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14322253
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2-methylisocitrate dehydratase
|
Class of enzymes
The enzyme 2-methylisocitrate dehydratase (EC 4.2.1.99) catalyzes the chemical reaction
(2"S",3"R")-3-hydroxybutane-1,2,3-tricarboxylate formula_0 ("Z")-but-2-ene-1,2,3-tricarboxylate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is (2"S",3"R")-3-hydroxybutane-1,2,3-tricarboxylate hydro-lyase [("Z")-but-2-ene-1,2,3-tricarboxylate-forming]. This enzyme is also called (2"S",3"R")-3-hydroxybutane-1,2,3-tricarboxylate hydro-lyase. This enzyme participates in propanoate metabolism.
References.
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14322281
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2-oxopent-4-enoate hydratase
|
InterPro Family
The enzyme 2-oxopent-4-enoate hydratase (EC 4.2.1.80) catalyzes the chemical reaction
4-hydroxy-2-oxopentanoate formula_0 2-oxopent-4-enoate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 4-hydroxy-2-oxopentanoate hydro-lyase (2-oxopent-4-enoate-forming). Other names in common use include 2-keto-4-pentenoate hydratase, OEH, 2-keto-4-pentenoate (vinylpyruvate)hydratase, and 4-hydroxy-2-oxopentanoate hydro-lyase. This enzyme participates in nine metabolic pathways: phenylalanine metabolism, benzoate degradation via hydroxylation, biphenyl degradation, toluene and xylene degradation, 1,4-dichlorobenzene degradation, fluorene degradation, carbazole degradation, ethylbenzene degradation, and styrene degradation.
References.
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https://en.wikipedia.org/wiki?curid=14322281
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14322304
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3alpha,7alpha,12alpha-trihydroxy-5beta-cholest-24-enoyl-CoA hydratase
|
Enzyme
The enzyme 3α,7α,12α-trihydroxy-5β-cholest-24-enoyl-CoA hydratase (EC 4.2.1.107) catalyzes the chemical reaction
(24"R",25"R")-3α,7α,12α,24-tetrahydroxy-5β-cholestanoyl-CoA formula_0
(24"E")-3α,7α,12α-trihydroxy-5β-cholest-24-enoyl-CoA + H2O
Nomenclature.
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is (24"R",25"R")-3α,7α,12α,24-tetrahydroxy-5beta-cholestanoyl-CoA hydro-lyase [(24"E")-3α,7α,12α-trihydroxy-5β-cholest-24-enoyl-CoA-forming]. Other names in common use include 46 kDa hydratase 2, and (24"R",25"R")-3α,7α,12α,24-tetrahydroxy-5β-cholestanoyl-CoA hydro-lyase.
References.
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Further reading.
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https://en.wikipedia.org/wiki?curid=14322304
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14323201
|
3-cyanoalanine hydratase
|
Class of enzymes
The enzyme 3-cyanoalanine hydratase (EC 4.2.1.65) catalyzes the chemical reaction
-asparagine formula_0 3-cyanoalanine + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -asparagine hydro-lyase (3-cyanoalanine-forming). Other names in common use include β-cyanoalanine hydrolase, β-cyanoalanine hydratase, β-CNAla hydrolase, β-CNA nitrilase, and -asparagine hydro-lyase. This enzyme participates in cyanoamino acid metabolism.
References.
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https://en.wikipedia.org/wiki?curid=14323201
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14323217
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3-dehydroquinate dehydratase
|
Class of enzymes
The enzyme 3-dehydroquinate dehydratase (EC 4.2.1.10) catalyzes the chemical reaction
3-dehydroquinate formula_0 3-dehydroshikimate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. This enzyme participates in phenylalanine, tyrosine and tryptophan biosynthesis.
Discovery.
The shikimate pathway was determined to be a major biosynthetic route for the production of aromatic amino acids through the research of Bernhard Davis and David Sprinson.
Role in the shikimate pathway.
3-Dehydroquinate Dehydratase is an enzyme that catalyzes the third step of the shikimate pathway. The shikimate pathway is a biosynthetic pathway that allows plants, fungi, and bacteria to produce aromatic amino acids. Mammals do not have this pathway, meaning that they must obtain these essential amino acids through their diet. Aromatic Amino acids include Phenylalanine, Tyrosine, and Tryptophan.
This enzyme dehydrates 3-Dehydroquinate, converting it to 3-Dehydroshikimate, as indicated in the adjacent diagram. This is the third step in the Shikimate pathway. It belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 3-dehydroquinate hydro-lyase (3-dehydroshikimate-forming). This enzyme is one of the few examples of convergent evolution. The two separate versions of this enzyme have different amino acid sequences.
3-Dehydroquinate dehydratase is also commonly referred to as Dehydroquinate dehydratase and DHQD. Other names include 3-dehydroquinate hydrolase, DHQase, 3-dehydroquinase, 5-dehydroquinase, dehydroquinase, 5-dehydroquinate dehydratase, 5-dehydroquinate hydro-lyase, and 3-dehydroquinate hydro-lyase.
Evolutionary origins.
Purposes of the products.
The aromatic amino acids produced by the shikimate acid pathway are used by higher plants as protein building blocks and as precursors for several secondary metabolites. Examples of such secondary metabolites are plant pigments and compounds to defend against herbivores, insects, and UV light. The specific aromatic secondary metabolites produced, as well as when and in what quantities they are produced in, varies across different types of plants. Mammals consume essential amino acids in their diets, converting them to precursors for important substances such as neurotransmitters.
Convergent evolution.
As mentioned previously, two classes of 3-Dehydroquinate Dehydratase exist, known as types I and II. These two versions have different amino acid sequences and different secondary structures. Type I is present in fungi, plants, and some bacteria, for the biosynthesis of chorismate. It catalyzes the cis-dehydration of 3-Dehydroquinate via a covalent imine intermediate. Type I is heat liable and has Km values in the low micromolar range. Type II is present in the quinate pathway of fungi and the shikimate pathway of most bacteria. It catalyzes a trans-dehydration using an enolate intermediate. It is heat stable and has Km values one or two orders of magnitude higher than the Type I Km values.
The best studied type I enzyme is from "Escherichia coli" (gene aroD) and related bacteria. It is a homodimeric protein. In fungi, dehydroquinase forms the core of the pentafunctional AROM complex, which catalyses five consecutive steps in the shikimate pathway. A histidine is involved in the catalytic mechanism.
Other purposes.
3-Dehydroquinate Dehydratase is also an enzyme present in the process of the degradation of quinate. Both 3-Dehydroquinate and 3-Dehydroshikimate are intermediates in the reaction mechanism. The following image shows this process in Quinate Degradation.
Applications.
The Shikimate pathway has become a focus of research into the development of herbicides and antimicrobial agents because it is an essential pathway in many plants, bacteria, and parasites but does not exist in mammals.
Inhibitors of the shikimate pathway in mycobacterium have the potential of treating tuberculosis.
Most of the 3-dehydroquinate-dehydratase in bacteria and higher plants is type I DHQD.
References.
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14323237
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3-dehydroquinate synthase
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Enzyme
The enzyme 3-dehydroquinate synthase (EC 4.2.3.4) catalyzes the chemical reaction
3-deoxy--"arabino"-hept-2-ulosonate 7-phosphate formula_0 3-dehydroquinate + phosphate
The protein uses NAD+ to catalyze the reaction. This reaction is part of the shikimate pathway which is involved in the biosynthesis of aromatic amino acids.
3-Dehydroquinate synthase belongs to the family of lyases, to be specific those carbon-oxygen lyases acting on phosphates. This enzyme participates in phenylalanine, tyrosine, and tryptophan biosynthesis. It employs one cofactor, cobalt (Co2+).
Background.
The shikimate pathway is composed of seven steps, each catalyzed by an enzyme. The shikimate pathway is responsible for producing the precursors for aromatic amino acids, which are essential to our diets because we cannot synthesize them in our bodies. Only plants, bacteria, and microbial eukaryotes are capable of producing aromatic amino acids. The pathway ultimately converts phosphoenolpyruvate and 4-erythrose phosphate into chorismate, the precursor to aromatic amino acids. 3-Dehydroquinate synthase is the enzyme that catalyzes reaction in the second step of this pathway. This second step of the reaction eliminates a phosphate from 3-deoxy-D-arabino-heptulosonate 7-phosphate, which results in 3-dehydroquinate. 3-Dehydroquinate synthase is a monomeric enzyme, and has a molecular weight of 39,000. 3-dehydroquinate synthase is activated by inorganic phosphate, and requires NAD+ for activity, although the reaction in total is neutral when catalyzed by an enzyme.
Function.
3-Dehydroquinate synthase utilizes a complex multi-step mechanism that includes alcohol oxidation, phosphate β-elimination, carbonyl reduction, ring opening, and intramolecular aldol condensation.
Dehydroquinate synthase requires NAD+ and a cobalt cofactor to catalyze the conversion of 3-deoxy-D-arabino-heptulosonate 7-phosphate into 3-dehydroquinate. Dehydroquinate synthase is of particular interest because of its complicated activity relative to its small size. In most bacteria, this enzyme has only one function. However, in fungi and protists, it is part of the pentafunctional AROM complex that comprises steps two, three, four, five and six of the shikimate pathway. Together with 3-dehydroquinate dehydratase, 3-dehydroquinate synthase forms the core of this complex.
Applications.
3-Dehydroquinate synthase catalyzes the second step in the shikimate pathway, which is essential for the production of aromatic amino acids in bacteria, plants, and fungi, but not mammals. This makes it an ideal target for new antimicrobial agents, anti-parasitic agents, and herbicides. Other enzymes in the shikimate pathway have already been targeted and put to use as herbicides.
Nomenclature.
The systematic name of this enzyme class is 3-deoxy--"arabino"-hept-2-ulosonate-7-phosphate phosphate-lyase (cyclizing; 3-dehydroquinate-forming). Other names in common use include 5-dehydroquinate synthase, 5-dehydroquinic acid synthetase, dehydroquinate synthase, 3-dehydroquinate synthetase, 3-deoxy-arabino-heptulosonate-7-phosphate phosphate-lyase, (cyclizing), and 3-deoxy-arabino-heptulonate-7-phosphate phosphate-lyase (cyclizing).
References.
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Further reading.
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14323255
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3-hydroxybutyryl-CoA dehydratase
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Class of enzymes
The enzyme 3-hydroxybutyryl-CoA dehydratase (EC 4.2.1.55) catalyzes the chemical reaction
(3"R")-3-hydroxybutanoyl-CoA formula_0 crotonoyl-CoA + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is (3"R")-3-hydroxybutanoyl-CoA hydro-lyase (crotonoyl-CoA-forming). Other names in common use include -3-hydroxybutyryl coenzyme A dehydratase, -3-hydroxybutyryl-CoA dehydratase, enoyl coenzyme A hydrase (), and (3"R")-3-hydroxybutanoyl-CoA hydro-lyase. This enzyme participates in butanoate metabolism.
References.
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14323279
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3-hydroxyoctanoyl-(acyl-carrier-protein) dehydratase
|
Class of enzymes
The enzyme 3-hydroxyoctanoyl-[acyl-carrier-protein] dehydratase (EC 4.2.1.59) catalyzes the chemical reaction
(3"R")-3-hydroxyoctanoyl-[acyl-carrier-protein] formula_0 oct-2-enoyl-[acyl-carrier-protein] + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is (3"R")-3-hydroxyoctanoyl-[acyl-carrier-protein] hydro-lyase (oct-2-enoyl-[acyl-carrier protein]-forming). Other names in common use include -3-hydroxyoctanoyl-[acyl carrier protein] dehydratase, -3-hydroxyoctanoyl-acyl carrier protein dehydratase, beta-hydroxyoctanoyl-acyl carrier protein dehydrase, beta-hydroxyoctanoyl thioester dehydratase, beta-hydroxyoctanoyl-ACP-dehydrase, and (3"R")-3-hydroxyoctanoyl-[acyl-carrier-protein] hydro-lyase.
References.
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14323297
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3-hydroxypalmitoyl-(acyl-carrier-protein) dehydratase
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Class of enzymes
In enzymology, a 3-hydroxypalmitoyl-[acyl-carrier-protein] dehydratase (EC 4.2.1.61) is an enzyme that catalyzes the chemical reaction
(3R)-3-hydroxypalmitoyl-[acyl-carrier-protein] formula_0 hexadec-2-enoyl-[acyl-carrier-protein] + H2O
Hence, this enzyme has one substrate, (3R)-3-hydroxypalmitoyl-[acyl-carrier-protein], and two products, hexadec-2-enoyl-[acyl-carrier-protein] and H2O.
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is (3R)-3-hydroxypalmitoyl-[acyl-carrier-protein] hydro-lyase (hexadec-2-enoyl-[acyl-carrier protein]-forming). Other names in common use include D-3-hydroxypalmitoyl-[acyl-carrier-protein] dehydratase, beta-hydroxypalmitoyl-acyl carrier protein dehydrase, beta-hydroxypalmitoyl thioester dehydratase, beta-hydroxypalmityl-ACP dehydrase, and (3R)-3-hydroxypalmitoyl-[acyl-carrier-protein] hydro-lyase. This enzyme participates in fatty acid biosynthesis.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 2PFF.
References.
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14323317
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4a-hydroxytetrahydrobiopterin dehydratase
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Enzyme
The enzyme 4a-hydroxytetrahydrobiopterin dehydratase (EC 4.2.1.96) catalyzes the chemical reaction
4a-hydroxytetrahydrobiopterin formula_0 6,7-dihydrobiopterin + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 4a-hydroxytetrahydrobiopterin hydro-lyase (6,7-dihydrobiopterin-forming). Other names in common use include 4a-hydroxy-tetrahydropterin dehydratase, pterin-4α-carbinolamine dehydratase, and 4a-hydroxytetrahydrobiopterin hydro-lyase.
Structural studies.
As of late 2007, 3 structures have been solved for this class of enzymes, with PDB accession codes 1DCO, 1DCP, and 1RU0.
References.
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https://en.wikipedia.org/wiki?curid=14323317
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14323329
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4-oxalmesaconate hydratase
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Class of enzymes
The enzyme 4-oxalmesaconate hydratase (EC 4.2.1.83) catalyzes the chemical reaction
2-hydroxy-4-oxobutane-1,2,4-tricarboxylate formula_0 (1"E",3"E")-4-hydroxybuta-1,3-diene-1,2,4-tricarboxylate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is (1"E",3"E")-4-hydroxybuta-1,3-diene-1,2,4-tricarboxylate 1,2-hydro-lyase (2-hydroxy-4-oxobutane-1,2,4-tricarboxylate-forming). Other names in common use include 4-carboxy-2-oxohexenedioate hydratase, 4-carboxy-2-oxobutane-1,2,4-tricarboxylate 2,3-hydro-lyase, oxalmesaconate hydratase, γ-oxalmesaconate hydratase, 4-carboxy-2-oxohexenedioate hydratase, and 2-hydroxy-4-oxobutane-1,2,4-tricarboxylate 2,3-hydro-lyase. This enzyme participates in benzoate degradation via hydroxylation.
References.
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14323352
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(4S)-limonene synthase
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Class of enzymes
The enzyme (4"S")-limonene synthase (EC 4.2.3.16) catalyzes the chemical reaction
geranyl diphosphate formula_0 (−)-(4"S")-limonene + diphosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is geranyl-diphosphate diphosphate-lyase [cyclizing, (−)-(4"S")-limonene-forming]. Other names in common use include (−)-(4"S")-limonene synthase, 4"S"-(−)-limonene synthase, geranyldiphosphate diphosphate lyase (limonene forming), geranyldiphosphate diphosphate lyase [cyclizing, and (4"S")-limonene-forming]. This enzyme participates in monoterpenoid biosynthesis.
References.
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14323369
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5alpha-hydroxysteroid dehydratase
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Class of enzymes
The enzyme 5α-hydroxysteroid dehydratase (EC 4.2.1.62) catalyzes the chemical reaction
5α-ergosta-7,22-diene-3β,5-diol formula_0 ergosterol + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 5α-ergosta-7,22-diene-3β,5-diol 5,6-hydro-lyase (ergosterol-forming). This enzyme is also called 5α-ergosta-7,22-diene-3β,5-diol 5,6-hydro-lyase.
References.
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14323397
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5-dehydro-4-deoxyglucarate dehydratase
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InterPro Family
The enzyme 5-dehydro-4-deoxyglucarate dehydratase (EC 4.2.1.41) catalyzes the chemical reaction
5-dehydro-4-deoxy--glucarate formula_0 2,5-dioxopentanoate + H2O + CO2
Enzyme class.
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 5-dehydro-4-deoxy--glucarate hydro-lyase (decarboxylating 2,5-dioxopentanoate-forming). Other names in common use include 5-keto-4-deoxy-glucarate dehydratase, deoxyketoglucarate dehydratase, -4-deoxy-5-ketoglucarate hydro-lyase, and 5-dehydro-4-deoxy--glucarate hydro-lyase (decarboxylating). This enzyme participates in ascorbate and aldarate metabolism.
References.
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14323556
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6-Pyruvoyltetrahydropterin synthase
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Class of enzymes
The enzyme 6-pyruvoyltetrahydropterin synthase (EC 4.2.3.12, PTPS) catalyzes the following chemical reaction:
7,8-Dihydroneopterin 3′-triphosphate formula_0 6-pyruvoyltetrahydropterin + triphosphate
This reaction is the second step (shown above) in the biosynthesis of tetrahydrobiopterin from GTP, which is used as a cofactor in the synthesis of aromatic amino acid monooxygenases and nitric oxide synthase PTPS converts 7,8-dihydroneopterin triphosphate to 6-pyruvoyltetrahydropterin (PTP) through the loss of the triphosphate group, a stereospecific reduction of the double bond between the top right nitrogen and carbon in the ring on the triphosphate on the right, the oxidation of the hydroxyl groups located on the first and second carbons of the side chain, and an internal base-catalyzed hydrogen transfer. ] 6-pyruvoyltetrahydropterin synthase (PTPS) can be found in the cytoplasm as well as the nucleus of cells according to immunohistochemical studies conducted. It has also been found that in higher species 6-pyruvoyltetrahydropterin synthase (PTPS) can undergo post-translational modification.
This enzyme participates in tetrahydrobiopterin biosynthesis.
Nomenclature.
This enzyme belongs to the family of lyases, to be specific, those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is 6-[(1S,2R)-1,2-dihydroxy-3′-triphosphooxypropyl]-7,8-dihydropterin triphosphate-lyase (6-pyruvoyl-5,6,7,8-tetrahydropterin-forming). Other names in common use include 2-amino-4-oxo-6-[(1S,2R)-1,2-dihydroxy-3-triphosphooxypropyl]-7,8-, and dihydroxypteridine triphosphate lyase.
Structure.
6-pyruvoyltetrahydropterin synthase (PTPS) is a hexamer with "D"3 symmetry, and dimensions 60 × 60 × 60 A ̊. It is composed of identical subunits formed from a dimer of trimers. A 12-stranded antiparallel b-barrel is formed by the trimer of dimers and creates a pore within PTPS, with a 6 to 12 A ̊ diameter. The trimers are connected by contact between the β-sheets of monomers, which are perpendicular to each other, separated by less than 4 Angstroms, and connected in three locations residues 20–24, 48–51, and 89–91.
One enzymatic active site is located where the three monomers come together in each subunit of the hexamer. Three histidine residues: His23, His48 and His50 create a transition metal binding site where Zn(II) binds and is the cause of enzymatic activity in the center of the pore. Above the Zn(II) ion are GluA133 and CysA42, which are catalytically important because they are close to the metal but do not bind to it. The lack of binding implies that the substrate binds to the Zn(II) inside the pore during catalysis.
Genetics.
This enzyme 6-pyruvoyltetrahydropterin synthase is encoded by the PTS gene. A mutation in the 6-PTS gene may be the cause of a hereditary dystonic disorder. There have been four mutations of the 6-PTS gene found. The mutations include two homozygous mutations, R25Q and I114V, and two compound heterozygous mutations, R16C and K120stop. The deficiency is only associated with the recessive gene being passed on from parent to child.
Clinical significance.
6-Pyruvoyltetrahydropterin synthase deficiency is the most common cause of a deficiency of tetrahydrobiopterin. Tetrahydrobiopterin deficiency leads to hyperphenylalaninemia and the inability to make neurotransmitters such as dopamine and serotonin. PTPS deficiency has been shown to lead to severe mental retardation, delayed motor development, and seizures. Low levels of tetrahydrobiopterin production, opposed to near complete lack of tetrahydrobiopterin may cause fluctuations in the symptoms experienced throughout the day.
References.
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Further reading.
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14323583
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Abietadiene synthase
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Class of enzymes
The enzyme abieta-7,13-diene synthase (EC 4.2.3.18) catalyzes the chemical reaction
(+)-copalyl diphosphate formula_0 abieta-7,13-diene + diphosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is (+)-copalyl-diphosphate diphosphate-lyase [cyclizing, abieta-7,13-diene-forming]. This enzyme is also called copalyl-diphosphate diphosphate-lyase (cyclizing). This enzyme participates in diterpenoid biosynthesis.
It has recently been shown (Keeling, "et al.", 2011) that the orthologous gene in Norway spruce ("Picea abies") does not produce abietadiene directly, but instead produces a thermally unstable allylic tertiary alcohol 13-hydroxy-8(14)- abietene, which readily dehydrates to abietadiene, levopimaradiene, palustradiene, and neoabietadiene, when analyzed by the commonly used gas chromatography. This has been confirmed in the other conifer species, lodgepole pine ("Pinus contorta") and Jack pine ("Pinus banksiana") (Hall "et al.", 2013).
References.
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14323615
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Acetylenecarboxylate hydratase
|
Class of enzymes
The enzyme acetylenecarboxylate hydratase (EC 4.2.1.27) catalyzes the chemical reaction
3-oxopropanoate formula_0 propynoate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 3-oxopropanoate hydro-lyase (propynoate-forming). Other names in common use include acetylenemonocarboxylate hydratase, alkynoate hydratase, acetylenemonocarboxylate hydrase, acetylenemonocarboxylic acid hydrase, malonate-semialdehyde dehydratase, and 3-oxopropanoate hydro-lyase. This enzyme participates in 3 metabolic pathways: beta-alanine metabolism, propanoate metabolism, and butanoate metabolism.
References.
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14323664
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Altronate dehydratase
|
The enzyme altronate dehydratase (EC 4.2.1.7) catalyzes the chemical reaction
-altronate formula_0 2-dehydro-3-deoxy--gluconate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -altronate hydro-lyase (2-dehydro-3-deoxy--gluconate-forming). This enzyme is also called -altronate hydro-lyase. This enzyme participates in pentose and glucuronate interconversions.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14323664
|
1432589
|
Schwarz lemma
|
Statement in complex analysis
In mathematics, the Schwarz lemma, named after Hermann Amandus Schwarz, is a result in complex analysis about holomorphic functions from the open unit disk to itself. The lemma is less celebrated than deeper theorems, such as the Riemann mapping theorem, which it helps to prove. It is, however, one of the simplest results capturing the rigidity of holomorphic functions.
Statement.
Let formula_0 be the open unit disk in the complex plane formula_1 centered at the origin, and let formula_2 be a holomorphic map such that formula_3 and formula_4 on formula_5.
Then formula_6 for all formula_7, and formula_8.
Moreover, if formula_9 for some non-zero formula_10 or formula_11, then formula_12 for some formula_13 with formula_14.
Proof.
The proof is a straightforward application of the maximum modulus principle on the function
formula_15
which is holomorphic on the whole of formula_16, including at the origin (because formula_17 is differentiable at the origin and fixes zero). Now if formula_18 denotes the closed disk of radius formula_19 centered at the origin, then the maximum modulus principle implies that, for formula_20, given any formula_21, there exists formula_22 on the boundary of formula_23 such that
formula_24
As formula_25 we get formula_26.
Moreover, suppose that formula_9 for some non-zero formula_27, or formula_11. Then, formula_28 at some point of formula_16. So by the maximum modulus principle, formula_29 is equal to a constant formula_30 such that formula_14. Therefore, formula_12, as desired.
Schwarz–Pick theorem.
A variant of the Schwarz lemma, known as the Schwarz–Pick theorem (after Georg Pick), characterizes the analytic automorphisms of the unit disc, i.e. bijective holomorphic mappings of the unit disc to itself:
Let formula_31 be holomorphic. Then, for all formula_32,
formula_33
and, for all formula_34,
formula_35
The expression
formula_36
is the distance of the points formula_37, formula_38 in the Poincaré metric, i.e. the metric in the Poincaré disc model for hyperbolic geometry in dimension two. The Schwarz–Pick theorem then essentially states that a holomorphic map of the unit disk into itself "decreases" the distance of points in the Poincaré metric. If equality holds throughout in one of the two inequalities above (which is equivalent to saying that the holomorphic map preserves the distance in the Poincaré metric), then formula_17 must be an analytic automorphism of the unit disc, given by a Möbius transformation mapping the unit disc to itself.
An analogous statement on the upper half-plane formula_39 can be made as follows:
Let formula_40 be holomorphic. Then, for all formula_41,
formula_42
This is an easy consequence of the Schwarz–Pick theorem mentioned above: One just needs to remember that the Cayley transform
formula_43 maps the upper half-plane formula_39 conformally onto the unit disc formula_5. Then, the map formula_44 is a holomorphic map from formula_5 onto formula_5. Using the Schwarz–Pick theorem on this map, and finally simplifying the results by using the formula for formula_45, we get the desired result. Also, for all formula_46,
formula_47
If equality holds for either the one or the other expressions, then formula_17 must be a Möbius transformation with real coefficients. That is, if equality holds, then
formula_48
with formula_49 and formula_50.
Proof of Schwarz–Pick theorem.
The proof of the Schwarz–Pick theorem follows from Schwarz's lemma and the fact that a Möbius transformation of the form
formula_51
maps the unit circle to itself. Fix formula_37 and define the Möbius transformations
formula_52
Since formula_53 and the Möbius transformation is invertible, the composition formula_54 maps formula_55 to formula_55 and the unit disk is mapped into itself. Thus we can apply Schwarz's lemma, which is to say
formula_56
Now calling formula_57 (which will still be in the unit disk) yields the desired conclusion
formula_58
To prove the second part of the theorem, we rearrange the left-hand side into the difference quotient and let formula_38 tend to formula_37.
Further generalizations and related results.
The Schwarz–Ahlfors–Pick theorem provides an analogous theorem for hyperbolic manifolds.
De Branges' theorem, formerly known as the Bieberbach Conjecture, is an important extension of the lemma, giving restrictions on the higher derivatives of formula_17 at formula_55 in case formula_17 is injective; that is, univalent.
