id
stringlengths 2
8
| title
stringlengths 1
130
| text
stringlengths 0
252k
| formulas
listlengths 1
823
| url
stringlengths 38
44
|
|---|---|---|---|---|
14650788
|
Chitobiosyldiphosphodolichol beta-mannosyltransferase
|
Class of enzymes
In enzymology, a chitobiosyldiphosphodolichol beta-mannosyltransferase (EC 2.4.1.142) is an enzyme that catalyzes the chemical reaction
GDP-mannose + chitobiosyldiphosphodolichol formula_0 GDP + beta-1,4-D-mannosylchitobiosyldiphosphodolichol
Thus, the two substrates of this enzyme are GDP-mannose and chitobiosyldiphosphodolichol, whereas its two products are GDP and beta-1,4-D-mannosylchitobiosyldiphosphodolichol.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is GDP-mannose:chitobiosyldiphosphodolichol beta-D-mannosyltransferase. Other names in common use include guanosine diphosphomannose-dolichol diphosphochitobiose, mannosyltransferase, and GDP-mannose-dolichol diphosphochitobiose mannosyltransferase. This enzyme participates in n-glycan biosynthesis and glycan structures - biosynthesis 1.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14650788
|
14650797
|
Cinnamate beta-D-glucosyltransferase
|
Enzyme
In enzymology, a cinnamate beta-D-glucosyltransferase (EC 2.4.1.177) is an enzyme that catalyzes the chemical reaction
UDP-glucose + trans-cinnamate formula_0 UDP + trans-cinnamoyl beta-D-glucoside
Thus, the two substrates of this enzyme are UDP-glucose and trans-cinnamate, whereas its two products are UDP and trans-cinnamoyl beta-D-glucoside.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:trans-cinnamate beta-D-glucosyltransferase. Other names in common use include uridine diphosphoglucose-cinnamate glucosyltransferase, and UDPG:t-cinnamate glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14650797
|
14650810
|
Cis-p-Coumarate glucosyltransferase
|
Enzyme
In enzymology, a "cis-p"-Coumarate glucosyltransferase (EC 2.4.1.209) is an enzyme that catalyzes the chemical reaction
UDP-glucose + "cis-p"-Coumarate formula_0 4'-O-beta-D-glucosyl-cis-p-coumarate + UDP
Thus, the two substrates of this enzyme are UDP-glucose and cis-p-coumarate, whereas its two products are 4'-O-beta-D-glucosyl-cis-p-coumarate and UDP.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:cis-p-coumarate beta-D-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14650810
|
14650822
|
Cis-zeatin O-beta-D-glucosyltransferase
|
Enzyme
In enzymology, a cis-zeatin O-beta-D-glucosyltransferase (EC 2.4.1.215) is an enzyme that catalyzes the chemical reaction
UDP-glucose + cis-zeatin formula_0 UDP + O-beta-D-glucosyl-cis-zeatin
Thus, the two substrates of this enzyme are UDP-glucose and cis-zeatin, whereas its two products are UDP and O-beta-D-glucosyl-cis-zeatin.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:cis-zeatin O-beta-D-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14650822
|
14650843
|
Coniferyl-alcohol glucosyltransferase
|
Enzyme
In enzymology, a coniferyl-alcohol glucosyltransferase (EC 2.4.1.111) is an enzyme that catalyzes the chemical reaction
UDP-glucose + coniferyl alcohol formula_0 UDP + coniferin
Thus, the two substrates of this enzyme are UDP-glucose and coniferyl alcohol, whereas its two products are UDP and coniferin.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:coniferyl-alcohol 4'-beta-D-glucosyltransferase. Other names in common use include uridine diphosphoglucose-coniferyl alcohol glucosyltransferase, and UDP-glucose coniferyl alcohol glucosyltransferase. This enzyme participates in phenylpropanoid biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14650843
|
1465085
|
Lindelöf hypothesis
|
In mathematics, the Lindelöf hypothesis is a conjecture by Finnish mathematician Ernst Leonard Lindelöf about the rate of growth of the Riemann zeta function on the critical line. This hypothesis is implied by the Riemann hypothesis. It says that for any "ε" > 0,
formula_0
as "t" tends to infinity (see big O notation). Since "ε" can be replaced by a smaller value, the conjecture can be restated as follows: for any positive "ε",
formula_1
The μ function.
If σ is real, then "μ"(σ) is defined to be the infimum of all real numbers "a" such that ζ(σ + "iT" ) = O("T" "a"). It is trivial to check that "μ"(σ) = 0 for σ > 1, and the functional equation of the zeta function implies that "μ"(σ) = "μ"(1 − σ) − σ + 1/2. The Phragmén–Lindelöf theorem implies that "μ" is a convex function. The Lindelöf hypothesis states "μ"(1/2) = 0, which together with the above properties of "μ" implies that "μ"(σ) is 0 for σ ≥ 1/2 and 1/2 − σ for σ ≤ 1/2.
Lindelöf's convexity result together with "μ"(1) = 0 and "μ"(0) = 1/2 implies that 0 ≤ "μ"(1/2) ≤ 1/4. The upper bound of 1/4 was lowered by Hardy and Littlewood to 1/6 by applying Weyl's method of estimating exponential sums to the approximate functional equation. It has since been lowered to slightly less than 1/6 by several authors using long and technical proofs, as in the following table:
Relation to the Riemann hypothesis.
Backlund (1918–1919) showed that the Lindelöf hypothesis is equivalent to the following statement about the zeros of the zeta function: for every "ε" > 0, the number of zeros with real part at least 1/2 + "ε" and imaginary part between "T" and "T" + 1 is o(log("T")) as "T" tends to infinity. The Riemann hypothesis implies that there are no zeros at all in this region and so implies the Lindelöf hypothesis. The number of zeros with imaginary part between "T" and "T" + 1 is known to be O(log("T")), so the Lindelöf hypothesis seems only slightly stronger than what has already been proved, but in spite of this it has resisted all attempts to prove it.
Means of powers (or moments) of the zeta function.
The Lindelöf hypothesis is equivalent to the statement that
formula_2
for all positive integers "k" and all positive real numbers ε. This has been proved for "k" = 1 or 2, but the case "k" = 3 seems much harder and is still an open problem.
There is a much more precise conjecture about the asymptotic behavior of the integral: it is believed that
formula_3
for some constants "c""k","j"&hairsp;. This has been proved by Littlewood for "k" = 1 and by Heath-Brown for "k" = 2
(extending a result of Ingham who found the leading term).
Conrey and Ghosh suggested the value
formula_4
for the leading coefficient when "k" is 6, and Keating and Snaith used random matrix theory to suggest some conjectures for the values of the coefficients for higher "k". The leading coefficients are conjectured to be the product of an elementary factor, a certain product over primes, and the number of "n" × "n" Young tableaux given by the sequence
1, 1, 2, 42, 24024, 701149020, ... (sequence in the OEIS).
Other consequences.
Denoting by "p""n" the "n"-th prime number, let formula_5 A result by Albert Ingham shows that the Lindelöf hypothesis implies that, for any "ε" > 0,
formula_6
if "n" is sufficiently large.
A prime gap conjecture stronger than Ingham's result is Cramér's conjecture, which asserts that
formula_7
The density hypothesis.
The density hypothesis says that formula_8, where formula_9 denote the number of zeros formula_10 of formula_11with formula_12 and formula_13, and it would follow from the Lindelöf hypothesis.
More generally let formula_14 then it is known that this bound roughly correspond to asymptotics for primes in short intervals of length formula_15.
Ingham showed that formula_16 in 1940, Huxley that formula_17 in 1971, and Guth and Maynard that formula_18 in 2024 (preprint) and these coincide on formula_19, therefore the latest work of Guth and Maynard gives the closest known value to formula_20 as we would expect from the Riemann hypothesis and improves the bound to formula_21 or equivalently the asymptotics to formula_22.
In theory improvements to Baker, Harman, and Pintz estimates for the Legendre conjecture and better Siegel zeros free regions could also be expected among others.
L-functions.
The Riemann zeta function belongs to a more general family of functions called L-functions.
In 2010, new methods to obtain sub-convexity estimates for L-functions in the PGL(2) case were given by Joseph Bernstein and Andre Reznikov and in the GL(1) and GL(2) case by Akshay Venkatesh and Philippe Michel and in 2021 for the GL("n") case by Paul Nelson.
Notes and references.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\zeta\\!\\left(\\frac{1}{2} + it\\right)\\! = O(t^\\varepsilon)"
},
{
"math_id": 1,
"text": "\\zeta\\!\\left(\\frac{1}{2} + it\\right)\\! = o(t^\\varepsilon)."
},
{
"math_id": 2,
"text": "\\frac{1}{T} \\int_0^T|\\zeta(1/2+it)|^{2k}\\,dt = O(T^{\\varepsilon})"
},
{
"math_id": 3,
"text": " \\int_0^T|\\zeta(1/2+it)|^{2k} \\, dt = T\\sum_{j=0}^{k^2}c_{k,j}\\log(T)^{k^2-j} + o(T)"
},
{
"math_id": 4,
"text": "\\frac{42}{9!}\\prod_ p \\left((1-p^{-1})^4(1+4p^{-1}+p^{-2})\\right)"
},
{
"math_id": 5,
"text": "g_n = p_{n + 1} - p_n.\\ "
},
{
"math_id": 6,
"text": "g_n\\ll p_n^{1/2+\\varepsilon}"
},
{
"math_id": 7,
"text": " g_n = O\\!\\left((\\log p_n)^2\\right)."
},
{
"math_id": 8,
"text": "N(\\sigma,T)\\le N^{2(1-\\sigma)+\\epsilon}"
},
{
"math_id": 9,
"text": "N(\\sigma,T)"
},
{
"math_id": 10,
"text": "\\rho"
},
{
"math_id": 11,
"text": "\\zeta(s)"
},
{
"math_id": 12,
"text": "\\mathfrak{R}(s)\\ge \\sigma"
},
{
"math_id": 13,
"text": "|\\mathfrak{I}(s)|\\le T"
},
{
"math_id": 14,
"text": "N(\\sigma,T)\\le N^{A(\\sigma)(1-\\sigma)+\\epsilon}"
},
{
"math_id": 15,
"text": "x^{1-1/A(\\sigma)}"
},
{
"math_id": 16,
"text": "A_I(\\sigma)=\\frac{3}{2-\\sigma}"
},
{
"math_id": 17,
"text": "A_H(\\sigma)=\\frac{3}{3\\sigma-1}"
},
{
"math_id": 18,
"text": "A_{GM}(\\sigma)=\\frac{15}{5\\sigma+3}"
},
{
"math_id": 19,
"text": "\\sigma_{I,GM}=7/10<\\sigma_{H,GM}=8/10<\\sigma_{I,H}=3/4"
},
{
"math_id": 20,
"text": "\\sigma=1/2"
},
{
"math_id": 21,
"text": "N(\\sigma,T)\\le N^{\\frac{30}{13}(1-\\sigma)+\\epsilon}"
},
{
"math_id": 22,
"text": "x^{17/30}"
}
] |
https://en.wikipedia.org/wiki?curid=1465085
|
14650862
|
Cyanidin 3-O-rutinoside 5-O-glucosyltransferase
|
Class of enzymes
In enzymology, a cyanidin 3-O-rutinoside 5-O-glucosyltransferase (EC 2.4.1.116) is an enzyme that catalyzes the chemical reaction
UDP-glucose + cyanidin 3-O-rutinoside formula_0 UDP + cyanidin 3-O-rutinoside 5-O-beta-D-glucoside
Thus, the two substrates of this enzyme are UDP-glucose and cyanidin 3-O-rutinoside, whereas its two products are UDP and cyanidin 3-O-rutinoside 5-O-beta-D-glucoside.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:cyanidin-3-O-beta-L-rhamnosyl-(1->6)-beta-D-glucoside 5-O-beta-D-glucosyltransferase. Other names in common use include uridine diphosphoglucose-cyanidin 3-rhamnosylglucoside, 5-O-glucosyltransferase, cyanidin-3-rhamnosylglucoside 5-O-glucosyltransferase, UDP-glucose:cyanidin-3-O-D-rhamnosyl-1,6-D-glucoside, and 5-O-D-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14650862
|
14650893
|
Cyanohydrin beta-glucosyltransferase
|
Class of enzymes
In enzymology, a cyanohydrin beta-glucosyltransferase (EC 2.4.1.85) is an enzyme that catalyzes the chemical reaction
UDP-D-glucose + (S)-4-hydroxymandelonitrile formula_0 UDP + (S)-4-hydroxymandelonitrile beta-D-glucoside
Thus, the two substrates of this enzyme are UDP-D-glucose and (S)-4-hydroxymandelonitrile, whereas its two products are UDP and (S)-4-hydroxymandelonitrile beta-D-glucoside.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-D-glucose:(S)-4-hydroxymandelonitrile beta-D-glucosyltransferase. Other names in common use include uridine diphosphoglucose-p-hydroxymandelonitrile, glucosyltransferase, UDP-glucose-p-hydroxymandelonitrile glucosyltransferase, uridine diphosphoglucose-cyanohydrin glucosyltransferase, uridine diphosphoglucose:aldehyde cyanohydrin, beta-glucosyltransferase, UDP-glucose:(S)-4-hydroxymandelonitrile beta-D-glucosyltransferase, UGT85B1, and UDP-glucose:p-hydroxymandelonitrile-O-glucosyltransferase. This enzyme participates in tyrosine metabolism and cyanoamino acid metabolism.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14650893
|
14650903
|
Cytokinin 7-beta-glucosyltransferase
|
Class of enzymes
In enzymology, a cytokinin 7-β-glucosyltransferase (EC 2.4.1.118) is an enzyme that catalyzes the chemical reaction
UDP-glucose + "N6"-alkylaminopurine formula_0 UDP + "N6"-alkylaminopurine-7-β-D-glucoside
Thus, the two substrates of this enzyme are UDP-glucose and "N6"-alkylaminopurine, whereas its two products are UDP and "N6"-alkylaminopurine-7-β-D-glucoside.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:"N6"-alkylaminopurine 7-glucosyltransferase. Other names in common use include uridine diphosphoglucose-zeatin 7-glucosyltransferase, and cytokinin 7-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14650903
|
14650920
|
Deoxyuridine phosphorylase
|
Class of enzymes
In enzymology, a deoxyuridine phosphorylase is an enzyme that catalyzes the chemical reaction
2'-deoxyuridine + phosphate formula_0 uracil + 2-deoxy-alpha-D-ribose 1-phosphate
Thus, the two substrates of this enzyme are 2'-deoxyuridine and phosphate, whereas its two products are uracil and 2-deoxy-alpha-D-ribose 1-phosphate.
No enzyme is known to be specific for this reaction, hence the EC number originally assigned to this enzyme function (EC 2.4.2.23) was deleted by the IUBMB in 2013. The reaction is catalysed by EC 2.4.2.2, pyrimidine-nucleoside phosphorylase, EC 2.4.2.3, uridine phosphorylase, and EC 2.4.2.4, thymidine phosphorylase.
These enzymes belong to the family of glycosyltransferases, specifically the pentosyltransferases. They participate in pyrimidine metabolism.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14650920
|
14650934
|
Dextransucrase
|
Class of enzymes
In enzymology, a dextransucrase (EC 2.4.1.5) is an enzyme that catalyzes the chemical reaction
sucrose + (1,6-alpha-D-glucosyl)n formula_0 D-fructose + (1,6-alpha-D-glucosyl)n+1
Thus, the two substrates of this enzyme are sucrose and (1,6-alpha-D-glucosyl)n, whereas its two products are D-fructose and (1,6-alpha-D-glucosyl)n+1.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is sucrose:1,6-alpha-D-glucan 6-alpha-D-glucosyltransferase. Other names in common use include sucrose 6-glucosyltransferase, SGE, CEP, and sucrose-1,6-alpha-glucan glucosyltransferase. This enzyme participates in starch and sucrose metabolism and two-component system - general.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14650934
|
14650953
|
Dextrin dextranase
|
Class of enzymes
In enzymology, a dextrin dextranase (EC 2.4.1.2) is an enzyme that catalyzes the chemical reaction
(1,4-alpha-D-glucosyl)n + (1,6-alpha-D-glucosyl)m formula_0 (1,4-alpha-D-glucosyl)n-1 + (1,6-alpha-D-glucosyl)m+1
Thus, the two substrates of this enzyme are (1,4-alpha-D-glucosyl)n and (1,6-alpha-D-glucosyl)m, whereas its two products are (1,4-alpha-D-glucosyl)n-1 and (1,6-alpha-D-glucosyl)m+1.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is 1,4-alpha-D-glucan:1,6-alpha-D-glucan 6-alpha-D-glucosyltransferase. Other names in common use include dextrin 6-glucosyltransferase, and dextran dextrinase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14650953
|
14650958
|
Rhind Mathematical Papyrus 2/n table
|
The Rhind Mathematical Papyrus, an ancient Egyptian mathematical work, includes a mathematical table for converting rational numbers of the form 2/"n" into Egyptian fractions (sums of distinct unit fractions), the form the Egyptians used to write fractional numbers. The text describes the representation of 50 rational numbers. It was written during the Second Intermediate Period of Egypt (approximately 1650–1550 BCE) by Ahmes, the first writer of mathematics whose name is known. Aspects of the document may have been copied from an unknown 1850 BCE text.
