD+, whereas its 3 products are 3,4-dihydroxybenzoate, CO2, and NADH.
This enzyme is a part of the terephthalate degradation pathway in bacteria.
Family.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (3S,4R)-3,4-dihydroxycyclohexa-1,5-diene-1,4-dicarboxylate:NAD+ oxidoreductase. Another name in common use is (1R,2S)-dihydroxy-3,5-cyclohexadiene-1,4-dicarboxylate dehydrogenase. This enzyme employs one cofactor, iron.
References.
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| https://en.wikipedia.org/wiki?curid=14040856 |
14040870 | 4-hydroxybenzoyl-CoA reductase | In enzymology, a 4-hydroxybenzoyl-CoA reductase (EC 1.3.7.9) is an enzyme found in some bacteria and archaea that catalyzes the chemical reaction
benzoyl-CoA + acceptor + H2O formula_0 4-hydroxybenzoyl-CoA + reduced acceptor
The 3 substrates of this enzyme are benzoyl-CoA, acceptor, and H2O, whereas its two products are 4-hydroxybenzoyl-CoA and reduced acceptor.
This enzyme participates in benzoate degradation via coa ligation.
Nomenclature.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with other acceptors. The systematic name of this enzyme class is benzoyl-CoA:acceptor oxidoreductase. Other names in common use include:
References.
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Further reading.
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| https://en.wikipedia.org/wiki?curid=14040870 |
14040892 | 5,6-dihydroxy-3-methyl-2-oxo-1,2,5,6-tetrahydroquinoline dehydrogenase | Class of enzymes
In enzymology, a 5,6-dihydroxy-3-methyl-2-oxo-1,2,5,6-tetrahydroquinoline dehydrogenase (EC 1.3.1.65) is an enzyme that catalyzes the chemical reaction
5,6-dihydroxy-3-methyl-2-oxo-1,2,5,6-tetrahydroquinoline + NAD+ formula_0 5,6-dihydroxy-3-methyl-2-oxo-1,2-dihydroquinoline + NADH + H+
Thus, the two substrates of this enzyme are 5,6-dihydroxy-3-methyl-2-oxo-1,2,5,6-tetrahydroquinoline and NAD+, whereas its 3 products are 5,6-dihydroxy-3-methyl-2-oxo-1,2-dihydroquinoline, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 5,6-dihydroxy-3-methyl-2-oxo-1,2,5,6-tetrahydroquinoline:NAD+ oxidoreductase.
References.
<templatestyles src="Reflist/styles.css" /> | [
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| https://en.wikipedia.org/wiki?curid=14040892 |
14040908 | 6-hydroxynicotinate reductase | Class of enzymes
In enzymology, a 6-hydroxynicotinate reductase (EC 1.3.7.1) is an enzyme that catalyzes the chemical reaction
6-oxo-1,4,5,6-tetrahydronicotinate + oxidized ferredoxin formula_0 6-hydroxynicotinate + reduced ferredoxin
Thus, the two substrates of this enzyme are 6-oxo-1,4,5,6-tetrahydronicotinate and oxidized ferredoxin, whereas its two products are 6-hydroxynicotinate and reduced ferredoxin.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-CH group of donor with an iron-sulfur protein as acceptor. The systematic name of this enzyme class is 6-oxo-1,4,5,6-tetrahydronicotinate:ferredoxin oxidoreductase. Other names in common use include 6-oxotetrahydronicotinate dehydrogenase, 6-hydroxynicotinic reductase, HNA reductase, and 1,4,5,6-tetrahydro-6-oxonicotinate:ferredoxin oxidoreductase.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
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| https://en.wikipedia.org/wiki?curid=14040908 |
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