The Koebe 1/4 theorem provides a related estimate in the case that formula_17 is univalent.
References.
"This article incorporates material from Schwarz lemma on PlanetMath, which is licensed under the ."
|
[
{
"math_id": 0,
"text": "\\mathbf{D} = \\{z : |z| < 1\\}"
},
{
"math_id": 1,
"text": "\\mathbb{C}"
},
{
"math_id": 2,
"text": "f : \\mathbf{D}\\rightarrow \\mathbb{C}"
},
{
"math_id": 3,
"text": "f(0) = 0"
},
{
"math_id": 4,
"text": "|f(z)|\\leq 1"
},
{
"math_id": 5,
"text": "\\mathbf{D}"
},
{
"math_id": 6,
"text": "|f(z)| \\leq |z|"
},
{
"math_id": 7,
"text": "z \\in \\mathbf{D}"
},
{
"math_id": 8,
"text": "|f'(0)| \\leq 1"
},
{
"math_id": 9,
"text": "|f(z)| = |z|"
},
{
"math_id": 10,
"text": "z"
},
{
"math_id": 11,
"text": "|f'(0)| = 1"
},
{
"math_id": 12,
"text": "f(z) = az"
},
{
"math_id": 13,
"text": "a \\in \\mathbb{C}"
},
{
"math_id": 14,
"text": "|a| = 1"
},
{
"math_id": 15,
"text": "g(z) = \\begin{cases}\n \\frac{f(z)}{z}\\, & \\mbox{if } z \\neq 0 \\\\\n f'(0) & \\mbox{if } z = 0,\n\\end{cases}"
},
{
"math_id": 16,
"text": "D"
},
{
"math_id": 17,
"text": "f"
},
{
"math_id": 18,
"text": "D_r = \\{z : |z| \\le r\\}"
},
{
"math_id": 19,
"text": "r"
},
{
"math_id": 20,
"text": "r < 1"
},
{
"math_id": 21,
"text": "z \\in D_r"
},
{
"math_id": 22,
"text": "z_r"
},
{
"math_id": 23,
"text": "D_r"
},
{
"math_id": 24,
"text": " |g(z)| \\le |g(z_r)| = \\frac{|f(z_r)|}{|z_r|} \\le \\frac{1}{r}."
},
{
"math_id": 25,
"text": "r \\rightarrow 1"
},
{
"math_id": 26,
"text": "|g(z)| \\leq 1"
},
{
"math_id": 27,
"text": "z \\in D"
},
{
"math_id": 28,
"text": "|g(z)| = 1"
},
{
"math_id": 29,
"text": "g(z)"
},
{
"math_id": 30,
"text": "a"
},
{
"math_id": 31,
"text": "f: \\mathbf{D}\\to\\mathbf{D}"
},
{
"math_id": 32,
"text": "z_1,z_2\\in\\mathbf{D}"
},
{
"math_id": 33,
"text": "\\left|\\frac{f(z_1)-f(z_2)}{1-\\overline{f(z_1)}f(z_2)}\\right| \\le \\left|\\frac{z_1-z_2}{1-\\overline{z_1}z_2}\\right|"
},
{
"math_id": 34,
"text": "z\\in\\mathbf{D}"
},
{
"math_id": 35,
"text": "\\frac{\\left|f'(z)\\right|}{1-\\left|f(z)\\right|^2} \\le \\frac{1}{1-\\left|z\\right|^2}."
},
{
"math_id": 36,
"text": " d(z_1,z_2)=\\tanh^{-1} \\left|\\frac{z_1-z_2}{1-\\overline{z_1}z_2}\\right| "
},
{
"math_id": 37,
"text": "z_1"
},
{
"math_id": 38,
"text": "z_2"
},
{
"math_id": 39,
"text": "\\mathbf{H}"
},
{
"math_id": 40,
"text": "f:\\mathbf{H}\\to\\mathbf{H}"
},
{
"math_id": 41,
"text": "z_1,z_2\\in\\mathbf{H}"
},
{
"math_id": 42,
"text": "\\left|\\frac{f(z_1)-f(z_2)}{\\overline{f(z_1)}-f(z_2)}\\right|\\le \\frac{\\left|z_1-z_2\\right|}{\\left|\\overline{z_1}-z_2\\right|}."
},
{
"math_id": 43,
"text": "W(z) = (z-i)/(z+i)"
},
{
"math_id": 44,
"text": "W\\circ f\\circ W^{-1}"
},
{
"math_id": 45,
"text": "W"
},
{
"math_id": 46,
"text": "z\\in\\mathbf{H}"
},
{
"math_id": 47,
"text": "\\frac{\\left|f'(z)\\right|}{\\text{Im}(f(z))} \\le \\frac{1}{\\text{Im}(z)}. "
},
{
"math_id": 48,
"text": "f(z)=\\frac{az+b}{cz+d}"
},
{
"math_id": 49,
"text": "a,b,c,d\\in\\mathbb{R}"
},
{
"math_id": 50,
"text": "ad-bc>0"
},
{
"math_id": 51,
"text": "\\frac{z-z_0}{\\overline{z_0}z-1}, \\qquad |z_0| < 1,"
},
{
"math_id": 52,
"text": "M(z)=\\frac{z_1-z}{1-\\overline{z_1}z}, \\qquad \\varphi(z)=\\frac{f(z_1)-z}{1-\\overline{f(z_1)}z}."
},
{
"math_id": 53,
"text": "M(z_1)=0"
},
{
"math_id": 54,
"text": "\\varphi(f(M^{-1}(z)))"
},
{
"math_id": 55,
"text": "0"
},
{
"math_id": 56,
"text": "\\left |\\varphi\\left(f(M^{-1}(z))\\right) \\right|=\\left|\\frac{f(z_1)-f(M^{-1}(z))}{1-\\overline{f(z_1)}f(M^{-1}(z))}\\right| \\le |z|."
},
{
"math_id": 57,
"text": "z_2=M^{-1}(z)"
},
{
"math_id": 58,
"text": "\\left|\\frac{f(z_1)-f(z_2)}{1-\\overline{f(z_1)}f(z_2)}\\right| \\le \\left|\\frac{z_1-z_2}{1-\\overline{z_1}z_2}\\right|."
}
] |
https://en.wikipedia.org/wiki?curid=1432589
|
1432664
|
Choice function
|
Mathematical function
A choice function (selector, selection) is a mathematical function "f" that is defined on some collection "X" of nonempty sets and assigns some element of each set "S" in that collection to "S" by "f"("S"); "f"("S") maps "S" to some element of "S". In other words, "f" is a choice function for "X" if and only if it belongs to the direct product of "X".
An example.
Let "X" = { {1,4,7}, {9}, {2,7} }. Then the function "f" defined by "f({1, 4, 7}) = 7, f({9}) = 9" and "f({2, 7}) = 2" is a choice function on "X".
History and importance.
Ernst Zermelo (1904) introduced choice functions as well as the axiom of choice (AC) and proved the well-ordering theorem, which states that every set can be well-ordered. AC states that every set of nonempty sets has a choice function. A weaker form of AC, the axiom of countable choice (ACω) states that every countable set of nonempty sets has a choice function. However, in the absence of either AC or ACω, some sets can still be shown to have a choice function.
Choice function of a multivalued map.
Given two sets "X" and "Y", let "F" be a multivalued map from "X" to "Y" (equivalently, formula_3 is a function from "X" to the power set of "Y").
A function formula_4 is said to be a selection of "F", if:
formula_5
The existence of more regular choice functions, namely continuous or measurable selections is important in the theory of differential inclusions, optimal control, and mathematical economics. See Selection theorem.
Bourbaki tau function.
Nicolas Bourbaki used epsilon calculus for their foundations that had a formula_6 symbol that could be interpreted as choosing an object (if one existed) that satisfies a given proposition. So if formula_7 is a predicate, then formula_8 is one particular object that satisfies formula_9 (if one exists, otherwise it returns an arbitrary object). Hence we may obtain quantifiers from the choice function, for example formula_10 was equivalent to formula_11.
However, Bourbaki's choice operator is stronger than usual: it's a "global" choice operator. That is, it implies the axiom of global choice. Hilbert realized this when introducing epsilon calculus.
Notes.
<templatestyles src="Reflist/styles.css" />
References.
"This article incorporates material from Choice function on PlanetMath, which is licensed under the ."
|
[
{
"math_id": 0,
"text": "X"
},
{
"math_id": 1,
"text": "X."
},
{
"math_id": 2,
"text": "\\bigcup X"
},
{
"math_id": 3,
"text": "F:X\\rightarrow\\mathcal{P}(Y)"
},
{
"math_id": 4,
"text": "f: X \\rightarrow Y"
},
{
"math_id": 5,
"text": "\\forall x \\in X \\, ( f(x) \\in F(x) ) \\,."
},
{
"math_id": 6,
"text": " \\tau "
},
{
"math_id": 7,
"text": " P(x) "
},
{
"math_id": 8,
"text": "\\tau_{x}(P)"
},
{
"math_id": 9,
"text": "P"
},
{
"math_id": 10,
"text": " P( \\tau_{x}(P))"
},
{
"math_id": 11,
"text": " (\\exists x)(P(x))"
}
] |
https://en.wikipedia.org/wiki?curid=1432664
|
14331278
|
Hildebrand solubility parameter
|
The Hildebrand solubility parameter (δ) provides a numerical estimate of the degree of interaction between materials and can be a good indication of solubility, particularly for nonpolar materials such as many polymers. Materials with similar values of δ are likely to be miscible.
Definition.
The Hildebrand solubility parameter is the square root of the cohesive energy density:
formula_0
The cohesive energy density is the amount of energy needed to completely remove unit volume of molecules from their neighbours to infinite separation (an ideal gas). This is equal to the heat of vaporization of the compound divided by its molar volume in the condensed phase. In order for a material to dissolve, these same interactions need to be overcome, as the molecules are separated from each other and surrounded by the solvent. In 1936 Joel Henry Hildebrand suggested the square root of the cohesive energy density as a numerical value indicating solvency behavior. This later became known as the "Hildebrand solubility parameter". Materials with similar solubility parameters will be able to interact with each other, resulting in solvation, miscibility or swelling.
Uses and limitations.
Its principal utility is that it provides simple predictions of phase equilibrium based on a single parameter that is readily obtained for most materials. These predictions are often useful for nonpolar and slightly polar (dipole moment < 2 debyes) systems without hydrogen bonding. It has found particular use in predicting solubility and swelling of polymers by solvents. More complicated three-dimensional solubility parameters, such as Hansen solubility parameters, have been proposed for polar molecules.
The principal limitation of the solubility parameter approach is that it applies only to associated solutions ("like dissolves like" or, technically speaking, positive deviations from Raoult's law); it cannot account for negative deviations from Raoult's law that result from effects such as solvation or the formation of electron donor–acceptor complexes. Like any simple predictive theory, it can inspire overconfidence; it is best used for screening with data used to verify the predictions.
Units.
The conventional units for the solubility parameter are (calories per cm3)1/2, or cal1/2 cm−3/2. The SI units are J1/2 m−3/2, equivalent to the pascal1/2. 1 calorie is equal to 4.184 J.
1 cal1/2 cm−3/2 = (523/125 J)1/2 (10−2 m)−3/2 = (4.184 J)1/2 (0.01 m)−3/2 = 2.045483 103 J1/2 m−3/2 = 2.045483 (106 J/m3)1/2= 2.045483 MPa1/2.
Given the non-exact nature of the use of δ, it is often sufficient to say that the number in MPa1/2 is about twice the number in cal1/2 cm−3/2.
Where the units are not given, for example, in older books, it is usually safe to assume the non-SI unit.
Examples.
From the table, poly(ethylene) has a solubility parameter of 7.9 cal1/2 cm−3/2. Good solvents are likely to be diethyl ether and hexane. (However, PE only dissolves at temperatures well above 100 °C.) Poly(styrene) has a solubility parameter of 9.1 cal1/2 cm−3/2, and thus ethyl acetate is likely to be a good solvent. Nylon 6,6 has a solubility parameter of 13.7 cal1/2 cm−3/2, and ethanol is likely to be the best solvent of those tabulated. However, the latter is polar, and thus we should be very cautions about using just the Hildebrand solubility parameter to make predictions.
References.
Notes.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\delta = \\sqrt{\\frac{\\Delta H_v - RT}{V_m}}."
}
] |
https://en.wikipedia.org/wiki?curid=14331278
|
14331851
|
Boundedly generated group
|
In mathematics, a group is called boundedly generated if it can be expressed as a finite product of cyclic subgroups. The property of bounded generation is also closely related with the congruence subgroup problem (see ).
Definitions.
A group "G" is called "boundedly generated" if there exists a finite subset "S" of "G" and a positive integer "m" such that every element "g" of "G" can be represented as a product of at most "m" powers of the elements of "S":
formula_0 where formula_1 and formula_2 are integers.
The finite set "S" generates "G", so a boundedly generated group is finitely generated.
An equivalent definition can be given in terms of cyclic subgroups. A group "G" is called "boundedly generated" if there is a finite family "C"1, …, "C""M" of not necessarily distinct cyclic subgroups such that "G" = "C"1…"C""M" as a set.
Properties.
A "pseudocharacter" on a discrete group "G" is defined to be a real-valued function "f" on a "G" such that
"f"("gh") − "f"("g") − "f"("h") is uniformly bounded and "f"("g""n") = "n"·"f"("g").
Free groups are not boundedly generated.
Several authors have stated in the mathematical literature that it is obvious that finitely generated free groups are not boundedly generated. This section contains various obvious and less obvious ways of proving this. Some of the methods, which touch on bounded cohomology, are important because they are geometric rather than algebraic, so can be applied to a wider class of groups, for example Gromov-hyperbolic groups.
Since for any "n" ≥ 2, the free group on 2 generators F2 contains the free group on "n" generators F"n" as a subgroup of finite index (in fact "n" − 1), once one non-cyclic free group on finitely many generators is known to be not boundedly generated, this will be true for all of them. Similarly, since SL2(Z) contains F2 as a subgroup of index 12, it is enough to consider SL2(Z). In other words, to show that no F"n" with "n" ≥ 2 has bounded generation, it is sufficient to prove this for one of them or even just for SL2(Z) .
Burnside counterexamples.
Since bounded generation is preserved under taking homomorphic images, if a single finitely generated group with at least two generators is known to be not boundedly generated, this will be true for the free group on the same number of generators, and hence for all free groups. To show that no (non-cyclic) free group has bounded generation, it is therefore enough to produce one example of a finitely generated group which is not boundedly generated, and any finitely generated infinite torsion group will work. The existence of such groups constitutes Golod and Shafarevich's negative solution of the generalized Burnside problem in 1964; later, other explicit examples of infinite finitely generated torsion groups were constructed by Aleshin, Olshanskii, and Grigorchuk, using automata. Consequently, free groups of rank at least two are not boundedly generated.
Symmetric groups.
The symmetric group S"n" can be generated by two elements, a 2-cycle and an "n"-cycle, so that it is a quotient group of F2. On the other hand, it is easy to show that the maximal order "M"("n") of an element in S"n" satisfies
log "M"("n") ≤ "n"/"e"
where "e" is Euler's number (Edmund Landau proved the more precise asymptotic estimate log "M"("n") ~ ("n" log "n")1/2). In fact if the cycles in a cycle decomposition of a permutation have length "N"1, ..., "N""k" with "N"1 + ··· + "N""k" = "n", then the order of the permutation divides the product "N"1 ··· "N""k", which in turn is bounded by ("n"/"k")"k", using the inequality of arithmetic and geometric means. On the other hand, ("n"/"x")"x" is maximized when "x" = "e". If F2 could be written as a product of "m" cyclic subgroups, then necessarily "n"! would have to be less than or equal to "M"("n")"m" for all "n", contradicting Stirling's asymptotic formula.
Hyperbolic geometry.
There is also a simple geometric proof that "G" = SL2(Z) is not boundedly generated. It acts by Möbius transformations on the upper half-plane H, with the Poincaré metric. Any compactly supported 1-form α on a fundamental domain of "G" extends uniquely to a "G"-invariant 1-form on H. If "z" is in H and γ is the geodesic from "z" to "g"("z"), the function defined by
formula_3
satisfies the first condition for a pseudocharacter since by the Stokes theorem
formula_4
where Δ is the geodesic triangle with vertices "z", "g"("z") and "h"−1("z"), and geodesics triangles have area bounded by π. The homogenized function
formula_5
defines a pseudocharacter, depending only on α. As is well known from the theory of dynamical systems, any orbit ("g""k"("z")) of a hyperbolic element "g" has limit set consisting of two fixed points on the extended real axis; it follows that the geodesic segment from "z" to "g"("z") cuts through only finitely many translates of the fundamental domain. It is therefore easy to choose α so that "f"α equals one on a given hyperbolic element and vanishes on a finite set of other hyperbolic elements with distinct fixed points. Since "G" therefore has an infinite-dimensional space of pseudocharacters, it cannot be boundedly generated.
Dynamical properties of hyperbolic elements can similarly be used to prove that any non-elementary Gromov-hyperbolic group is not boundedly generated.
Brooks pseudocharacters.
Robert Brooks gave a combinatorial scheme to produce pseudocharacters of any free group F"n"; this scheme was later shown to yield
an infinite-dimensional family of pseudocharacters (see ). Epstein and Fujiwara later extended these results to all non-elementary Gromov-hyperbolic groups.
Gromov boundary.
This simple folklore proof uses dynamical properties of the action of hyperbolic elements on the Gromov boundary of a Gromov-hyperbolic group. For the special case of the free group F"n", the boundary (or space of ends) can be identified with the space "X" of semi-infinite reduced words
"g"1 "g"2 ···
in the generators and their inverses. It gives a natural compactification of the tree, given by the Cayley graph with respect to the generators. A sequence of semi-infinite words converges to another such word provided that the initial segments agree after a certain stage, so that "X" is compact (and metrizable). The free group acts by left multiplication on the semi-infinite words. Moreover, any element "g" in F"n" has exactly two fixed points "g" ±∞, namely the reduced infinite words given by the limits of "g"&hairsp;"n" as "n" tends to ±∞. Furthermore, "g"&hairsp;"n"·"w" tends to "g" ±∞ as "n" tends to ±∞ for any semi-infinite word "w"; and more generally if "w""n" tends to "w" ≠ "g" ±∞, then "g"&hairsp;"n"·"w""n" tends to "g"&hairsp;+∞ as "n" tends to ∞.
If F"n" were boundedly generated, it could be written as a product of cyclic groups C"i"
generated by elements "h""i". Let "X"0 be the countable subset given by the finitely many F"n"-orbits
of the fixed points "h""i" ±∞, the fixed points of the "h""i" and all their conjugates. Since "X" is uncountable, there
is an element of "g" with fixed points outside "X"0 and a point "w" outside "X"0 different from these fixed points. Then for
some subsequence ("g""m") of ("g""n")
"g""m" = "h"1"n"("m",1) ··· "h""k""n"("m","k"), with each "n"("m","i"&hairsp;) constant or strictly monotone.
On the one hand, by successive use of the rules for computing limits of the form "h"&hairsp;"n"·"w""n", the limit of the right hand side applied to "x" is necessarily a fixed point of one of the conjugates of the "h""i"'s. On the other hand, this limit also must be "g"&hairsp;+∞, which is not one of these points, a contradiction.
|
[
{
"math_id": 0,
"text": "g = s_1^{k_1} \\cdots s_m^{k_m},"
},
{
"math_id": 1,
"text": "s_i \\in S"
},
{
"math_id": 2,
"text": "k_i"
},
{
"math_id": 3,
"text": "F(g)\\equiv F_{\\alpha,z}(g)=\\int_{\\gamma}\\, \\alpha"
},
{
"math_id": 4,
"text": "F(gh) - F(g)-F(h) = \\int_{\\Delta}\\, d\\alpha,"
},
{
"math_id": 5,
"text": "f_\\alpha(g) = \\lim_{n\\rightarrow \\infty} F_{\\alpha,z}(g^n)/n"
}
] |
https://en.wikipedia.org/wiki?curid=14331851
|
143320
|
PCI Express
|
Computer expansion bus standard
PCI Express (Peripheral Component Interconnect Express), officially abbreviated as PCIe or PCI-e, is a high-speed serial computer expansion bus standard, designed to replace the older PCI, PCI-X and AGP bus standards. It is the common motherboard interface for personal computers' graphics cards, capture cards, sound cards, hard disk drive host adapters, SSDs, Wi-Fi, and Ethernet hardware connections. PCIe has numerous improvements over the older standards, including higher maximum system bus throughput, lower I/O pin count and smaller physical footprint, better performance scaling for bus devices, a more detailed error detection and reporting mechanism (Advanced Error Reporting, AER), and native hot-swap functionality. More recent revisions of the PCIe standard provide hardware support for I/O virtualization.
The PCI Express electrical interface is measured by the number of simultaneous lanes. (A lane is a single send/receive line of data, analogous to a "one-lane road" having one lane of traffic in both directions.) The interface is also used in a variety of other standards — most notably the laptop expansion card interface called ExpressCard. It is also used in the storage interfaces of SATA Express, U.2 (SFF-8639) and M.2.
Format specifications are maintained and developed by the PCI-SIG (PCI Special Interest Group) — a group of more than 900 companies that also maintains the conventional PCI specifications.
Architecture.
Conceptually, the PCI Express bus is a high-speed serial replacement of the older PCI/PCI-X bus. One of the key differences between the PCI Express bus and the older PCI is the bus topology; PCI uses a shared parallel bus architecture, in which the PCI host and all devices share a common set of address, data, and control lines. In contrast, PCI Express is based on point-to-point topology, with separate serial links connecting every device to the root complex (host). Because of its shared bus topology, access to the older PCI bus is arbitrated (in the case of multiple masters), and limited to one master at a time, in a single direction. Furthermore, the older PCI clocking scheme limits the bus clock to the slowest peripheral on the bus (regardless of the devices involved in the bus transaction). In contrast, a PCI Express bus link supports full-duplex communication between any two endpoints, with no inherent limitation on concurrent access across multiple endpoints.
In terms of bus protocol, PCI Express communication is encapsulated in packets. The work of packetizing and de-packetizing data and status-message traffic is handled by the transaction layer of the PCI Express port (described later). Radical differences in electrical signaling and bus protocol require the use of a different mechanical form factor and expansion connectors (and thus, new motherboards and new adapter boards); PCI slots and PCI Express slots are not interchangeable. At the software level, PCI Express preserves backward compatibility with PCI; legacy PCI system software can detect and configure newer PCI Express devices without explicit support for the PCI Express standard, though new PCI Express features are inaccessible.
The PCI Express link between two devices can vary in size from one to 16 lanes. In a multi-lane link, the packet data is striped across lanes, and peak data throughput scales with the overall link width. The lane count is automatically negotiated during device initialization and can be restricted by either endpoint. For example, a single-lane PCI Express (x1) card can be inserted into a multi-lane slot (x4, x8, etc.), and the initialization cycle auto-negotiates the highest mutually supported lane count. The link can dynamically down-configure itself to use fewer lanes, providing a failure tolerance in case bad or unreliable lanes are present. The PCI Express standard defines link widths of x1, x2, x4, x8, and x16. Up to and including PCIe 5.0, x12, and x32 links were defined as well but never used. This allows the PCI Express bus to serve both cost-sensitive applications where high throughput is not needed, and performance-critical applications such as 3D graphics, networking (10 Gigabit Ethernet or multiport Gigabit Ethernet), and enterprise storage (SAS or Fibre Channel). Slots and connectors are only defined for a subset of these widths, with link widths in between using the next larger physical slot size.
As a point of reference, a PCI-X (133 MHz 64-bit) device and a PCI Express 1.0 device using four lanes (x4) have roughly the same peak single-direction transfer rate of 1064 MB/s. The PCI Express bus has the potential to perform better than the PCI-X bus in cases where multiple devices are transferring data simultaneously, or if communication with the PCI Express peripheral is bidirectional.
Interconnect.
PCI Express devices communicate via a logical connection called an "interconnect" or "link". A link is a point-to-point communication channel between two PCI Express ports allowing both of them to send and receive ordinary PCI requests (configuration, I/O or memory read/write) and interrupts (INTx, MSI or MSI-X). At the physical level, a link is composed of one or more "lanes". Low-speed peripherals (such as an 802.11 Wi-Fi card) use a single-lane (x1) link, while a graphics adapter typically uses a much wider and therefore faster 16-lane (x16) link.
Lane.
A lane is composed of two differential signaling pairs, with one pair for receiving data and the other for transmitting. Thus, each lane is composed of four wires or signal traces. Conceptually, each lane is used as a full-duplex byte stream, transporting data packets in eight-bit "byte" format simultaneously in both directions between endpoints of a link. Physical PCI Express links may contain 1, 4, 8 or 16 lanes. Lane counts are written with an "x" prefix (for example, "x8" represents an eight-lane card or slot), with x16 being the largest size in common use. Lane sizes are also referred to via the terms "width" or "by" e.g., an eight-lane slot could be referred to as a "by 8" or as "8 lanes wide."
For mechanical card sizes, see below.
Serial bus.
The bonded serial bus architecture was chosen over the traditional parallel bus because of the inherent limitations of the latter, including half-duplex operation, excess signal count, and inherently lower bandwidth due to timing skew. Timing skew results from separate electrical signals within a parallel interface traveling through conductors of different lengths, on potentially different printed circuit board (PCB) layers, and at possibly different signal velocities. Despite being transmitted simultaneously as a single word, signals on a parallel interface have different travel duration and arrive at their destinations at different times. When the interface clock period is shorter than the largest time difference between signal arrivals, recovery of the transmitted word is no longer possible. Since timing skew over a parallel bus can amount to a few nanoseconds, the resulting bandwidth limitation is in the range of hundreds of megahertz.
A serial interface does not exhibit timing skew because there is only one differential signal in each direction within each lane, and there is no external clock signal since clocking information is embedded within the serial signal itself. As such, typical bandwidth limitations on serial signals are in the multi-gigahertz range. PCI Express is one example of the general trend toward replacing parallel buses with serial interconnects; other examples include Serial ATA (SATA), USB, Serial Attached SCSI (SAS), FireWire (IEEE 1394), and RapidIO. In digital video, examples in common use are DVI, HDMI, and DisplayPort.
Multichannel serial design increases flexibility with its ability to allocate fewer lanes for slower devices.
Form factors.
PCI Express (standard).
A PCI Express card fits into a slot of its physical size or larger (with x16 as the largest used), but may not fit into a smaller PCI Express slot; for example, a x16 card may not fit into a x4 or x8 slot. Some slots use open-ended sockets to permit physically longer cards and negotiate the best available electrical and logical connection.