Table.
The following table gives the expansions listed in the papyrus.
This part of the Rhind Mathematical Papyrus was spread over nine sheets of papyrus.
Explanations.
Any rational number has infinitely many different possible expansions as a sum of unit fractions, and since the discovery of the Rhind Mathematical Papyrus mathematicians have struggled to understand how the ancient Egyptians might have calculated the specific expansions shown in this table.
Suggestions by Gillings included five different techniques. Problem 61 in the Rhind Mathematical Papyrus gives one formula:
formula_0, which can be stated equivalently as formula_1 ("n" divisible by 3 in the latter equation).
Other possible formulas are:
formula_2 ("n" divisible by 5)
formula_3 (where "k" is the average of "m" and "n")
formula_4. This formula yields the decomposition for "n" = 101 in the table.
Ahmes was suggested to have converted 2/"p" (where "p" was a prime number) by two methods, and three methods to convert 2/"pq" composite denominators. Others have suggested only one method was used by Ahmes which used multiplicative factors similar to least common multiples. A detailed and simple explanation of how the 2/"p" table may have been decomposed was provided by Abdulrahman Abdulaziz.
Comparison to other table texts.
An older ancient Egyptian papyrus contained a similar table of Egyptian fractions; the Lahun Mathematical Papyri, written around 1850 BCE, is about the age of one unknown source for the Rhind papyrus. The Kahun 2/"n" fractions were identical to the fraction decompositions given in the Rhind Papyrus' 2/"n" table.
The Egyptian Mathematical Leather Roll (EMLR), circa 1900 BCE, lists decompositions of fractions of the form 1/"n" into other unit fractions. The table consisted of 26 unit fraction series of the form 1/"n" written as sums of other rational numbers.
The Akhmim wooden tablet wrote fractions in the form 1/"n" in terms of sums of hekat rational numbers, 1/3, 1/7, 1/10, 1/11 and 1/13. In this document a two-part set of fractions was written in terms of Eye of Horus fractions which were fractions of the form and remainders expressed in terms of a unit called "ro". The answers were checked by multiplying the initial divisor by the proposed solution and checking that the resulting answer was 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 5 "ro", which equals 1.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": " \\frac{2}{3n} = \\frac{1}{2n} + \\frac{1}{6n} "
},
{
"math_id": 1,
"text": "\\frac{2}{n} = \\frac{1}{2} \\frac{1}{n} +\\frac{3}{2} \\frac{1}{n}"
},
{
"math_id": 2,
"text": "\\,\\frac{2}{n}\\; = \\;\\frac{1}{3} \\frac{1}{n} +\\frac{5}{3} \\frac{1}{n}"
},
{
"math_id": 3,
"text": "\\!\\frac{2}{mn}\\! = \\frac{1}{m}\\!\\frac{1}{k} +\\frac{1}{n} \\frac{1}{k}"
},
{
"math_id": 4,
"text": "\\,\\frac{2}{n}\\; = \\,\\frac{1}{n} + \\frac{1}{2n} + \\frac{1}{3n} + \\frac{1}{6n}"
}
] |
https://en.wikipedia.org/wiki?curid=14650958
|
14650971
|
Digalactosyldiacylglycerol synthase
|
Class of enzymes
In enzymology, a digalactosyldiacylglycerol synthase (EC 2.4.1.241) is an enzyme that catalyzes the chemical reaction
UDP-galactose + 3-(beta-D-galactosyl)-1,2-diacyl-sn-glycerol formula_0 UDP + 3-[alpha-D-galactosyl-(1->6)-beta-D-galactosyl]-1,2-diacyl-sn- glycerol
Thus, the two substrates of this enzyme are UDP-galactose and 3-(beta-D-galactosyl)-1,2-diacyl-sn-glycerol, whereas its 3 products are UDP, 3-[alpha-D-galactosyl-(1->6)-beta-D-galactosyl]-1,2-diacyl-sn-, and glycerol.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:3-(beta-D-galactosyl)-1,2-diacyl-sn-glycerol 6-alpha-galactosyltransferase. Other names in common use include DGD1, DGD2, DGDG synthase (ambiguous), UDP-galactose-dependent DGDG synthase, UDP-galactose-dependent digalactosyldiacylglycerol synthase, and UDP-galactose:MGDG galactosyltransferase. This enzyme participates in glycerolipid metabolism.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14650971
|
14650996
|
Diglucosyl diacylglycerol synthase
|
Class of enzymes
In enzymology, a diglucosyl diacylglycerol synthase (EC 2.4.1.208) is an enzyme that catalyzes the chemical reaction
UDP-glucose + 1,2-diacyl-3-O-(alpha-D-glucopyranosyl)-sn-glycerol formula_0 1,2-diacyl-3-O-(alpha-D-glucopyranosyl(1->2)-O-alpha-D- glucopyranosyl)sn-glycerol + UDP
Thus, the two substrates of this enzyme are UDP-glucose and 1,2-diacyl-3-O-(alpha-D-glucopyranosyl)-sn-glycerol, whereas its 2 products are 1,2-diacyl-3-O-(alpha-D-glucopyranosyl(1-2)-O-alpha-D-glucopyranosyl)sn-glycerol, and UDP.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:1,2-diacyl-3-O-(alpha-D-glucopyranosyl)-sn-glycerol (1->2) glucosyltransferase. Other names in common use include monoglucosyl diacylglycerol (1->2) glucosyltransferase, MGlcDAG (1->2) glucosyltransferase, and DGlcDAG synthase. It employs one cofactor, magnesium.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14650996
|
14651018
|
Dioxotetrahydropyrimidine phosphoribosyltransferase
|
Class of enzymes
In enzymology, a dioxotetrahydropyrimidine phosphoribosyltransferase (EC 2.4.2.20) is an enzyme that catalyzes the chemical reaction
a 2,4-dioxotetrahydropyrimidine D-ribonucleotide + diphosphate formula_0 a 2,4-dioxotetrahydropyrimidine + 5-phospho-alpha-D-ribose 1-diphosphate
Thus, the two substrates of this enzyme are 2,4-dioxotetrahydropyrimidine D-ribonucleotide and diphosphate, whereas its two products are 2,4-dioxotetrahydropyrimidine and 5-phospho-alpha-D-ribose 1-diphosphate.
This enzyme belongs to the family of glycosyltransferases, specifically the pentosyltransferases. The systematic name of this enzyme class is 2,4-dioxotetrahydropyrimidine-nucleotide:diphosphate phospho-alpha-D-ribosyltransferase. Other names in common use include dioxotetrahydropyrimidine-ribonucleotide pyrophosphorylase, dioxotetrahydropyrimidine phosphoribosyl transferase, and dioxotetrahydropyrimidine ribonucleotide pyrophosphorylase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651018
|
14651042
|
Dolichyl-diphosphooligosaccharide–protein glycotransferase
|
Class of enzymes
In enzymology, a dolichyl-diphosphooligosaccharide–protein glycotransferase (EC 2.4.99.18) is an enzyme that catalyzes the chemical reaction
dolichyl diphosphooligosaccharide + protein L-asparagine formula_0 dolichyl diphosphate + a glycoprotein with the oligosaccharide chain attached by N-glycosyl linkage to protein L-asparagine
Thus, the two substrates of this enzyme are dolichyl diphosphooligosaccharide and protein L-asparagine, whereas its 3 products are dolichyl diphosphate, glycoprotein with the oligosaccharide chain attached by N-glycosyl, and linkage to protein L-asparagine.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is dolichyl-diphosphooligosaccharide:protein-L-asparagine oligopolysaccharidotransferase. Other names in common use include dolichyldiphosphooligosaccharide-protein glycosyltransferase, asparagine N-glycosyltransferase, dolichyldiphosphooligosaccharide-protein oligosaccharyltransferase, dolichylpyrophosphodiacetylchitobiose-protein glycosyltransferase, oligomannosyltransferase, oligosaccharide transferase, dolichyldiphosphoryloligosaccharide-protein, and oligosaccharyltransferase. This enzyme participates in n-glycan biosynthesis and glycan structures - biosynthesis 1.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651042
|
14651059
|
Dolichyl-phosphate alpha-N-acetylglucosaminyltransferase
|
Class of enzymes
In enzymology, a dolichyl-phosphate alpha-N-acetylglucosaminyltransferase (EC 2.4.1.153) is an enzyme that catalyzes the chemical reaction
UDP-N-acetyl-D-glucosamine + dolichyl phosphate formula_0 UDP + dolichyl N-acetyl-alpha-D-glucosaminyl phosphate
Thus, the two substrates of this enzyme are UDP-N-acetyl-D-glucosamine and dolichyl phosphate, whereas its two products are UDP and dolichyl N-acetyl-alpha-D-glucosaminyl phosphate.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-N-acetyl-D-glucosamine:dolichyl-phosphate alpha-N-acetyl-D-glucosaminyltransferase. Other names in common use include uridine diphosphoacetylglucosamine-dolichol phosphate, acetylglucosaminyltransferase, dolichyl phosphate acetylglucosaminyltransferase, dolichyl phosphate N-acetylglucosaminyltransferase, UDP-N-acetylglucosamine-dolichol phosphate, and N-acetylglucosaminyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651059
|
14651080
|
Dolichyl-phosphate beta-D-mannosyltransferase
|
Class of enzymes
In enzymology, a dolichyl-phosphate beta-D-mannosyltransferase (EC 2.4.1.83) is an enzyme that catalyzes the chemical reaction
GDP-mannose + dolichyl phosphate formula_0 GDP + dolichyl D-mannosyl phosphate
Thus, the two substrates of this enzyme are GDP-mannose and dolichyl phosphate, whereas its two products are GDP and dolichyl D-mannosyl phosphate.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is GDP-mannose:dolichyl-phosphate beta-D-mannosyltransferase. Other names in common use include GDP-Man:DolP mannosyltransferase, dolichyl mannosyl phosphate synthase, dolichyl-phospho-mannose synthase, GDP-mannose:dolichyl-phosphate mannosyltransferase, guanosine diphosphomannose-dolichol phosphate mannosyltransferase, dolichol phosphate mannose synthase, dolichyl phosphate mannosyltransferase, dolichyl-phosphate mannose synthase, GDP-mannose-dolichol phosphate mannosyltransferase, GDP-mannose-dolichylmonophosphate mannosyltransferase, mannosylphosphodolichol synthase, and mannosylphosphoryldolichol synthase. This enzyme participates in n-glycan biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651080
|
14651095
|
Dolichyl-phosphate beta-glucosyltransferase
|
Class of enzymes
In enzymology, a dolichyl-phosphate beta-glucosyltransferase (EC 2.4.1.117) is an enzyme that catalyzes the chemical reaction
UDP-glucose + dolichyl phosphate formula_0 UDP + dolichyl beta-D-glucosyl phosphate
Thus, the two substrates of this enzyme are UDP-glucose and dolichyl phosphate, whereas its two products are UDP and dolichyl beta-D-glucosyl phosphate.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:dolichyl-phosphate beta-D-glucosyltransferase. Other names in common use include polyprenyl phosphate:UDP-D-glucose glucosyltransferase, UDP-glucose dolichyl-phosphate glucosyltransferase, uridine diphosphoglucose-dolichol glucosyltransferase, UDP-glucose:dolichol phosphate glucosyltransferase, UDP-glucose:dolicholphosphoryl glucosyltransferase, UDP-glucose:dolichyl monophosphate glucosyltransferase, and UDP-glucose:dolichyl phosphate glucosyltransferase. This enzyme participates in n-glycan biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651095
|
14651109
|
Dolichyl-phosphate D-xylosyltransferase
|
Class of enzymes
In enzymology, a dolichyl-phosphate D-xylosyltransferase (EC 2.4.2.32) is an enzyme that catalyzes the chemical reaction
UDP-D-xylose + dolichyl phosphate formula_0 UDP + dolichyl D-xylosyl phosphate
Thus, the two substrates of this enzyme are UDP-D-xylose and dolichyl phosphate, whereas its two products are UDP and dolichyl D-xylosyl phosphate.
This enzyme belongs to the family of glycosyltransferases, specifically the pentosyltransferases. The systematic name of this enzyme class is UDP-D-xylose:dolichyl-phosphate D-xylosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651109
|
14651140
|
Dolichyl-phosphate-mannose-protein mannosyltransferase
|
Class of enzymes
In enzymology, a dolichyl-phosphate-mannose-protein mannosyltransferase (EC 2.4.1.109) is an enzyme that catalyzes the chemical reaction
dolichyl phosphate D-mannose + protein formula_0 dolichyl phosphate + O-D-mannosylprotein
Thus, the two substrates of this enzyme are dolichyl phosphate D-mannose and protein, whereas its two products are dolichyl phosphate and O-D-mannosylprotein.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is dolichyl-phosphate-D-mannose:protein O-D-mannosyltransferase. Other names in common use include dolichol phosphomannose-protein mannosyltransferase, and protein O-D-mannosyltransferase. A human gene that codes for this enzyme is POMT1.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651140
|
14651155
|
Dolichyl-xylosyl-phosphate—protein xylosyltransferase
|
Class of enzymes
In enzymology, a dolichyl-xylosyl-phosphate-protein xylosyltransferase (EC 2.4.2.33) is an enzyme that catalyzes the chemical reaction
dolichyl D-xylosyl phosphate + protein formula_0 dolichyl phosphate + D-xylosylprotein
Thus, the two substrates of this enzyme are dolichyl D-xylosyl phosphate and protein, whereas its two products are dolichyl phosphate and D-xylosylprotein.
This enzyme belongs to the family of glycosyltransferases, specifically the pentosyltransferases. The systematic name of this enzyme class is dolichyl-D-xylosyl-phosphate:protein D-xylosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651155
|
14651168
|
Flavanone 7-O-beta-glucosyltransferase
|
Class of enzymes
In enzymology, a flavanone 7-O-beta-glucosyltransferase (EC 2.4.1.185) is an enzyme that catalyzes the chemical reaction
UDP-glucose + a flavanone formula_0 UDP + a flavanone 7-O-beta-D-glucoside
Thus, the two substrates of this enzyme are UDP-glucose and flavanone, whereas its two products are UDP and flavanone 7-O-beta-D-glucoside.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:flavanone 7-O-beta-D-glucosyltransferase. Other names in common use include uridine diphosphoglucose-flavanone 7-O-glucosyltransferase, naringenin 7-O-glucosyltransferase, and hesperetin 7-O-glucosyl-transferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651168
|
14651184
|
Flavanone 7-O-glucoside 2"-O-beta-L-rhamnosyltransferase
|
Class of enzymes
In enzymology, a flavanone 7-O-glucoside 2"-O-beta-L-rhamnosyltransferase (EC 2.4.1.236) is an enzyme that catalyzes the chemical reaction
UDP-L-rhamnose + a flavanone 7-O-glucoside formula_0 UDP + a flavanone 7-O-[beta-L-rhamnosyl-(1->2)-beta-D-glucoside]
Thus, the two substrates of this enzyme are UDP-L-rhamnose and flavanone 7-O-glucoside, whereas its two products are UDP and flavanone 7-O-[beta-L-rhamnosyl-(1->2)-beta-D-glucoside].
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-L-rhamnose:flavanone-7-O-glucoside 2"-O-beta-L-rhamnosyltransferase. Other names in common use include UDP-rhamnose:flavanone-7-O-glucoside-2"-O-rhamnosyltransferase, and 1->2 UDP-rhamnosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651184
|
14651195
|
Flavone 7-O-beta-glucosyltransferase
|
Class of enzymes
In enzymology, a flavone 7-O-beta-glucosyltransferase (EC 2.4.1.81) is an enzyme that catalyzes the chemical reaction
UDP-glucose + 5,7,3',4'-tetrahydroxyflavone formula_0 UDP + 7-O-beta-D-glucosyl-5,7,3',4'-tetrahydroxyflavone
Thus, the two substrates of this enzyme are UDP-glucose and 5,7,3',4'-tetrahydroxyflavone (luteolin), whereas its two products are UDP and 7-O-beta-D-glucosyl-5,7,3',4'-tetrahydroxyflavone (cynaroside).
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:5,7,3',4'-tetrahydroxyflavone 7-O-beta-D-glucosyltransferase. Other names in common use include UDP-glucose-apigenin beta-glucosyltransferase, UDP-glucose-luteolin beta-D-glucosyltransferase, uridine diphosphoglucose-luteolin glucosyltransferase, uridine diphosphoglucose-apigenin 7-O-glucosyltransferase, and UDP-glucosyltransferase. This enzyme participates in flavonoid biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651195
|
1465121
|
Kuder–Richardson formulas
|
In psychometrics, the Kuder–Richardson formulas, first published in 1937, are a measure of internal consistency reliability for measures with dichotomous choices. They were developed by Kuder and Richardson.
Kuder–Richardson Formula 20 (KR-20).
The name of this formula stems from the fact that is the twentieth formula discussed in Kuder and Richardson's seminal paper on test reliability.
It is a special case of Cronbach's α, computed for dichotomous scores. It is often claimed that a high KR-20 coefficient (e.g., > 0.90) indicates a homogeneous test. However, like Cronbach's α, homogeneity (that is, unidimensionality) is actually an assumption, not a conclusion, of reliability coefficients. It is possible, for example, to have a high KR-20 with a multidimensional scale, especially with a large number of items.
Values can range from 0.00 to 1.00 (sometimes expressed as 0 to 100), with high values indicating that the examination is likely to correlate with alternate forms (a desirable characteristic). The KR-20 may be affected by difficulty of the test, the spread in scores and the length of the examination.
In the case when scores are not tau-equivalent (for example when there is not homogeneous but rather examination items of increasing difficulty) then the KR-20 is an indication of the lower bound of internal consistency (reliability).
The formula for KR-20 for a test with "K" test items numbered "i" = 1 to "K" is
formula_0
where "pi" is the proportion of correct responses to test item "i", "qi" is the proportion of incorrect responses to test item "i" (so that "pi" + "qi" = 1), and the variance for the denominator is
formula_1
where "n" is the total sample size.
If it is important to use unbiased operators then the sum of squares should be divided by degrees of freedom ("n" − 1) and the probabilities are multiplied by formula_2
Kuder–Richardson Formula 21 (KR-21).
Often discussed in tandem with KR-20, is Kuder–Richardson Formula 21 (KR-21). KR-21 is a simplified version of KR-20, which can be used when the difficulty of all items on the test are known to be equal. Like KR-20, KR-21 was first set forth as the twenty-first formula discussed in Kuder and Richardson's 1937 paper.
The formula for KR-21 is as such:
formula_3
Similarly to KR-20, K is equal to the number of items. Difficulty level of the items ("p"), is assumed to be the same for each item, however, in practice, KR-21 can be applied by finding the average item difficulty across the entirety of the test. KR-21 tends to be a more conservative estimate of reliability than KR-20, which in turn is a more conservative estimate than Cronbach's "α".
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "r= \\frac{K}{K-1} \\left[ 1 - \\frac{\\sum_{i=1}^K p_i q_i}{\\sigma^2_X} \\right] "
},
{
"math_id": 1,
"text": "\\sigma^2_X = \\frac{\\sum_{i=1}^n (X_i-\\bar{X})^2\\,{}}{n}."
},
{
"math_id": 2,
"text": "n/(n-1)."
},
{
"math_id": 3,
"text": "r= \\frac{K}{K-1} \\left[ 1 - \\frac{Kp(1-p)}{\\sigma^2_X} \\right] "
}
] |
https://en.wikipedia.org/wiki?curid=1465121
|
14651217
|
Flavone apiosyltransferase
|
Class of enzymes
In enzymology, a flavone apiosyltransferase (EC 2.4.2.25) is an enzyme that catalyzes the chemical reaction
UDP-apiose + 5,7,4'-trihydroxyflavone 7-O-beta-D-glucoside formula_0 UDP + 5,7,4'-trihydroxyflavone 7-O-[beta-D-apiosyl-(1->2)-beta-D-glucoside]
Thus, the two substrates of this enzyme are UDP-apiose and 5,7,4'-trihydroxyflavone 7-O-beta-D-glucoside, whereas its 3 products are UDP, 5,7,4'-trihydroxyflavone (apigenin), and 7-O-[beta-D-apiosyl-(1->2)-beta-D-glucoside].
This enzyme belongs to the family of glycosyltransferases, specifically the pentosyltransferases. The systematic name of this enzyme class is UDP-apiose:5,4'-dihydroxyflavone 7-O-beta-D-glucoside 2"-O-beta-D-apiofuranosyltransferase. Other names in common use include uridine diphosphoapiose-flavone apiosyltransferase, and UDP-apiose:7-O-(beta-D-glucosyl)-flavone apiosyltransferase. This enzyme participates in flavonoid biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651217
|
14651241
|
Flavonol-3-O-glucoside glucosyltransferase
|
Class of enzymes
In enzymology, a flavonol-3-O-glucoside glucosyltransferase (EC 2.4.1.239) is an enzyme that catalyzes the chemical reaction
UDP-glucose + a flavonol 3-O-beta-D-glucoside formula_0 UDP + a flavonol 3-O-beta-D-glucosyl-(1->2)-beta-D-glucoside
Thus, the two substrates of this enzyme are UDP-glucose and flavonol 3-O-beta-D-glucoside, whereas its two products are UDP and flavonol 3-O-beta-D-glucosyl-(1→2)-beta-D-glucoside.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:flavonol-3-O-glucoside 2"-O-beta-D-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651241
|
14651266
|
Flavonol-3-O-glucoside L-rhamnosyltransferase
|
Class of enzymes
In enzymology, a flavonol-3-O-glucoside L-rhamnosyltransferase (EC 2.4.1.159) is an enzyme that catalyzes the chemical reaction
UDP-L-rhamnose + a flavonol 3-O-D-glucoside formula_0 UDP + a flavonol 3-O-[beta-L-rhamnosyl-(1->6)-beta-D-glucoside]
Thus, the two substrates of this enzyme are UDP-L-rhamnose and flavonol 3-O-D-glucoside, whereas its two products are UDP and flavonol 3-O-[beta-L-rhamnosyl-(1->6)-beta-D-glucoside].
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-L-rhamnose:flavonol-3-O-D-glucoside 6"-O-L-rhamnosyltransferase. Other names in common use include uridine diphosphorhamnose-flavonol 3-O-glucoside, rhamnosyltransferase, and UDP-rhamnose:flavonol 3-O-glucoside rhamnosyltransferase. This enzyme participates in flavonoid biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651266
|
14651276
|
Flavonol 3-O-glucosyltransferase
|
Class of enzymes
In enzymology, a flavonol 3-O-glucosyltransferase (EC 2.4.1.91) is an enzyme that catalyzes the chemical reaction
UDP-glucose + a flavonol formula_0 UDP + a flavonol 3-O-beta-D-glucoside
Thus, the two substrates of this enzyme are UDP-glucose and flavonol, whereas its two products are UDP and flavonol 3-O-beta-D-glucoside. The flavonoids that can act as substrates within this reaction include quercetin, kaempferol, dihydrokaempferol, kaempferid, fisetin, and isorhamnetin. Flavonol 3-O-glucosyltransferase is a hexosyl group transfer enzyme.
This enzyme is known by the systematic name UPD-glucose:flavonol 3-O-D glucosyltransferase, and it participates in flavonoid biosynthesis and causes the formation of anthocyanins. Anthocyanins produce a purple color in the plant tissues that they are present in.
It is an enzyme found most notably in grapes ("Vitis vinifera"). This enzyme is found within a number of other plants as well—such as snapdragons ("Antirrhinum majus"), kale ("Brassica oleracea"), and grapefruit ("Citrus x paradisi").
Pathways.
This enzyme is involved in the biosynthesis of secondary metabolites. The primary function of this enzyme within its pathway is binding a glucoside onto a flavonol molecule, forming a flavonol 3-O-glucoside. It is through this mechanism that the enzyme converts anthocyanidins to anthocyanins as a part of the phenylpropanoid pathway. One specific example would be this enzymes actions on pelargonidin. Flavonol 3-O-glucosyltransferase binds the glucoside to this protein, making pelargonidin 3-O-glucoside. This enzyme is also involved in the flavone glycoside pathway, and daphnetin modification in some organisms. The role of the enzyme in these pathways is, again, to bind a glucoside to the substrate to construct a flavonol 3-O-glucoside.
Nomenclature.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:flavonol 3-O-D-glucosyltransferase. Other names in common use include:
Among those, UFGT is divided into UDP-glucose: Flavonoid 3-O-glucosyltransferase (UF3GT) and UDP-glucose: Flavonoid 5-O-glucosyltransferase (UF5GT), which are responsible for the glucosylation of anthocyanins to produce stable molecules.
Inhibitors and Structure of the Enzyme.
Some of the inhibitors of this enzyme include CaCl2, CoCl2, Cu+2, CuCl2, KCl, Mg+2, and Mn+2. The primary active site residue of this enzyme is Asp181, as determined by studies of how mutations affect enzyme capacity. There are several documentations of the crystalline structure of flavonol 3-O-glucosyltransferase (2C1X, 2C1Z, and 2C9Z), and, based on these renderings of the enzyme, there is only one subunit in the quaternary structure of the molecule.
References.
<templatestyles src="Reflist/styles.css" />
Further reading.
<templatestyles src="Refbegin/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651276
|
14651297
|
Flavonol-3-O-glycoside glucosyltransferase
|
Class of enzymes
In enzymology, a flavonol-3-O-glycoside glucosyltransferase (EC 2.4.1.240) is an enzyme that catalyzes the chemical reaction
UDP-glucose + a flavonol 3-O-beta-D-glucosyl-(1->2)-beta-D-glucoside formula_0 UDP + a flavonol 3-O-beta-D-glucosyl-(1->2)-beta-D-glucosyl-(1->2)-beta-D-glucoside
Thus, the two substrates of this enzyme are UDP-glucose and flavonol 3-O-beta-D-glucosyl-(1->2)-beta-D-glucoside, whereas its 3 products are UDP, flavonol, and 3-O-beta-D-glucosyl-(1->2)-beta-D-glucosyl-(1->2)-beta-D-glucoside.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:flavonol-3-O-beta-D-glucosyl-(1->2)-beta-D-glucoside 2-O-beta-D-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651297
|
14651313
|
Flavonol-3-O-glycoside xylosyltransferase
|
Class of enzymes
In enzymology, a flavonol-3-O-glycoside xylosyltransferase (EC 2.4.2.35) is an enzyme that catalyzes the chemical reaction
UDP-D-xylose + a flavonol 3-O-glycoside formula_0 UDP + a flavonol 3-[-D-xylosyl-(1->2)-beta-D-glycoside]
Thus, the two substrates of this enzyme are UDP-D-xylose and flavonol 3-O-glycoside, whereas its two products are UDP and flavonol 3-[-D-xylosyl-(1->2)-beta-D-glycoside].
This enzyme belongs to the family of glycosyltransferases, specifically the pentosyltransferases. The systematic name of this enzyme class is UDP-D-xylose:flavonol-3-O-glycoside 2"-O-beta-D-xylosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651313
|
14651338
|
Flavonol 7-O-beta-glucosyltransferase
|
Class of enzymes
In enzymology, a flavonol 7-O-beta-glucosyltransferase (EC 2.4.1.237) is an enzyme that catalyzes the chemical reaction
UDP-glucose + a flavonol formula_0 UDP + a flavonol 7-O-beta-D-glucoside
Thus, the two substrates of this enzyme are UDP-glucose and flavonol, whereas its two products are UDP and flavonol 7-O-beta-D-glucoside.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:flavonol 7-O-beta-D-glucosyltransferase. This enzyme is also called UDP-glucose:flavonol 7-O-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651338
|
14651352
|
Fucosylgalactoside 3-alpha-galactosyltransferase
|
Class of enzymes
In enzymology, a fucosylgalactoside 3-alpha-galactosyltransferase (EC 2.4.1.37) is an enzyme that catalyzes the chemical reaction
UDP-galactose + alpha-L-fucosyl-(1->2)-D-galactosyl-R formula_0 UDP + alpha-D-galactosyl-(1->3)-[alpha-L-fucosyl(1->2)]-D-galactosyl-R
Thus, the two substrates of this enzyme are UDP-galactose and alpha-L-fucosyl-(1->2)-D-galactosyl-R, whereas its two products are UDP and alpha-D-galactosyl-(1->3)-[alpha-L-fucosyl(1->2)]-D-galactosyl-R.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:alpha-L-fucosyl-(1->2)-D-galactoside 3-alpha-D-galactosyltransferase. Other names in common use include UDP-galactose:O-alpha-L-fucosyl(1->2)D-galactose, alpha-D-galactosyltransferase, UDPgalactose:glycoprotein-alpha-L-fucosyl-(1,2)-D-galactose, 3-alpha-D-galactosyltransferase, [blood group substance] alpha-galactosyltransferase, blood-group substance B-dependent galactosyltransferase, glycoprotein-fucosylgalactoside alpha-galactosyltransferase, histo-blood group B transferase, and histo-blood substance B-dependent galactosyltransferase. This enzyme participates in 3 metabolic pathways: glycosphingolipid biosynthesis - lactoseries, glycosphingolipid biosynthesis - neo-lactoseries, and glycan structures - biosynthesis 2.
Structural studies.
As of late 2007, 7 structures have been solved for this class of enzymes, with PDB accession codes 1R7U, 1R7X, 1R80, 1R82, 2A8W, 2PGV, and 2PGY.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651352
|
14651370
|
Galactinol—raffinose galactosyltransferase
|
Class of enzymes
In enzymology, a galactinol-raffinose galactosyltransferase (EC 2.4.1.67) is an enzyme that catalyzes the chemical reaction
alpha-D-galactosyl-(1→3)-1D-myo-inositol + raffinose formula_0 myo-inositol + stachyose
Thus, the two substrates of this enzyme are α-D-galactosyl-(1→3)-1D-myo-inositol and raffinose, whereas its two products are myo-inositol and stachyose.
This enzyme participates in galactose metabolism.
Nomenclature.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is alpha-D-galactosyl-(1→3)-myo-inositol:raffinose galactosyltransferase. Other names in common use include galactinol-raffinose galactosyltransferase, and stachyose synthetase.
References.
<templatestyles src="Refbegin/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651370
|
14651379
|
Galactinol—sucrose galactosyltransferase
|
Class of enzymes
In enzymology, a galactinol-sucrose galactosyltransferase (EC 2.4.1.82) is an enzyme that catalyzes the chemical reaction
alpha-D-galactosyl-(1->3)-1D-myo-inositol + sucrose formula_0 myo-inositol + raffinose
Thus, the two substrates of this enzyme are alpha-D-galactosyl-(1->3)-1D-myo-inositol and sucrose, whereas its two products are myo-inositol and raffinose.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is alpha-D-galactosyl-(1->3)-myo-inositol:sucrose 6-alpha-D-galactosyltransferase. Other names in common use include 1-alpha-D-galactosyl-myo-inositol:sucrose, and 6-alpha-D-galactosyltransferase. This enzyme participates in galactose metabolism.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651379
|
14651392
|
Galactogen 6beta-galactosyltransferase
|
Class of enzymes
In enzymology, a galactogen 6beta-galactosyltransferase (EC 2.4.1.205) is an enzyme that catalyzes the chemical reaction
UDP-galactose + galactogen formula_0 UDP + 1,6-beta-D-galactosylgalactogen
Thus, the two substrates of this enzyme are UDP-galactose and galactogen, whereas its two products are UDP and 1,6-beta-D-galactosylgalactogen.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:galactogen beta-1,6-D-galactosyltransferase. Other names in common use include uridine diphosphogalactose-galactogen galactosyltransferase, 1,6-D-galactosyltransferase, and beta-(1-6)-D-galactosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651392
|
14651410
|
Galactolipid galactosyltransferase
|
Class of enzymes
In enzymology, a galactolipid galactosyltransferase (EC 2.4.1.184) is an enzyme that catalyzes the chemical reaction
2 3-(beta-D-galactosyl)-1,2-diacyl-sn-glycerol formula_0 3-[alpha-D-galactosyl-(1->6)-beta-D-galactosyl]-1,2-diacyl-sn- glycerol + 1,2-diacyl-sn-glycerol
Hence, this enzyme has one substrate, 3-(beta-D-galactosyl)-1,2-diacyl-sn-glycerol, but 3 products: 3-[alpha-D-galactosyl-(1->6)-beta-D-galactosyl]-1,2-diacyl-sn-, glycerol, and 1,2-diacyl-sn-glycerol.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is 3-(beta-D-galactosyl)-1,2-diacyl-sn-glycerol:mono-3-(beta-D-galactos yl)-1,2-diacyl-sn-glycerol beta-D-galactosyltransferase. Other names in common use include galactolipid-galactolipid galactosyltransferase, galactolipid:galactolipid galactosyltransferase, interlipid galactosyltransferase, GGGT, DGDG synthase (ambiguous), and digalactosyldiacylglycerol synthase (ambiguous). This enzyme participates in glycerolipid metabolism.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651410
|
14651427
|
Galactoside 2-alpha-L-fucosyltransferase
|
Class of enzymes
In enzymology, a galactoside 2-alpha-L-fucosyltransferase (EC 2.4.1.69) is an enzyme that catalyzes the chemical reaction
GDP-beta-L-fucose + beta-D-galactosyl-R formula_0 GDP + alpha-L-fucosyl-1,2-beta-D-galactosyl-R
Thus, the two substrates of this enzyme are GDP-beta-L-fucose and beta-D-galactosyl-R, whereas its two products are GDP and alpha-L-fucosyl-1,2-beta-D-galactosyl-R.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases.