The number of lanes actually connected to a slot may also be fewer than the number supported by the physical slot size. An example is a x16 slot that runs at x4, which accepts any x1, x2, x4, x8 or x16 card, but provides only four lanes. Its specification may read as "x16 (x4 mode)", while "mechanical @ electrical" notation (e.g. "x16 @ x4") is also common. The advantage is that such slots can accommodate a larger range of PCI Express cards without requiring motherboard hardware to support the full transfer rate. Standard mechanical sizes are x1, x4, x8, and x16. Cards using a number of lanes other than the standard mechanical sizes need to physically fit the next larger mechanical size (e.g. an x2 card uses the x4 size, or an x12 card uses the x16 size).
The cards themselves are designed and manufactured in various sizes. For example, solid-state drives (SSDs) that come in the form of PCI Express cards often use HHHL (half height, half length) and FHHL (full height, half length) to describe the physical dimensions of the card.
Non-standard video card form factors.
Modern (since c. 2012) gaming video cards usually exceed the height as well as thickness specified in the PCI Express standard, due to the need for more capable and quieter cooling fans, as gaming video cards often emit hundreds of watts of heat. Modern computer cases are often wider to accommodate these taller cards, but not always. Since full-length cards (312 mm) are uncommon, modern cases sometimes cannot fit those. The thickness of these cards also typically occupies the space of 2 PCIe slots. In fact, even the methodology of how to measure the cards varies between vendors, with some including the metal bracket size in dimensions and others not.
For instance, comparing three high-end video cards released in 2020: a Sapphire Radeon RX 5700 XT card measures 135 mm in height (excluding the metal bracket), which exceeds the PCIe standard height by 28 mm, another Radeon RX 5700 XT card by XFX measures 55 mm thick (i.e. 2.7 PCI slots at 20.32 mm), taking up 3 PCIe slots, while an Asus GeForce RTX 3080 video card takes up two slots and measures 140.1mm × 318.5mm × 57.8mm, exceeding PCI Express' maximum height, length, and thickness respectively.
Pinout.
The following table identifies the conductors on each side of the edge connector on a PCI Express card. The solder side of the printed circuit board (PCB) is the A-side, and the component side is the B-side. PRSNT1# and PRSNT2# pins must be slightly shorter than the rest, to ensure that a hot-plugged card is fully inserted. The WAKE# pin uses full voltage to wake the computer, but must be pulled high from the standby power to indicate that the card is wake capable.
Power.
Slot power.
All PCI express cards may consume up to at (). The amount of +12 V and total power they may consume depends on the form factor and the role of the card:
6- and 8-pin power connectors.
Optional connectors add (6-pin) or (8-pin) of +12 V power for up to total (2 × 75 W + 1 × 150 W).
Some cards use two 8-pin connectors, but this has not been standardized yet as of 2018[ [update]], therefore such cards must not carry the official PCI Express logo. This configuration allows 375 W total (1 × 75 W + 2 × 150 W) and will likely be standardized by PCI-SIG with the PCI Express 4.0 standard. The 8-pin PCI Express connector could be confused with the EPS12V connector, which is mainly used for powering SMP and multi-core systems. The power connectors are variants of the Molex Mini-Fit Jr. series connectors.
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PCI Express Mini Card.
PCI Express Mini Card (also known as Mini PCI Express, Mini PCIe, Mini PCI-E, mPCIe, and PEM), based on PCI Express, is a replacement for the Mini PCI form factor. It is developed by the PCI-SIG. The host device supports both PCI Express and USB 2.0 connectivity, and each card may use either standard. Most laptop computers built after 2005 use PCI Express for expansion cards; however, as of 2015[ [update]], many vendors are moving toward using the newer M.2 form factor for this purpose.
Due to different dimensions, PCI Express Mini Cards are not physically compatible with standard full-size PCI Express slots; however, passive adapters exist that let them be used in full-size slots.
Physical dimensions.
Dimensions of PCI Express Mini Cards are 30 mm × 50.95 mm (width × length) for a Full Mini Card. There is a 52-pin edge connector, consisting of two staggered rows on a 0.8 mm pitch. Each row has eight contacts, a gap equivalent to four contacts, then a further 18 contacts. Boards have a thickness of 1.0 mm, excluding the components. A "Half Mini Card" (sometimes abbreviated as HMC) is also specified, having approximately half the physical length of 26.8 mm. There are also half size mini PCIe cards that are 30 x 31.90 mm which is about half the length of a full size mini PCIe card.
Electrical interface.
PCI Express Mini Card edge connectors provide multiple connections and buses:
Mini-SATA (mSATA) variant.
Despite sharing the Mini PCI Express form factor, an mSATA slot is not necessarily electrically compatible with Mini PCI Express. For this reason, only certain notebooks are compatible with mSATA drives. Most compatible systems are based on Intel's Sandy Bridge processor architecture, using the Huron River platform. Notebooks such as Lenovo's ThinkPad T, W and X series, released in March–April 2011, have support for an mSATA SSD card in their WWAN card slot. The ThinkPad Edge E220s/E420s, and the Lenovo IdeaPad Y460/Y560/Y570/Y580 also support mSATA. On the contrary, the L-series among others can only support M.2 cards using the PCIe standard in the WWAN slot.
Some notebooks (notably the Asus Eee PC, the Apple MacBook Air, and the Dell mini9 and mini10) use a variant of the PCI Express Mini Card as an SSD. This variant uses the reserved and several non-reserved pins to implement SATA and IDE interface passthrough, keeping only USB, ground lines, and sometimes the core PCIe x1 bus intact. This makes the "miniPCIe" flash and solid-state drives sold for netbooks largely incompatible with true PCI Express Mini implementations.
Also, the typical Asus miniPCIe SSD is 71 mm long, causing the Dell 51 mm model to often be (incorrectly) referred to as half length. A true 51 mm Mini PCIe SSD was announced in 2009, with two stacked PCB layers that allow for higher storage capacity. The announced design preserves the PCIe interface, making it compatible with the standard mini PCIe slot. No working product has yet been developed.
Intel has numerous desktop boards with the PCIe x1 Mini-Card slot that typically do not support mSATA SSD. A list of desktop boards that natively support mSATA in the PCIe x1 Mini-Card slot (typically multiplexed with a SATA port) is provided on the Intel Support site.
PCI Express M.2.
M.2 replaces the mSATA standard and Mini PCIe. Computer bus interfaces provided through the M.2 connector are PCI Express 3.0 (up to four lanes), Serial ATA 3.0, and USB 3.0 (a single logical port for each of the latter two). It is up to the manufacturer of the M.2 host or device to choose which interfaces to support, depending on the desired level of host support and device type.
PCI Express External Cabling.
"PCI Express External Cabling" (also known as "External PCI Express", "Cabled PCI Express", or "ePCIe") specifications were released by the PCI-SIG in February 2007.
Standard cables and connectors have been defined for x1, x4, x8, and x16 link widths, with a transfer rate of 250 MB/s per lane. The PCI-SIG also expects the norm to evolve to reach 500 MB/s, as in PCI Express 2.0. An example of the uses of Cabled PCI Express is a metal enclosure, containing a number of PCIe slots and PCIe-to-ePCIe adapter circuitry. This device would not be possible had it not been for the ePCIe specification.
PCI Express OCuLink.
"OCuLink" (standing for "optical-copper link", since "Cu" is the chemical symbol for copper) is an extension for the "cable version of PCI Express". Version 1.0 of OCuLink, released in Oct 2015, supports up to 4 PCIe 3.0 lanes (3.9 GB/s) over copper cabling; a fiber optic version may appear in the future.
The most recent version of OCuLink, OCuLink-2, supports up to 16 GB/s (PCIe 4.0 x8) while the maximum bandwidth of a USB 4 cable is 10GB/s.
While initially intended for use in laptops for the connection of powerful external GPU boxes, OCuLink's popularity lies primarily in its use for PCIe interconnections in servers, a more prevalent application.
Derivative forms.
Numerous other form factors use, or are able to use, PCIe. These include:
The PCIe slot connector can also carry protocols other than PCIe. Some 9xx series Intel chipsets support Serial Digital Video Out, a proprietary technology that uses a slot to transmit video signals from the host CPU's integrated graphics instead of PCIe, using a supported add-in.
The PCIe transaction-layer protocol can also be used over some other interconnects, which are not electrically PCIe:
History and revisions.
While in early development, PCIe was initially referred to as "HSI" (for "High Speed Interconnect"), and underwent a name change to "3GIO" (for "3rd Generation I/O") before finally settling on its PCI-SIG name "PCI Express". A technical working group named the "Arapaho Work Group" (AWG) drew up the standard. For initial drafts, the AWG consisted only of Intel engineers; subsequently, the AWG expanded to include industry partners.
Since, PCIe has undergone several large and smaller revisions, improving on performance and other features.
Comparison table.
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PCI Express 1.0a.
In 2003, PCI-SIG introduced PCIe 1.0a, with a per-lane data rate of 250 MB/s and a transfer rate of 2.5 gigatransfers per second (GT/s).
Transfer rate is expressed in transfers per second instead of bits per second because the number of transfers includes the overhead bits, which do not provide additional throughput; PCIe 1.x uses an 8b/10b encoding scheme, resulting in a 20% (= 2/10) overhead on the raw channel bandwidth. So in the PCIe terminology, transfer rate refers to the encoded bit rate: 2.5 GT/s is 2.5 Gbit/s on the encoded serial link. This corresponds to 2.0 Gbit/s of pre-coded data or 250 MB/s, which is referred to as throughput in PCIe.
PCI Express 1.1.
In 2005, PCI-SIG introduced PCIe 1.1. This updated specification includes clarifications and several improvements, but is fully compatible with PCI Express 1.0a. No changes were made to the data rate.
PCI Express 2.0.
PCI-SIG announced the availability of the PCI Express Base 2.0 specification on 15 January 2007. The PCIe 2.0 standard doubles the transfer rate compared with PCIe 1.0 to 5GT/s and the per-lane throughput rises from 250 MB/s to 500 MB/s. Consequently, a 16-lane PCIe connector (x16) can support an aggregate throughput of up to 8 GB/s.
PCIe 2.0 motherboard slots are fully backward compatible with PCIe v1.x cards. PCIe 2.0 cards are also generally backward compatible with PCIe 1.x motherboards, using the available bandwidth of PCI Express 1.1. Overall, graphic cards or motherboards designed for v2.0 work, with the other being v1.1 or v1.0a.
The PCI-SIG also said that PCIe 2.0 features improvements to the point-to-point data transfer protocol and its software architecture.
Intel's first PCIe 2.0 capable chipset was the X38 and boards began to ship from various vendors (Abit, Asus, Gigabyte) as of 21 October 2007. AMD started supporting PCIe 2.0 with its AMD 700 chipset series and nVidia started with the MCP72. All of Intel's prior chipsets, including the Intel P35 chipset, supported PCIe 1.1 or 1.0a.
Like 1.x, PCIe 2.0 uses an 8b/10b encoding scheme, therefore delivering, per-lane, an effective 4 Gbit/s max. transfer rate from its 5 GT/s raw data rate.
PCI Express 2.1.
PCI Express 2.1 (with its specification dated 4 March 2009) supports a large proportion of the management, support, and troubleshooting systems planned for full implementation in PCI Express 3.0. However, the speed is the same as PCI Express 2.0. The increase in power from the slot breaks backward compatibility between PCI Express 2.1 cards and some older motherboards with 1.0/1.0a, but most motherboards with PCI Express 1.1 connectors are provided with a BIOS update by their manufacturers through utilities to support backward compatibility of cards with PCIe 2.1.
PCI Express 3.0.
PCI Express 3.0 Base specification revision 3.0 was made available in November 2010, after multiple delays. In August 2007, PCI-SIG announced that PCI Express 3.0 would carry a bit rate of 8 gigatransfers per second (GT/s), and that it would be backward compatible with existing PCI Express implementations. At that time, it was also announced that the final specification for PCI Express 3.0 would be delayed until Q2 2010. New features for the PCI Express 3.0 specification included a number of optimizations for enhanced signaling and data integrity, including transmitter and receiver equalization, PLL improvements, clock data recovery, and channel enhancements of currently supported topologies.
Following a six-month technical analysis of the feasibility of scaling the PCI Express interconnect bandwidth, PCI-SIG's analysis found that 8 gigatransfers per second could be manufactured in mainstream silicon process technology, and deployed with existing low-cost materials and infrastructure, while maintaining full compatibility (with negligible impact) with the PCI Express protocol stack.
PCI Express 3.0 upgraded the encoding scheme to 128b/130b from the previous 8b/10b encoding, reducing the bandwidth overhead from 20% of PCI Express 2.0 to approximately 1.54% (= 2/130). PCI Express 3.0's 8 GT/s bit rate effectively delivers 985 MB/s per lane, nearly doubling the lane bandwidth relative to PCI Express 2.0.
On 18 November 2010, the PCI Special Interest Group officially published the finalized PCI Express 3.0 specification to its members to build devices based on this new version of PCI Express.
PCI Express 3.1.
In September 2013, PCI Express 3.1 specification was announced for release in late 2013 or early 2014, consolidating various improvements to the published PCI Express 3.0 specification in three areas: power management, performance and functionality. It was released in November 2014.
PCI Express 4.0.
On 29 November 2011, PCI-SIG preliminarily announced PCI Express 4.0, providing a 16 GT/s bit rate that doubles the bandwidth provided by PCI Express 3.0 to 31.5 GB/s in each direction for a 16-lane configuration, while maintaining backward and forward compatibility in both software support and used mechanical interface. PCI Express 4.0 specs also bring OCuLink-2, an alternative to Thunderbolt. OCuLink version 2 has up to 16 GT/s (16GB/s total for x8 lanes), while the maximum bandwidth of a Thunderbolt 3 link is 5GB/s.
In June 2016 Cadence, PLDA and Synopsys demonstrated PCIe 4.0 physical-layer, controller, switch and other IP blocks at the PCI SIG’s annual developer’s conference.
Mellanox Technologies announced the first 100Gbit/s network adapter with PCIe 4.0 on 15 June 2016, and the first 200Gbit/s network adapter with PCIe 4.0 on 10 November 2016.
In August 2016, Synopsys presented a test setup with FPGA clocking a lane to PCIe 4.0 speeds at the Intel Developer Forum. Their IP has been licensed to several firms planning to present their chips and products at the end of 2016.
On the IEEE Hot Chips Symposium in August 2016 IBM announced the first CPU with PCIe 4.0 support, POWER9.
PCI-SIG officially announced the release of the final PCI Express 4.0 specification on 8 June 2017. The spec includes improvements in flexibility, scalability, and lower-power.
On 5 December 2017 IBM announced the first system with PCIe 4.0 slots, Power AC922.
NETINT Technologies introduced the first NVMe SSD based on PCIe 4.0 on 17 July 2018, ahead of Flash Memory Summit 2018
AMD announced on 9 January 2019 its upcoming Zen 2-based processors and X570 chipset would support PCIe 4.0. AMD had hoped to enable partial support for older chipsets, but instability caused by motherboard traces not conforming to PCIe 4.0 specifications made that impossible.
Intel released their first mobile CPUs with PCI Express 4.0 support in mid-2020, as a part of the Tiger Lake microarchitecture.
PCI Express 5.0.
In June 2017, PCI-SIG announced the PCI Express 5.0 preliminary specification. Bandwidth was expected to increase to 32GT/s, yielding 63GB/s in each direction in a 16-lane configuration. The draft spec was expected to be standardized in 2019. Initially, 25.0 GT/s was also considered for technical feasibility.
On 7 June 2017 at PCI-SIG DevCon, Synopsys recorded the first demonstration of PCI Express 5.0 at 32 GT/s.
On 31 May 2018, PLDA announced the availability of their XpressRICH5 PCIe 5.0 Controller IP based on draft 0.7 of the PCIe 5.0 specification on the same day.
On 10 December 2018, the PCI SIG released version 0.9 of the PCIe 5.0 specification to its members,
and on 17 January 2019, PCI SIG announced the version 0.9 had been ratified, with version 1.0 targeted for release in the first quarter of 2019.
On 29 May 2019, PCI-SIG officially announced the release of the final PCI Express 5.0 specification.
On 20 November 2019, Jiangsu Huacun presented the first PCIe 5.0 Controller HC9001 in a 12 nm manufacturing process. Production started in 2020.
On 17 August 2020, IBM announced the Power10 processor with PCIe 5.0 and up to 32 lanes per single-chip module (SCM) and up to 64 lanes per double-chip module (DCM).
On 9 September 2021, IBM announced the Power E1080 Enterprise server with planned availability date 17 September. It can have up to 16 Power10 SCMs with maximum of 32 slots per system which can act as PCIe 5.0 x8 or PCIe 4.0 x16. Alternatively they can be used as PCIe 5.0 x16 slots for optional optical CXP converter adapters connecting to external PCIe expansion drawers.
On 27 October 2021, Intel announced the 12th Gen Intel Core CPU family, the world's first consumer x86-64 processors with PCIe 5.0 (up to 16 lanes) connectivity.
On 22 March 2022, Nvidia announced Nvidia Hopper GH100 GPU, the world's first PCIe 5.0 GPU.
On 23 May 2022, AMD announced its Zen 4 architecture with support for up to 24 lanes of PCIe 5.0 connectivity on consumer platforms and 128 lanes on server platforms.
PCI Express 6.0.
On 18 June 2019, PCI-SIG announced the development of PCI Express 6.0 specification. Bandwidth is expected to increase to 64GT/s, yielding 128GB/s in each direction in a 16-lane configuration, with a target release date of 2021. The new standard uses 4-level pulse-amplitude modulation (PAM-4) with a low-latency forward error correction (FEC) in place of non-return-to-zero (NRZ) modulation. Unlike previous PCI Express versions, forward error correction is used to increase data integrity and PAM-4 is used as line code so that two bits are transferred per transfer. With 64GT/s data transfer rate (raw bit rate), up to 121GB/s in each direction is possible in x16 configuration.
On 24 February 2020, the PCI Express 6.0 revision 0.5 specification (a "first draft" with all architectural aspects and requirements defined) was released.
On 5 November 2020, the PCI Express 6.0 revision 0.7 specification (a "complete draft" with electrical specifications validated via test chips) was released.
On 6 October 2021, the PCI Express 6.0 revision 0.9 specification (a "final draft") was released.
On 11 January 2022, PCI-SIG officially announced the release of the final PCI Express 6.0 specification.
On 18 March 2024, Nvidia announced Nvidia Blackwell GB100 GPU, the world's first PCIe 6.0 GPU.
PAM-4 coding results in a vastly higher bit error rate (BER) of 10−6 (vs. 10−12 previously), so in place of 128b/130b encoding, a 3-way interlaced forward error correction (FEC) is used in addition to cyclic redundancy check (CRC). A fixed 256 byte Flow Control Unit (FLIT) block carries 242 bytes of data, which includes variable-sized transaction level packets (TLP) and data link layer payload (DLLP); remaining 14 bytes are reserved for 8-byte CRC and 6-byte FEC. 3-way Gray code is used in PAM-4/FLIT mode to reduce error rate; the interface does not switch to NRZ and 128/130b encoding even when retraining to lower data rates.
PCI Express 7.0.
On 21 June 2022, PCI-SIG announced the development of PCI Express 7.0 specification. It will deliver 128 GT/s raw bit rate and up to 242 GB/s per direction in x16 configuration, using the same PAM4 signaling as version 6.0. Doubling of the data rate will be achieved by fine-tuning channel parameters to decrease signal losses and improve power efficiency, but signal integrity is expected to be a challenge. The specification is expected to be finalized in 2025.
On 2 April 2024, PCI-SIG announced the release of PCIe 7.0 specification version 0.5; PCI Express 7.0 remains on track for release in 2025.
Extensions and future directions.
Some vendors offer PCIe over fiber products, with active optical cables (AOC) for PCIe switching at increased distance in PCIe expansion drawers, or in specific cases where transparent PCIe bridging is preferable to using a more mainstream standard (such as InfiniBand or Ethernet) that may require additional software to support it.
"Thunderbolt" was co-developed by Intel and Apple as a general-purpose high speed interface combining a logical PCIe link with DisplayPort and was originally intended as an all-fiber interface, but due to early difficulties in creating a consumer-friendly fiber interconnect, nearly all implementations are copper systems. A notable exception, the Sony VAIO Z VPC-Z2, uses a nonstandard USB port with an optical component to connect to an outboard PCIe display adapter. Apple has been the primary driver of Thunderbolt adoption through 2011, though several other vendors have announced new products and systems featuring Thunderbolt. Thunderbolt 3 forms the basis of the USB4 standard.
"Mobile PCIe" specification (abbreviated to "M-PCIe") allows PCI Express architecture to operate over the MIPI Alliance's M-PHY physical layer technology. Building on top of already existing widespread adoption of M-PHY and its low-power design, Mobile PCIe lets mobile devices use PCI Express.
Draft process.
There are 5 primary releases/checkpoints in a PCI-SIG specification:
Historically, the earliest adopters of a new PCIe specification generally begin designing with the Draft 0.5 as they can confidently build up their application logic around the new bandwidth definition and often even start developing for any new protocol features. At the Draft 0.5 stage, however, there is still a strong likelihood of changes in the actual PCIe protocol layer implementation, so designers responsible for developing these blocks internally may be more hesitant to begin work than those using interface IP from external sources.
Hardware protocol summary.
The PCIe link is built around dedicated unidirectional couples of serial (1-bit), point-to-point connections known as "lanes". This is in sharp contrast to the earlier PCI connection, which is a bus-based system where all the devices share the same bidirectional, 32-bit or 64-bit parallel bus.
PCI Express is a layered protocol, consisting of a "transaction layer", a "data link layer", and a "physical layer". The Data Link Layer is subdivided to include a media access control (MAC) sublayer. The Physical Layer is subdivided into logical and electrical sublayers. The Physical logical-sublayer contains a physical coding sublayer (PCS). The terms are borrowed from the IEEE 802 networking protocol model.
Physical layer.
The PCIe Physical Layer ("PHY", "PCIEPHY", "PCI Express PHY", or "PCIe PHY") specification is divided into two sub-layers, corresponding to electrical and logical specifications. The logical sublayer is sometimes further divided into a MAC sublayer and a PCS, although this division is not formally part of the PCIe specification. A specification published by Intel, the PHY Interface for PCI Express (PIPE), defines the MAC/PCS functional partitioning and the interface between these two sub-layers. The PIPE specification also identifies the "physical media attachment" (PMA) layer, which includes the serializer/deserializer (SerDes) and other analog circuitry; however, since SerDes implementations vary greatly among ASIC vendors, PIPE does not specify an interface between the PCS and PMA.
At the electrical level, each lane consists of two unidirectional differential pairs operating at 2.5, 5, 8, 16 or 32 Gbit/s, depending on the negotiated capabilities. Transmit and receive are separate differential pairs, for a total of four data wires per lane.
A connection between any two PCIe devices is known as a "link", and is built up from a collection of one or more "lanes". All devices must minimally support single-lane (x1) link. Devices may optionally support wider links composed of up to 32 lanes. This allows for very good compatibility in two ways:
In both cases, PCIe negotiates the highest mutually supported number of lanes. Many graphics cards, motherboards and BIOS versions are verified to support x1, x4, x8 and x16 connectivity on the same connection.
The width of a PCIe connector is 8.8 mm, while the height is 11.25 mm, and the length is variable. The fixed section of the connector is 11.65 mm in length and contains two rows of 11 pins each (22 pins total), while the length of the other section is variable depending on the number of lanes. The pins are spaced at 1 mm intervals, and the thickness of the card going into the connector is 1.6 mm.
Data transmission.
PCIe sends all control messages, including interrupts, over the same links used for data. The serial protocol can never be blocked, so latency is still comparable to conventional PCI, which has dedicated interrupt lines. When the problem of IRQ sharing of pin based interrupts is taken into account and the fact that message signaled interrupts (MSI) can bypass an I/O APIC and be delivered to the CPU directly, MSI performance ends up being substantially better.
Data transmitted on multiple-lane links is interleaved, meaning that each successive byte is sent down successive lanes. The PCIe specification refers to this interleaving as "data striping". While requiring significant hardware complexity to synchronize (or deskew) the incoming striped data, striping can significantly reduce the latency of the "n"th byte on a link. While the lanes are not tightly synchronized, there is a limit to the "lane to lane skew" of 20/8/6 ns for 2.5/5/8 GT/s so the hardware buffers can re-align the striped data. Due to padding requirements, striping may not necessarily reduce the latency of small data packets on a link.
As with other high data rate serial transmission protocols, the clock is embedded in the signal. At the physical level, PCI Express 2.0 utilizes the 8b/10b encoding scheme (line code) to ensure that strings of consecutive identical digits (zeros or ones) are limited in length. This coding was used to prevent the receiver from losing track of where the bit edges are. In this coding scheme every eight (uncoded) payload bits of data are replaced with 10 (encoded) bits of transmit data, causing a 20% overhead in the electrical bandwidth. To improve the available bandwidth, PCI Express version 3.0 instead uses 128b/130b encoding (1.54% overhead). Line encoding limits the run length of identical-digit strings in data streams and ensures the receiver stays synchronised to the transmitter via clock recovery.
A desirable balance (and therefore spectral density) of 0 and 1 bits in the data stream is achieved by XORing a known binary polynomial as a "scrambler" to the data stream in a feedback topology. Because the scrambling polynomial is known, the data can be recovered by applying the XOR a second time. Both the scrambling and descrambling steps are carried out in hardware.
Dual simplex in PCIe means there are two simplex channels on every PCIe lane. Simplex means communication is only possible in one direction. By having two simplex channels, two-way communication is made possible. One differential pair is used for each channel.
Data link layer.
The data link layer performs three vital services for the PCIe link:
On the transmit side, the data link layer generates an incrementing sequence number for each outgoing TLP. It serves as a unique identification tag for each transmitted TLP, and is inserted into the header of the outgoing TLP. A 32-bit cyclic redundancy check code (known in this context as Link CRC or LCRC) is also appended to the end of each outgoing TLP.
On the receive side, the received TLP's LCRC and sequence number are both validated in the link layer. If either the LCRC check fails (indicating a data error), or the sequence-number is out of range (non-consecutive from the last valid received TLP), then the bad TLP, as well as any TLPs received after the bad TLP, are considered invalid and discarded. The receiver sends a negative acknowledgement message (NAK) with the sequence-number of the invalid TLP, requesting re-transmission of all TLPs forward of that sequence-number. If the received TLP passes the LCRC check and has the correct sequence number, it is treated as valid. The link receiver increments the sequence-number (which tracks the last received good TLP), and forwards the valid TLP to the receiver's transaction layer. An ACK message is sent to remote transmitter, indicating the TLP was successfully received (and by extension, all TLPs with past sequence-numbers.)