This enzyme participates in 4 metabolic pathways: glycosphingolipid biosynthesis - lactoseries, glycosphingolipid biosynthesis - neo-lactoseries, glycosphingolipid biosynthesis - globoseries, and glycan structures - biosynthesis 2.
Nomenclature.
The systematic name of this enzyme class is:
Other names in common use include:
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651427
|
14651445
|
Galactosyldiacylglycerol alpha-2,3-sialyltransferase
|
Class of enzymes
In enzymology, a galactosyldiacylglycerol alpha-2,3-sialyltransferase (EC 2.4.99.5) is an enzyme that catalyzes the chemical reaction
CMP-N-acetylneuraminate + 1,2-diacyl-3-beta-D-galactosyl-sn-glycerol formula_0 CMP + 1,2-diacyl-3-[3-(alpha-D-N-acetylneuraminyl)-beta-D-galactosyl]-sn- glycerol
Thus, the two substrates of this enzyme are CMP-N-acetylneuraminate and 1,2-diacyl-3-beta-D-galactosyl-sn-glycerol, whereas its 3 products are CMP, 1,2-diacyl-3-[3-(alpha-D-N-acetylneuraminyl)-beta-D-galactosyl]-sn-, and glycerol.
This enzyme belongs to the family of transferases, specifically those glycosyltransferases that do not transfer hexosyl or pentosyl groups. The systematic name of this enzyme class is CMP-N-acetylneuraminate:1,2-diacyl-3-beta-D-galactosyl-sn-glycerol N-acetylneuraminyltransferase. This enzyme participates in glycerolipid metabolism.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651445
|
14651482
|
Galactosylgalactosylxylosylprotein 3-beta-glucuronosyltransferase
|
Class of enzymes
In enzymology, a galactosylgalactosylxylosylprotein 3-beta-glucuronosyltransferase (EC 2.4.1.135) is an enzyme that catalyzes the chemical reaction
UDP-glucuronate + 3-beta-D-galactosyl-4-beta-D-galactosyl-O-beta-D-xylosylprotein formula_0 UDP + 3-beta-D-glucuronosyl-3-beta-D-galactosyl-4-beta-D-galactosyl-O- beta-D-xylosylprotein
Thus, the two substrates of this enzyme are UDP-glucuronate and 3-beta-D-galactosyl-4-beta-D-galactosyl-O-beta-D-xylosylprotein, whereas its 3 products are UDP, 3-beta-D-glucuronosyl-3-beta-D-galactosyl-4-beta-D-galactosyl-O-, and beta-D-xylosylprotein.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucuronate:3-beta-D-galactosyl-4-beta-D-galactosyl-O-beta-D-xyl osyl-protein D-glucuronosyltransferase. Other names in common use include glucuronosyltransferase I, and uridine diphosphate glucuronic acid:acceptor glucuronosyltransferase. This enzyme participates in chondroitin sulfate biosynthesis and glycan structures - biosynthesis 1. It employs one cofactor, manganese.
Structural studies.
As of late 2007, 4 structures have been solved for this class of enzymes, with PDB accession codes 1V82, 1V83, 1V84, and 2D0J.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651482
|
14651502
|
Galactosylxylosylprotein 3-beta-galactosyltransferase
|
Class of enzymes
In enzymology, a galactosylxylosylprotein 3-beta-galactosyltransferase (EC 2.4.1.134) is an enzyme that catalyzes the chemical reaction
UDP-galactose + 4-beta-D-galactosyl-O-beta-D-xylosylprotein formula_0 UDP + 3-beta-D-galactosyl-4-beta-D-galactosyl-O-beta-D-xylosylprotein
Thus, the two substrates of this enzyme are UDP-galactose and 4-beta-D-galactosyl-O-beta-D-xylosylprotein, whereas its two products are UDP and 3-beta-D-galactosyl-4-beta-D-galactosyl-O-beta-D-xylosylprotein.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:4-beta-D-galactosyl-O-beta-D-xylosylprotein 3-beta-D-galactosyltransferase. Other names in common use include galactosyltransferase II, and uridine diphosphogalactose-galactosylxylose galactosyltransferase. This enzyme participates in chondroitin sulfate biosynthesis and glycan structures - biosynthesis 1. It employs one cofactor, manganese.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651502
|
14651523
|
Gallate 1-beta-glucosyltransferase
|
Class of enzymes
In enzymology, a gallate 1-beta-glucosyltransferase (EC 2.4.1.136) is an enzyme that catalyzes the chemical reaction
UDP-glucose + gallate formula_0 UDP + 1-galloyl-beta-D-glucose
Thus, the two substrates of this enzyme are UDP-glucose and gallate, whereas its two products are UDP and 1-galloyl-beta-D-glucose.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:gallate beta-D-glucosyltransferase. Other names in common use include UDP-glucose-vanillate 1-glucosyltransferase, UDPglucose:vanillate 1-O-glucosyltransferase, and UDPglucose:gallate glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651523
|
14651538
|
Ganglioside galactosyltransferase
|
Class of enzymes
In enzymology, a ganglioside galactosyltransferase (EC 2.4.1.62) is an enzyme that catalyzes the chemical reaction
UDP-galactose + N-acetyl-D-galactosaminyl-(N-acetylneuraminyl)-D-galactosyl-1,4-beta-D-glucosyl-N-acylsphingosine formula_0 UDP + D-galactosyl-1,3-beta-N-acetyl-D-galactosaminyl-(N-acetylneuraminyl)-D-galactosyl-D-glucosyl-N-acylsphingosine
The 2 substrates of this enzyme are UDP-galactose and N-acetyl-D-galactosaminyl-(N-acetylneuraminyl)-D-galactosyl-1,4-beta-D-glucosyl-N-acylsphingosine, whereas its 2 products are UDP and D-galactosyl-1,3-beta-N-acetyl-D-galactosaminyl-(N-acetylneuraminyl)-D-galactosyl-D-glucosyl-N-acylsphingosine.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:N-acetyl-D-galactosaminyl-(N-acetylneuraminyl)-D-galac tosyl-D-glucosyl-N-acylsphingosine beta-1,3-D-galactosyltransferase. Other names in common use include UDP-galactose-ceramide galactosyltransferase, uridine diphosphogalactose-ceramide galactosyltransferase, UDP galactose-LAC Tet-ceramide alpha-galactosyltransferase, UDP-galactose-GM2 galactosyltransferase, uridine diphosphogalactose-GM2 galactosyltransferase, uridine diphosphate D-galactose:glycolipid galactosyltransferase, UDP-galactose:N-acetylgalactosaminyl-(N-acetylneuraminyl), galactosyl-glucosyl-ceramide galactosyltransferase, UDP-galactose-GM2 ganglioside galactosyltransferase, and GM1-synthase. This enzyme participates in glycosphingolipid biosynthesis - ganglioseries and glycan structures - biosynthesis 2.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651538
|
14651559
|
Gibberellin beta-D-glucosyltransferase
|
Class of enzymes
In enzymology, a gibberellin beta-D-glucosyltransferase (EC 2.4.1.176) is an enzyme that catalyzes the chemical reaction
UDP-glucose + gibberellin formula_0 UDP + gibberellin 2-O-beta-D-glucoside
Thus, the two substrates of this enzyme are UDP-glucose and gibberellin, whereas its two products are UDP and gibberellin 2-O-beta-D-glucoside.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:gibberellin 2-O-beta-D-glucosyltransferase. Other names in common use include uridine diphosphoglucose-gibberellate 7-glucosyltransferase, and uridine diphosphoglucose-gibberellate 3-O-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651559
|
14651574
|
Globoside alpha-N-acetylgalactosaminyltransferase
|
Class of enzymes
In enzymology, a globoside alpha-N-acetylgalactosaminyltransferase (EC 2.4.1.88) is an enzyme that catalyzes the chemical reaction
UDP-N-acetyl-D-galactosamine + N-acetyl-D-galactosaminyl-1,3-D-galactosyl-1,4-D-galactosyl-1,4-D- glucosylceramide formula_0 UDP + N-acetyl-D-galactosaminyl-N-acetyl-D-galactosaminyl-1,3-D- galactosyl-1,4-D-galactosyl-1,4-D-glucosylceramide
The 3 substrates of this enzyme are UDP-N-acetyl-D-galactosamine, N-acetyl-D-galactosaminyl-1,3-D-galactosyl-1,4-D-galactosyl-1,4-D-, and glucosylceramide, whereas its 3 products are UDP, N-acetyl-D-galactosaminyl-N-acetyl-D-galactosaminyl-1,3-D-, and galactosyl-1,4-D-galactosyl-1,4-D-glucosylceramide.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-N-acetyl-D-galactosamine:N-acetyl-D-galactosaminyl-1,3-D-galacto syl-1,4-D-galactosyl-1,4-D-glucosylceramide alpha-N-acetyl-D-galactosaminyltransferase. Other names in common use include uridine diphosphoacetylgalactosamine-globoside, alpha-acetylgalactosaminyltransferase, Forssman synthase, and globoside acetylgalactosaminyltransferase. This enzyme participates in glycosphingolipid biosynthesis - globoseries and glycan structures - biosynthesis 2.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651574
|
14651586
|
Globotriaosylceramide 3-beta-N-acetylgalactosaminyltransferase
|
Class of enzymes
In enzymology, a globotriaosylceramide 3-beta-N-acetylgalactosaminyltransferase (EC 2.4.1.79) is an enzyme that catalyzes the chemical reaction
UDP-N-acetyl-D-galactosamine + alpha-D-galactosyl-(1->4)-beta-D-galactosyl-(1->4)-beta-D-glucosyl- (11)-ceramide formula_0 UDP + N-acetyl-beta-D-galactosaminyl-(1->3)-alpha-D-galactosyl-(1->4)- beta-D-galactosyl-(1->4)-beta-D-glucosyl-(11)-ceramide
The 3 substrates of this enzyme are UDP-N-acetyl-D-galactosamine, alpha-D-galactosyl-(1->4)-beta-D-galactosyl-(1->4)-beta-D-glucosyl-, and (11)-ceramide, whereas its 3 products are UDP, N-acetyl-beta-D-galactosaminyl-(1->3)-alpha-D-galactosyl-(1->4)-, and beta-D-galactosyl-(1->4)-beta-D-glucosyl-(11)-ceramide.
Wrongly characterized previously as globotriosylceramide beta-1,6-N-acetylgalactosaminyl-transferase (EC 2.4.1.154
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-N-acetyl-D-galactosamine:alpha-D-galactosyl-(1->4)-beta-D-galact osyl-(1->4)-beta-D-glucosyl-(11)-ceramide III3-beta-N-acetyl-D-galactosaminyltransferase. This enzyme participates in glycosphingolipid biosynthesis - globoseries and glycan structures - biosynthesis 2.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651586
|
14651604
|
Glucomannan 4-beta-mannosyltransferase
|
Class of enzymes
In enzymology, a glucomannan 4-beta-mannosyltransferase (EC 2.4.1.32) is an enzyme that catalyzes the chemical reaction
GDP-mannose + (glucomannan)n formula_0 GDP + (glucomannan)n+1
Thus, the two substrates of this enzyme are GDP-mannose and (glucomannan)n, whereas its two products are GDP and (glucomannan)n+1, a noncellulosic polysaccharide which is used in the formation of cell walls.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is GDPmannose:glucomannan 1,4-beta-D-mannosyltransferase. Other names in common use include GDP-man-beta-mannan manosyltransferase, and glucomannan-synthase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651604
|
14651620
|
Glucosaminylgalactosylglucosylceramide beta-galactosyltransferase
|
Class of enzymes
In enzymology, a glucosaminylgalactosylglucosylceramide beta-galactosyltransferase (EC 2.4.1.86) is an enzyme that catalyzes the chemical reaction
UDP-galactose + N-acetyl-beta-D-glucosaminyl-(1->3)-beta-D-galactosyl-(1->4)-beta-D- glucosyl-(11)-ceramide formula_0 UDP + beta-D-galactosyl-(1->3)-N-acetyl-beta-D-glucosaminyl-(1->3)-beta-D- galactosyl-(1->4)-beta-D-glucosyl-(11)-ceramide
The 3 substrates of this enzyme are UDP-galactose, N-acetyl-beta-D-glucosaminyl-(1->3)-beta-D-galactosyl-(1->4)-beta-D-, and glucosyl-(11)-ceramide, whereas its 3 products are UDP, beta-D-galactosyl-(1->3)-N-acetyl-beta-D-glucosaminyl-(1->3)-beta-D-, and galactosyl-(1->4)-beta-D-glucosyl-(11)-ceramide.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:N-acetyl-beta-D-glucosaminyl-(1->3)-beta-D-galactosyl- (1->4)-beta-D-glucosylceramide 3-beta-D-galactosyltransferase. Other names in common use include uridine, diphosphogalactose-acetyl-glucosaminylgalactosylglucosylceramide, galactosyltransferase, GalT-4, paragloboside synthase, glucosaminylgalactosylglucosylceramide 4-beta-galactosyltransferase, lactotriaosylceramide 4-beta-galactosyltransferase, UDP-galactose:N-acetyl-D-glucosaminyl-1,3-D-galactosyl-1,4-D-, glucosylceramide beta-D-galactosyltransferase, and UDP-Gal:LcOse3Cer(beta 1-4)galactosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651620
|
14651643
|
Glucosylglycerol-phosphate synthase
|
Class of enzymes
In enzymology, a glucosylglycerol-phosphate synthase (EC 2.4.1.213) is an enzyme that catalyzes the chemical reaction
ADP-glucose + sn-glycerol 3-phosphate formula_0 2-(beta-D-glucosyl)-sn-glycerol 3-phosphate + ADP
Thus, the two substrates of this enzyme are ADP-glucose and sn-glycerol 3-phosphate, whereas its two products are 2-(beta-D-glucosyl)-sn-glycerol 3-phosphate and ADP.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is ADP-glucose:sn-glycerol-3-phosphate 2-beta-D-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651643
|
14651686
|
Glycoprotein 2-beta-D-xylosyltransferase
|
Class of enzymes
In enzymology, a glycoprotein 2-beta-D-xylosyltransferase (EC 2.4.2.38) is an enzyme that catalyzes the chemical reaction
UDP-D-xylose + N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N- acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D- mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-N-acetyl-beta-D- glucosaminyl}asparagine formula_0 UDP + N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N- acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-[beta-D- xylosyl-(1->2)]-beta-D-mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl- (1->4)-N-acetyl-beta-D-glucosaminyl}asparagine
The 5 substrates of this enzyme are UDP-D-xylose, N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N-, acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D-, mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-N-acetyl-beta-D-, and glucosaminyl}asparagine, whereas its 5 products are UDP, N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N-, acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)-beta-D-, xylosyl-(1->2)]-beta-D-mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-, and (1->4)-N-acetyl-beta-D-glucosaminyl}asparagine.
This enzyme belongs to the family of glycosyltransferases, specifically the pentosyltransferases. The systematic name of this enzyme class is UDP-D-xylose:glycoprotein (D-xylose to the 3,6-disubstituted mannose of N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N-a cetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D-man nosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-N-acetyl-beta-D-glu cosaminyl}asparagine) 2-beta-D-xylosyltransferase. Other names in common use include beta1,2-xylosyltransferase, UDP-D-xylose:glycoprotein (D-xylose to the 3,6-disubstituted mannose, of, 4-N-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N-, acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D-, mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-N-acetyl-beta-D-, and glucosaminyl}asparagine) 2-beta-D-xylosyltransferase. This enzyme participates in glycan structures - biosynthesis 1.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651686
|
14651709
|
Glycoprotein 3-alpha-L-fucosyltransferase
|
Class of enzymes
In enzymology, a glycoprotein 3-alpha-L-fucosyltransferase (EC 2.4.1.214) is an enzyme that catalyzes the chemical reaction
GDP-L-fucose + N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N- acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D- mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-N-acetyl-beta-D- glucosaminyl}asparagine formula_0 GDP + N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N- acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D- mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-[alpha-L- fucosyl-(1->3)]-N-acetyl-beta-D-glucosaminyl}asparagine
The 5 substrates of this enzyme are GDP-L-fucose, N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N-, acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D-, mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-N-acetyl-beta-D-, and glucosaminyl}asparagine, whereas its 5 products are GDP, N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N-, acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D-, mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-[alpha-L-, and fucosyl-(1->3)]-N-acetyl-beta-D-glucosaminyl}asparagine.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is GDP-L-fucose:glycoprotein (L-fucose to asparagine-linked N-acetylglucosamine of N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N-a cetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D-man nosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-N-acetyl-beta-D-glu cosaminyl}asparagine) 3-alpha-L-fucosyl-transferase. Other names in common use include GDP-L-Fuc:N-acetyl-beta-D-glucosaminide alpha1,3-fucosyltransferase, GDP-L-Fuc:Asn-linked GlcNAc alpha1,3-fucosyltransferase, GDP-fucose:beta-N-acetylglucosamine (Fuc to, (Fucalpha1->6GlcNAc)-Asn-peptide) alpha1->3-fucosyltransferase, GDP-L-fucose:glycoprotein (L-fucose to asparagine-linked, N-acetylglucosamine of, 4-N-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N-, acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D-, mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-N-acetyl-beta-D-, and glucosaminyl}asparagine) 3-alpha-L-fucosyl-transferase. This enzyme participates in glycan structures - biosynthesis 1.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651709
|
14651727
|
Glycoprotein 6-alpha-L-fucosyltransferase
|
InterPro Family
In enzymology, a glycoprotein 6-alpha-L-fucosyltransferase (EC 2.4.1.68) is an enzyme that catalyzes the chemical reaction
GDP-L-fucose + N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N- acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D- mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-N-acetyl-beta-D- glucosaminyl}asparagine formula_0 GDP + N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N- acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D- mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-[alpha-L- fucosyl-(1->6)]-N-acetyl-beta-D-glucosaminyl}asparagine
The 2 substrates of this enzyme are GDP-L-fucose and N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D-mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-N-acetyl-beta-D-glucosaminyl}asparagine, and its 2 products are GDP and N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D-mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-[alpha-L-fucosyl-(1->6)]-N-acetyl-beta-D-glucosaminyl}asparagine.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is GDP-L-fucose:glycoprotein (L-fucose to asparagine-linked N-acetylglucosamine of N4-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N-a cetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D-man nosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-N-acetyl-beta-D-glu cosaminyl}asparagine) 6-alpha-L-fucosyltransferase. Other names in common use include GDP-fucose-glycoprotein fucosyltransferase, GDP-L-Fuc:N-acetyl-beta-D-glucosaminide alpha1->6fucosyltransferase, GDP-L-fucose-glycoprotein fucosyltransferase, glycoprotein fucosyltransferase, guanosine diphosphofucose-glycoprotein fucosyltransferase, GDP-L-fucose:glycoprotein (L-fucose to asparagine-linked, N-acetylglucosamine of, 4-N-{N-acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->3)-[N-, acetyl-beta-D-glucosaminyl-(1->2)-alpha-D-mannosyl-(1->6)]-beta-D-, mannosyl-(1->4)-N-acetyl-beta-D-glucosaminyl-(1->4)-N-acetyl-beta-D-, glucosaminyl}asparagine) 6-alpha-L-fucosyltransferase, and FucT. This enzyme participates in 3 metabolic pathways: n-glycan biosynthesis, keratan sulfate biosynthesis, and glycan structures - biosynthesis 1.
Structural studies.
As of late 2007, 3 structures have been solved for this class of enzymes, with PDB accession codes 2DE0, 2HHC, and 2HLH.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651727
|
14651747
|
Glycoprotein-N-acetylgalactosamine 3-beta-galactosyltransferase
|
Class of enzymes
In enzymology, a glycoprotein-N-acetylgalactosamine 3-beta-galactosyltransferase (EC 2.4.1.122) is an enzyme that catalyzes the chemical reaction
UDP-galactose + glycoprotein N-acetyl-D-galactosamine formula_0 UDP + glycoprotein D-galactosyl-1,3-N-acetyl-D-galactosamine
Thus, the two substrates of this enzyme are UDP-galactose and glycoprotein N-acetyl-D-galactosamine, whereas its two products are UDP and glycoprotein D-galactosyl-1,3-N-acetyl-D-galactosamine.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:glycoprotein-N-acetyl-D-galactosamine 3-beta-D-galactosyltransferase. This enzyme is also called uridine diphosphogalactose-mucin beta-(1->3)-galactosyltransferase. This enzyme participates in o-glycan biosynthesis and glycan structures - biosynthesis 1.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651747
|
14651761
|
Glycosaminoglycan galactosyltransferase
|
Class of enzymes
In enzymology, a glycosaminoglycan galactosyltransferase (EC 2.4.1.74) is an enzyme that catalyzes the chemical reaction
UDP-galactose + glycosaminoglycan formula_0 UDP + D-galactosylglycosaminoglycan
Thus, the two substrates of this enzyme are UDP-galactose and glycosaminoglycan, whereas its two products are UDP and D-galactosylglycosaminoglycan.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:glycosaminoglycan D-galactosyltransferase. This enzyme is also called uridine diphosphogalactose-mucopolysaccharide galactosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651761
|
14651786
|
Guanosine phosphorylase
|
Class of enzymes
In enzymology, a guanosine phosphorylase (EC 2.4.2.15) is an enzyme that catalyzes the chemical reaction
guanosine + phosphate formula_0 guanine + alpha-D-ribose 1-phosphate
Thus, the two substrates of this enzyme are guanosine and phosphate, whereas its two products are guanine and alpha-D-ribose 1-phosphate.
This enzyme belongs to the family of glycosyltransferases, specifically the pentosyltransferases. The systematic name of this enzyme class is guanosine:phosphate alpha-D-ribosyltransferase. This enzyme participates in purine metabolism.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14651786
|
14653734
|
Theta solvent
|
In a polymer solution, a theta solvent (or θ solvent) is a solvent in which polymer coils act like ideal chains, assuming exactly their random walk coil dimensions. Therefore, the Mark–Houwink equation exponent is formula_0 in a theta solvent. Thermodynamically, the excess chemical potential of mixing between a polymer and a theta solvent is zero.
Physical interpretation.
The conformation assumed by a polymer chain in dilute solution can be modeled as a random walk of monomer subunits using a freely jointed chain model. However, this model does not account for steric effects. Real polymer coils are more closely represented by a self-avoiding walk because conformations in which different chain segments occupy the same space are not physically possible. This excluded volume effect causes the polymer to expand.
Chain conformation is also affected by solvent quality. The intermolecular interactions between polymer chain segments and coordinated solvent molecules have an associated energy of interaction which can be positive or negative. For a "good solvent", interactions between polymer segments and solvent molecules are energetically favorable, and will cause polymer coils to expand. For a "poor solvent", polymer-polymer self-interactions are preferred, and the polymer coils will contract. The quality of the solvent depends on both the chemical compositions of the polymer and solvent molecules and the solution temperature.
Theta temperature.
If a solvent is precisely poor enough to cancel the effects of excluded volume expansion, the theta (θ) condition is satisfied. For a given polymer-solvent pair, the theta condition is satisfied at a certain temperature, called the theta (θ) temperature or theta point. A solvent at this temperature is called a theta solvent.
In general, measurements of the properties of polymer solutions depend on the solvent. However, when a theta solvent is used, the measured characteristics are independent of the solvent. They depend only on short-range properties of the polymer such as the bond length, bond angles, and sterically favorable rotations. The polymer chain will behave exactly as predicted by the random walk or ideal chain model. This makes experimental determination of important quantities such as the root mean square end-to-end distance or the radius of gyration much simpler.
Additionally, the theta condition is also satisfied in the bulk amorphous polymer phase. Thus, the conformations adopted by polymers dissolved in theta solvents are identical to those adopted in bulk polymer polymerization .
Thermodynamic definition.
Thermodynamically, the excess chemical potential of mixing between a theta solvent and a polymer is zero. Equivalently, the enthalpy of mixing is zero, making the solution ideal.
One cannot measure the chemical potential by any direct means, but one can correlate it to the solution's osmotic pressure (formula_1) and the solvent's partial specific volume (formula_2):
formula_3
One can use a virial expansion to express how osmotic pressure depends on concentration:
formula_4
"M" is the molecular weight of the polymer
"R" is the gas constant
"T" is the absolute temperature
"B" is the second virial coefficient
This relationship with osmotic pressure is one way to determine the theta condition or theta temperature for a solvent.
The change in the chemical potential when the two are mixed has two terms: ideal and excess:
formula_5
The second virial coefficient, B, is proportional to the excess chemical potential of mixing:
formula_6
B reflects the energy of binary interactions between solvent molecules and segments of polymer chain. When B > 0, the solvent is "good," and when B < 0, the solvent is "poor". For a theta solvent, the second virial coefficient is zero because the excess chemical potential is zero; otherwise it would fall outside the definition of a theta solvent. A solvent at its theta temperature is, in this way, analogous to a real gas at its Boyle temperature.
Similar relationships exist for other experimental techniques, including light scattering, intrinsic viscosity measurement, sedimentation equilibrium, and cloud point titration.
|
[
{
"math_id": 0,
"text": "1/2"
},
{
"math_id": 1,
"text": "\\Pi"
},
{
"math_id": 2,
"text": "v_s"
},
{
"math_id": 3,
"text": "\\Delta\\mu_1 = -v_s\\Pi"
},
{
"math_id": 4,
"text": "\\frac{\\Pi}{RT} = \\frac{c}{M} + Bc^2 + B_3c^3..."
},
{
"math_id": 5,
"text": "\\Delta\\mu_1=\\Delta\\mu_1^{ideal}+\\Delta\\mu_1^{excess}"
},
{
"math_id": 6,
"text": "B=\\frac{-\\Delta\\mu_1^{excess}}{{v_s}{c^2}}"
}
] |
https://en.wikipedia.org/wiki?curid=14653734
|
14653762
|
Tukey's range test
|
Statistical test for multiple comparisons
Tukey's range test, also known as Tukey's test, Tukey method, Tukey's honest significance test, or Tukey's HSD (honestly significant difference) test,
is a single-step multiple comparison procedure and statistical test. It can be used to correctly interpret the statistical significance of the difference between means that have been selected for comparison because of their extreme values.
The method was initially developed and introduced by John Tukey for use in Analysis of Variance (ANOVA), and usually has only been taught in connection with ANOVA. However, the studentized range distribution used to determine the level of significance of the differences considered in Tukey's test has vastly broader application: It is useful for researchers who have searched their collected data for remarkable differences between groups, but then cannot validly determine how significant their discovered stand-out difference is using standard statistical distributions used for other conventional statistical tests, for which the data must have been selected at random. Since when stand-out data is compared it was by definition "not" selected at random, but rather specifically chosen because it was extreme, it needs a different, stricter interpretation provided by the likely frequency and size of the studentized range; the modern practice of "data mining" is an example where it is used.
Development.
The test is named after John Tukey,
it compares all possible pairs of means, and is based on a studentized range distribution (q) (this distribution is similar to the distribution of t from the t-test. See below).
Tukey's test compares the means of every treatment to the means of every other treatment; that is, it applies simultaneously to the set of all pairwise comparisons
formula_0
and identifies any difference between two means that is greater than the expected standard error. The confidence coefficient for the set, when all sample sizes are equal, is exactly formula_1 for any formula_2 For unequal sample sizes, the confidence coefficient is greater than formula_3 In other words, the Tukey method is conservative when there are unequal sample sizes.
This test is often followed by the Compact Letter Display (CLD) statistical procedure to render the output of this test more transparent to non-statistician audiences.
The test statistic.
Tukey's test is based on a formula very similar to that of the t-test. In fact, Tukey's test is essentially a t-test, except that it corrects for family-wise error rate.
The formula for Tukey's test is
formula_4
where YA and YB are the two means being compared, and SE is the standard error for the sum of the means. The value qs is the sample's test statistic. (The notation means the absolute value of x; the magnitude of x with the sign set to +, regardless of the original sign of x.)
This qs test statistic can then be compared to a q value for the chosen significance level α from a table of the studentized range distribution. If the qs value is "larger" than the critical value qα obtained from the distribution, the two means are said to be significantly different at level
Since the null hypothesis for Tukey's test states that all means being compared are from the same population (i.e. "μ"1
"μ"2
"μ"3
"μk" ), the means should be normally distributed (according to the central limit theorem) with the same model standard deviation σ, estimated by the merged standard error, formula_5 for all the samples; its calculation is discussed in the following sections. This gives rise to the normality assumption of Tukey's test.
The studentized range (q) distribution.
The Tukey method uses the studentized range distribution. Suppose that we take a sample of size n from each of k populations with the same normal distribution and suppose that formula_6 is the smallest of these sample means and formula_7 is the largest of these sample means, and suppose S2 is the pooled sample variance from these samples. Then the following random variable has a Studentized range distribution:
formula_8
This definition of the statistic q given above is the basis of the critically significant value for qα discussed below, and is based on these three factors:
formula_9 the Type I error rate, or the probability of rejecting a true null hypothesis;
formula_10 the number of sub-populations being compared;
formula_11 the number of degrees of freedom for each mean
( df
"N" − "k" ) where N is the total number of observations.)
The distribution of q has been tabulated and appears in many textbooks on statistics. In some tables the distribution of q has been tabulated without the formula_12 factor. To understand which table it is, we can compute the result for and compare it to the result of the Student's t-distribution with the same degrees of freedom and the
In addition, R offers a cumulative distribution function (codice_0) and a quantile function (codice_1)
Confidence limits.
The Tukey confidence limits for all pairwise comparisons with confidence coefficient of at least
formula_13
Notice that the point estimator and the estimated variance are the same as those for a single pairwise comparison. The only difference between the confidence limits for simultaneous comparisons and those for a single comparison is the multiple of the estimated standard deviation.
Also note that the sample sizes must be equal when using the studentized range approach. formula_14 is the standard deviation of the entire design, not just that of the two groups being compared. It is possible to work with unequal sample sizes. In this case, one has to calculate the estimated standard deviation for each pairwise comparison as formalized by Clyde Kramer in 1956, so the procedure for unequal sample sizes is sometimes referred to as the Tukey–Kramer method which is as follows:
formula_15
where and are the sizes of groups i and j respectively. The degrees of freedom for the whole design is also applied.
Comparing ANOVA and Tukey–Kramer tests.
Both ANOVA and Tukey–Kramer tests are based on the same assumptions. However, these two tests for k groups (i.e. "μ"1
"μ"2
"μk" ) may result in logical contradictions when even if the assumptions do hold.
It is possible to generate a set of pseudorandom samples of strictly negative measure such that hypothesis is rejected at significance level formula_16 while is not rejected even at formula_17
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": " \\mu_i - \\mu_j\\ ,"
},
{
"math_id": 1,
"text": "\\ 1 - \\alpha\\ "
},
{
"math_id": 2,
"text": "\\ \\alpha ~:~ 0 \\le \\alpha \\le 1 ~."
},
{
"math_id": 3,
"text": "\\ 1 - \\alpha ~."
},
{
"math_id": 4,
"text": " q_\\mathsf{s} = \\frac{\\ \\left| Y_\\mathsf{A} - Y_\\mathsf{B} \\right|\\ }{\\ \\mathsf{SE}\\ }\\ ,"
},
{
"math_id": 5,
"text": "\\ \\mathsf{SE}\\ ,"
},
{
"math_id": 6,
"text": "\\ \\bar{y}_\\mathsf{min}\\ "
},
{
"math_id": 7,
"text": "\\ \\bar{y}_\\mathsf{max}\\ "
},
{
"math_id": 8,
"text": " q \\equiv \\frac{\\ \\overline{y}_\\mathsf{max} - \\overline{y}_\\mathsf{min}\\ }{\\ S\\sqrt{2/n}\\ }"
},
{
"math_id": 9,
"text": "\\ \\alpha~ \\quad "
},
{
"math_id": 10,
"text": "\\ k~ \\quad"
},
{
"math_id": 11,
"text": "\\ \\mathsf{df} \\quad"
},
{
"math_id": 12,
"text": "\\ \\sqrt{2\\ }\\ "
},
{
"math_id": 13,
"text": " \\bar{y}_{i\\bullet} - \\bar{y}_{j\\bullet}\\ \\pm\\ \\frac{\\ q_{\\ \\alpha\\ ;\\ k\\ ;\\ N-k}\\ }{\\ \\sqrt{2\\ }\\ }\\ \\widehat{\\sigma}_\\varepsilon\\ \\sqrt{\\frac{2}{n}\\ } \\quad : \\quad i,\\ j = 1, \\ldots, k \\quad i\\neq j ~."