If the transmitter receives a NAK message, or no acknowledgement (NAK or ACK) is received until a timeout period expires, the transmitter must retransmit all TLPs that lack a positive acknowledgement (ACK). Barring a persistent malfunction of the device or transmission medium, the link-layer presents a reliable connection to the transaction layer, since the transmission protocol ensures delivery of TLPs over an unreliable medium.
In addition to sending and receiving TLPs generated by the transaction layer, the data-link layer also generates and consumes data link layer packets (DLLPs). ACK and NAK signals are communicated via DLLPs, as are some power management messages and flow control credit information (on behalf of the transaction layer).
In practice, the number of in-flight, unacknowledged TLPs on the link is limited by two factors: the size of the transmitter's replay buffer (which must store a copy of all transmitted TLPs until the remote receiver ACKs them), and the flow control credits issued by the receiver to a transmitter. PCI Express requires all receivers to issue a minimum number of credits, to guarantee a link allows sending PCIConfig TLPs and message TLPs.
Transaction layer.
PCI Express implements split transactions (transactions with request and response separated by time), allowing the link to carry other traffic while the target device gathers data for the response.
PCI Express uses credit-based flow control. In this scheme, a device advertises an initial amount of credit for each received buffer in its transaction layer. The device at the
opposite end of the link, when sending transactions to this device, counts the number of credits each TLP consumes from its account. The sending device may only transmit a TLP when doing so does not make its consumed credit count exceed its credit limit. When the receiving device finishes processing the TLP from its buffer, it signals a return of credits to the sending device, which increases the credit limit by the restored amount. The credit counters are modular counters, and the comparison of consumed credits to credit limit requires modular arithmetic. The advantage of this scheme (compared to other methods such as wait states or handshake-based transfer protocols) is that the latency of credit return does not affect performance, provided that the credit limit is not encountered. This assumption is generally met if each device is designed with adequate buffer sizes.
PCIe 1.x is often quoted to support a data rate of 250 MB/s in each direction, per lane. This figure is a calculation from the physical signaling rate (2.5 gigabaud) divided by the encoding overhead (10 bits per byte). This means a sixteen lane (x16) PCIe card would then be theoretically capable of 16x250 MB/s = 4 GB/s in each direction. While this is correct in terms of data bytes, more meaningful calculations are based on the usable data payload rate, which depends on the profile of the traffic, which is a function of the high-level (software) application and intermediate protocol levels.
Like other high data rate serial interconnect systems, PCIe has a protocol and processing overhead due to the additional transfer robustness (CRC and acknowledgements). Long continuous unidirectional transfers (such as those typical in high-performance storage controllers) can approach >95% of PCIe's raw (lane) data rate. These transfers also benefit the most from increased number of lanes (x2, x4, etc.) But in more typical applications (such as a USB or Ethernet controller), the traffic profile is characterized as short data packets with frequent enforced acknowledgements. This type of traffic reduces the efficiency of the link, due to overhead from packet parsing and forced interrupts (either in the device's host interface or the PC's CPU). Being a protocol for devices connected to the same printed circuit board, it does not require the same tolerance for transmission errors as a protocol for communication over longer distances, and thus, this loss of efficiency is not particular to PCIe.
Efficiency of the link.
As for any "network like" communication links, some of the "raw" bandwidth is consumed by protocol overhead:
A PCIe 1.x lane for example offers a data rate on top of the physical layer of 250 MB/s (simplex). This is not the payload bandwidth but the physical layer bandwidth – a PCIe lane has to carry additional information for full functionality.
The Gen2 overhead is then 20, 24, or 28 bytes per transaction.
The Gen3 overhead is then 22, 26 or 30 bytes per transaction.
The formula_0 for a 128 byte payload is 86%, and 98% for a 1024 byte payload. For small accesses like register settings (4 bytes), the efficiency drops as low as 16%.
The maximum payload size (MPS) is set on all devices based on smallest maximum on any device in the chain. If one device has an MPS of 128 bytes, "all" devices of the tree must set their MPS to 128 bytes. In this case the bus will have a peak efficiency of 86% for writes.3
Applications.
PCI Express operates in consumer, server, and industrial applications, as a motherboard-level interconnect (to link motherboard-mounted peripherals), a passive backplane interconnect and as an expansion card interface for add-in boards.
In virtually all modern (as of 2012[ [update]]) PCs, from consumer laptops and desktops to enterprise data servers, the PCIe bus serves as the primary motherboard-level interconnect, connecting the host system-processor with both integrated peripherals (surface-mounted ICs) and add-on peripherals (expansion cards). In most of these systems, the PCIe bus co-exists with one or more legacy PCI buses, for backward compatibility with the large body of legacy PCI peripherals.
As of 2013[ [update]], PCI Express has replaced AGP as the default interface for graphics cards on new systems. Almost all models of graphics cards released since 2010 by AMD (ATI) and Nvidia use PCI Express. Nvidia used the high-bandwidth data transfer of PCIe for its Scalable Link Interface (SLI) technology, which allowed multiple graphics cards of the same chipset and model number to run in tandem, allowing increased performance. This interface has, since, been discontinued. AMD has also developed a multi-GPU system based on PCIe called CrossFire. AMD, Nvidia, and Intel have released motherboard chipsets that support as many as four PCIe x16 slots, allowing tri-GPU and quad-GPU card configurations.
External GPUs.
Theoretically, external PCIe could give a notebook the graphics power of a desktop, by connecting a notebook with any PCIe desktop video card (enclosed in its own external housing, with a power supply and cooling); this is possible with an ExpressCard or Thunderbolt interface. An ExpressCard interface provides bit rates of 5 Gbit/s (0.5 GB/s throughput), whereas a Thunderbolt interface provides bit rates of up to 40 Gbit/s (5 GB/s throughput).
In 2006, Nvidia developed the Quadro Plex external PCIe family of GPUs that can be used for advanced graphic applications for the professional market. These video cards require a PCI Express x8 or x16 slot for the host-side card, which connects to the Plex via a VHDCI carrying eight PCIe lanes.
In 2008, AMD announced the ATI XGP technology, based on a proprietary cabling system that is compatible with PCIe x8 signal transmissions. This connector is available on the Fujitsu Amilo and the Acer Ferrari One notebooks. Fujitsu launched their AMILO GraphicBooster enclosure for XGP soon thereafter. Around 2010 Acer launched the Dynavivid graphics dock for XGP.
In 2010, external card hubs were introduced that can connect to a laptop or desktop through a PCI ExpressCard slot. These hubs can accept full-sized graphics cards. Examples include MSI GUS, Village Instrument's ViDock, the Asus XG Station, Bplus PE4H V3.2 adapter, as well as more improvised DIY devices. However such solutions are limited by the size (often only x1) and version of the available PCIe slot on a laptop.
The Intel Thunderbolt interface has provided a new option to connect with a PCIe card externally. Magma has released the ExpressBox 3T, which can hold up to three PCIe cards (two at x8 and one at x4). MSI also released the Thunderbolt GUS II, a PCIe chassis dedicated for video cards. Other products such as the Sonnet's Echo Express and mLogic's mLink are Thunderbolt PCIe chassis in a smaller form factor.
In 2017, more fully featured external card hubs were introduced, such as the Razer Core, which has a full-length PCIe x16 interface.
Storage devices.
The PCI Express protocol can be used as data interface to flash memory devices, such as memory cards and solid-state drives (SSDs).
The XQD card is a memory card format utilizing PCI Express, developed by the CompactFlash Association, with transfer rates of up to 1 GB/s.
Many high-performance, enterprise-class SSDs are designed as PCI Express RAID controller cards. Before NVMe was standardized, many of these cards utilized proprietary interfaces and custom drivers to communicate with the operating system; they had much higher transfer rates (over 1 GB/s) and IOPS (over one million I/O operations per second) when compared to Serial ATA or SAS drives. For example, in 2011 OCZ and Marvell co-developed a native PCI Express solid-state drive controller for a PCI Express 3.0 x16 slot with maximum capacity of 12 TB and a performance of to 7.2 GB/s sequential transfers and up to 2.52 million IOPS in random transfers.
SATA Express was an interface for connecting SSDs through SATA-compatible ports, optionally providing multiple PCI Express lanes as a pure PCI Express connection to the attached storage device. M.2 is a specification for internally mounted computer expansion cards and associated connectors, which also uses multiple PCI Express lanes.
PCI Express storage devices can implement both AHCI logical interface for backward compatibility, and NVM Express logical interface for much faster I/O operations provided by utilizing internal parallelism offered by such devices. Enterprise-class SSDs can also implement SCSI over PCI Express.
Cluster interconnect.
Certain data-center applications (such as large computer clusters) require the use of fiber-optic interconnects due to the distance limitations inherent in copper cabling. Typically, a network-oriented standard such as Ethernet or Fibre Channel suffices for these applications, but in some cases the overhead introduced by routable protocols is undesirable and a lower-level interconnect, such as InfiniBand, RapidIO, or NUMAlink is needed. Local-bus standards such as PCIe and HyperTransport can in principle be used for this purpose, but as of 2015[ [update]], solutions are only available from niche vendors such as Dolphin ICS, and TTTech Auto.
Competing protocols.
Other communications standards based on high bandwidth serial architectures include InfiniBand, RapidIO, HyperTransport, Intel QuickPath Interconnect, the Mobile Industry Processor Interface (MIPI), and NVLink. Differences are based on the trade-offs between flexibility and extensibility vs latency and overhead. For example, making the system hot-pluggable, as with Infiniband but not PCI Express, requires that software track network topology changes.
Another example is making the packets shorter to decrease latency (as is required if a bus must operate as a memory interface). Smaller packets mean packet headers consume a higher percentage of the packet, thus decreasing the effective bandwidth. Examples of bus protocols designed for this purpose are RapidIO and HyperTransport.
targeted by design as a system interconnect (local bus) rather than a device interconnect or routed network protocol. Additionally, its design goal of software transparency constrains the protocol and raises its latency somewhat.
Delays in PCIe 4.0 implementations led to the Gen-Z consortium, the CCIX effort and an open Coherent Accelerator Processor Interface (CAPI) all being announced by the end of 2016.
On 11 March 2019, Intel presented Compute Express Link (CXL), a new interconnect bus, based on the PCI Express 5.0 physical layer infrastructure. The initial promoters of the CXL specification included: Alibaba, Cisco, Dell EMC, Facebook, Google, HPE, Huawei, Intel and Microsoft.
Integrators list.
The PCI-SIG Integrators List lists products made by PCI-SIG member companies that have passed compliance testing. The list include switches, bridges, NICs, SSDs, etc.
See also.
<templatestyles src="Div col/styles.css"/>
Notes.
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References.
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"text": "\\text{Packet Efficiency} = \\frac{\\text{Payload}}{\\text{Payload} + \\text{Overhead}}"
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https://en.wikipedia.org/wiki?curid=143320
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14333272
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Dominance-based rough set approach
|
The dominance-based rough set approach (DRSA) is an extension of rough set theory for multi-criteria decision analysis (MCDA), introduced by Greco, Matarazzo and Słowiński. The main change compared to the classical rough sets is the substitution for the indiscernibility relation by a dominance relation, which permits one to deal with inconsistencies typical to consideration of criteria and preference-ordered decision classes.
Multicriteria classification (sorting).
Multicriteria classification (sorting) is one of the problems considered within MCDA and can be stated as follows: given a set of objects evaluated by a set of criteria (attributes with preference-order domains), assign these objects to some pre-defined and preference-ordered decision classes, such that each object is assigned to exactly one class. Due to the preference ordering, improvement of evaluations of an object on the criteria should not worsen its class assignment. The sorting problem is very similar to the problem of classification, however, in the latter, the objects are evaluated by regular attributes and the decision classes are not necessarily preference ordered. The problem of multicriteria classification is also referred to as ordinal classification problem with monotonicity constraints and often appears in real-life application when ordinal and monotone properties follow from the domain knowledge about the problem.
As an illustrative example, consider the problem of evaluation in a high school. The director of the school wants to assign students ("objects") to three classes: "bad", "medium" and "good" (notice that class "good" is preferred to "medium" and "medium" is preferred to "bad"). Each student is described by three criteria: level in Physics, Mathematics and Literature, each taking one of three possible values "bad", "medium" and "good". Criteria are preference-ordered and improving the level from one of the subjects should not result in worse global evaluation (class).
As a more serious example, consider classification of bank clients, from the viewpoint of bankruptcy risk, into classes "safe" and "risky". This may involve such characteristics as "return on equity (ROE)", "return on investment (ROI)" and "return on sales (ROS)". The domains of these attributes are not simply ordered but involve a preference order since, from the viewpoint of bank managers, greater values of ROE, ROI or ROS are better for clients being analysed for bankruptcy risk . Thus, these attributes are criteria. Neglecting this information in knowledge discovery may lead to wrong conclusions.
Data representation.
Decision table.
In DRSA, data are often presented using a particular form of decision table. Formally, a DRSA decision table is a 4-tuple formula_0, where formula_1 is a finite set of objects, formula_2 is a finite set of criteria, formula_3 where formula_4 is the domain of the criterion formula_5 and formula_6 is an "information function" such that formula_7 for every formula_8. The set formula_2 is divided into "condition criteria" (set formula_9) and the "decision criterion" ("class") formula_10. Notice, that formula_11 is an evaluation of object formula_12 on criterion formula_13, while formula_14 is the class assignment (decision value) of the object. An example of decision table is shown in Table 1 below.
Outranking relation.
It is assumed that the domain of a criterion formula_15 is completely preordered by an outranking relation formula_16; formula_17 means that formula_12 is at least as good as (outranks) formula_18 with respect to the criterion formula_5. Without loss of generality, we assume that the domain of formula_5 is a subset of reals, formula_19, and that the outranking relation is a simple order between real numbers formula_20 such that the following relation holds: formula_21. This relation is straightforward for gain-type ("the more, the better") criterion, e.g. "company profit". For cost-type ("the less, the better") criterion, e.g. "product price", this relation can be satisfied by negating the values from formula_4.
Decision classes and class unions.
Let formula_22. The domain of decision criterion, formula_23 consist of formula_24 elements (without loss of generality we assume formula_25) and induces a partition of formula_1 into formula_24 classes formula_26, where formula_27. Each object formula_28 is assigned to one and only one class formula_29. The classes are preference-ordered according to an increasing order of class indices, i.e. for all formula_30 such that formula_31, the objects from formula_32 are strictly preferred to the objects from formula_33. For this reason, we can consider the upward and downward unions of classes, defined respectively, as:
formula_34
Main concepts.
Dominance.
We say that formula_12 dominates formula_18 with respect to formula_35, denoted by formula_36, if formula_12 is better than formula_18 on every criterion from formula_37, formula_38. For each formula_35, the dominance relation formula_39 is reflexive and transitive, i.e. it is a partial pre-order. Given formula_35 and formula_28, let
formula_40
formula_41
represent P"-dominating set and P"-dominated set with respect to formula_28, respectively.
Rough approximations.
The key idea of the rough set philosophy is approximation of one knowledge by another knowledge. In DRSA, the knowledge being approximated is a collection of upward and downward unions of decision classes and the "granules of knowledge" used for approximation are "P"-dominating and "P"-dominated sets.
The P"-lower and the P"-upper approximation of formula_42 with respect to formula_35, denoted as formula_43 and formula_44, respectively, are defined as:
formula_45
formula_46
Analogously, the "P"-lower and the "P"-upper approximation of formula_47 with respect to formula_35, denoted as formula_48 and formula_49, respectively, are defined as:
formula_50
formula_51
Lower approximations group the objects which "certainly" belong to class union formula_52 (respectively formula_53). This certainty comes from the fact, that object formula_28 belongs to the lower approximation formula_54 (respectively formula_55), if no other object in formula_1 contradicts this claim, i.e. every object formula_56 which "P"-dominates formula_12, also belong to the class union formula_52 (respectively formula_53). Upper approximations group the objects which "could belong" to formula_52 (respectively formula_53), since object formula_28 belongs to the upper approximation formula_57 (respectively formula_58), if there exist another object formula_56 "P"-dominated by formula_12 from class union formula_52 (respectively formula_53).
The "P"-lower and "P"-upper approximations defined as above satisfy the following properties for all formula_59 and for any formula_35:
formula_60
formula_61
The "P"-boundaries ("P-doubtful regions") of formula_62 and formula_63 are defined as:
formula_64
formula_65
Quality of approximation and reducts.
The ratio
formula_66
defines the quality of approximation of the partition formula_67 into classes by means of the set of criteria formula_37. This ratio express the relation between all the "P"-correctly classified objects and all the objects in the table.
Every minimal subset formula_35 such that formula_68 is called a reduct of formula_69 and is denoted by formula_70. A decision table may have more than one reduct. The intersection of all reducts is known as the "core".
Decision rules.
On the basis of the approximations obtained by means of the dominance relations, it is possible to induce a generalized description of the preferential information contained in the decision table, in terms of decision rules. The decision rules are expressions of the form "if" [condition] "then" [consequent], that represent a form of dependency between condition criteria and decision criteria. Procedures for generating decision rules from a decision table use an inductive learning principle. We can distinguish three types of rules: certain, possible and approximate. Certain rules are generated from lower approximations of unions of classes; possible rules are generated from upper approximations of unions of classes and approximate rules are generated from boundary regions.
Certain rules has the following form:
if formula_71 and formula_72 and formula_73 then formula_74
if formula_75 and formula_76 and formula_77 then formula_78
Possible rules has a similar syntax, however the "consequent" part of the rule has the form: formula_12 "could belong to" formula_62 or the form: formula_12 "could belong to" formula_63.
Finally, approximate rules has the syntax:
if formula_71 and formula_72 and formula_79 and formula_80 and formula_81 and formula_77
then formula_82
The certain, possible and approximate rules represent certain, possible and ambiguous knowledge extracted from the decision table.
Each decision rule should be minimal. Since a decision rule is an implication, by a minimal decision rule we understand such an implication that there is no other implication with an antecedent of at least the same weakness (in other words, rule using a subset of elementary conditions or/and weaker elementary conditions) and a consequent of at least the same strength (in other words, rule assigning objects to the same union or sub-union of classes).
A set of decision rules is "complete" if it is able to cover all objects from the decision table in such a way that consistent objects are re-classified to their original classes and inconsistent objects are classified to clusters of classes referring to this inconsistency. We call "minimal" each set of decision rules that is complete and non-redundant, i.e. exclusion of any rule from this set makes it non-complete.
One of three induction strategies can be adopted to obtain a set of decision rules:
The most popular rule induction algorithm for dominance-based rough set approach is DOMLEM, which generates minimal set of rules.
Example.
Consider the following problem of high school students’ evaluations:
Each object (student) is described by three criteria formula_83, related to the levels in Mathematics, Physics and Literature, respectively. According to the decision attribute, the students are divided into three preference-ordered classes: formula_84, formula_85 and formula_86. Thus, the following unions of classes were approximated:
Notice that evaluations of objects formula_91 and formula_92 are inconsistent, because formula_91 has better evaluations on all three criteria than formula_92 but worse global score.
Therefore, lower approximations of class unions consist of the following objects:
formula_93
formula_94
formula_95
formula_96
Thus, only classes formula_87 and formula_89 cannot be approximated precisely. Their upper approximations are as follows:
formula_97
formula_98
while their boundary regions are:
formula_99
Of course, since formula_88 and formula_90 are approximated precisely, we have formula_100, formula_101 and formula_102
The following minimal set of 10 rules can be induced from the decision table:
The last rule is approximate, while the rest are certain.
Extensions.
Multicriteria choice and ranking problems.
The other two problems considered within multi-criteria decision analysis, multicriteria choice and ranking problems, can also be solved using dominance-based rough set approach. This is done by converting the decision table into pairwise comparison table (PCT).
Variable-consistency DRSA.
The definitions of rough approximations are based on a strict application of the dominance principle. However, when defining non-ambiguous objects, it is reasonable to accept a limited proportion of negative examples, particularly for large decision tables. Such extended version of DRSA is called Variable-Consistency DRSA model (VC-DRSA)
Stochastic DRSA.
In real-life data, particularly for large datasets, the notions of rough approximations were found to be excessively restrictive. Therefore, an extension of DRSA, based on stochastic model (Stochastic DRSA), which allows inconsistencies to some degree, has been introduced. Having stated the probabilistic model for ordinal classification problems with monotonicity constraints, the concepts of lower approximations are extended to the
stochastic case. The method is based on estimating the conditional probabilities using the nonparametric maximum likelihood method which leads
to the problem of isotonic regression.
Stochastic dominance-based rough sets can also be regarded as a sort of variable-consistency model.
Software.
4eMka2 is a decision support system for multiple criteria classification problems based on dominance-based rough sets (DRSA). JAMM is a much more advanced successor of 4eMka2. Both systems are freely available for non-profit purposes on the Laboratory of Intelligent Decision Support Systems (IDSS) website.
References.
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"text": "V=\\bigcup {}_{q \\in Q} V_q"
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"text": "V_q\\,\\!"
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"text": "q\\,\\!"
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"text": "f(x,q) \\in V_q"
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"text": "(x,q) \\in U \\times Q"
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"math_id": 9,
"text": "C \\neq \\emptyset"
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{
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"text": "d\\,\\!"
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{
"math_id": 11,
"text": "f(x,q)\\,\\!"
},
{
"math_id": 12,
"text": "x\\,\\!"
},
{
"math_id": 13,
"text": "q \\in C"
},
{
"math_id": 14,
"text": "f(x,d)\\,\\!"
},
{
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"text": "q \\in Q"
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"text": "\\succeq_q"
},
{
"math_id": 17,
"text": "x \\succeq_q y"
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{
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"text": "y\\,\\!"
},
{
"math_id": 19,
"text": "V_q \\subseteq \\mathbb{R}"
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{
"math_id": 20,
"text": "\\geq\\,\\!"
},
{
"math_id": 21,
"text": "x \\succeq_q y \\iff f(x,q) \\geq f(y,q)"
},
{
"math_id": 22,
"text": "T = \\{1,\\ldots,n\\}\\,\\!"
},
{
"math_id": 23,
"text": "V_d\\,\\!"
},
{
"math_id": 24,
"text": "n\\,\\!"
},
{
"math_id": 25,
"text": "V_d = T\\,\\!"
},
{
"math_id": 26,
"text": "\\textbf{Cl}=\\{Cl_t, t \\in T\\}"
},
{
"math_id": 27,
"text": "Cl_t = \\{x \\in U \\colon f(x,d) = t\\}"
},
{
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"text": "x \\in U"
},
{
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"text": "Cl_t, t \\in T"
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"text": "r,s \\in T"
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"text": "r \\geq s\\,\\!"
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"text": "Cl_r\\,\\!"
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"text": "Cl_s\\,\\!"
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"text": "\nCl^{\\geq}_t = \\bigcup_{s \\geq t} Cl_s \\qquad Cl^{\\leq}_t= \\bigcup_{s \\leq t} Cl_s \\qquad t \\in T\n"
},
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"text": "P \\subseteq C"
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"text": " x D_p y\\,\\!"
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"text": "P\\,\\!"
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"text": "x \\succeq_q y, \\, \\forall q \\in P"
},
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"text": "D_P\\,\\!"
},
{
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"text": "\nD_P^+(x) = \\{y \\in U \\colon y D_p x \\}\n"
},
{
"math_id": 41,
"text": "\nD_P^-(x) = \\{y \\in U \\colon x D_p y \\}\n"
},
{
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"text": "Cl_t^{\\geq}, t \\in T"
},
{
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"text": "\\underline{P}(Cl_t^{\\geq})"
},
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"text": "\\overline{P}(Cl_t^{\\geq})"
},
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"text": "\n\\underline{P}(Cl_t^{\\geq}) = \\{x \\in U \\colon D_P^+(x) \\subseteq Cl_t^{\\geq} \\}\n"
},
{
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"text": "\n\\overline{P}(Cl_t^{\\geq}) = \\{x \\in U \\colon D_P^-(x) \\cap Cl_t^{\\geq} \\neq \\emptyset\\}\n"
},
{
"math_id": 47,
"text": "Cl_t^{\\leq}, t \\in T"
},
{
"math_id": 48,
"text": "\\underline{P}(Cl_t^{\\leq})"
},
{
"math_id": 49,
"text": "\\overline{P}(Cl_t^{\\leq})"
},
{
"math_id": 50,
"text": "\n\\underline{P}(Cl_t^{\\leq}) = \\{x \\in U \\colon D_P^-(x) \\subseteq Cl_t^{\\leq} \\}\n"
},
{
"math_id": 51,
"text": "\n\\overline{P}(Cl_t^{\\leq}) = \\{x \\in U \\colon D_P^+(x) \\cap Cl_t^{\\leq} \\neq \\emptyset\\}\n"
},
{
"math_id": 52,
"text": "Cl^{\\ge}_t"
},
{
"math_id": 53,
"text": "Cl^{\\le}_t"
},
{
"math_id": 54,
"text": "\\underline{P}(Cl^{\\ge}_t)"
},
{
"math_id": 55,
"text": "\\underline{P}(Cl^{\\le}_t)"
},
{
"math_id": 56,
"text": "y \\in U"
},
{
"math_id": 57,
"text": "\\overline{P}(Cl^{\\ge}_t)"
},
{
"math_id": 58,
"text": "\\overline{P}(Cl^{\\le}_t)"
},
{
"math_id": 59,
"text": "t \\in T"
},
{
"math_id": 60,
"text": "\n\\underline{P}(Cl_t^{\\geq}) \\subseteq Cl_t^{\\geq} \\subseteq \\overline{P}(Cl_t^{\\geq})\n"
},
{
"math_id": 61,
"text": "\n\\underline{P}(Cl_t^{\\leq}) \\subseteq Cl_t^{\\leq} \\subseteq \\overline{P}(Cl_t^{\\leq})\n"
},
{
"math_id": 62,
"text": "Cl_t^{\\geq}"
},
{
"math_id": 63,
"text": "Cl_t^{\\leq}"
},
{
"math_id": 64,
"text": "\nBn_P(Cl_t^{\\geq}) = \\overline{P}(Cl_t^{\\geq})-\\underline{P}(Cl_t^{\\geq})\n"
},
{
"math_id": 65,
"text": "\nBn_P(Cl_t^{\\leq}) = \\overline{P}(Cl_t^{\\leq})-\\underline{P}(Cl_t^{\\leq})\n"
},
{
"math_id": 66,
"text": "\n\\gamma_P(\\textbf{Cl}) = \\frac{\\left|U - \\left( \\left( \\bigcup_{t \\in T} Bn_P(Cl_t^{\\geq}) \\right) \\cup \\left( \\bigcup_{t \\in T} Bn_P(Cl_t^{\\leq}) \\right) \\right)\\right|}{|U|}\n"
},
{
"math_id": 67,
"text": "\\textbf{Cl}\\,\\!"
},
{
"math_id": 68,
"text": "\\gamma_P(\\mathbf{Cl}) = \\gamma_C(\\mathbf{Cl})\\,\\!"
},
{
"math_id": 69,
"text": "C\\,\\!"
},
{
"math_id": 70,
"text": "RED_{\\mathbf{Cl}}(P)"
},
{
"math_id": 71,
"text": "f(x,q_1) \\geq r_1\\,\\!"
},
{
"math_id": 72,
"text": "f(x,q_2) \\geq r_2\\,\\!"
},
{
"math_id": 73,
"text": "\\ldots f(x,q_p) \\geq r_p\\,\\!"
},
{
"math_id": 74,
"text": "x \\in Cl_t^{\\geq}"
},
{
"math_id": 75,
"text": "f(x,q_1) \\leq r_1\\,\\!"
},
{
"math_id": 76,
"text": "f(x,q_2) \\leq r_2\\,\\!"
},
{
"math_id": 77,
"text": "\\ldots f(x,q_p) \\leq r_p\\,\\!"
},
{
"math_id": 78,
"text": "x \\in Cl_t^{\\leq}"
},
{
"math_id": 79,
"text": "\\ldots f(x,q_k) \\geq r_k\\,\\!"
},
{
"math_id": 80,
"text": "f(x,q_{k+1}) \\leq r_{k+1}\\,\\!"
},
{
"math_id": 81,
"text": "f(x,q_{k+2}) \\leq r_{k+2}\\,\\!"
},
{
"math_id": 82,
"text": "x \\in Cl_s \\cup Cl_{s+1} \\cup Cl_t"
},
{
"math_id": 83,
"text": "q_1,q_2,q_3\\,\\!"
},
{
"math_id": 84,
"text": "Cl_1 = \\{bad\\}"
},
{
"math_id": 85,
"text": "Cl_2 = \\{medium\\}"
},
{
"math_id": 86,
"text": "Cl_3 = \\{good\\}"
},
{
"math_id": 87,
"text": "Cl_1^{\\leq}"
},
{
"math_id": 88,
"text": "Cl_2^{\\leq}"
},
{
"math_id": 89,
"text": "Cl_2^{\\geq}"
},
{
"math_id": 90,
"text": "Cl_3^{\\geq}"
},
{
"math_id": 91,
"text": "x_4\\,\\!"
},
{
"math_id": 92,
"text": "x_6\\,\\!"
},
{
"math_id": 93,
"text": "\\underline{P}(Cl_1^{\\leq}) = \\{x_1,x_5\\}"
},
{
"math_id": 94,
"text": "\\underline{P}(Cl_2^{\\leq}) = \\{x_1,x_2,x_3,x_4,x_5,x_6,x_8\\} = Cl_2^{\\leq}"
},
{
"math_id": 95,
"text": "\\underline{P}(Cl_2^{\\geq}) = \\{x_2,x_3,x_7,x_8,x_9,x_{10}\\}"
},
{
"math_id": 96,
"text": "\\underline{P}(Cl_3^{\\geq}) = \\{x_7,x_9,x_{10}\\} = Cl_3^{\\geq}"
},
{
"math_id": 97,
"text": "\\overline{P}(Cl_1^{\\leq}) = \\{x_1,x_4,x_5,x_6\\}"
},
{
"math_id": 98,
"text": "\\overline{P}(Cl_2^{\\geq}) = \\{x_2,x_3,x_4,x_6,x_7,x_8,x_9,x_{10}\\}"
},
{
"math_id": 99,
"text": "Bn_P(Cl_1^{\\leq}) = Bn_P(Cl_2^{\\geq}) = \\{x_4,x_6\\}"
},
{
"math_id": 100,
"text": "\\overline{P}(Cl_2^{\\leq})=Cl_2^{\\leq}"
},
{
"math_id": 101,
"text": "\\overline{P}(Cl_3^{\\geq})=Cl_3^{\\geq}"
},
{
"math_id": 102,
"text": "Bn_P(Cl_2^{\\leq}) = Bn_P(Cl_3^{\\geq}) = \\emptyset"
},
{
"math_id": 103,
"text": "Physics \\leq bad"
},
{
"math_id": 104,
"text": "student \\leq bad"
},
{
"math_id": 105,
"text": "Literature \\leq bad"
},
{
"math_id": 106,
"text": "Physics \\leq medium"
},
{
"math_id": 107,
"text": "Math \\leq medium"
},
{
"math_id": 108,
"text": "Math \\leq bad"
},
{
"math_id": 109,
"text": "student \\leq medium"
},
{
"math_id": 110,
"text": "Literature \\leq medium"
},
{
"math_id": 111,
"text": "Literature \\geq good"
},
{
"math_id": 112,
"text": "Math \\geq medium"
},
{
"math_id": 113,
"text": "student \\geq good"
},
{
"math_id": 114,
"text": "Physics \\geq good"
},
{
"math_id": 115,
"text": "Math \\geq good"
},
{
"math_id": 116,
"text": "student \\geq medium"
},
{
"math_id": 117,
"text": "Physics \\geq medium"
},
{
"math_id": 118,
"text": "student = bad \\lor medium"
}
] |
https://en.wikipedia.org/wiki?curid=14333272
|
14333702
|
Arabinonate dehydratase
|
The enzyme arabinonate dehydratase (EC 4.2.1.5) catalyzes the chemical reaction
-arabinonate formula_0 2-dehydro-3-deoxy--arabinonate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -arabinonate hydro-lyase (2-dehydro-3-deoxy--arabinonate-forming). This enzyme is also called -arabinonate hydro-lyase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14333702
|
14333758
|
ATP-dependent NAD(P)H-hydrate dehydratase
|
The enzyme ATP-dependent NAD(P)H-hydrate dehydratase (EC 4.2.1.93) catalyzes the chemical reactions
ATP + (6"S")-6-β-hydroxy-1,4,5,6-tetrahydronicotinamide-adenine dinucleotide formula_0 ADP + phosphate + NADH
ATP + (6"S")-6-β-hydroxy-1,4,5,6-tetrahydronicotinamide-adenine dinucleotide phosphate formula_0 ADP + phosphate + NADPH
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is (6"S")-6-β-hydroxy-1,4,5,6-tetrahydronicotinamide-adenine-dinucleotide hydro-lyase (ATP-hydrolysing; NADH-forming). Other names in common use include reduced nicotinamide adenine dinucleotide hydrate dehydratase, ATP-dependent H4NAD(P)+OH dehydratase, (6"S")-β-6-hydroxy-1,4,5,6-tetrahydronicotinamide-adenine-, and dinucleotide hydro-lyase (ATP-hydrolysing).
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14333758
|
14333774
|
Bile-acid 7alpha-dehydratase
|
The enzyme bile-acid 7α-dehydratase (EC 4.2.1.106) catalyzes the chemical reaction
7α,12α-dihydroxy-3-oxochol-4-enoate formula_0 12α-hydroxy-3-oxochola-4,6-dienoate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 7α,12α-dihydroxy-3-oxochol-4-enoate hydro-lyase (12α-hydroxy-3-oxochola-4,6-dienoate-forming). This enzyme is also called 7α,12α-dihydroxy-3-oxochol-4-enoate hydro-lyase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14333774
|
14333889
|
Carboxymethyloxysuccinate lyase
|
The enzyme carboxymethyloxysuccinate lyase (EC 4.2.99.12) catalyzes the chemical reaction
carboxymethyloxysuccinate formula_0 fumarate + glycolate
This enzyme belongs to the family of lyases, specifically the "catch-all" class of lyases that cleave carbon-oxygen bonds. The systematic name of this enzyme class is carboxymethyloxysuccinate glycolate-lyase (fumarate-forming). Other names in common use include carbon-oxygen lyase, and carboxymethyloxysuccinate glycolate-lyase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14333889
|
14333899
|
Carnitine dehydratase
|
Enzyme
In enzymology, a carnitine dehydratase (EC 4.2.1.89) is an enzyme that catalyzes the chemical reaction
L-carnitine formula_0 4-(trimethylammonio)but-2-enoate + H2O
Hence, this enzyme has one substrate, L-carnitine, and two products, 4-(trimethylammonio)but-2-enoate and H2O.
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is L-carnitine hydro-lyase [4-(trimethylammonio)but-2-enoate-forming]. This enzyme is also called L-carnitine hydro-lyase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14333899
|
14333914
|
Casbene synthase
|
Enzyme
The enzyme casbene synthase (EC 4.2.3.8) catalyzes the chemical reaction
geranylgeranyl diphosphate formula_0 casbene + diphosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is geranylgeranyl-diphosphate diphosphate-lyase (cyclizing, casbene-forming). Other names in common use include casbene synthetase, and geranylgeranyl-diphosphate diphosphate-lyase (cyclizing). This enzyme participates in diterpenoid biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14333914
|
14333931
|
CDP-glucose 4,6-dehydratase
|
The enzyme CDP-glucose 4,6-dehydratase (EC 4.2.1.45) catalyzes the chemical reaction
CDP-glucose formula_0 CDP-4-dehydro-6-deoxy--glucose + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. This enzyme participates in starch and sucrose metabolism. It employs one cofactor, NAD+.
Nomenclature.
The systematic name of this enzyme class is CDP-glucose 4,6-hydro-lyase (CDP-4-dehydro-6-deoxy--glucose-forming). Other names in common use include:
Structural studies.
As of late 2007, two structures have been solved for this class of enzymes, with PDB accession codes 1RKX and 1WVG.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14333931
|
14334029
|
Chorismate synthase
|
The enzyme chorismate synthase (EC 4.2.3.5) catalyzes the chemical reaction
5-"O"-(1-carboxyvinyl)-3-phosphoshikimate formula_0 chorismate + phosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is 5-"O"-(1-carboxyvinyl)-3-phosphoshikimate phosphate-lyase (chorismate-forming). This enzyme is also called 5-"O"-(1-carboxyvinyl)-3-phosphoshikimate phosphate-lyase. This enzyme participates in phenylalanine, tyrosine and tryptophan biosynthesis.
Chorismate synthase catalyzes the last of the seven steps in the shikimate pathway which is used in prokaryotes, fungi and plants for the biosynthesis of aromatic amino acids. It catalyzes the 1,4-trans elimination of the phosphate group from 5-enolpyruvylshikimate-3-phosphate (EPSP) to form chorismate which can then be used in phenylalanine, tyrosine or tryptophan biosynthesis. Chorismate synthase requires the presence of a reduced flavin mononucleotide (FMNH2 or FADH2) for its activity. Chorismate synthase from various sources shows a high degree of sequence conservation. It is a protein of about 360 to 400 amino-acid residues.
Biological and practical function.
The shikimate pathway synthesises precursors to aromatic amino acids, as well as other aromatic compounds that have various involvement with processes such as "UV protection, electron transport, signaling, communication, plant defense, and the wound response". Because humans lack the shikimate pathway, but it is required for the survival of many microorganisms, the pathway and chorismate synthase in particular are considered to be potential targets for new antimicrobial treatments. For example, chorismate synthase is known to be essential to the survival of "Mycobacterium tuberculosis", making the enzyme an attractive antibiotic target for control of this pathogen.
Structural studies.
As of late 2007, 9 structures have been solved for this class of enzymes, with PDB accession codes 1Q1L, 1QXO, 1R52, 1R53, 1SQ1, 1UM0, 1UMF, 1ZTB, and 2G85.
The crystal structure of chorismate synthase is a homotetramer with one
FMN molecule non-covalently bound to each of the four monomers.
Each monomer is made up of 9 alpha helices and 18 beta strands and the core
is assembled in a unique beta-alpha-beta sandwich fold. The active sites for FMN-binding are made up of clusters of flexible loops and the area around these regions have highly positive electromagnetic potential. There are two histidine residues located at the active site which are thought to protonate the reduced flavin molecule and the leaving phosphate group of the substrate.
Mechanism.
The formation of chorismate from EPSP involves two eliminations, of phosphate and a proton (H+), from the substrate. In the first step of catalysis, phosphate is eliminated, assisted by proton transfer from a conserved histidine residue. At the same time, an electron is transferred from the FMN to the substrate, forming an FMN radical and a substrate radical. Next, the FMN radical rearranges, and then a hydrogen atom is transferred to FMN from the substrate, eliminating both radicals and generating the product. The reduced FMN then re-tautomerizes to its active form by donating a proton to a second conserved histidine. Although the chorismate synthase reaction is FMN-dependent, there is no net redox change between substrate and product; the FMN merely acts as a catalyst.
Two classes of chorismate synthase exist, differing in how the reduced state of the FMN cofactor is maintained. Bifunctional chorismate synthase is present in fungi and contains an NAD(P)H-dependent flavin reductase domain. Monofunctional chorismate synthase is found in plants and "E.coli" and lacks a flavin reductase domain. It depends on a separate reductase enzyme to reduce the FMN.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334029
|
14334051
|
Citrate dehydratase
|
In enzymology, a citrate dehydratase (EC 4.2.1.4) is an enzyme that catalyzes the chemical reaction
citrate formula_0 cis-aconitate + H2O
Hence, this enzyme has one substrate, citrate, and two products, cis-aconitate and H2O.
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is citrate hydro-lyase (cis-aconitate-forming). This enzyme is also called citrate hydro-lyase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334051
|
14334072
|
Crotonoyl-(acyl-carrier-protein) hydratase
|
In enzymology, a crotonoyl-[acyl-carrier-protein] hydratase (EC 4.2.1.58) is an enzyme that catalyzes the chemical reaction
(3R)-3-hydroxybutanoyl-[acyl-carrier-protein] formula_0 but-2-enoyl-[acyl-carrier-protein] + H2O
Hence, this enzyme has one substrate, (3R)-3-hydroxybutanoyl-[acyl-carrier-protein], and two products, but-2-enoyl-[acyl-carrier-protein] and H2O.
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is (3R)-3-hydroxybutanoyl-[acyl-carrier-protein] hydro-lyase (but-2-enoyl-[acyl-carrier protein]-forming). Other names in common use include (3R)-3-hydroxybutanoyl-[acyl-carrier-protein] hydro-lyase, beta-hydroxybutyryl acyl carrier protein dehydrase, beta-hydroxybutyryl acyl carrier protein (ACP) dehydrase, beta-hydroxybutyryl acyl carrier protein dehydrase, enoyl acyl carrier protein hydrase, crotonyl acyl carrier protein hydratase, 3-hydroxybutyryl acyl carrier protein dehydratase, beta-hydroxybutyryl acyl carrier, and protein dehydrase. This enzyme participates in fatty acid biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334072
|
14334122
|
Cyanamide hydratase
|
The enzyme cyanamide hydratase (EC 4.2.1.69) catalyzes the chemical reaction
urea formula_0 cyanamide + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is urea hydro-lyase (cyanamide-forming). This enzyme is also called urea hydro-lyase. This enzyme participates in atrazine degradation.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334122
|
14334137
|
Cyanide hydratase
|
Type of enzyme
The enzyme cyanide hydratase (EC 4.2.1.66) catalyzes the chemical reaction
formamide formula_0 cyanide + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is formamide hydro-lyase (cyanide-forming). Other names in common use include formamide dehydratase, and formamide hydro-lyase. This enzyme participates in cyanoamino acid metabolism.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334137
|
14334164
|
Cyclohexa-1,5-dienecarbonyl-CoA hydratase
|
The enzyme cyclohexa-1,5-dienecarbonyl-CoA hydratase (EC 4.2.1.100) catalyzes the chemical reaction
6-hydroxycyclohex-1-enecarbonyl-CoA formula_0 cyclohexa-1,5-dienecarbonyl-CoA + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 6-hydroxycyclohex-1-enecarbonyl-CoA (cyclohexa-1,5-dienecarbonyl-CoA-forming). Other names in common use include cyclohexa-1,5-diene-1-carbonyl-CoA hydratase, dienoyl-CoA hydratase, and cyclohexa-1,5-dienecarbonyl-CoA hydro-lyase (incorrect). This enzyme participates in benzoate degradation via CoA ligation.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334164
|
14334183
|
Cyclohexyl-isocyanide hydratase
|
The enzyme cyclohexyl-isocyanide hydratase (EC 4.2.1.103) catalyzes the chemical reaction
"N"-cyclohexylformamide formula_0 cyclohexyl isocyanide + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is N"-cyclohexylformamide hydro-lyase (cyclohexyl-isocyanide-forming). Other names in common use include isonitrile hydratase, and N"-cyclohexylformamide hydro-lyase. This enzyme participates in caprolactam degradation.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334183
|
14334236
|
D-fuconate dehydratase
|
The enzyme -fuconate dehydratase (EC 4.2.1.67) catalyzes the chemical reaction.
-fuconate formula_0 2-dehydro-3-deoxy--fuconate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -fuconate hydro-lyase (2-dehydro-3-deoxy--fuconate-forming). This enzyme is also called -fuconate hydro-lyase. This enzyme participates in fructose and mannose metabolism.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334236
|
14334247
|
D-glutamate cyclase
|
The enzyme -glutamate cyclase (EC 4.2.1.48) catalyzes the chemical reaction
-glutamate formula_0 5-oxo-proline + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -glutamate hydro-lyase (cyclizing; 5-oxo--proline-forming). This enzyme is also called -glutamate hydro-lyase (cyclizing). This enzyme participates in -glutamine and -glutamate metabolism.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334247
|
14334273
|
Dihydroxy-acid dehydratase
|
The enzyme dihydroxy-acid dehydratase (EC 4.2.1.9) catalyzes the chemical reaction
2,3-dihydroxy-3-methylbutanoate formula_0 3-methyl-2-oxobutanoate + H2O
This enzyme participates in valine, leucine and isoleucine biosynthesis and pantothenate and coenzyme A (CoA) biosynthesis.
Nomenclature.
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 2,3-dihydroxy-3-methylbutanoate hydro-lyase (3-methyl-2-oxobutanoate-forming). Other names in common use include
References.
<templatestyles src="Reflist/styles.css" />
Further reading.
<templatestyles src="Refbegin/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334273
|
14334295
|
Dimethylmaleate hydratase
|
Class of enzymes
The enzyme dimethylmaleate hydratase (EC 4.2.1.85) catalyzes the chemical reaction
(2"R",3"S")-2,3-dimethylmalate formula_0 dimethylmaleate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is (2"R",3"S")-2,3-dimethylmalate hydro-lyase (dimethylmaleate-forming). This enzyme is also called (2"R",3"S")-2,3-dimethylmalate hydro-lyase. This enzyme participates in c5-branched dibasic acid metabolism. It employs one cofactor, iron.
References.
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334295
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14334331
|
D(−)-tartrate dehydratase
|
Enzyme
The enzyme (−)-tartrate dehydratase (EC 4.2.1.81) catalyzes the chemical reaction
("S,S")-tartrate formula_0 oxaloacetate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is ("S,S")-tartrate hydro-lyase (oxaloacetate-forming). Other names in common use include -tartrate dehydratase, and ("S,S")-tartrate hydro-lyase. It has 2 cofactors: iron and manganese.
Structural studies.
As of late 2007, two structures have been solved for this class of enzymes, with PDB accession codes 2DW6 and 2DW7.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334331
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14334351
|
DTDP-glucose 4,6-dehydratase
|
The enzyme dTDP-glucose 4,6-dehydratase (EC 4.2.1.46) catalyzes the chemical reaction
dTDP-glucose formula_0 dTDP-4-dehydro-6-deoxy--glucose + H2O
Structure and mechanism of action.
The first protein structures of a dTDP-glucose 4,6-dehydratase (RmlB) were completed by Jim Thoden in the Hazel Holden lab (University of Wisconsin–Madison) and Simon Allard in the Jim Naismith lab (University of St Andrews). Further structural, mutagenic, and enzymatic studies by both groups, along with important mechanistic work by the W. Wallace Cleland and Perry Frey groups have led to a good understanding of this enzyme. In brief summary, the enzyme is a dimeric protein with a Rossmann fold; it uses the tightly bound coenzyme NAD+ for transiently oxidizing the substrate, activating it for the dehydration step.
Nomenclature.
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is dTDP-glucose 4,6-hydro-lyase (dTDP-4-dehydro-6-deoxy--glucose-forming). Other names in common use include thymidine diphosphoglucose oxidoreductase, TDP-glucose oxidoreductase, RmlB, DESIV, and dTDP-glucose 4,6-hydro-lyase. This enzyme participates in 4 metabolic pathways: nucleotide sugars metabolism, streptomycin biosynthesis, polyketide sugar unit biosynthesis, and biosynthesis of vancomycin group antibiotics.
References.
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Further reading.
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334351
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14334366
|
Ectoine synthase
|
The enzyme ectoine synthase (EC ) catalyzes the chemical reaction
(2"S")-4-acetamido-2-aminobutanoate formula_0 -ectoine + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is (2"S")-4-acetamido-2-aminobutanoate (-ectoine-forming). Other names in common use include N"-acetyldiaminobutyrate dehydratase, N"-acetyldiaminobutanoate dehydratase, -ectoine synthase, EctC, and 4-"N"-acetyl--2,4-diaminobutanoate hydro-lyase (-ectoine-forming). This enzyme participates in glycine, serine and threonine metabolism.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334366
|
14334381
|
(−)-endo-fenchol synthase
|
Class of enzymes
The enzyme (−)-"endo"-Fenchol synthase (EC 4.2.3.10) catalyzes the chemical reaction
geranyl diphosphate + H2O formula_0 (−)-"endo"-fenchol + diphosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is geranyl-diphosphate diphosphate-lyase [cyclizing, (−)-endo-fenchol-forming]. Other names in common use include (−)-"endo"-fenchol cyclase, and geranyl pyrophosphate:(−)-"endo"-fenchol cyclase. This enzyme participates in monoterpenoid biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334381
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14334394
|
Ent-kaurene synthase
|
The enzyme "ent"-kaurene synthase (EC 4.2.3.19) catalyzes the chemical reaction
"ent"-copalyl diphosphate formula_0 "ent"-kaurene + diphosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is ent"-copalyl-diphosphate diphosphate-lyase (cyclizing, "ent"-kaurene-forming). Other names in common use include ent"-kaurene synthase B, "ent"-kaurene synthetase B, "ent"-copalyl-diphosphate diphosphate-lyase, and (cyclizing). This enzyme participates in diterpenoid biosynthesis.
In "Stevia".
In "Stevia" spp., "ent"-kaurene synthase is a required part of the biosynthesis of steviol. Hajihashemi "et al.", 2013 find that it is involved in the drought stress response and – because it mimics drought stress – paclobutrazol toxicity. Both inhbit transcription of steviol glycoside synthesis genes including "ent"-kaurene synthase. This is believed to reduce steviol content in the final plant product.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334394
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14334411
|
Ethanolamine-phosphate phospho-lyase
|
The enzyme ethanolamine-phosphate phospho-lyase (EC 4.2.3.2) catalyzes the chemical reaction
ethanolamine phosphate + H2O formula_0 acetaldehyde + NH3 + phosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is ethanolamine-phosphate phosphate-lyase (deaminating; acetaldehyde-forming). Other names in common use include O"-phosphoethanolamine-phospholyase, amino alcohol "O"-phosphate phospholyase, O"-phosphorylethanol-amine phospho-lyase, and ethanolamine-phosphate phospho-lyase (deaminating). It employs one cofactor, pyridoxal phosphate.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334411
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14334415
|
Grzegorczyk hierarchy
|
Functions in computability theory
The Grzegorczyk hierarchy (, ), named after the Polish logician Andrzej Grzegorczyk, is a hierarchy of functions used in computability theory. Every function in the Grzegorczyk hierarchy is a primitive recursive function, and every primitive recursive function appears in the hierarchy at some level. The hierarchy deals with the rate at which the values of the functions grow; intuitively, functions in lower levels of the hierarchy grow slower than functions in the higher levels.
Definition.
First we introduce an infinite set of functions, denoted "Ei" for some natural number "i". We define
formula_0
formula_1 is the addition function, and formula_2 is a unary function which squares its argument and adds two. Then, for each "n" greater than 1, formula_3, i.e. the "x"-th iterate of formula_4 evaluated at 2.
From these functions we define the Grzegorczyk hierarchy. formula_5, the "n"-th set in the hierarchy, contains the following functions:
In other words, formula_5 is the closure of set formula_12 with respect to function composition and limited recursion (as defined above).
Properties.
These sets clearly form the hierarchy
formula_13
because they are closures over the formula_14's and formula_15.
They are strict subsets. In other words
formula_16
because the hyperoperation formula_17 is in formula_5 but not in formula_18.
Notably, both the function formula_24 and the characteristic function of the predicate formula_25 from the Kleene normal form theorem are definable in a way such that they lie at level formula_19 of the Grzegorczyk hierarchy. This implies in particular that every recursively enumerable set is enumerable by some formula_19-function.
Relation to primitive recursive functions.
The definition of formula_5 is the same as that of the primitive recursive functions, PR, except that recursion is "limited" (formula_9 for some "j" in formula_5) and the functions formula_26 are explicitly included in formula_5. Thus the Grzegorczyk hierarchy can be seen as a way to "limit" the power of primitive recursion to different levels.
It is clear from this fact that all functions in any level of the Grzegorczyk hierarchy are primitive recursive functions (i.e. formula_27) and thus:
formula_28
It can also be shown that all primitive recursive functions are in some level of the hierarchy, thus
formula_29
and the sets formula_30 partition the set of primitive recursive functions, PR.
Meyer and Ritchie introduced another hierarchy subdividing the primitive recursive functions, based on the nesting depth of loops needed to write a LOOP program that computes the function. For a natural number formula_31, let formula_32 denote the set of functions computable by a LOOP program with codice_0 and codice_1 commands nested no deeper than formula_31 levels. Fachini and Maggiolo-Schettini showed that formula_32 coincides with formula_33 for all integers formula_34.p.63
Extensions.
The Grzegorczyk hierarchy can be extended to transfinite ordinals. Such extensions define a fast-growing hierarchy. To do this, the generating functions formula_35 must be recursively defined for limit ordinals (note they have already been recursively defined for successor ordinals by the relation formula_36). If there is a standard way of defining a "fundamental sequence" formula_37, whose limit ordinal is formula_38, then the generating functions can be defined formula_39. However, this definition depends upon a standard way of defining the fundamental sequence. suggests a standard way for all ordinals "α" < ε0.
The original extension was due to Martin Löb and Stan S. Wainer and is sometimes called the Löb–Wainer hierarchy.
Notes.