},
{
"math_id": 14,
"text": "\\ \\widehat{\\sigma}_\\varepsilon\\ "
},
{
"math_id": 15,
"text": " \\bar{y}_{i\\bullet} - \\bar{y}_{j\\bullet}\\ \\pm\\ \\frac{\\ q_{\\ \\alpha\\ ;\\ k\\ ;\\ N-k}\\ }{\\ \\sqrt{2\\ }\\ }\\ \\widehat{\\sigma}_\\varepsilon\\ \\sqrt{\\ \\frac{\\ 1\\ }{ n_i }\\ +\\ \\frac{\\ 1\\ }{ n_j }\\ }\\ "
},
{
"math_id": 16,
"text": "\\ 1 - \\alpha > 0.95\\ "
},
{
"math_id": 17,
"text": "\\ 1 - \\alpha = 0.975 ~."
}
] |
https://en.wikipedia.org/wiki?curid=14653762
|
14655845
|
Complex-base system
|
Positional numeral system
In arithmetic, a complex-base system is a positional numeral system whose radix is an imaginary (proposed by Donald Knuth in 1955) or complex number (proposed by S. Khmelnik in 1964 and Walter F. Penney in 1965).
In general.
Let formula_0 be an integral domain formula_1, and formula_2 the (Archimedean) absolute value on it.
A number formula_3 in a positional number system is represented as an expansion
formula_4
where
The cardinality formula_5 is called the "level of decomposition".
A positional number system or coding system is a pair
formula_6
with radix formula_7 and set of digits formula_8, and we write the standard set of digits with formula_9 digits as
formula_10
Desirable are coding systems with the features:
In the real numbers.
In this notation our standard decimal coding scheme is denoted by
formula_21
the standard binary system is
formula_22
the negabinary system is
formula_23
and the balanced ternary system is
formula_24
All these coding systems have the mentioned features for formula_11 and formula_25, and the last two do not require a sign.
In the complex numbers.
Well-known positional number systems for the complex numbers include the following (formula_26 being the imaginary unit):
formula_29, the quater-imaginary base, proposed by Donald Knuth in 1955.
formula_31 (see also the section Base −1 ± i below).
formula_38
formula_44
Binary systems.
"Binary" coding systems of complex numbers, i.e. systems with the digits formula_47, are of practical interest.
Listed below are some coding systems formula_48 (all are special cases of the systems above) and resp. codes for the (decimal) numbers −1, 2, −2, i.
The standard binary (which requires a sign, first line) and the "negabinary" systems (second line) are also listed for comparison. They do not have a genuine expansion for i.
As in all positional number systems with an "Archimedean" absolute value, there are some numbers with multiple representations. Examples of such numbers are shown in the right column of the table. All of them are repeating fractions with the repetend marked by a horizontal line above it.
If the set of digits is minimal, the set of such numbers has a measure of 0. This is the case with all the mentioned coding systems.
The almost binary quater-imaginary system is listed in the bottom line for comparison purposes. There, real and imaginary part interleave each other.
Base −1 ± i.
Of particular interest are the quater-imaginary base (base 2i) and the base −1 ± i systems discussed below, both of which can be used to finitely represent the Gaussian integers without sign.
Base −1 ± i, using digits 0 and 1, was proposed by S. Khmelnik in 1964 and Walter F. Penney in 1965.
Connection to the twindragon.
The rounding region of an integer – i.e., a set formula_49 of complex (non-integer) numbers that share the integer part of their representation in this system – has in the complex plane a fractal shape: the twindragon (see figure). This set formula_49 is, by definition, all points that can be written as formula_50 with formula_51. formula_49 can be decomposed into 16 pieces congruent to formula_52. Notice that if formula_49 is rotated counterclockwise by 135°, we obtain two adjacent sets congruent to formula_53, because formula_54. The rectangle formula_55 in the center intersects the coordinate axes counterclockwise at the following points: formula_56, formula_57, and formula_58, and formula_59. Thus, formula_49 contains all complex numbers with absolute value ≤ .
As a consequence, there is an injection of the complex rectangle
formula_60
into the interval formula_61 of real numbers by mapping
formula_62
with formula_63.
Furthermore, there are the two mappings
formula_64
and
formula_65
both surjective, which give rise to a surjective (thus space-filling) mapping
formula_66
which, however, is not continuous and thus "not" a space-filling "curve". But a very close relative, the Davis-Knuth dragon, is continuous and a space-filling curve.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "D"
},
{
"math_id": 1,
"text": "\\subset \\C"
},
{
"math_id": 2,
"text": "|\\cdot|"
},
{
"math_id": 3,
"text": "X\\in D"
},
{
"math_id": 4,
"text": " X = \\pm \\sum_{\\nu}^{ } x_\\nu \\rho^\\nu,"
},
{
"math_id": 5,
"text": "R:=|Z|"
},
{
"math_id": 6,
"text": "\\left\\langle \\rho, Z \\right\\rangle"
},
{
"math_id": 7,
"text": "\\rho"
},
{
"math_id": 8,
"text": "Z"
},
{
"math_id": 9,
"text": "R"
},
{
"math_id": 10,
"text": "Z_R := \\{0, 1, 2,\\dotsc, {R-1}\\}."
},
{
"math_id": 11,
"text": "\\Z"
},
{
"math_id": 12,
"text": "\\Z[\\mathrm i]"
},
{
"math_id": 13,
"text": "\\Z[\\tfrac{-1+\\mathrm i\\sqrt7}2]"
},
{
"math_id": 14,
"text": "K:=\\operatorname{Quot}(D)"
},
{
"math_id": 15,
"text": "K:=\\R"
},
{
"math_id": 16,
"text": "K:=\\C"
},
{
"math_id": 17,
"text": "X"
},
{
"math_id": 18,
"text": "\\nu \\to -\\infty"
},
{
"math_id": 19,
"text": "R=|\\rho|"
},
{
"math_id": 20,
"text": "R=|\\rho|^2"
},
{
"math_id": 21,
"text": "\\left\\langle 10, Z_{10} \\right\\rangle,"
},
{
"math_id": 22,
"text": "\\left\\langle 2, Z_2 \\right\\rangle,"
},
{
"math_id": 23,
"text": "\\left\\langle -2, Z_2 \\right\\rangle,"
},
{
"math_id": 24,
"text": "\\left\\langle 3, \\{-1,0,1\\} \\right\\rangle."
},
{
"math_id": 25,
"text": "\\R"
},
{
"math_id": 26,
"text": "\\mathrm i"
},
{
"math_id": 27,
"text": "\\left\\langle\\sqrt{R},Z_R\\right\\rangle"
},
{
"math_id": 28,
"text": "\\left\\langle\\pm \\mathrm i \\sqrt{2},Z_2\\right\\rangle"
},
{
"math_id": 29,
"text": "\\left\\langle\\pm 2\\mathrm i,Z_4\\right\\rangle"
},
{
"math_id": 30,
"text": "\\left\\langle\\sqrt{2}e^{\\pm \\tfrac{\\pi}2 \\mathrm i}=\\pm \\mathrm i\\sqrt{2},Z_2\\right\\rangle"
},
{
"math_id": 31,
"text": "\\left\\langle\\sqrt{2}e^{\\pm \\tfrac{3 \\pi}4 \\mathrm i}=-1\\pm\\mathrm i,Z_2\\right\\rangle"
},
{
"math_id": 32,
"text": "\\left\\langle\\sqrt{R}e^{\\mathrm i\\varphi},Z_R\\right\\rangle"
},
{
"math_id": 33,
"text": "\\varphi=\\pm \\arccos{(-\\beta/(2\\sqrt{R}))}"
},
{
"math_id": 34,
"text": "\\beta<\\min(R, 2\\sqrt{R})"
},
{
"math_id": 35,
"text": "\\beta_{ }^{ }"
},
{
"math_id": 36,
"text": "\\beta=1"
},
{
"math_id": 37,
"text": "R=2"
},
{
"math_id": 38,
"text": "\\left\\langle\\tfrac{-1+\\mathrm i\\sqrt7}2,Z_2\\right\\rangle."
},
{
"math_id": 39,
"text": "\\left\\langle 2e^{\\tfrac{\\pi}3 \\mathrm i},A_4:=\\left\\{0,1,e^{\\tfrac{2 \\pi}3 \\mathrm i},e^{-\\tfrac{2 \\pi}3 \\mathrm i}\\right\\}\\right\\rangle"
},
{
"math_id": 40,
"text": "\\left\\langle-R,A_R^2\\right\\rangle"
},
{
"math_id": 41,
"text": "A_R^2"
},
{
"math_id": 42,
"text": "r_\\nu=\\alpha_\\nu^1+\\alpha_\\nu^2\\mathrm i"
},
{
"math_id": 43,
"text": "\\alpha_\\nu^{ } \\in Z_R"
},
{
"math_id": 44,
"text": "\\left\\langle -2, \\{0,1,\\mathrm i,1+\\mathrm i\\}\\right\\rangle."
},
{
"math_id": 45,
"text": "\\left\\langle\\rho=\\rho_2,Z_2\\right\\rangle"
},
{
"math_id": 46,
"text": "\\rho_2=\\begin{cases}\n (-2)^{\\tfrac{\\nu}2} & \\text{if } \\nu \\text{ even,}\\\\\n (-2)^{\\tfrac{\\nu-1}2}\\mathrm i & \\text{if } \\nu \\text{ odd.}\n\\end{cases}"
},
{
"math_id": 47,
"text": "Z_2=\\{0,1\\}"
},
{
"math_id": 48,
"text": "\\langle \\rho, Z_2 \\rangle"
},
{
"math_id": 49,
"text": "S"
},
{
"math_id": 50,
"text": "\\textstyle \\sum_{k\\geq 1}x_k (\\mathrm i-1)^{-k}"
},
{
"math_id": 51,
"text": "x_k\\in Z_2"
},
{
"math_id": 52,
"text": "\\tfrac14 S"
},
{
"math_id": 53,
"text": "\\tfrac{1}{\\sqrt{2}}S"
},
{
"math_id": 54,
"text": "(\\mathrm i-1)S=S\\cup(S+1)"
},
{
"math_id": 55,
"text": "R\\subset S"
},
{
"math_id": 56,
"text": "\\tfrac2{15}\\gets 0.\\overline{00001100}"
},
{
"math_id": 57,
"text": "\\tfrac1{15} \\mathrm i\\gets 0.\\overline{00000011}"
},
{
"math_id": 58,
"text": "-\\tfrac8{15}\\gets 0.\\overline{11000000}"
},
{
"math_id": 59,
"text": "-\\tfrac4{15} \\mathrm i\\gets 0.\\overline{00110000}"
},
{
"math_id": 60,
"text": "[-\\tfrac8{15},\\tfrac2{15}]\\times[-\\tfrac4{15},\\tfrac1{15}]\\mathrm i"
},
{
"math_id": 61,
"text": "[0,1)"
},
{
"math_id": 62,
"text": "\\textstyle \\sum_{k\\geq 1}x_k (\\mathrm i-1)^{-k} \\mapsto \\sum_{k\\geq 1}x_k b^{-k}"
},
{
"math_id": 63,
"text": "b > 2"
},
{
"math_id": 64,
"text": "\\begin{array}{lll}\nZ_2^\\N & \\to & S \\\\\n\\left(x_k\\right)_{k\\in\\N} & \\mapsto & \\sum_{k\\geq 1}x_k (\\mathrm i-1)^{-k}\n\\end{array}"
},
{
"math_id": 65,
"text": "\\begin{array}{lll}\nZ_2^\\N & \\to & [0,1) \\\\\n\\left(x_k\\right)_{k\\in\\N} & \\mapsto & \\sum_{k\\geq 1}x_k 2^{-k}\n\\end{array}"
},
{
"math_id": 66,
"text": "[0,1) \\qquad \\to \\qquad S "
}
] |
https://en.wikipedia.org/wiki?curid=14655845
|
14656451
|
Kernelization
|
In computer science, a kernelization is a technique for designing efficient algorithms that achieve their efficiency by a preprocessing stage in which inputs to the algorithm are replaced by a smaller input, called a "kernel". The result of solving the problem on the kernel should either be the same as on the original input, or it should be easy to transform the output on the kernel to the desired output for the original problem.
Kernelization is often achieved by applying a set of reduction rules that cut away parts of the instance that are easy to handle. In parameterized complexity theory, it is often possible to prove that a kernel with guaranteed bounds on the size of a kernel (as a function of some parameter associated to the problem) can be found in polynomial time. When this is possible, it results in a fixed-parameter tractable algorithm whose running time is the sum of the (polynomial time) kernelization step and the (non-polynomial but bounded by the parameter) time to solve the kernel. Indeed, every problem that can be solved by a fixed-parameter tractable algorithm can be solved by a kernelization algorithm of this type. This is also true for approximate kernelization.
Example: vertex cover.
A standard example for a kernelization algorithm is the kernelization of the vertex cover problem by S. Buss.
In this problem, the input is an undirected graph formula_0 together with a number formula_1. The output is a set of at most formula_1 vertices that includes an endpoint of every edge in the graph, if such a set exists, or a failure exception if no such set exists. This problem is NP-hard. However, the following reduction rules may be used to kernelize it:
An algorithm that applies these rules repeatedly until no more reductions can be made necessarily terminates with a kernel that has at most formula_4 edges and (because each edge has at most two endpoints and there are no isolated vertices) at most formula_6 vertices. This kernelization may be implemented in linear time. Once the kernel has been constructed, the vertex cover problem may be solved by a brute force search algorithm that tests whether each subset of the kernel is a cover of the kernel.
Thus, the vertex cover problem can be solved in time formula_7 for a graph with formula_8 vertices and formula_9 edges, allowing it to be solved efficiently when formula_1 is small even if formula_8 and formula_9 are both large.
Although this bound is fixed-parameter tractable, its dependence on the parameter is higher than might be desired. More complex kernelization procedures can improve this bound, by finding smaller kernels, at the expense of greater running time in the kernelization step. In the vertex cover example, kernelization algorithms are known that produce kernels with at most formula_10 vertices.
One algorithm that achieves this improved bound exploits the half-integrality of the linear program relaxation of vertex cover due to Nemhauser and Trotter. Another kernelization algorithm achieving that bound is based on what is known as the crown reduction rule and uses alternating path arguments. The currently best known kernelization algorithm in terms of the number of vertices is due to and achieves formula_11 vertices for any fixed constant formula_12.
It is not possible, in this problem, to find a kernel of size formula_13, unless P = NP, for such a kernel would lead to a polynomial-time algorithm for the NP-hard vertex cover problem. However, much stronger bounds on the kernel size can be proven in this case: unless coNP formula_14 NP/poly (believed unlikely by complexity theorists), for every formula_15 it is impossible in polynomial time to find kernels with formula_16 edges.
It is unknown for vertex cover whether kernels with formula_17 vertices for some formula_15 would have any unlikely complexity-theoretic consequences.
Definition.
In the literature, there is no clear consensus on how kernelization should be formally defined and there are subtle differences in the uses of that expression.
Downey–Fellows notation.
In the notation of , a "parameterized problem" is a subset formula_18 describing a decision problem.
A kernelization for a parameterized problem formula_19 is an algorithm that takes an instance formula_20 and maps it in time polynomial in formula_21 and formula_1 to an instance formula_22 such that
The output formula_22 of kernelization is called a kernel. In this general context, the "size" of the string formula_23 just refers to its length.
Some authors prefer to use the number of vertices or the number of edges as the size measure in the context of graph problems.
Flum–Grohe notation.
In the notation of , a "parameterized problem" consists of a decision problem formula_26 and a function formula_27, the parameterization. The "parameter" of an instance formula_28 is the number formula_29.
A kernelization for a parameterized problem formula_19 is an algorithm that takes an instance formula_28 with parameter formula_1 and maps it in polynomial time to an instance formula_30 such that
Note that in this notation, the bound on the size of formula_30 implies that the parameter of formula_30 is also bounded by a function in formula_1.
The function formula_24 is often referred to as the size of
the kernel. If formula_31, it is said that formula_19 admits a polynomial kernel. Similarly, for formula_32, the problem admits linear kernel.
Kernelizability and fixed-parameter tractability are equivalent.
A problem is fixed-parameter tractable if and only if it is kernelizable and decidable.
That a kernelizable and decidable problem is fixed-parameter tractable can be seen from the definition above:
First the kernelization algorithm, which runs in time formula_33 for some c, is invoked to generate a kernel of size formula_34.
The kernel is then solved by the algorithm that proves that the problem is decidable.
The total running time of this procedure is formula_35, where formula_36 is the running time for the algorithm used to solve the kernels.
Since formula_37 is computable, e.g. by using the assumption that formula_34 is computable and testing all possible inputs of length formula_34, this implies that the problem is fixed-parameter tractable.