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References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": " \n\\begin{array}{lcl}\nE_0(x,y) & = & x + y \\\\\nE_1(x) & = & x^2 + 2 \\\\\nE_{n+2}(0) & = & 2 \\\\\nE_{n+2}(x+1) & = & E_{n+1}(E_{n+2}(x)) \\\\\n\\end{array}\n"
},
{
"math_id": 1,
"text": "E_0"
},
{
"math_id": 2,
"text": "E_1"
},
{
"math_id": 3,
"text": "E_n(x)=E^{x}_{n-1}(2)"
},
{
"math_id": 4,
"text": "E_{n-1}"
},
{
"math_id": 5,
"text": "\\mathcal{E}^n"
},
{
"math_id": 6,
"text": " p_i^m(t_1, t_2, \\dots, t_m) = t_i "
},
{
"math_id": 7,
"text": " f(\\bar{u}) = h(g_1(\\bar{u}), g_2(\\bar{u}), \\dots, g_m(\\bar{u})) "
},
{
"math_id": 8,
"text": "\\bar{u}"
},
{
"math_id": 9,
"text": "f(t, \\bar{u}) \\leq j(t, \\bar{u})"
},
{
"math_id": 10,
"text": "f(0, \\bar{u}) = g(\\bar{u})"
},
{
"math_id": 11,
"text": "f(t+1, \\bar{u}) = h(t,\\bar{u},f(t,\\bar{u}))"
},
{
"math_id": 12,
"text": "B_n = \\{Z, S, (p_i^m)_{i \\le m}, E_k : k < n\\}"
},
{
"math_id": 13,
"text": " \\mathcal{E}^0 \\subseteq \\mathcal{E}^1 \\subseteq \\mathcal{E}^2 \\subseteq \\cdots "
},
{
"math_id": 14,
"text": "B_n"
},
{
"math_id": 15,
"text": " B_0 \\subseteq B_1 \\subseteq B_2 \\subseteq \\cdots"
},
{
"math_id": 16,
"text": " \\mathcal{E}^0 \\subsetneq \\mathcal{E}^1 \\subsetneq \\mathcal{E}^2 \\subsetneq \\cdots "
},
{
"math_id": 17,
"text": "H_n"
},
{
"math_id": 18,
"text": "\\mathcal{E}^{n-1}"
},
{
"math_id": 19,
"text": "\\mathcal{E}^0"
},
{
"math_id": 20,
"text": "\\mathcal{E}^1"
},
{
"math_id": 21,
"text": "\\mathcal{E}^2"
},
{
"math_id": 22,
"text": "\\mathcal{E}^3"
},
{
"math_id": 23,
"text": "\\mathcal{E}^4"
},
{
"math_id": 24,
"text": "U"
},
{
"math_id": 25,
"text": "T"
},
{
"math_id": 26,
"text": "(E_k)_{k<n}"
},
{
"math_id": 27,
"text": " \\mathcal{E}^n \\subseteq \\mathsf{PR} "
},
{
"math_id": 28,
"text": " \\bigcup_n{\\mathcal{E}^n} \\subseteq \\mathsf{PR} "
},
{
"math_id": 29,
"text": " \\bigcup_n{\\mathcal{E}^n} = \\mathsf{PR} "
},
{
"math_id": 30,
"text": " \\mathcal{E}^0, \\mathcal{E}^1 - \\mathcal{E}^0, \\mathcal{E}^2 - \\mathcal{E}^1, \\dots, \\mathcal{E}^n - \\mathcal{E}^{n-1}, \\dots "
},
{
"math_id": 31,
"text": "i"
},
{
"math_id": 32,
"text": "\\mathcal{L}_i"
},
{
"math_id": 33,
"text": "\\mathcal{E}_{i+1}"
},
{
"math_id": 34,
"text": "i>1"
},
{
"math_id": 35,
"text": "E_\\alpha"
},
{
"math_id": 36,
"text": " E_{\\alpha+1}(n) = E_\\alpha^n(2) "
},
{
"math_id": 37,
"text": "\\lambda_m"
},
{
"math_id": 38,
"text": "\\lambda"
},
{
"math_id": 39,
"text": " E_\\lambda(n) = E_{\\lambda_n}(n) "
}
] |
https://en.wikipedia.org/wiki?curid=14334415
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14334444
|
Galactarate dehydratase
|
The enzyme galactarate dehydratase (EC 4.2.1.42) catalyzes the chemical reaction
-galactarate formula_0 5-dehydro-4-deoxy--glucarate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -galactarate hydro-lyase (5-dehydro-4-deoxy--glucarate-forming). This enzyme is also called -galactarate hydro-lyase. This enzyme participates in ascorbate and aldarate metabolism.
References.
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14334444
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14334671
|
Galactonate dehydratase
|
The enzyme galactonate dehydratase (EC 4.2.1.6) catalyzes the chemical reaction
-galactonate formula_0 2-dehydro-3-deoxy--galactonate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -galactonate hydro-lyase (2-dehydro-3-deoxy--alactonate-forming). Other names in common use include -galactonate dehydrase, -galactonate dehydratase, and -galactonate hydro-lyase. This enzyme participates in galactose metabolism.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14334671
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14334698
|
GDP-mannose 4,6-dehydratase
|
The enzyme GDP-mannose 4,6-dehydratase (EC 4.2.1.47) catalyzes the chemical reaction
GDP-mannose formula_0 GDP-4-dehydro-6-deoxy--mannose + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is GDP-mannose 4,6-hydro-lyase (GDP-4-dehydro-6-deoxy--mannose-forming). Other names in common use include guanosine 5'-diphosphate--mannose oxidoreductase, guanosine diphosphomannose oxidoreductase, guanosine diphosphomannose 4,6-dehydratase, GDP--mannose dehydratase, GDP--mannose 4,6-dehydratase, Gmd, and GDP-mannose 4,6-hydro-lyase. This enzyme participates in fructose and mannose metabolism. It employs one cofactor, NAD+.
GDP-Mannose 4, 6-Dehydratase Reaction.
The enzyme GDP-Mannose 4, 6-Dehydratase is in the lyase family of enzymes, specifically the hydro-lyases. Other names in use include guanosine 5'-diphosphate-D-mannose oxidoreductase, guanosine diphosphomannose oxidoreductase, guanosine diphosphomannose 4,6-dehydratase, GDP-D-mannose dehydratase, GDP-D-mannose 4,6-dehydratase, GMD, and GDP-mannose 4,6-hydro-lyase. The enzyme is a part of the GDP-Fucose de novo synthesis pathway and catalyzes the first step in the process that gives us GDP-Fucose which is essential for the transfer of Fucose sugars. Its primary structure contains 372 amino acids. This is an essential enzyme in that fucose plays a major role in cell immunity and signaling. Currently GDP-Mannose 4, 6-Dehydratase is not the target of any available drugs, however it is being experimentally targeted with the drug Guanosine-5'-Diphosphate. The chemical reaction of GDP-Mannose 4, 6-Dehydratase is as shown:
GDP-mannose ↔ GDP-4-dehydro-6-deoxy-D-mannose + H2O
Factors In The Reaction.
The enzymes substrate, what the enzyme is acting on, is the GDP-Mannose substance. No other substrates are use this enzyme for reactions.
When the enzyme undergoes its catalyzing process the main product is gets is when it converts GDP-mannose to GDP-4-dehydro-6-deoxy-D-mannose which is then subsequently converted to GDP-Fucose which is crucial for the body to process correctly. It acts as an intermediate step between GDP-Mannose and GDP-Fucose.
In the reaction that the enzyme uses it requires only one cofactor, a compound required for activation, which is NADP(+) however it is uncertain if this compound truly activates the enzyme.
GDP-Fucose is an allosteric inhibitor of the enzyme.
GDP-Fucose Biosynthesis Pathway.
The enzyme GDP-Mannose 4, 6-Dehydratase is only present in one pathway that we know of. This pathway is the GDP-mannose-dependent de novo pathway which provides most of the bodies GDP-Fucose whereas minor amounts come from fucose salvaging in the body.
In the pathway the enzyme is in an intermediate step that converts GDP-Mannose to GDP-4-dehydro-6-deoxy-D-mannose which is then converted into GDP-Fucose which is absolutely crucial to the body. The product of this pathway is fucosyltransferases which is then used in a different pathway that creates fucosylated glycans which is used for cell signaling and immunity in the body. Fucose is a deoxyhexose that is present in a wide variety of organisms. In most mammals, fucose-containing glycans have important roles in blood transfusion reactions, selectin-mediated leukocyte-endothelial adhesion, host-microbe interactions, and numerous ontogenic events. Along with those the body uses fucose as signaling branches of a cell and also as identification systems in immunity. However the enzyme only works at its top levels under normal body conditions. Increased pH or heat could severely denature the protein causing the enzyme to malfunction.
GDP-Mannose 4, 6-dehydratase Structure.
The enzyme contains four different subunits. Here is a link for a 3-D view of the enzyme http://www.rcsb.org/pdb/explore/jmol.do?structureId=1RPN&bionumber=1
Structural studies.
As of late 2007, 5 structures have been solved for this class of enzymes, with PDB accession codes 1DB3, 1N7G, 1N7H, 1RPN, and 1T2A.
References.
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14334698
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14334721
|
Germacrene-A synthase
|
The enzyme germacrene-A synthase (EC 4.2.3.23) catalyzes the chemical reaction
(2"E",6"E")-farnesyl diphosphate formula_0 (+)-("R")-gemacrene A + diphosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is (2"E",6"E")-farnesyl-diphosphate diphosphate-lyase [(+)-("R")-germacrene-A-forming]. Other names in common use include germacrene A synthase, (+)-germacrene A synthase, (+)-(10"R")-germacrene A synthase, GAS, 2-"trans",6-"trans"-farnesyl-diphosphate diphosphate-lyase, (germacrene-A-forming).
References.
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14334721
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14334743
|
Glucarate dehydratase
|
The enzyme glucarate dehydratase (EC 4.2.1.40) catalyzes the chemical reaction
-glucarate formula_0 5-dehydro-4-deoxy--glucarate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -glucarate hydro-lyase (5-dehydro-4-deoxy--glucarate-forming). Other names in common use include -glucarate dehydratase, and -glucarate hydro-lyase. This enzyme participates in ascorbate and aldarate metabolism.
Structural studies.
As of late 2007, 7 structures have been solved for this class of enzymes, with PDB accession codes 1BQG, 1EC7, 1EC8, 1EC9, 1ECQ, 1JCT, and 1JDF.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334743
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14334767
|
Gluconate dehydratase
|
Class of enzymes
The enzyme gluconate dehydratase (EC 4.2.1.39) catalyzes the chemical reaction
-gluconate formula_0 2-dehydro-3-deoxy--gluconate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -gluconate hydro-lyase (2-dehydro-3-deoxy-D-gluconate-forming). Other names in common use include -gluconate dehydratase, and -gluconate hydro-lyase. This enzyme participates in the pentose phosphate pathway.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 1QJ4.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334767
|
14334827
|
Glycerol dehydratase
|
Class of enzymes
In enzymology, a glycerol dehydratase (EC 4.2.1.30) catalyzes the chemical reaction
glycerol formula_0 3-hydroxypropanal + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is glycerol hydro-lyase (3-hydroxypropanol-forming). Other names in common use include glycerol dehydrase, and glycerol hydro-lyase. This enzyme participates in glycerolipid metabolism. It employs one cofactor, cobalamin.
Structural studies.
As of late 2007, two structures have been solved for this class of enzymes, with PDB accession codes 1IWP and 1MMF.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14334827
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14335197
|
Homoaconitate hydratase
|
Enzyme
The enzyme homoaconitate hydratase (EC 4.2.1.36) catalyzes the chemical reaction
(1"R",2"S")-1-hydroxybutane-1,2,4-tricarboxylate formula_0 ("Z")-but-1-ene-1,2,4-tricarboxylate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is (1"R",2"S")-1-hydroxybutane-1,2,4-tricarboxylate hydro-lyase [("Z")-but-1-ene-1,2,4-tricarboxylate-forming]. Other names in common use include homoaconitase, "cis"-homoaconitase, HACN, Lys4, LysF, and 2-hydroxybutane-1,2,4-tricarboxylate hydro-lyase (incorrect). This enzyme participates in lysine biosynthesis.
References.
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14335197
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14335245
|
Hydroperoxide dehydratase
|
The enzyme hydroperoxide dehydratase (EC 4.2.1.92) catalyzes the chemical reaction
(9"Z",11"E",14"Z")-(13"S")-hydroperoxyoctadeca-9,11,14-trienoate formula_0 (9"Z")-(13"S")-12,13-epoxyoctadeca-9,11-dienoate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is (9"Z",11"E",14"Z")-(13"S")-hydroperoxyoctadeca-9,11,14-trienoate 12,13-hydro-lyase [(9"Z")-(13"S")-12,13-epoxyoctadeca-9,11-dienoate-forming]. Other names in common use include hydroperoxide isomerase, linoleate hydroperoxide isomerase, linoleic acid hydroperoxide isomerase, HPI, (9"Z",11"E",14"Z")-(13"S")-hydroperoxyoctadeca-9,11,14-trienoate, and 12,13-hydro-lyase.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 1U5U.
References.
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[
{
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14335262
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Imidazoleglycerol-phosphate dehydratase
|
The enzyme imidazoleglycerol-phosphate dehydratase (EC 4.2.1.19) catalyzes the chemical reaction
-erythro-1-(imidazol-4-yl)glycerol 3-phosphate formula_0 3-(imidazol-4-yl)-2-oxopropyl phosphate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -"erythro"-1-(imidazol-4-yl)glycerol-3-phosphate hydro-lyase [3-(imidazol-4-yl)-2-oxopropyl-phosphate-forming]. Other names in common use include IGP dehydratase, and -"erythro"-1-(imidazol-4-yl)glycerol 3-phosphate hydro-lyase. This enzyme participates in histidine metabolism as it is involved in the 6th step of histidine biosynthesis as part of a nine step cyclical pathway.
There are two isoforms of IGPD; IGPD1 and IGPD2. The different isoforms are highly conserved with only 8 amino acids differing between them. These subtle differences however affect their activity but as yet it is unknown how.
In most organisms IGPD is a monofunctional protein of about 22 to 29 kD. In some bacteria such as "Escherichia coli", it is the C-terminal domain of a bifunctional protein that include a histidinol-phosphatase domain. In "E. coli", this is the protein encoded by the "hisB" gene.
Inhibition.
Certain compounds that inhibit IGPD have been used as herbicides as animals do not have this protein. One of these inhibitors is 3-Amino-1,2,4-triazole (3-AT), which has also been used as a competitive inhibitor of the product of the yeast HIS3 gene (another IGPD), e.g. in the yeast two-hybrid system.
Structural studies.
As of late 2007, 3 structures have been solved for this class of enzymes, with PDB accession codes 1RHY, 2AE8, and 2F1D.
References.
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[
{
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https://en.wikipedia.org/wiki?curid=14335262
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14335329
|
Isohexenylglutaconyl-CoA hydratase
|
The enzyme isohexenylglutaconyl-CoA hydratase (EC 4.2.1.57) catalyzes the chemical reaction
3-hydroxy-3-(4-methylpent-3-en-1-yl)glutaryl-CoA formula_0 3-(4-methylpent-3-en-1-yl)pent-2-enedioyl-CoA + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 3-hydroxy-3-(4-methylpent-3-en-1-yl)glutaryl-CoA hydro-lyase [3-(4-methylpent-3-en-1-yl)pent-2-enedioyl-CoA-forming]. Other names in common use include 3-hydroxy-3-isohexenylglutaryl-CoA-hydrolase, isohexenylglutaconyl coenzyme A hydratase, β-isohexenylglutaconyl-CoA-hydratase, and 3-hydroxy-3-(4-methylpent-3-en-1-yl)glutaryl-CoA hydro-lyase.
References.
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{
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https://en.wikipedia.org/wiki?curid=14335329
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14335346
|
Isoprene synthase
|
The enzyme isoprene synthase (EC 4.2.3.27) catalyzes the chemical reaction
prenyl pyrophosphate formula_0 isoprene + diphosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is prenyl-diphosphate diphosphate-lyase (isoprene-forming). Other names in common use include ISPC, and ISPS.
References.
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{
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https://en.wikipedia.org/wiki?curid=14335346
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14335363
|
Itaconyl-CoA hydratase
|
The enzyme itaconyl-CoA hydratase (EC 4.2.1.56) catalyzes the chemical reaction
citramalyl-CoA formula_0 itaconyl-CoA + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is citramalyl-CoA hydro-lyase (itaconyl-CoA-forming). Other names in common use include itaconyl coenzyme A hydratase, and citramalyl-CoA hydro-lyase. This enzyme participates in c5-branched dibasic acid metabolism.
References.
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{
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https://en.wikipedia.org/wiki?curid=14335363
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14335390
|
Kievitone hydratase
|
The enzyme kievitone hydratase (EC 4.2.1.95) catalyzes the chemical reaction
kievitone hydrate formula_0 kievitone + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is kievitone-hydrate hydro-lyase (kievitone-forming). Other names in common use include KHase, and kievitone-hydrate hydro-lyase.
References.
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{
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https://en.wikipedia.org/wiki?curid=14335390
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14335415
|
Lactoyl-CoA dehydratase
|
The enzyme lactoyl-CoA dehydratase (EC 4.2.1.54) catalyzes the chemical reaction
lactoyl-CoA formula_0 acryloyl-CoA + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is lactoyl-CoA hydro-lyase (acryloyl-CoA-forming). Other names in common use include lactoyl coenzyme A dehydratase, lactyl-coenzyme A dehydrase, lactyl CoA dehydratase, acrylyl coenzyme A hydratase, and lactoyl-CoA hydro-lyase. This enzyme participates in propanoate metabolism and styrene degradation.
References.
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{
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https://en.wikipedia.org/wiki?curid=14335415
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14335429
|
L-arabinonate dehydratase
|
The enzyme -arabinonate dehydratase (EC 4.2.1.25) catalyzes the chemical reaction
-arabinonate formula_0 2-dehydro-3-deoxy--arabinonate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -arabinonate hydro-lyase (2-dehydro-3-deoxy--arabinonate-forming). Other names in common use include -arabonate dehydrase, -arabonate dehydratase, and -arabinonate hydro-lyase. This enzyme participates in ascorbate and aldarate metabolism.
References.
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{
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https://en.wikipedia.org/wiki?curid=14335429
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14335477
|
L-fuconate dehydratase
|
The enzyme -fuconate dehydratase (EC 4.2.1.68) catalyzes the chemical reaction
-fuconate formula_0 2-dehydro-3-deoxy--fuconate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -fuconate hydro-lyase (2-dehydro-3-deoxy--fuconate-forming). This enzyme is also called -fuconate hydro-lyase.
References.
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{
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https://en.wikipedia.org/wiki?curid=14335477
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14335499
|
Long-chain-enoyl-CoA hydratase
|
The enzyme long-chain-enoyl-CoA hydratase (EC 4.2.1.74) catalyzes the chemical reaction
(3"S")-3-hydroxyacyl-CoA formula_0 "trans"-2-enoyl-CoA + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is long-chain-(3"S")-3-hydroxyacyl-CoA hydro-lyase. This enzyme is also called long-chain enoyl coenzyme A hydratase. This enzyme participates in fatty acid elongation in mitochondria and fatty acid metabolism.
References.
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14335527
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L-rhamnonate dehydratase
|
The enzyme rhamnonate dehydratase (EC 4.2.1.90) catalyzes the chemical reaction
-rhamnonate formula_0 2-dehydro-3-deoxy-L-rhamnonate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -rhamnonate hydro-lyase (2-dehydro-3-deoxy--rhamnonate-forming). This enzyme is also called rhamnonate hydro-lyase. This enzyme participates in fructose and mannose metabolism.
Structural studies.
As of late 2007, 4 structures have been solved for this class of enzymes, with PDB accession codes 2GSH, 2OZ3, 2P0I, and 2P3Z.
References.
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14335547
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L(+)-tartrate dehydratase
|
The enzyme (+)-tartrate dehydratase (EC 4.2.1.32) catalyzes the chemical reaction
("R,R")-tartrate formula_0 oxaloacetate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is ("R,R")-tartrate hydro-lyase (oxaloacetate-forming). Other names in common use include tartrate dehydratase, tartaric acid dehydrase, -tartrate dehydratase, -(+)-tartaric acid dehydratase, and ("R,R")-tartrate hydro-lyase. This enzyme participates in glyoxylate and dicarboxylate metabolism. It has 2 cofactors: iron, and Thiol.
References.
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14335566
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Maleate hydratase
|
The enzyme maleate hydratase (EC 4.2.1.31) catalyzes the chemical reaction
("R")-malate formula_0 maleate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is ("R")-malate hydro-lyase (maleate-forming). Other names in common use include -malate hydro-lyase, malease, and ("R")-malate hydro-lyase. This enzyme participates in butanoate metabolism.
References.
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14335590
|
Mannonate dehydratase
|
The enzyme mannonate dehydratase (EC 4.2.1.8) catalyzes the chemical reaction
-mannonate formula_0 2-dehydro-3-deoxy--gluconate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -mannonate hydro-lyase (2-dehydro-3-deoxy--gluconate-forming). Other names in common use include mannonic hydrolase, mannonate hydrolyase, altronic hydro-lyase, altronate hydrolase, -mannonate hydrolyase, and -mannonate hydro-lyase. This enzyme participates in pentose and glucuronate interconversions.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 1TZ9.
References.
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14335614
|
Methylglyoxal synthase
|
Class of enzymes
The enzyme methylglyoxal synthase (EC 4.2.3.3) catalyzes the chemical reaction
glycerone phosphate formula_0 2-oxopropanal + phosphate
Attempts to observe reversibility of this reaction have been unsuccessful.
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is glycerone-phosphate phosphate-lyase (methylglyoxal-forming). Other names in common use include methylglyoxal synthetase, and glycerone-phosphate phospho-lyase. This enzyme participates in pyruvate metabolism and is constitutively expressed.
Structural studies.
As of late 2007, 7 structures have been solved for this class of enzymes, with PDB accession codes 1B93, 1EGH, 1IK4, 1S89, 1S8A, 1VMD, and 1WO8.
Methylglyoxal synthase (MGS) is a 152-amino acid homohexamer that has a molecular weight of approximately 67,000 kD. The total solvent-accessible surface area of the MGS homohexamer is 18,510 square Angstroms, roughly 40% of the total possible surface area if the subunits were separated. Each monomer consists of five alpha helices surrounding five beta sheets. Of these, two antiparallel beta sheets and one alpha helix are located in a subdomain where the N-terminus and C-terminus are in close juxtaposition. The homohexamer exhibits a threefold axis perpendicular to a twofold axis. Within the wide V-groove, there are twelve hydrogen bonds and six salt bridges between the monomers in the presence of phosphate binding. In the absence of phosphate binding, ten hydrogen bonds and two salt bridges hold the monomers together. At the peak interfaces, ten hydrogen bonds and no salt bridges connect the monomers regardless of phosphate binding.
The MGS homohexamer is slightly asymmetrical. All three monomers within the asymmetrical region contain a formate molecule within their respective actives sites. Only one of the monomers within the asymmetrical region is additionally bound to a phosphate.
The active site contains many conserved residues for function (Asp, His, Thr) and structure (Gly, Pro). Inorganic phosphate interacts with Lys23, Thr45, Thr47, Thr48, and Gly66. Formate interacts with His19, His98, and Asp71. The active site is exposed to the solvent via a perpendicular channel that consists of Arg150, Tyr146, Asp20, Pro67, His98, and His19.
Although mechanistically similar to triosephosphate isomerase (TIM), MGS contains widely dissimilar protein folding that prevents structural alignment with TIM which suggests convergent evolution of their chemical reactions. However, Asp71 in MGS may act similarly to the Glu165, the catalytic base in TIM. Additionally, His19 and His98 may perform the role of the electrophilic catalyst similar to His95 in TIM. CheB methylesterase has the highest structural similarity with MGS.
Mechanism.
Methylglyoxal synthase is highly specific for DHAP with Km 0.47mM at its optimal pH of 7.5. Contrary to early reports, the purified enzyme does not react with other glycolytic metabolites such as glyceraldehyde-3-phosphate or fructose 1,6-diphosphate. The mechanism of MGS is similar to that of TIM; both enzymes react with dihydroxyacetone phosphate to form an ene-diol phosphate intermediate as the first step of their reaction pathways. However, the second step involves the elimination of phosphate to form methylglyoxal instead of reprotonation to form glyceraldehyde-3-phosphate. The overall reaction is characterized as an intramolecular oxidation-reduction followed by a dephosphorylation. The C-3 of DHAP is oxidized to an aldehyde, while C-1, which bears the phosphate ester, is dephosphorylated and reduced to a methyl group. MGS does not require the use of metal ions or a Schiff base as part of catalysis.
The enzyme first uses Asp71 to specifically abstract the pro-S hydrogen from the C-3 of DHAP to form an ene-diol(ate)-enzyme intermediate, unlike the abstraction of C-3 pro-R hydrogen in TIM by Glu165. A second base deprotonates the hydroxyl group, leading to the collapse of the en-diol(ate) to form the 2-hydroxy 2-propenal enol intermediate along with dissociation of inorganic phosphate (–OPO3) through the cleavage of a C-O bond rather than an O-P bond. This deprotonation is catalyzed by either Asp71 or Asp101. Protonation of the methylene group of the enolate is non-stereospecific. The reaction products are released sequentially with methylglyoxal leaving before the inorganic phosphate. MGS is responsible for the racemic mixture of lactate in cells; the production of methylglyoxal and its further metabolism yields L-(+)-lactate and D-(-)-lactate, while deletion of the MGS gene leads to observation of optically pure D-(-)-lactate.
Regulation.
Binding of phosphate to the enzyme increases its cooperativity via structural changes that open three DHAP-binding sites. At higher concentrations, however, phosphate acts as a competitive allosteric inhibitor to turn off enzymatic activity, suggesting that diversion to methylglyoxal production occurs under conditions of phosphate starvation. This inhibition is believed to be caused by bound phosphate and formate mimicking the reaction intermediates (enolate and inorganic phosphate). Additionally, phosphate binding causes rotation of threonine residues that close the active site.
Ser55 in the active site of MGS is responsible for discriminating the binding of an inorganic phosphate from the phosphate group of the substrate (DHAP) by hydrogen bonding and undergoing a conformational change of location. Transmittance of the allosteric signal is determined to pass through Arg97 and Val101 because none of these are located in the active site, yet mutations at these residues negates any inhibitory effect of phosphate binding. Pro82 is necessary to transmit the signal from one subunit to the Ar97 and Val101 of another subunit. The induction of salt-bridge formation between Asp10 and Arg140 is an additional inter-subunit signal transmission pathway for organisms that retain the last 10 amino acids of the monomer peptide. The final acceptor of this allosteric signal is the catalytic Gly56 within the active site.
Inorganic pyrophosphate has 95% the ability of phosphate in inhibiting MGS. 3-phosphoglycerate and phosphoenolpyruvate also have 50% and 70% inhibition, respectively. 2-phosphoglycolate also acts as a competitive inhibitor by mimicking the ene-diolate intermediate. ATP has been shown to have weak inhibition in some bacterial strains. The reaction product, methylglyoxal, does not exhibit any feedback inhibition on MGS.
Biological function.
Methylglyoxal synthase provides an alternative catabolic pathway for triose phosphates created in glycolysis. It has activity levels similar to that of glyceraldehyde-3-phosphate dehydrogenase from glycolysis, suggesting an interplay between the two enzymes in the breakdown of triose phosphates. Indeed, MGS is strongly inhibited by phosphate concentrations that are close to the Km of phosphate serving as substrate for glyceraldehyde-3-phosphate dehydrogenase and is, therefore, inactive at normal intracellular conditions. Triose phosphate catabolism switches over to MGS when phosphate concentrations are too low for glyceraldehyde-3-phosphate dehydrogenase activity.
In situations when glycolysis is restricted by phosphate starvation, the switch to MGS serves to release phosphate from glycolytic metabolites for glyceraldehyde-3-phosphate dehydrogenase and to produce methylglyoxal, which is converted to pyruvate via lactate with the uncoupling of ATP synthesis. This interplay between the two enzymes allows the cell to shift triose catabolism between the formation of 1,3-bisphosphoglycerate and methylglyoxal based on available phosphates.
Other applications.
For fuel ethanol production, complete metabolism of complex combinations of sugars in "E. coli" by synthetic biocatalysts is necessary. Deletion of the methylglyoxal synthase gene in "E. coli" increases fermentation rate of ethanogenic E. coli by promoting the co-metabolism of sugar mixtures containing the five principal sugars found in biomass (glucose, xylose, arabinose, galactose, and mannose). This suggests that MGS production of methylglyoxal plays a role in controlling expression of sugar-specific transporters and catabolic genes in native E.coli.
MGS also has industrial importance in the production of lactate, hydroxyacetone (acetol), and 1,2-propandiol. Introduction of the MGS gene in bacteria that natively lack MGS increased useful production of 1,2-propandiol by 141%.
For biotechnological and synthetic applications, phosphate binding helps to stabilize and protect the enzyme against cold- and heat-induced denaturation. His-His interaction via the insertion of one histidine residue between Arg22 and His23 is also known to confer greater thermostability by increasing its half-life 4.6-fold.
References.
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Further reading.
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14335634
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Methylthioribulose 1-phosphate dehydratase
|
The enzyme methylthioribulose 1-phosphate dehydratase (EC .2.1.109) catalyzes the chemical reaction
5-(methylsulfanyl)-)ribulose 1-phosphate formula_0 5-(methylthio)-2,3-dioxopentyl phosphate + H2
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 5-methyl-5-thio-D-ribulose-1-phosphate 4-hydro-lyase [5-(methylthio)-2,3-dioxopentyl-phosphate-forming]. Other names in common use include 1-PMT-ribulose dehydratase, and "S"-methyl-5-thio-D-ribulose-1-phosphate hydro-lyase. This enzyme participates in methionine metabolism.
References.
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14335651
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Myo-inosose-2 dehydratase
|
The enzyme "myo"-inosose-2 dehydratase (EC 4.2.1.44) catalyzes the chemical reaction
2,4,6/3,5-pentahydroxycyclohexanone formula_0 3,5/4-trihydroxycyclohexa-1,2-dione + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 2,4,6/3,5-pentahydroxycyclohexanone hydro-lyase (3,5/4-trihydroxycyclohexa-1,2-dione-forming). Other names in common use include inosose 2,3-dehydratase, ketoinositol dehydratase, and 2,4,6/3,5-pentahydroxycyclohexanone hydro-lyase. This enzyme participates in inositol phosphate metabolism. It has 2 cofactors: manganese, and Cobalt.
References.
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https://en.wikipedia.org/wiki?curid=14335651
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14335675
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Myrcene synthase
|
The enzyme myrcene synthase (EC 4.2.3.15) catalyzes the chemical reaction
geranyl diphosphate formula_0 myrcene + diphosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is geranyl-diphosphate diphosphate-lyase (myrcene-forming). This enzyme participates in monoterpenoid biosynthesis.
References.
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14335699
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Octopamine dehydratase
|
The enzyme octopamine dehydratase (EC 4.2.1.87) catalyzes the chemical reaction
1-(4-hydroxyphenyl)-2-aminoethanol formula_0 (4-hydroxyphenyl)acetaldehyde + NH3
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 1-(4-hydroxyphenyl)-2-aminoethanol hydro-lyase [deaminating (4-hydroxyphenyl)acetaldehyde-forming]. Other names in common use include octopamine hydrolyase, and octopamine hydro-lyase (deaminating).
References.
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143357
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Medical ultrasound
|
Diagnostic and therapeutic technique
Medical ultrasound includes diagnostic techniques (mainly imaging techniques) using ultrasound, as well as therapeutic applications of ultrasound. In diagnosis, it is used to create an image of internal body structures such as tendons, muscles, joints, blood vessels, and internal organs, to measure some characteristics (e.g. distances and velocities) or to generate an informative audible sound. The usage of ultrasound to produce visual images for medicine is called medical ultrasonography or simply sonography, or echography. The practice of examining pregnant women using ultrasound is called obstetric ultrasonography, and was an early development of clinical ultrasonography. The machine used is called an ultrasound machine, a sonograph or an echograph. The visual image formed using this technique is called an ultrasonogram, a sonogram or an echogram.
Ultrasound is composed of sound waves with frequencies greater than 20,000 Hz, which is by approximation the upper threshold of human hearing. Ultrasonic images, also known as sonograms, are created by sending pulses of ultrasound into tissue using a probe. The ultrasound pulses echo off tissues with different reflection properties and are returned to the probe which records and displays them as an image.
A general-purpose ultrasonic transducer may be used for most imaging purposes but some situations may require the use of a specialized transducer. Most ultrasound examination is done using a transducer on the surface of the body, but improved visualization is often possible if a transducer can be placed inside the body. For this purpose, special-use transducers, including transvaginal, endorectal, and transesophageal transducers are commonly employed. At the extreme, very small transducers can be mounted on small diameter catheters and placed within blood vessels to image the walls and disease of those vessels.
Types.
The imaging mode refers to probe and machine settings that result in specific dimensions of the ultrasound image.
Several modes of ultrasound are used in medical imaging:
Most machines convert two-way time to imaging depth using as assumed speed of sound of 1540 m/s. As the actual speed of sound varies greatly in different tissue types, an ultrasound image is therefore not a true tomographic representation of the body.
Three-dimensional imaging is done by combining B-mode images, using dedicated rotating or stationary probes. This has also been referred to as C-mode.
An imaging technique refers to a method of signal generation and processing that results in a specific application.
Most imaging techniques are operating in B-mode.
*B-flow is an imaging technique that digitally highlights moving reflectors (mainly red blood cells) while suppressing the signals from the surrounding stationary tissue. It aims to visualize flowing blood and surrounding stationary tissues simultaneously. It is thus an alternative or complement to Doppler ultrasonography in visualizing blood flow.
Therapeutic ultrasound aimed at a specific tumor or calculus is not an imaging mode. However, for positioning a treatment probe to focus on a specific region of interest, A-mode and B-mode are typically used, often during treatment.
Advantages and drawbacks.
Compared to other medical imaging modalities, ultrasound has several advantages. It provides images in real-time, is portable, and can consequently be brought to the bedside. It is substantially lower in cost than other imaging strategies. Drawbacks include various limits on its field of view, the need for patient cooperation, dependence on patient physique, difficulty imaging structures obscured by bone, air or gases, and the necessity of a skilled operator, usually with professional training.
Uses.
Sonography (ultrasonography) is widely used in medicine. It is possible to perform both diagnosis and therapeutic procedures, using ultrasound to guide interventional procedures such as biopsies or to drain collections of fluid, which can be both diagnostic and therapeutic. Sonographers are medical professionals who perform scans which are traditionally interpreted by radiologists, physicians who specialize in the application and interpretation of medical imaging modalities, or by cardiologists in the case of cardiac ultrasonography (echocardiography). Sonography is effective for imaging soft tissues of the body. Superficial structures such as muscle, tendon, testis, breast, thyroid and parathyroid glands, and the neonatal brain are imaged at higher frequencies (7–18 MHz), which provide better linear (axial) and horizontal (lateral) resolution. Deeper structures such as liver and kidney are imaged at lower frequencies (1–6 MHz) with lower axial and lateral resolution as a price of deeper tissue penetration.
Anesthesiology.
In anesthesiology, ultrasound is commonly used to guide the placement of needles when injecting local anesthetic solutions in the proximity of nerves identified within the ultrasound image (nerve block). It is also used for vascular access such as cannulation of large central veins and for difficult arterial cannulation. Transcranial Doppler is frequently used by neuro-anesthesiologists for obtaining information about flow-velocity in the basal cerebral vessels.
Angiology (vascular).
In angiology or vascular medicine, duplex ultrasound (B Mode imaging combined with Doppler flow measurement) is used to diagnose arterial and venous disease. This is particularly important in potential neurologic problems, where carotid ultrasound is commonly used for assessing blood flow and potential or suspected stenosis in the carotid arteries, while transcranial Doppler is used for imaging flow in the intracerebral arteries.
Intravascular ultrasound ("IVUS") uses a specially designed catheter with a miniaturized ultrasound probe attached to its distal end, which is then threaded inside a blood vessel. The proximal end of the catheter is attached to computerized ultrasound equipment and allows the application of ultrasound technology, such as a piezoelectric transducer or capacitive micromachined ultrasonic transducer, to visualize the endothelium of blood vessels in living individuals.
In the case of the common and potentially, serious problem of blood clots in the deep veins of the leg, ultrasound plays a key diagnostic role, while ultrasonography of chronic venous insufficiency of the legs focuses on more superficial veins to assist with planning of suitable interventions to relieve symptoms or improve cosmetics.
Cardiology (heart).
Echocardiography is an essential tool in cardiology, assisting in evaluation of heart valve function, such as stenosis or insufficiency, strength of cardiac muscle contraction, and hypertrophy or dilatation of the main chambers. (ventricle and atrium)
Emergency medicine.
Point of care ultrasound has many applications in emergency medicine. These include differentiating cardiac from pulmonary causes of acute breathlessness, and the Focused Assessment with Sonography for Trauma (FAST) exam, extended to include assessment for significant hemoperitoneum or pericardial tamponade after trauma (EFAST). Other uses include assisting with differentiating causes of abdominal pain such as gallstones and kidney stones. Emergency Medicine Residency Programs have a substantial history of promoting the use of bedside ultrasound during physician training.
Gastroenterology/Colorectal surgery.
Both abdominal and endoanal ultrasound are frequently used in gastroenterology and colorectal surgery. In abdominal sonography, the major organs of the abdomen such as the pancreas, aorta, inferior vena cava, liver, gall bladder, bile ducts, kidneys, and spleen may be imaged. However, sound waves may be blocked by gas in the bowel and attenuated to differing degrees by fat, sometimes limiting diagnostic capabilities. The appendix can sometimes be seen when inflamed (e.g.: appendicitis) and ultrasound is the initial imaging choice, avoiding radiation if possible, although it frequently needs to be followed by other imaging methods such as CT. Endoanal ultrasound is used particularly in the investigation of anorectal symptoms such as fecal incontinence or obstructed defecation. It images the immediate perianal anatomy and is able to detect occult defects such as tearing of the anal sphincter.
Hepatology.
Ultrasonography of liver tumors allows for both detection and characterization.
Ultrasound imaging studies are often obtained during the evaluation process of Fatty liver disease. Ultrasonography reveals a "bright" liver with increased echogenicity. Pocket-sized ultrasound devices might be used as point-of-care screening tools to diagnose liver steatosis.
Gynecology and obstetrics.
Gynecologic ultrasonography examines female pelvic organs (specifically the uterus, ovaries, and fallopian tubes) as well as the bladder, adnexa, and pouch of Douglas. It uses transducers designed for approaches through the lower abdominal wall, curvilinear and sector, and specialty transducers such as transvaginal ultrasound.
Obstetrical sonography was originally developed in the late 1950s and 1960s by Sir Ian Donald and is commonly used during pregnancy to check the development and presentation of the fetus. It can be used to identify many conditions that could be potentially harmful to the mother and/or baby possibly remaining undiagnosed or with delayed diagnosis in the absence of sonography. It is currently believed that the risk of delayed diagnosis is greater than the small risk, if any, associated with undergoing an ultrasound scan. However, its use for non-medical purposes such as fetal "keepsake" videos and photos is discouraged.
Obstetric ultrasound is primarily used to:
According to the European Committee of Medical Ultrasound Safety (ECMUS)
<templatestyles src="Template:Blockquote/styles.css" />Ultrasonic examinations should only be performed by competent personnel who are trained and updated in safety matters. Ultrasound produces heating, pressure changes and mechanical disturbances in tissue. Diagnostic levels of ultrasound can produce temperature rises that are hazardous to sensitive organs and the embryo/fetus. Biological effects of non-thermal origin have been reported in animals but, to date, no such effects have been demonstrated in humans, except when a micro-bubble contrast agent is present.Nonetheless, care should be taken to use low power settings and avoid pulsed wave scanning of the fetal brain unless specifically indicated in high risk pregnancies.
Figures released for the period 2005–2006 by the UK Government (Department of Health) show that non-obstetric ultrasound examinations constituted more than 65% of the total number of ultrasound scans conducted.
Hemodynamics (blood circulation).
Blood velocity can be measured in various blood vessels, such as middle cerebral artery or descending aorta, by relatively inexpensive and low risk ultrasound Doppler probes attached to portable monitors. These provide non-invasive or transcutaneous (non-piercing) minimal invasive blood flow assessment. Common examples are transcranial Doppler, esophageal Doppler and suprasternal Doppler.
Otolaryngology (head and neck).
Most structures of the neck, including the thyroid and parathyroid glands, lymph nodes, and salivary glands, are well-visualized by high-frequency ultrasound with exceptional anatomic detail. Ultrasound is the preferred imaging modality for thyroid tumors and lesions, and its use is important in the evaluation, preoperative planning, and postoperative surveillance of patients with thyroid cancer. Many other benign and malignant conditions in the head and neck can be differentiated, evaluated, and managed with the help of diagnostic ultrasound and ultrasound-guided procedures.
Neonatology.
In neonatology, transcranial Doppler can be used for basic assessment of intracerebral structural abnormalities, suspected hemorrhage, ventriculomegaly or hydrocephalus and anoxic insults (periventricular leukomalacia). It can be performed through the soft spots in the skull of a newborn infant (Fontanelle) until these completely close at about 1 year of age by which time they have formed a virtually impenetrable acoustic barrier to ultrasound. The most common site for cranial ultrasound is the anterior fontanelle. The smaller the fontanelle, the more the image is compromised.
Lung ultrasound has been found to be useful in diagnosing common neonatal respiratory diseases such as transient tachypnea of the newborn, respiratory distress syndrome, congenital pneumonia, meconium aspiration syndrome, and pneumothorax. A neonatal lung ultrasound score, first described by Brat et al., has been found to highly correlate with oxygenation in the newborn.
Ophthalmology (<templatestyles src="Template:Visible anchor/styles.css" />eyes).
In ophthalmology and optometry, there are two major forms of eye exam using ultrasound:
Pulmonology (lungs).
Ultrasound is used to assess the lungs in a variety of settings including critical care, emergency medicine, trauma surgery, as well as general medicine. This imaging modality is used at the bedside or examination table to evaluate a number of different lung abnormalities as well as to guide procedures such as thoracentesis, (drainage of pleural fluid (effusion)), needle aspiration biopsy, and catheter placement. Although air present in the lungs does not allow good penetration of ultrasound waves, interpretation of specific artifacts created on the lung surface can be used to detect abnormalities.
Urinary tract.
Ultrasound is routinely used in urology to determine the amount of fluid retained in a patient's bladder. In a pelvic sonogram, images include the uterus and ovaries or urinary bladder in females. In males, a sonogram will provide information about the bladder, prostate, or testicles (for example to urgently distinguish epididymitis from testicular torsion). In young males, it is used to distinguish more benign testicular masses (varicocele or hydrocele) from testicular cancer, which is curable but must be treated to preserve health and fertility. There are two methods of performing pelvic sonography – externally or internally. The internal pelvic sonogram is performed either transvaginally (in a woman) or transrectally (in a man). Sonographic imaging of the pelvic floor can produce important diagnostic information regarding the precise relationship of abnormal structures with other pelvic organs and it represents a useful hint to treat patients with symptoms related to pelvic prolapse, double incontinence and obstructed defecation. It is also used to diagnose and, at higher frequencies, to treat (break up) kidney stones or kidney crystals (nephrolithiasis).
Penis and scrotum.
Scrotal ultrasonography is used in the evaluation of testicular pain, and can help identify solid masses.
Ultrasound is an excellent method for the study of the penis, such as indicated in trauma, priapism, erectile dysfunction or suspected Peyronie's disease.
Musculoskeletal.
Musculoskeletal ultrasound is used to examine tendons, muscles, nerves, ligaments, soft tissue masses, and bone surfaces.
It is helpful in diagnosing ligament sprains, muscles strains and joint pathology. It is an alternative or supplement to x-ray imaging in detecting fractures of the wrist, elbow and shoulder for patients up to 12 years (Fracture sonography).
Quantitative ultrasound is an adjunct musculoskeletal test for myopathic disease in children; estimates of lean body mass in adults; proxy measures of muscle quality (i.e., tissue composition) in older adults with sarcopenia
Ultrasound can also be used for needle guidance in muscle or joint injections, as in ultrasound-guided hip joint injection.
Kidneys.
In nephrology, ultrasonography of the kidneys is essential in the diagnosis and management of kidney-related diseases. The kidneys are easily examined, and most pathological changes are distinguishable with ultrasound. It is an accessible, versatile, relatively economic, and fast aid for decision-making in patients with renal symptoms and for guidance in renal intervention. Using B-mode imaging, assessment of renal anatomy is easily performed, and US is often used as image guidance for renal interventions. Furthermore, novel applications in renal US have been introduced with contrast-enhanced ultrasound (CEUS), elastography and fusion imaging. However, renal US has certain limitations, and other modalities, such as CT (CECT) and MRI, should be considered for supplementary imaging in assessing renal disease.
Venous access.
Intravenous access, for the collection of blood samples to assist in diagnosis or laboratory investigation including blood culture, or for administration of intravenous fluids for fluid maintenance of replacement or blood transfusion in sicker patients, is a common medical procedure. The need for intravenous access occurs in the outpatient laboratory, in the inpatient hospital units, and most critically in the Emergency Room and Intensive Care Unit. In many situations, intravenous access may be required repeatedly or over a significant time period. In these latter circumstances, a needle with an overlying catheter is introduced into the vein and the catheter is then inserted securely into the vein while the needle is withdrawn.
The chosen veins are most frequently selected from the arm, but in challenging situations, a deeper vein from the neck (external jugular vein) or upper arm (subclavian vein) may need to be used.
There are many reasons why the selection of a suitable vein may be problematic.
These include, but are not limited to, obesity, previous injury to veins from inflammatory reaction to previous 'blood draws', previous injury to veins from recreational drug use.
In these challenging situations, the insertion of a catheter into a vein has been greatly assisted by the use of ultrasound. The ultrasound unit may be 'cart-based' or 'handheld' using a linear transducer with a frequency of 10 to 15 megahertz. In most circumstances, choice of vein will be limited by the requirement that the vein is within 1.5 cms. from the skin surface.
The transducer may be placed longitudinally or transversely over the chosen vein.
Ultrasound training for intravenous cannulation is offered in most ultrasound training programs.
Mechanism.
The creation of an image from sound has three steps – transmitting a sound wave, receiving echoes, and interpreting those echoes.
Producing a sound wave.
A sound wave is typically produced by a piezoelectric transducer encased in a plastic housing. Strong, short electrical pulses from the ultrasound machine drive the transducer at the desired frequency. The frequencies can vary between 1 and 18 MHz, though frequencies up to 50–100 megahertz have been used experimentally in a technique known as biomicroscopy in special regions, such as the anterior chamber of the eye.
Older technology transducers focused their beam with physical lenses. Contemporary technology transducers use digital antenna array techniques (piezoelectric elements in the transducer produce echoes at different times) to enable the ultrasound machine to change the direction and depth of focus. Near the transducer, the width of the ultrasound beam almost equals to the width of the transducer, after reaching a distance from the transducer (near zone length or Fresnel zone), the beam width narrows to half of the transducer width, and after that the width increases (far zone length or Fraunhofer's zone), where the lateral resolution decreases. Therefore, the wider the transducer width and the higher the frequency of ultrasound, the longer the Fresnel zone, and the lateral resolution can be maintained at a greater depth from the transducer. Ultrasound waves travel in pulses. Therefore, a shorter pulse length requires higher bandwidth (greater number of frequencies) to constitute the ultrasound pulse.
As stated, the sound is focused either by the shape of the transducer, a lens in front of the transducer, or a complex set of control pulses from the ultrasound scanner, in the beamforming or spatial filtering technique. This focusing produces an arc-shaped sound wave from the face of the transducer. The wave travels into the body and comes into focus at a desired depth.
Materials on the face of the transducer enable the sound to be transmitted efficiently into the body (often a rubbery coating, a form of impedance matching). In addition, a water-based gel is placed between the patient's skin and the probe to facilitate ultrasound transmission into the body. This is because air causes total reflection of ultrasound; impeding the transmission of ultrasound into the body.
The sound wave is partially reflected from the layers between different tissues or scattered from smaller structures. Specifically, sound is reflected anywhere where there are acoustic impedance changes in the body: e.g. blood cells in blood plasma, small structures in organs, etc. Some of the reflections return to the transducer.
Receiving the echoes.
The return of the sound wave to the transducer results in the same process as sending the sound wave, in reverse. The returned sound wave vibrates the transducer and the transducer turns the vibrations into electrical pulses that travel to the ultrasonic scanner where they are processed and transformed into a digital image.
Forming the image.
To make an image, the ultrasound scanner must determine two characteristics from each received echo:
Once the ultrasonic scanner determines these two, it can locate which pixel in the image to illuminate and with what intensity.
Transforming the received signal into a digital image may be explained by using a blank spreadsheet as an analogy. First picture a long, flat transducer at the top of the sheet. Send pulses down the 'columns' of the spreadsheet (A, B, C, etc.). Listen at each column for any return echoes. When an echo is heard, note how long it took for the echo to return. The longer the wait, the deeper the row (1,2,3, etc.). The strength of the echo determines the brightness setting for that cell (white for a strong echo, black for a weak echo, and varying shades of grey for everything in between.) When all the echoes are recorded on the sheet, a greyscale image has been accomplished.
In modern ultrasound systems, images are derived from the combined reception of echoes by multiple elements, rather than a single one. These elements in the transducer array work together to receive signals, a process essential for optimizing the ultrasonic beam's focus and producing detailed images. One predominant method for this is "delay-and-sum" beamforming. The time delay applied to each element is calculated based on the geometrical relationship between the imaging point, the transducer, and receiver positions. By integrating these time-adjusted signals, the system pinpoints focus onto specific tissue regions, enhancing image resolution and clarity. The utilization of multiple element reception combined with the delay-and-sum principles underpins the high-quality images characteristic of contemporary ultrasound scans.
Displaying the image.
Images from the ultrasound scanner are transferred and displayed using the DICOM standard. Normally, very little post processing is applied.
Sound in the body.
Ultrasonography (sonography) uses a probe containing multiple acoustic transducers to send pulses of sound into a material. Whenever a sound wave encounters a material with a different density (acoustical impedance), some of the sound wave is scattered but part is reflected back to the probe and is detected as an echo. The time it takes for the echo to travel back to the probe is measured and used to calculate the depth of the tissue interface causing the echo. The greater the difference between acoustic impedances, the larger the echo is. If the pulse hits gases or solids, the density difference is so great that most of the acoustic energy is reflected and it becomes impossible to progress further.
The frequencies used for medical imaging are generally in the range of 1 to 18 MHz Higher frequencies have a correspondingly smaller wavelength, and can be used to make more detailed sonograms. However, the attenuation of the sound wave is increased at higher frequencies, so penetration of deeper tissues necessitates a lower frequency (3–5 MHz).
Penetrating deep into the body with sonography is difficult. Some acoustic energy is lost each time an echo is formed, but most of it (approximately formula_0) is lost from acoustic absorption. (See Acoustic attenuation for further details on modeling of acoustic attenuation and absorption.)
The speed of sound varies as it travels through different materials, and is dependent on the acoustical impedance of the material. However, the sonographic instrument assumes that the acoustic velocity is constant at 1540 m/s. An effect of this assumption is that in a real body with non-uniform tissues, the beam becomes somewhat de-focused and image resolution is reduced.
To generate a 2-D image, the ultrasonic beam is swept. A transducer may be swept mechanically by rotating or swinging or a 1-D phased array transducer may be used to sweep the beam electronically. The received data is processed and used to construct the image. The image is then a 2-D representation of the slice into the body.
3-D images can be generated by acquiring a series of adjacent 2-D images. Commonly a specialized probe that mechanically scans a conventional 2-D image transducer is used. However, since the mechanical scanning is slow, it is difficult to make 3D images of moving tissues. Recently, 2-D phased array transducers that can sweep the beam in 3-D have been developed. These can image faster and can even be used to make live 3-D images of a beating heart.
Doppler ultrasonography is used to study blood flow and muscle motion. The different detected speeds are represented in color for ease of interpretation, for example leaky heart valves: the leak shows up as a flash of unique color. Colors may alternatively be used to represent the amplitudes of the received echoes.
Expansions.
An additional expansion of ultrasound is bi-planar ultrasound, in which the probe has two 2D planes perpendicular to each other, providing more efficient localization and detection. Furthermore, an omniplane probe can rotate 180° to obtain multiple images. In 3D ultrasound, many 2D planes are digitally added together to create a 3-dimensional image of the object.
Doppler ultrasonography.
Doppler ultrasonography employs the Doppler effect to assess whether structures (usually blood) are moving towards or away from the probe, and their relative velocity. By calculating the frequency shift of a particular sample volume, flow in an artery or a jet of blood flow over a heart valve, its speed and direction can be determined and visualized, as an example. "Color Doppler" is the measurement of velocity by color scale. Color Doppler images are generally combined with gray scale (B-mode) images to display "duplex ultrasonography" images. Uses include:
Contrast ultrasonography (ultrasound contrast imaging).