The other direction, that a fixed-parameter tractable problem is kernelizable and decidable is a bit more involved. Assume that the question is non-trivial, meaning that there is at least one instance that is in the language, called formula_38, and at least one instance that is not in the language, called formula_39; otherwise, replacing any instance by the empty string is a valid kernelization. Assume also that the problem is fixed-parameter tractable, i.e., it has an algorithm that runs in at most formula_40 steps on instances formula_41, for some constant formula_12 and some function formula_34. To kernelize an input, run this algorithm on the given input for at most formula_42 steps. If it terminates with an answer, use that answer to select either formula_38 or formula_39 as the kernel. If, instead, it exceeds the formula_42 bound on the number of steps without terminating, then return formula_20 itself as the kernel. Because formula_20 is only returned as a kernel for inputs with formula_43, it follows that the size of the kernel produced in this way is at most formula_44. This size bound is computable, by the assumption from fixed-parameter tractability that formula_34 is computable.
Kernelization for structural parameterizations.
While the parameter formula_1 in the examples above is chosen as the size of the desired solution, this is not necessary. It is also possible to choose a structural complexity measure of the input as the parameter value, leading to so-called structural parameterizations. This approach is fruitful for instances whose solution size is large, but for which some other complexity measure is bounded. For example, the "feedback vertex number" of an undirected graph formula_0 is defined as the minimum cardinality of a set of vertices whose removal makes formula_0 acyclic. The vertex cover problem parameterized by the feedback vertex number of the input graph has a polynomial kernelization: There is a polynomial-time algorithm that, given a graph formula_0 whose feedback vertex number is formula_1, outputs a graph formula_53 on formula_54 vertices such that a minimum vertex cover in formula_53 can be transformed into a minimum vertex cover for formula_0 in polynomial time. The kernelization algorithm therefore guarantees that instances with a small feedback vertex number formula_1 are reduced to small instances.
Notes.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "G"
},
{
"math_id": 1,
"text": "k"
},
{
"math_id": 2,
"text": "k>0"
},
{
"math_id": 3,
"text": "v"
},
{
"math_id": 4,
"text": "k^2"
},
{
"math_id": 5,
"text": "k=0"
},
{
"math_id": 6,
"text": "2k^2"
},
{
"math_id": 7,
"text": "O(2^{2k^2}+n+m)"
},
{
"math_id": 8,
"text": "n"
},
{
"math_id": 9,
"text": "m"
},
{
"math_id": 10,
"text": "2k"
},
{
"math_id": 11,
"text": "2k-c\\log k"
},
{
"math_id": 12,
"text": "c"
},
{
"math_id": 13,
"text": "O(\\log k)"
},
{
"math_id": 14,
"text": "\\subseteq"
},
{
"math_id": 15,
"text": "\\epsilon>0"
},
{
"math_id": 16,
"text": "O(k^{2-\\epsilon})"
},
{
"math_id": 17,
"text": "(2-\\epsilon)k"
},
{
"math_id": 18,
"text": "L\\subseteq\\Sigma^*\\times\\N"
},
{
"math_id": 19,
"text": "L"
},
{
"math_id": 20,
"text": "(x,k)"
},
{
"math_id": 21,
"text": "|x|"
},
{
"math_id": 22,
"text": "(x',k')"
},
{
"math_id": 23,
"text": "x'"
},
{
"math_id": 24,
"text": "f"
},
{
"math_id": 25,
"text": "k'"
},
{
"math_id": 26,
"text": "L\\subseteq\\Sigma^*"
},
{
"math_id": 27,
"text": "\\kappa:\\Sigma^*\\to\\N"
},
{
"math_id": 28,
"text": "x"
},
{
"math_id": 29,
"text": "\\kappa(x)"
},
{
"math_id": 30,
"text": "y"
},
{
"math_id": 31,
"text": "f=k^{O(1)}"
},
{
"math_id": 32,
"text": "f={O(k)}"
},
{
"math_id": 33,
"text": "O(|x|^c)"
},
{
"math_id": 34,
"text": "f(k)"
},
{
"math_id": 35,
"text": "g(f(k)) + O(|x|^c)"
},
{
"math_id": 36,
"text": "g(n)"
},
{
"math_id": 37,
"text": "g(f(k))"
},
{
"math_id": 38,
"text": "I_{yes}"
},
{
"math_id": 39,
"text": "I_{no}"
},
{
"math_id": 40,
"text": "f(k) \\cdot |x|^c"
},
{
"math_id": 41,
"text": "(x, k)"
},
{
"math_id": 42,
"text": "|x|^{c+1}"
},
{
"math_id": 43,
"text": "f(k)\\cdot |x|^c > |x|^{c+1}"
},
{
"math_id": 44,
"text": "\\max\\{|I_{yes}|, |I_{no}|, f(k)\\}"
},
{
"math_id": 45,
"text": "O(k^2)"
},
{
"math_id": 46,
"text": "\\varepsilon >0"
},
{
"math_id": 47,
"text": "O(k^{2-\\varepsilon})"
},
{
"math_id": 48,
"text": "\\text{coNP}\\subseteq\\text{NP/poly}"
},
{
"math_id": 49,
"text": "d"
},
{
"math_id": 50,
"text": "O(k^{d})"
},
{
"math_id": 51,
"text": "O(k^{d-\\varepsilon})"
},
{
"math_id": 52,
"text": "4k^2"
},
{
"math_id": 53,
"text": "G'"
},
{
"math_id": 54,
"text": "O(k^3)"
}
] |
https://en.wikipedia.org/wiki?curid=14656451
|
1465823
|
Fan-Tan
|
Gambling game long played in China
Fan-Tan, or fantan () is a gambling game long played in China. It is a game of pure chance.
The game is played by placing two handfuls of small objects on a board and guessing the remaining count when divided by four. After players have cast bets on values of 1 through 4, the dealer or croupier repeatedly removes four objects from the board until only one, two, three or four beans remain, determining the winner.
History.
The game may have arisen during third and fourth centuries, during the period of the Northern and Southern dynasties. It then spread through southern China during the Qing dynasty. The name fantan dates back only to the mid-nineteenth century. Before that time, "fantan" was known as , , , or . It was prominent during the Late Qing and Republican period in Canton and the Pearl River Delta region. The game was also played in the Philippines under the name "Capona".
After 1850, "fantan" spread overseas as a side effect of the massive Cantonese emigration. As a rule, in places where a significant number of Cantonese migrants could be found, "fantan" was also present. Fan-tan was very popular among Chinese migrants in America, as most of them were of Cantonese origin. Jacob Riis, in his famous book about the underbelly of New York, "How the Other Half Lives" (1890), wrote of entering a Chinatown fan-tan parlor: "At the first foot-fall of leather soles on the steps the hum of talk ceases, and the group of celestials, crouching over their game of fan tan, stop playing and watch the comer with ugly looks. Fan tan is their ruling passion." The large Chinatown in San Francisco was also home to dozens of fan-tan houses in the 19th century. The city's former police commissioner Jesse B. Cook wrote that in 1889 Chinatown had 50 fan-tan games, and that "in the 50 fan tan gambling houses the tables numbered from one to 24, according to the size of the room."
California amended Section 330 of the California Penal Code in 1885, adding fan-tan to its list of banned games; this coincided with the general rise of anti-Chinese sentiment in the United States, as fan-tan was considered a differentiating vice on par with opium use and the direct cause of property crime and violence. Raids on fan-tan parlors were regularly featured in contemporary news articles, with police in some cases posing as Chinese to infiltrate the games. In San Jose, California, a typo in a local printed law led to charges being dismissed against several bettors. Despite its illegality, it was estimated that 100 fan-tan parlors were operating in San Francisco's Chinatown around the turn of the 20th century.
Because of the police raids, fan-tan parlors adopted double-entrance security measures: after entering through the street doors, a bettor would have to pass through a hallway and a second interior set of doors. If the guard posted on the exterior doors did not recognize the prospective bettor or the guard raised an alarm in the event of a raid, the interior doors, often heavily reinforced with iron, would be shut and barred, giving the fan-tan patrons and parlor time to dismantle the game, conceal evidence, and flee the premises.
Fan-tan is no longer as popular as it once was, having been replaced by modern casino games like Baccarat, and other traditional Chinese games such as Mah Jong and Pai Gow. Fan-tan is still played at some Macau casinos.
The game.
The game is operated by two people: the "tán kún" or croupier, who stands by the table at position no. 1, and the "ho kún" (clerk or cashier), who stands to the left of the "tán kún".
A square is marked in the center of an ordinary table, or a square piece of metal is laid on it, the sides being marked 1, 2, 3 and 4 in anti-clockwise order; alternatively, the sides may be marked 0 through 3, with 0 taking the place of 4. The banker puts on the table a double handful of small objects (buttons, beads, coins, dried beans, or similar articles), which he covers with a metal bowl. When all bets are placed, the bowl is removed and the "tán kún" uses a small bamboo stick to remove the objects from the heap, four at a time, until the final batch is reached.
If the final batch contains four objects, those who wagered on position 4 (and specific bets that include position 4) win; if three, the backers of No. 3 win; if two, the backers of No. 2 win and if one the backers of No. 1 win. A variant substitutes dice instead of counting the objects by fours; the remainder after dividing the sum of the dice by four is used to determine the winning positions.
Betting.
Fan-Tan uses a fixed-odds betting system where all winning wagers are paid according to the true odds of success. The pool of money used to pay off bets is the total amount wagered on all positions, less a house commission, which ranges from 5% to 25% depending on the time and place. Because the prizes are paid entirely out of the wagers, the game is relatively inexpensive to operate.
Culin (1891) describes four potential bets:
In the modern game, the "Hong" (row) bet is usually replaced by two alternative three-number bets. The first of these is the "Tan" or "Nga Tan" bet (). Two positions are chosen as the "primary" wager, and one position is chosen as the "secondary" "push" wager; there are twelve possible combinations of this type of bet, and each position has six corresponding "primary" and three "secondary" wagers. For example, the six bets that include position 1 as the "primary" wager are 1-24, 1-23, 1-32; 1-42, 1-43, and 1-34; and the three bets that include position 1 as the "secondary" "push" wager are 2-41, 2-31, and 3-41, so any single position will result in a win for <templatestyles src="Fraction/styles.css" />6⁄12 of the "Tan" bets and a push for <templatestyles src="Fraction/styles.css" />3⁄12 of them.
The second three-number bet that can be made is an all-"primary" wager, known as "Sheh Sam Hong", sometimes romanized as "Shen Sam Hong" ( or ), where any one of the three numbers will win. There are four combinations of the three numbers: 1-2-3, 2-3-4, 3-4-1, or 4-1-2, so any single position will result in a win for <templatestyles src="Fraction/styles.css" />3⁄4 of the "SSH" bets. The payout for the "Tan" and "SSH" bets is correspondingly lower, based on the increased odds of winning, and the two modern three-number bets also generally require a higher minimum stake because of the lower payout.
<templatestyles src="Reflist/styles.css" />
Currently, in Macau casinos, the house commission is uniformly set at 5%. For example, assume that bettors have wagered a total of $100 on each position as "Fan" bets, meaning the total of all wagers is $400 for all positions; the true odds of winning this specific wager are 1 in 4. The total payout to the bettors who chose the winning position would be $400 (the total wagered on all positions). Based on the amount wagered on the winning position, $100, the net payout is 3 to 1: $100 wagered, $300 returned in addition to the original wager. However, the house commission of 5% means the winning bettor(s) are paid a total of $285 ($300 less 5%), providing a total commission of $15 to the house for the game.
Odds and payout.
The net payout for each bet is determined by the true odds. The odds of winning for each type of bet is determined by considering the total number of potential bets within that type, and if how many of those bets will win, lose, or push for a given position outcome; the sum of the odds for any single bet (win + lose + push) is always one. The net payout for each bet is calculated as , less the cut for the house. The odds of the "push" or secondary positions only affect the calculation of net payout by reducing the number of losing bets because when the result is a push, the original wager is returned without loss.
For example, the "Fan" bet on a single position only wins <templatestyles src="Fraction/styles.css" />1⁄4 of the time, i.e., only when that specific position is selected; consequently, there is a <templatestyles src="Fraction/styles.css" />3⁄4 chance of losing the "Fan" wager. The net payout is = 3, before the cut for the house is taken. Assuming a 5% cut, the final payout for a "Fan" win is 95% of 3×, or 2.85× the amount bet. Similarly, the odds of winning a "Tan" bet are <templatestyles src="Fraction/styles.css" />6⁄12 and the odds of losing a "Tan" bet are <templatestyles src="Fraction/styles.css" />3⁄12 (a push will occur for the remaining <templatestyles src="Fraction/styles.css" />3⁄12), so the net payout is = <templatestyles src="Fraction/styles.css" />1⁄2, before the cut for the house is taken.
The net return is the product of the odds of winning and final payout (after the cut for the house is taken), less the odds of losing. Again, the odds of a push are not considered. For example, for the "Fan" bet, the net return is formula_0, meaning the house receives 3.75% of each "Fan" bet, on average. In contrast, for the "Tan" bet, the net return is formula_1, and the house receives 1.25% of each "Tan" bet.
Cultural references.
Fan Tan Alley in the Chinatown of Victoria, British Columbia is named for the numerous gaming parlors that once lined it. It is the narrowest street in North America, at just wide
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\frac{1}{4}\\cdot{2.85}-\\frac{3}{4}=-0.0375"
},
{
"math_id": 1,
"text": "\\frac{6}{12}\\cdot{\\frac{0.95}{2}}-\\frac{3}{12}=-0.0125"
}
] |
https://en.wikipedia.org/wiki?curid=1465823
|
14659380
|
Columnar jointing
|
Polygonal stone columns
Columnar jointing is a geological structure where sets of intersecting closely spaced fractures, referred to as joints, result in the formation of a regular array of polygonal prisms, or columns. Columnar jointing occurs in many types of igneous rocks and forms as the rock cools and contracts. Columnar jointing can occur in cooling lava flows and ashflow tuffs (ignimbrites), as well as in some shallow intrusions. Columnar jointing also occurs rarely in sedimentary rocks, due to a combination of dissolution and reprecipitation of interstitial minerals (often quartz or cryptocrystalline silica) by hot, hydrothermal fluids and the expansion and contraction of the rock unit, both resulting from the presence of a nearby magmatic intrusion.
The columns can vary from 3 meters to a few centimeters in diameter, and can be as much as 30 meters tall. They are typically parallel and straight, but can also be curved and vary in diameter. An array of regular, straight, and larger-diameter columns is called a colonnade; an irregular, less-straight, and smaller-diameter array is termed an entablature. The number of sides of the individual columns can vary from 3 to 8, with 6 sides being the most common.
Physics.
When lava cools into basalt, much heat still remains. As it cools down further, the basalt contracts, and it forms cracks to release the tensile energy. It then is cooled down further by groundwater boiling and reflux.
When the cracks first form at the surface, the cracks are dominated by T-junctions, like mudcracks, because they were formed individually. One crack would form and move across the surface, until it hits upon a previous crack, forming a T-junction.
Then, these cracks extend downwards in a moving front that is roughly planar and parallel to the surface. As it moves, the crack pattern anneals to become lower in energy. The speed "v" at which the front moves is determined by the groundwater flow rate. After the front moves a few meters deep, it would evolve into a hexagonal grid with roughly equal width "L". The width "L" is determined by the basalt's material properties, and the speed "v" at which the front moves.
Scaling.
Define Péclet number formula_0 where formula_1 is the thermal diffusivity of the material. For all columnar jointing, the value of "Pe" is around 0.2, and thus the shape and speed of all columnar joints are similar after scaling. A scaled model can be made by drying cornstarch a centimeter thick, which creates columns about 1 mm wide.
For basalt, formula_2. For cornstarch, formula_3.
Places.
Some famous locations in the United States where columnar jointing can be found are Devils Tower in Wyoming, Devils Postpile in California and the Columbia River flood basalts in Oregon, Washington and Idaho. Other famous places include the Giant's Causeway in Northern Ireland, Fingal's Cave on the island of Staffa, Scotland and the Stuðlagil Canyon, Iceland.
Devils Tower.
Devils Tower in Wyoming in the United States is about 40 million years old and high. Geologists agree that the rock forming Devils Tower solidified from an intrusion, but it has not been established whether the magma from this intrusion ever reached the surface. Most columns are 6-sided, but 4, 5, and 7-sided ones can also be found.
Giant's Causeway.
The Giant's Causeway (Irish: "Clochán An Aifir") on the north Antrim coast of Northern Ireland was created by volcanic activity 60 million years ago, and consists of over 40,000 columns. According to a legend, the giant Finn McCool created the Giant's Causeway, as a causeway to Scotland.
Sōunkyō Gorge.
Sōunkyō Gorge, a part of the town of Kamikawa, Hokkaido, Japan, features a stretch of columnar jointing, which is the result of an eruption of the Daisetsuzan Volcanic Group 30,000 years ago.
Deccan Traps.
The late Cretaceous Deccan Traps of India constitute one of the largest volcanic provinces of Earth, and examples of columnar jointing can be found in St. Mary's Island in the state of Karnataka.
High Island Reservoir.