A contrast medium for medical ultrasonography is a formulation of encapsulated gaseous microbubbles to increase echogenicity of blood, discovered by Dr. Raymond Gramiak in 1968 and named contrast-enhanced ultrasound. This contrast medical imaging modality is used throughout the world, for echocardiography in particular in the United States and for ultrasound radiology in Europe and Asia.
Microbubbles-based contrast media is administered intravenously into the patient blood stream during the ultrasonography examination. Due to their size, the microbubbles remain confined in blood vessels without extravasating towards the interstitial fluid. An ultrasound contrast media is therefore purely intravascular, making it an ideal agent to image organ microvasculature for diagnostic purposes. A typical clinical use of contrast ultrasonography is detection of a hypervascular metastatic tumor, which exhibits a contrast uptake (kinetics of microbubbles concentration in blood circulation) faster than healthy biological tissue surrounding the tumor. Other clinical applications using contrast exist, as in echocardiography to improve delineation of left ventricle for visualizing contractibility of heart muscle after a myocardial infarction. Finally, applications in quantitative perfusion (relative measurement of blood flow) have emerged for identifying early patient response to anti-cancerous drug treatment (methodology and clinical study by Dr. Nathalie Lassau in 2011), enabling the best oncological therapeutic options to be determined.
In oncological practice of medical contrast ultrasonography, clinicians use 'parametric imaging of vascular signatures' invented by Dr. Nicolas Rognin in 2010. This method is conceived as a cancer aided diagnostic tool, facilitating characterization of a suspicious tumor (malignant versus benign) in an organ. This method is based on medical computational science to analyze a time sequence of ultrasound contrast images, a digital video recorded in real-time during patient examination. Two consecutive signal processing steps are applied to each pixel of the tumor:
Once signal processing in each pixel is completed, a color spatial map of the parameter is displayed on a computer monitor, summarizing all vascular information of the tumor in a single image called a parametric image (see last figure of press article as clinical examples). This parametric image is interpreted by clinicians based on predominant colorization of the tumor: red indicates a suspicion of malignancy (risk of cancer), green or yellow – a high probability of benignity. In the first case (suspicion of malignant tumor), the clinician typically prescribes a biopsy to confirm the diagnostic or a CT scan examination as a second opinion. In the second case (quasi-certain of benign tumor), only a follow-up is needed with a contrast ultrasonography examination a few months later. The main clinical benefits are to avoid a systemic biopsy (with inherent risks of invasive procedures) of benign tumors or a CT scan examination exposing the patient to X-ray radiation. The parametric imaging of vascular signatures method proved to be effective in humans for characterization of tumors in the liver. In a cancer screening context, this method might be potentially applicable to other organs such as breast or prostate.
Molecular ultrasonography (ultrasound molecular imaging).
The current future of contrast ultrasonography is in molecular imaging with potential clinical applications expected in cancer screening to detect malignant tumors at their earliest stage of appearance. Molecular ultrasonography (or ultrasound molecular imaging) uses targeted microbubbles originally designed by Dr Alexander Klibanov in 1997; such targeted microbubbles specifically bind or adhere to tumoral microvessels by targeting biomolecular cancer expression (overexpression of certain biomolecules that occurs during neo-angiogenesis or inflammation in malignant tumors). As a result, a few minutes after their injection in blood circulation, the targeted microbubbles accumulate in the malignant tumor; facilitating its localization in a unique ultrasound contrast image. In 2013, the very first exploratory clinical trial in humans for prostate cancer was completed at Amsterdam in the Netherlands by Dr. Hessel Wijkstra.
In molecular ultrasonography, the technique of acoustic radiation force (also used for shear wave elastography) is applied in order to literally push the targeted microbubbles towards microvessels wall; first demonstrated by Dr. Paul Dayton in 1999. This allows maximization of binding to the malignant tumor; the targeted microbubbles being in more direct contact with cancerous biomolecules expressed at the inner surface of tumoral microvessels. At the stage of scientific preclinical research, the technique of acoustic radiation force was implemented as a prototype in clinical ultrasound systems and validated "in vivo" in 2D and 3D imaging modes.
Elastography (ultrasound elasticity imaging).
Ultrasound is also used for elastography, which is a relatively new imaging modality that maps the elastic properties of soft tissue. This modality emerged in the last two decades. Elastography is useful in medical diagnoses as it can discern healthy from unhealthy tissue for specific organs/growths. For example, cancerous tumors will often be harder than the surrounding tissue, and diseased livers are stiffer than healthy ones.
There are many ultrasound elastography techniques.
Interventional ultrasonography.
Interventional ultrasonography involves biopsy, emptying fluids, intrauterine Blood transfusion (Hemolytic disease of the newborn).
Compression ultrasonography.
Compression ultrasonography is when the probe is pressed against the skin. This can bring the target structure closer to the probe, increasing spatial resolution of it. Comparison of the shape of the target structure before and after compression can aid in diagnosis.
It is used in ultrasonography of deep venous thrombosis, wherein absence of vein compressibility is a strong indicator of thrombosis. Compression ultrasonography has both high sensitivity and specificity for detecting proximal deep vein thrombosis in symptomatic patients. Results are not reliable when the patient is asymptomatic, for example in high risk postoperative orthopedic patients.
Panoramic ultrasonography.
Panoramic ultrasonography is the digital stitching of multiple ultrasound images into a broader one. It can display an entire abnormality and show its relationship to nearby structures on a single image.
Multiparametric ultrasonography.
Multiparametric ultrasonography (mpUSS) combines multiple ultrasound techniques to produce a composite result. For example, one study combined B-mode, colour Doppler, real-time elastography, and contrast-enhanced ultrasound, achieving an accuracy similar to that of multiparametric MRI.
Speed-of-Sound Imaging.
Speed-of-sound (SoS) imaging aims to find the spatial distribution of the SoS within the tissue. The idea is to find relative delay measurements for different transmission events and solve the limited-angle tomographic reconstruction problem using delay measurements and transmission geometry. Compared to shear-wave elastography, SoS imaging has better ex-vivo tissue differentiation for benign and malignant tumors.
Attributes.
As with all imaging modalities, ultrasonography has positive and negative attributes.
Risks and side-effects.
Ultrasonography is generally considered safe imaging, with the World Health Organizations stating:
"Diagnostic ultrasound is recognized as a safe, effective, and highly flexible imaging modality capable of providing clinically relevant information about most parts of the body in a rapid and cost-effective fashion".
Diagnostic ultrasound studies of the fetus are generally considered to be safe during pregnancy. However, this diagnostic procedure should be performed only when there is a valid medical indication, and the lowest possible ultrasonic exposure setting should be used to gain the necessary diagnostic information under the "as low as reasonably practicable" or ALARP principle.
Although there is no evidence that ultrasound could be harmful to the fetus, medical authorities typically strongly discourage the promotion, selling, or leasing of ultrasound equipment for making "keepsake fetal videos".
Regulation.
Diagnostic and therapeutic ultrasound equipment is regulated in the US by the Food and Drug Administration, and worldwide by other national regulatory agencies. The FDA limits acoustic output using several metrics; generally, other agencies accept the FDA-established guidelines.
Currently, New Mexico, Oregon, and North Dakota are the only US states that regulate diagnostic medical sonographers. Certification examinations for sonographers are available in the US from three organizations: the American Registry for Diagnostic Medical Sonography, Cardiovascular Credentialing International and the American Registry of Radiologic Technologists.
The primary regulated metrics are Mechanical Index (MI), a metric associated with the cavitation bio-effect, and Thermal Index (TI) a metric associated with the tissue heating bio-effect. The FDA requires that the machine not exceed established limits, which are reasonably conservative in an effort to maintain diagnostic ultrasound as a safe imaging modality. This requires self-regulation on the part of the manufacturer in terms of machine calibration.
Ultrasound-based pre-natal care and sex screening technologies were launched in India in the 1980s. With concerns about its misuse for sex-selective abortion, the Government of India passed the Pre-natal Diagnostic Techniques Act (PNDT) in 1994 to distinguish and regulate legal and illegal uses of ultrasound equipment. The law was further amended as the Pre-Conception and Pre-natal Diagnostic Techniques (Regulation and Prevention of Misuse) (PCPNDT) Act in 2004 to deter and punish prenatal sex screening and sex selective abortion. It is currently illegal and a punishable crime in India to determine or disclose the sex of a fetus using ultrasound equipment.
Use in other animals.
Ultrasound is also a valuable tool in veterinary medicine, offering the same non-invasive imaging that helps in the diagnosis and monitoring of conditions in animals.
History.
After the French physicist Pierre Curie's discovery of piezoelectricity in 1880, ultrasonic waves could be deliberately generated for industry. In 1940, the American acoustical physicist Floyd Firestone devised the first ultrasonic echo imaging device, the Supersonic Reflectoscope, to detect internal flaws in metal castings. In 1941, Austrian neurologist Karl Theo Dussik, in collaboration with his brother, Friedrich, a physicist, was likely the first person to image the human body ultrasonically, outlining the ventricles of a human brain. Ultrasonic energy was first applied to the human body for medical purposes by Dr George Ludwig at the Naval Medical Research Institute, Bethesda, Maryland, in the late 1940s. English-born physicist John Wild (1914–2009) first used ultrasound to assess the thickness of bowel tissue as early as 1949; he has been described as the "father of medical ultrasound". Subsequent advances took place concurrently in several countries but was not until 1961 when David Robinson and George Kossoff's work at the Australian Department of Health resulted in the first commercially practical water bath ultrasonic scanner. In 1963 Meyerdirk & Wright launched production of the first commercial, hand-held, articulated arm, compound contact B-mode scanner, which made ultrasound generally available for medical use.
France.
Léandre Pourcelot, a researcher and teacher at INSA (Institut National des Sciences Appliquées), Lyon, co-published a report in 1965 at the Académie des sciences, "Effet Doppler et mesure du débit sanguin" ("Doppler effect and measure of the blood flow"), the basis of his design of a Doppler flow meter in 1967.
Scotland.
Parallel developments in Glasgow, Scotland by Professor Ian Donald and colleagues at the Glasgow Royal Maternity Hospital (GRMH) led to the first diagnostic applications of the technique. Donald was an obstetrician with a self-confessed "childish interest in machines, electronic and otherwise", who, having treated the wife of one of the company's directors, was invited to visit the Research Department of boilermakers Babcock & Wilcox at Renfrew. He adapted their industrial ultrasound equipment to conduct experiments on various anatomical specimens and assess their ultrasonic characteristics. Together with the medical physicist Tom Brown. and fellow obstetrician John MacVicar, Donald refined the equipment to enable differentiation of pathology in live volunteer patients. These findings were reported in "The Lancet" on 7 June 1958 as "Investigation of Abdominal Masses by Pulsed Ultrasound" – possibly one of the most important papers published in the field of diagnostic medical imaging.
At GRMH, Professor Donald and James Willocks then refined their techniques to obstetric applications including fetal head measurement to assess the size and growth of the fetus. With the opening of the new Queen Mother's Hospital in Yorkhill in 1964, it became possible to improve these methods even further. Stuart Campbell's pioneering work on fetal cephalometry led to it acquiring long-term status as the definitive method of study of foetal growth. As the technical quality of the scans was further developed, it soon became possible to study pregnancy from start to finish and diagnose its many complications such as multiple pregnancy, fetal abnormality and "placenta praevia". Diagnostic ultrasound has since been imported into practically every other area of medicine.
Sweden.
Medical ultrasonography was used in 1953 at Lund University by cardiologist Inge Edler and Gustav Ludwig Hertz's son Carl Hellmuth Hertz, who was then a graduate student at the university's department of nuclear physics.
Edler had asked Hertz if it was possible to use radar to look into the body, but Hertz said this was impossible. However, he said, it might be possible to use ultrasonography. Hertz was familiar with using ultrasonic reflectoscopes of the American acoustical physicist Floyd Firestone's invention for nondestructive materials testing, and together Edler and Hertz developed the idea of applying this methodology in medicine.
The first successful measurement of heart activity was made on October 29, 1953, using a device borrowed from the ship construction company Kockums in Malmö. On December 16 the same year, the method was applied to generate an echo-encephalogram (ultrasonic probe of the brain). Edler and Hertz published their findings in 1954.
United States.
In 1962, after about two years of work, Joseph Holmes, William Wright, and Ralph Meyerdirk developed the first compound contact B-mode scanner. Their work had been supported by U.S. Public Health Services and the University of Colorado. Wright and Meyerdirk left the university to form Physionic Engineering Inc., which launched the first commercial hand-held articulated arm compound contact B-mode scanner in 1963. This was the start of the most popular design in the history of ultrasound scanners.
In the late 1960s Gene Strandness and the bio-engineering group at the University of Washington conducted research on Doppler ultrasound as a diagnostic tool for vascular disease. Eventually, they developed technologies to use duplex imaging, or Doppler in conjunction with B-mode scanning, to view vascular structures in real time while also providing hemodynamic information.
The first demonstration of color Doppler was by Geoff Stevenson, who was involved in the early developments and medical use of Doppler shifted ultrasonic energy.
Manufacturers.
Major manufacturers of Medical Ultrasound Devices and Equipment are:
Explanatory notes.
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References.
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References.
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https://en.wikipedia.org/wiki?curid=14335726
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Lysase enzyme
The enzyme oligogalacturonide lyase (EC 4.2.2.6) catalyzes the chemical reaction
4-(4-deoxy-β--gluc-4-enuronosyl)-D-galacturonate formula_0 2 5-dehydro-4-deoxy--glucuronate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on polysaccharides. The systematic name of this enzyme class is oligogalacturonide lyase. Other names in common use include oligogalacturonate lyase, unsaturated oligogalacturonate transeliminase, and OGTE. This enzyme participates in pentose and glucuronate interconversions.
References.
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[
{
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"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14335748
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14335830
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Pentalenene synthase
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The enzyme pentalenene synthase (EC 4.2.3.7) catalyzes the chemical reaction
(2"E",6"E")-farnesyl diphosphate formula_0 pentalenene + diphosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is (2"E",6"E")-farnesyl-diphosphate diphosphate-lyase (cyclizing, pentalenene-forming). This enzyme is also called pentalenene synthetase.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
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"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14335830
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14335844
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Phaseollidin hydratase
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The enzyme phaseollidin hydratase (EC 4.2.1.97) catalyzes the chemical reaction
phaseollidin hydrate formula_0 phaseollidin + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is phaseollidin-hydrate hydro-lyase (phaseollidin-forming). This enzyme is also called phaseollidin-hydrate hydro-lyase.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14335844
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14335864
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Phosphogluconate dehydratase
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The enzyme phosphogluconate dehydratase (EC 4.2.1.12) catalyzes the chemical reaction
6-phospho--gluconate formula_0 2-dehydro-3-deoxy-6-phospho--gluconate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 6-phospho--gluconate hydro-lyase (2-dehydro-3-deoxy-6-phospho--gluconate-forming). Other names in common use include 6-phosphogluconate dehydratase, 6-phosphogluconic dehydrase, gluconate-6-phosphate dehydratase, gluconate 6-phosphate dehydratase, 6-phosphogluconate dehydrase, and 6-phospho-gluconate hydro-lyase. This enzyme participates in the Entner–Doudoroff pathway.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 2GP4.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14335864
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14335912
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Pinene synthase
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In enzymology, a pinene synthase (EC 4.2.3.14) is an enzyme that catalyzes the chemical reaction
geranyl diphosphate formula_0 pinene + diphosphate
Hence, this enzyme has one substrate, geranyl diphosphate, and two products, pinene and diphosphate.
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is geranyl-diphosphate diphosphate-lyase (cyclizing, pinene-forming). Other names in common use include beta-geraniolene synthase, (−)-(1S,5S)-pinene synthase, and geranyldiphosphate diphosphate lyase (pinene forming). This enzyme participates in monoterpenoid biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14335912
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14335986
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Prephenate dehydratase
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The enzyme prephenate dehydratase (EC 4.2.1.51) catalyzes the chemical reaction
prephenate formula_0 phenylpyruvate + H2O + CO2
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is prephenate hydro-lyase (decarboxylating; phenylpyruvate-forming). This enzyme is also called prephenate hydro-lyase (decarboxylating). This enzyme participates in phenylalanine, tyrosine and tryptophan biosynthesis.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 2QMX.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14335986
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14336010
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Propanediol dehydratase
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The enzyme propanediol dehydratase (EC 4.2.1.28) catalyzes the chemical reaction
propane-1,2-diol formula_0 propanal + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is propane-1,2-diol hydro-lyase (propanal-forming). Other names in common use include meso-2,3-butanediol dehydrase, diol dehydratase, -1,2-propanediol hydro-lyase, diol dehydrase, adenosylcobalamin-dependent diol dehydratase, propanediol dehydrase, coenzyme B12-dependent diol dehydrase, 1,2-propanediol dehydratase, dioldehydratase, and propane-1,2-diol hydro-lyase. This enzyme participates in glycerolipid metabolism. It employs one cofactor, cobamide.
Structural studies.
As of late 2007, 7 structures have been solved for this class of enzymes, with PDB accession codes 1DIO, 1EEX, 1EGM, 1EGV, 1IWB, 1UC4, and 1UC5.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14336010
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14336153
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Protoaphin-aglucone dehydratase (cyclizing)
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The enzyme protoaphin-aglucone dehydratase (cyclizing) (EC 4.2.1.73) catalyzes the chemical reaction
protoaphin aglucone formula_0 xanthoaphin + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is protoaphin-aglucone hydro-lyase (cyclizing; xanthoaphin-forming). Other names in common use include protoaphin dehydratase, protoaphin dehydratase (cyclizing), and protoaphin-aglucone hydro-lyase (cyclizing).
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14336153
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14336176
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Pseudouridylate synthase
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The enzyme pseudouridylate synthase (EC 4.2.1.70) catalyzes the chemical reaction
uracil + -ribose 5-phosphate formula_0 pseudouridine 5′-phosphate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is uracil hydro-lyase (adding -ribose 5-phosphate pseudouridine-5′-phosphate-forming). Other names in common use include pseudouridylic acid synthetase, pseudouridine monophosphate synthetase, 5-ribosyluracil 5-phosphate synthetase, pseudouridylate synthetase, upsilonUMP synthetase, and uracil hydro-lyase (adding -ribose 5-phosphate). This enzyme participates in pyrimidine metabolism.
Structural studies.
As of late 2007, 22 structures have been solved for this class of enzymes, with PDB accession codes 1DJ0, 1K8W, 1KSK, 1KSL, 1KSV, 1PRZ, 1QYU, 1R3E, 1R3F, 1SB7, 1SGV, 1SI7, 1SZW, 1V9F, 1V9K, 1VIO, 1XPI, 1Z2Z, 1ZE1, 1ZE2, 1ZL3, and 2I82.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14336176
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14336199
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Pyrazolylalanine synthase
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The enzyme pyrazolylalanine synthase (EC 4.2.1.50) catalyzes the chemical reaction
-serine + pyrazole formula_0 3-(pyrazol-1-yl)--alanine + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is -serine hydro-lyase [adding pyrazole 3-(pyrazol-1-yl)--alanine-forming]. Other names in common use include β-pyrazolylalaninase, β-(1-pyrazolyl)alanine synthase, and -serine hydro-lyase (adding pyrazole). It employs one cofactor, pyridoxal phosphate.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
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https://en.wikipedia.org/wiki?curid=14336199
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14336224
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(R)-2-methylmalate dehydratase
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Class of enzymes
The enzyme("R")-2-methylmalate dehydratase (EC 4.2.1.35) catalyzes the chemical reaction
("R")-2-methylmalate formula_0 2-methylmaleate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is ("R")-2-methylmalate hydro-lyase (2-methylmaleate-forming). Other names in common use include citraconate hydratase, citraconase, citramalate hydro-lyase, (−)-citramalate hydro-lyase, and ("R")-2-methylmalate hydro-lyase. This enzyme participates in valine, leucine and isoleucine biosynthesis and c5-branched dibasic acid metabolism. It employs one cofactor, iron.
References.
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
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https://en.wikipedia.org/wiki?curid=14336224
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14336239
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(R)-limonene synthase
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Class of enzymes
The enzyme ("R")-limonene synthase (EC 4.2.3.20) catalyzes the reversible chemical reaction
Description.
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is Geranyl-diphosphate diphosphate-lyase [cyclizing, (+)-(4"R")-limonene-forming]. Other names in common use include Limonene synthase, and Geranyldiphosphate diphosphate lyase [(+)-("R")-limonene-forming].
The enzyme participates in monoterpenoid biosynthesis and is localized to Leucoplasts of oil gland secretory cells.
References.
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Further reading.
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
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https://en.wikipedia.org/wiki?curid=14336239
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14336255
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R-linalool synthase
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The enzyme "R"-linalool synthase (EC 4.2.3.26) catalyzes the chemical reaction
geranyl diphosphate + H2O formula_0 (3"R")-linalool + diphosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is geranyl-diphosphate diphosphate-lyase [(3"R")-linalool-forming]. Other names in common use include (3"R")-linalool synthase, and (−)-3"R"-linalool synthase.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14336255
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14336284
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(S)-2-methylmalate dehydratase
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Class of enzymes
The enzyme ("S")-2-methylmalate dehydratase (EC 4.2.1.34) catalyzes the chemical reaction:
("S")-2-methylmalate formula_0 2-methylfumarate + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is
("S")-2-methylmalate hydro-lyase (2-methylfumarate-forming). Other names in common use include mesaconate hydratase, (+)-citramalate hydro-lyase, L-citramalate hydrolase, citramalate dehydratase, (+)-citramalic hydro-lyase, mesaconate mesaconase, mesaconase, and ("S")-2-methylmalate hydro-lyase.
This enzyme participates in c5-branched dibasic acid metabolism. In addition, the family of lyases which is also an enzyme catalyzes the breaking the elimination reaction of the variety of amounts of chemical bonds from hydrolysis (a substitution reaction ) and oxidation, which forms a new double bond or a new ring structure.
References.
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
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https://en.wikipedia.org/wiki?curid=14336284
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14336320
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Sabinene-hydrate synthase
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The enzyme sabinene-hydrate synthase (EC 4.2.3.11) catalyzes the chemical reaction
geranyl diphosphate + H2O formula_0 sabinene hydrate + diphosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is geranyl-diphosphate diphosphate-lyase (cyclizing, sabinene-hydrate-forming). This enzyme is also called sabinene hydrate cyclase. This enzyme participates in monoterpenoid biosynthesis.
References.
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14336320
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14336341
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Scytalone dehydratase
|
The enzyme scytalone dehydratase (EC 4.2.1.94) catalyzes the chemical reaction
scytalone formula_0 1,3,8-trihydroxynaphthalene + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is scytalone 7,8-hydro-lyase (1,3,8-trihydroxynaphthalene-forming). This enzyme is also called scytalone 7,8-hydro-lyase.
Structural studies.
As of late 2007, 8 structures have been solved for this class of enzymes, with PDB accession codes 1IDP, 1STD, 2STD, 3STD, 4STD, 5STD, 6STD, and 7STD.
References.
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14336341
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14336354
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S-linalool synthase
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The enzyme "S"-linalool synthase (EC 4.2.3.25) catalyzes the chemical reaction
geranyl diphosphate + H2O formula_0 (3"S")-linalool + diphosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is geranyl-diphosphate diphosphate-lyase [(3"S")-linalool-forming]. Other names in common use include LIS, Lis, and 3"S"-linalool synthase.
References.
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14336354
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14336373
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(S)-norcoclaurine synthase
|
Class of enzymes
The enzyme ("S")-norcoclaurine synthase (EC 4.2.1.78) catalyzes the chemical reaction
4-hydroxyphenylacetaldehyde + 4-(2-aminoethyl)benzene-1,2-diol (Dopamine) formula_0 ("S")-norcoclaurine + H2O
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 4-hydroxyphenylacetaldehyde hydro-lyase [adding dopamine ("S")-norcoclaurine-forming]. Other names in common use include ("S")-norlaudanosoline synthase, and 4-hydroxyphenylacetaldehyde hydro-lyase (adding dopamine). This enzyme participates in benzylisoquinoline alkaloid biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14336373
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14336393
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Synephrine dehydratase
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The enzyme synephrine dehydratase (EC 4.2.1.88) catalyzes the chemical reaction
("R")-synephrine formula_0 (4-hydroxyphenyl)acetaldehyde + methylamine
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is ("R")-synephrine hydro-lyase (methylamine-forming).
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14336393
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14336413
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Taxadiene synthase
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The enzyme taxadiene synthase (EC 4.2.3.17) catalyzes the chemical reaction
geranylgeranyl diphosphate formula_0 taxa-4,11-diene + diphosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is geranylgeranyl-diphosphate diphosphate-lyase (cyclizing, taxa-4,11-diene-forming). Other names in common use include geranylgeranyl-diphosphate diphosphate-lyase (cyclizing, and taxadiene-forming). This enzyme participates in diterpenoid biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14336413
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14336439
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Threonine synthase
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The enzyme threonine synthase (EC 4.2.3.1) catalyzes the chemical reaction
"O"-phospho--homoserine + H2O formula_0 -threonine + phosphate
This enzyme belongs to the family of lyases, specifically those carbon-oxygen lyases acting on phosphates. The systematic name of this enzyme class is O"-phospho--homoserine phosphate-lyase (adding water -threonine-forming). Other names in common use include threonine synthetase, and O"-phospho--homoserine phospho-lyase (adding water). This enzyme participates in glycine, serine and threonine metabolism, and vitamin B6 metabolism. It employs one cofactor, pyridoxal phosphate.
Structural studies.
As of late 2007, 7 structures have been solved for this class of enzymes, with PDB accession codes 1UIM, 1UIN, 1V7C, 1VB3, 2C2B, 2C2G, and 2D1F.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14336439
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14336460
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Trans-feruloyl-CoA hydratase
|
In enzymology, a trans-feruloyl-CoA hydratase (EC 4.2.1.101) is an enzyme that catalyzes the chemical reaction
4-hydroxy-3-methoxyphenyl-beta-hydroxypropanoyl-CoA formula_0 trans-feruloyl-CoA + H2O
Hence, this enzyme has one substrate, 4-hydroxy-3-methoxyphenyl-beta-hydroxypropanoyl-CoA, and two products, trans-feruloyl-CoA and H2O.
This enzyme belongs to the family of lyases, specifically the hydro-lyases, which cleave carbon-oxygen bonds. The systematic name of this enzyme class is 4-hydroxy-3-methoxyphenyl-beta-hydroxypropanoyl-CoA hydro-lyase (trans-feruloyl-CoA-forming). This enzyme is also called trans-feruloyl-CoA hydro-lyase (incorrect).
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 2J5I.
References.
<templatestyles src="Reflist/styles.css" />
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[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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https://en.wikipedia.org/wiki?curid=14336460
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