Formed in Cretaceous, the columnar rocks are found around the reservoir and the islands nearby in Sai Kung, Hong Kong. It is special that the rocks are not mafic, but felsic tuff instead.
Makhtesh Ramon.
The columnar jointed sandstone of the "HaMinsara" (Carpentry Shop) in the makhtesh (erosion cirque) of Makhtesh Ramon, Negev desert, Israel.
Cerro Kõi.
There are several examples of columnar jointed sandstones in the greater Asunción region of Paraguay. The best known is Cerro Kõi in Areguá, but there are also several quarries in Luque.
Mars.
Several exposures of columnar jointing have been discovered on the planet Mars by the High Resolution Imaging Science Experiment (HiRISE) camera, which is carried by the Mars Reconnaissance Orbiter (MRO).
Sawn Rocks.
Sawn Rocks, in Mount Kaputar National Park close to Narrabri, New South Wales, Australia, features 40 meters of columnar jointing above the creek and 30 meters below the surface.
Basaltic Prisms of Santa María Regla.
Alexander von Humboldt documented the prisms located in Huasca de Ocampo, in the Mexican state of Hidalgo.
Columnar basalt of Tawau (Batu Bersusun).
At Kampung Balung Cocos, Tawau, Malaysia, the river flows through the area of columnar basalt. One section is seen vertically high on river bank. The rest lies on river bank. The water flows from the lowest area forming waterfall.
Gorge of Garni, Armenia.
The Garni Gorge is situated 23 km east of Yerevan, Armenia, just below the village of the same name. This portion of the Garni Gorge is typically referred to as the "Symphony of the Stones." On a promontory above the gorge the first-century AD Temple of Garni may be seen.
Stuðlagil Canyon, Iceland.
The Stuðlagil Canyon, situated 45 miles west of Egilsstaðir, showing a view of columnar joint basalts rock formations and the blue-green water that runs through it.
|
[
{
"math_id": 0,
"text": "Pe = \\frac{Lv}{D}"
},
{
"math_id": 1,
"text": "D"
},
{
"math_id": 2,
"text": "Pe \\approx 0.35"
},
{
"math_id": 3,
"text": "Pe \\approx 0.1"
}
] |
https://en.wikipedia.org/wiki?curid=14659380
|
1465944
|
Fisher effect
|
Tendency for nominal interest rate to follow changes in inflation
In economics, the Fisher effect is the tendency for nominal interest rates to change to follow the inflation rate. It is named after the economist Irving Fisher, who first observed and explained this relationship. Fisher proposed that the real interest rate is independent of monetary measures (known as the Fisher hypothesis), therefore, the nominal interest rate will adjust to accommodate any changes in expected inflation.
Derivation.
The "nominal" interest rate is the accounting interest rate – the percentage by which the amount of dollars (or other currency) owed by a borrower to a lender grows over time, while the "real" interest rate is the percentage by which the real purchasing power of the loan grows over time. In other words, the real interest rate is the nominal interest rate adjusted for the effect of inflation on the purchasing power of the outstanding loan.
The relation between nominal and real interest rates, and inflation, is approximately given by the Fisher equation:
formula_0
The equation states that the real interest rate (formula_1), is equal to the nominal interest rate (formula_2) minus the expected inflation rate (formula_3).
The equation is an approximation; however, the difference with the correct value is small as long as the interest rate and the inflation rate is low. The discrepancy becomes large if either the nominal interest rate or the inflation rate is high. The accurate equation can be expressed using periodic compounding as:
formula_4
If the real rate formula_1 is assumed to be constant, the nominal rate formula_2 must change point-for-point when formula_3 rises or falls. Thus, the Fisher effect states that there will be a one-for-one adjustment of the nominal interest rate to the expected inflation rate.
The implication of the conjectured constant real rate is that monetary events such as monetary policy actions will have no effect on the real economy—for example, no effect on real spending by consumers on consumer durables and by businesses on machinery and equipment.
Alternative hypotheses.
Some contrary models assert that, for example, a rise in expected inflation would increase current real spending contingent on any nominal rate and hence increase income, limiting the rise in the nominal interest rate that would be necessary to re-equilibrate money demand with money supply at any time. In this scenario, a rise in expected inflation formula_3 results in only a smaller rise in the nominal interest rate formula_2 and thus a decline in the real interest rate formula_1. It has also been contended that the Fisher hypothesis may break down in times of both quantitative easing and financial sector recapitalisation.
Related concepts.
The international Fisher effect predicts an international exchange rate drift entirely based on the respective national nominal interest rates. A related concept is "Fisher parity".
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "r = i - \\pi^e"
},
{
"math_id": 1,
"text": "r"
},
{
"math_id": 2,
"text": "i"
},
{
"math_id": 3,
"text": "\\pi^e"
},
{
"math_id": 4,
"text": "1+i =(1+r)\\times (1+\\pi^e)"
}
] |
https://en.wikipedia.org/wiki?curid=1465944
|
14660594
|
Heteroglycan alpha-mannosyltransferase
|
Class of enzymes
In enzymology, a heteroglycan alpha-mannosyltransferase (EC 2.4.1.48) is an enzyme that catalyzes the chemical reaction
GDP-mannose + heteroglycan formula_0 GDP + 2(or 3)-alpha-D-mannosyl-heteroglycan
Thus, the two substrates of this enzyme are GDP-mannose and heteroglycan, whereas its 3 products are GDP, 2-alpha-D-mannosyl-heteroglycan, and 3-alpha-D-mannosyl-heteroglycan.
This enzyme belongs to the family of glycosyltransferases, to be specific the hexosyltransferases. The systematic name of this enzyme class is GDP-mannose:heteroglycan 2-(or 3-)-alpha-D-mannosyltransferase. Other names in common use include GDP mannose alpha-mannosyltransferase, and guanosine diphosphomannose-heteroglycan alpha-mannosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660594
|
14660607
|
Hydroquinone glucosyltransferase
|
Class of enzymes
In enzymology, a hydroquinone glucosyltransferase (EC 2.4.1.218) is an enzyme that catalyzes the chemical reaction
UDP-glucose + hydroquinone formula_0 UDP + hydroquinone-O-beta-D-glucopyranoside
Thus, the two substrates of this enzyme are UDP-glucose and hydroquinone, whereas its two products are UDP and hydroquinone-O-beta-D-glucopyranoside.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:hydroquinone-O-beta-D-glucosyltransferase. Other names in common use include arbutin synthase, and hydroquinone:O-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660607
|
14660622
|
Hydroxyanthraquinone glucosyltransferase
|
Class of enzymes
In enzymology, a hydroxyanthraquinone glucosyltransferase (EC 2.4.1.181) is an enzyme that catalyzes the chemical reaction
UDP-glucose + an hydroxyanthraquinone formula_0 UDP + a glucosyloxyanthraquinone
Thus, the two substrates of this enzyme are UDP-glucose and hydroxyanthraquinone, whereas its two products are UDP and glucosyloxyanthraquinone.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:hydroxyanthraquinone O-glucosyltransferase. Other names in common use include uridine diphosphoglucose-anthraquinone glucosyltransferase, and anthraquinone-specific glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660622
|
14660670
|
Hydroxycinnamate 4-beta-glucosyltransferase
|
Class of enzymes
In enzymology, a hydroxycinnamate 4-beta-glucosyltransferase (EC 2.4.1.126) is an enzyme that catalyzes the chemical reaction
UDP-glucose + trans-4-hydroxycinnamate formula_0 UDP + 4-O-beta-D-glucosyl-4-hydroxycinnamate
Thus, the two substrates of this enzyme are UDP-glucose and trans-4-hydroxycinnamate (p-coumaric acid), whereas its two products are UDP and 4-O-beta-D-glucosyl-4-hydroxycinnamate.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:trans-4-hydroxycinnamate 4-O-beta-D-glucosyltransferase. Other names in common use include uridine diphosphoglucose-hydroxycinnamate glucosyltransferase, UDP-glucose-hydroxycinnamate glucosyltransferase, and hydroxycinnamoyl glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660670
|
14660681
|
Hydroxymandelonitrile glucosyltransferase
|
Class of enzymes
In enzymology, a hydroxymandelonitrile glucosyltransferase (EC 2.4.1.178) is an enzyme that catalyzes the chemical reaction
UDP-glucose + 4-hydroxymandelonitrile formula_0 UDP + taxiphyllin
Thus, the two substrates of this enzyme are UDP-glucose and 4-hydroxymandelonitrile, whereas its two products are UDP and taxiphyllin.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:4-hydroxymandelonitrile glucosyltransferase. Other names in common use include cyanohydrin glucosyltransferase, and uridine diphosphoglucose-cyanohydrin glucosyltransferase. This enzyme participates in tyrosine metabolism.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660681
|
14660705
|
Indole-3-acetate beta-glucosyltransferase
|
Class of enzymes
In enzymology, an indole-3-acetate beta-glucosyltransferase (EC 2.4.1.121) is an enzyme that catalyzes the chemical reaction
UDP-glucose + (indol-3-yl)acetate formula_0 UDP + 1-O-(indol-3-yl)acetyl-beta-D-glucose
Thus, the two substrates of this enzyme are UDP-glucose and (indol-3-yl)acetate, whereas its two products are UDP and 1-O-(indol-3-yl)acetyl-beta-D-glucose.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:(indol-3-yl)acetate beta-D-glucosyltransferase. Other names in common use include uridine diphosphoglucose-indoleacetate glucosyltransferase, UDPG-indol-3-ylacetyl glucosyl transferase, UDP-glucose:indol-3-ylacetate glucosyltransferase, indol-3-ylacetylglucose synthase, UDP-glucose:indol-3-ylacetate glucosyl-transferase, IAGlu synthase, IAA-glucose synthase, and UDP-glucose:indole-3-acetate beta-D-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660705
|
14660722
|
Indolylacetylinositol arabinosyltransferase
|
Class of enzymes
In enzymology, an indolylacetylinositol arabinosyltransferase (EC 2.4.2.34) is an enzyme that catalyzes the chemical reaction
UDP-L-arabinose + (indol-3-yl)acetyl-1D-myo-inositol formula_0 UDP + (indol-3-yl)acetyl-myo-inositol 3-L-arabinoside
Thus, the two substrates of this enzyme are UDP-L-arabinose and indol-3-ylacetyl-1D-myo-inositol, whereas its two products are UDP and (indol-3-yl)acetyl-myo-inositol 3-L-arabinoside.
This enzyme belongs to the family of glycosyltransferases, specifically the pentosyltransferases. The systematic name of this enzyme class is UDP-L-arabinose:(indol-3-yl)acetyl-myo-inositol L-arabinosyltransferase. Other names in common use include arabinosylindolylacetylinositol synthase, UDP-L-arabinose:indol-3-ylacetyl-myo-inositol, and L-arabinosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660722
|
14660736
|
Indolylacetyl-myo-inositol galactosyltransferase
|
Class of enzymes
In enzymology, an indolylacetyl-myo-inositol galactosyltransferase (EC 2.4.1.156) is an enzyme that catalyzes the chemical reaction
UDP-galactose + (indol-3-yl)acetyl-myo-inositol formula_0 UDP + 5-O-(indol-3-yl)acetyl-myo-inositol D-galactoside
Thus, the two substrates of this enzyme are UDP-galactose and indol-3-ylacetyl-myo-inositol, whereas its two products are UDP and 5-O-(indol-3-yl)acetyl-myo-inositol D-galactoside.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:(indol-3-yl)acetyl-myo-inositol 5-O-D-galactosyltransferase. Other names in common use include uridine diphosphogalactose-indolylacetylinositol, galactosyltransferase, indol-3-ylacetyl-myo-inositol galactoside synthase, UDP-galactose:indol-3-ylacetyl-myo-inositol, and 5-O-D-galactosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660736
|
14660753
|
Indoxyl-UDPG glucosyltransferase
|
Class of enzymes
In enzymology, an indoxyl-UDPG glucosyltransferase (EC 2.4.1.220) is an enzyme that catalyzes the chemical reaction
UDP-glucose + indoxyl formula_0 UDP + indican
Thus, the two substrates of this enzyme are UDP-glucose and indoxyl, whereas its two products are UDP and indican.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:indoxyl 3-O-beta-D-glucosyltransferase. This enzyme is also called indoxyl-UDPG-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660753
|
14660771
|
Inositol 3-alpha-galactosyltransferase
|
InterPro Family
In enzymology, an inositol 3-alpha-galactosyltransferase (EC 2.4.1.123) is an enzyme that catalyzes the chemical reaction
UDP-galactose + myo-inositol formula_0 UDP + O-alpha-D-galactosyl-(1->3)-1D-myo-inositol
Thus, the two substrates of this enzyme are UDP-galactose and myo-inositol, whereas its two products are UDP and O-alpha-D-galactosyl-(1->3)-1D-myo-inositol.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:myo-inositol 3-alpha-D-galactosyltransferase. Other names in common use include UDP-D-galactose:inositol galactosyltransferase, UDP-galactose:myo-inositol 1-alpha-D-galactosyltransferase, UDPgalactose:myo-inositol 1-alpha-D-galactosyltransferase, galactinol synthase, inositol 1-alpha-galactosyltransferase, and uridine diphosphogalactose-inositol galactosyltransferase. This enzyme participates in galactose metabolism.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660771
|
14660796
|
Inulosucrase
|
Class of enzymes
In enzymology, an inulosucrase (EC 2.4.1.9) is an enzyme that catalyzes the chemical reaction
sucrose + (2,1-beta-D-fructosyl)n formula_0 glucose + (2,1-beta-D-fructosyl)n+1
Thus, the two substrates of this enzyme are sucrose and (2,1-beta-D-fructosyl)n, whereas its two products are glucose and (2,1-beta-D-fructosyl)n+1.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is sucrose:2,1-beta-D-fructan 1-beta-D-fructosyltransferase. This enzyme is also called sucrose 1-fructosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660796
|
14660810
|
Isoflavone 7-O-glucosyltransferase
|
Class of enzymes
In enzymology, an isoflavone 7-O-glucosyltransferase (EC 2.4.1.170) is an enzyme that catalyzes the chemical reaction
UDP-glucose + an isoflavone formula_0 UDP + an isoflavone 7-O-beta-D-glucoside
Thus, the two substrates of this enzyme are UDP-glucose and isoflavone, whereas its two products are UDP and isoflavone 7-O-beta-D-glucoside.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:isoflavone 7-O-beta-D-glucosyltransferase. Other names in common use include uridine diphosphoglucose-isoflavone 7-O-glucosyltransferase, UDPglucose-favonoid 7-O-glucosyltransferase, and UDPglucose:isoflavone 7-O-glucosyltransferase. This enzyme participates in isoflavonoid biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660810
|
14660843
|
Isovitexin beta-glucosyltransferase
|
Class of enzymes
In enzymology, an isovitexin beta-glucosyltransferase (EC 2.4.1.106) is an enzyme that catalyzes the chemical reaction
UDP-glucose + isovitexin formula_0 UDP + isovitexin 2"-O-beta-D-glucoside
Thus, the two substrates of this enzyme are UDP-glucose and isovitexin, whereas its two products are UDP and isovitexin 2"-O-beta-D-glucoside.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:isovitexin 2"-O-beta-D-glucosyltransferase. This enzyme is also called uridine diphosphoglucose-isovitexin 2"-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660843
|
14660868
|
Kaempferol 3-O-galactosyltransferase
|
Class of enzymes
In enzymology, a kaempferol 3-O-galactosyltransferase (EC 2.4.1.234) is an enzyme that catalyzes the chemical reaction
UDP-galactose + kaempferol formula_0 UDP + kaempferol 3-O-beta-D-galactoside
Thus, the two substrates of this enzyme are UDP-galactose and kaempferol, whereas its two products are UDP and trifolin.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:kaempferol 3-O-beta-D-galactosyltransferase. This enzyme is also called F3GalTase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660868
|
14660895
|
Kojibiose phosphorylase
|
Class of enzymes
In enzymology, a kojibiose phosphorylase (EC 2.4.1.230) is an enzyme that catalyzes the chemical reaction
2-alpha-D-glucosyl-D-glucose + phosphate formula_0 D-glucose + beta-D-glucose 1-phosphate
Thus, the two substrates of this enzyme are kojibiose and phosphate, whereas its two products are D-glucose and beta-D-glucose 1-phosphate.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is 2-alpha-D-glucosyl-D-glucose:phosphate beta-D-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660895
|
14660914
|
Lactosylceramide 1,3-N-acetyl-beta-D-glucosaminyltransferase
|
Class of enzymes
In enzymology, a lactosylceramide 1,3-N-anning-beta-D-glrofelucosaminyltlolferase (EC 2.4.1.206) is an enzyme that catalyzes the chemical reaction
UDP-N-acetyl-D-glucosamine + D-galactosyl-1,4-beta-D-glucosylceramide formula_0 UDP + N-acetyl-D-glucosaminyl-1,3-beta-D-galactosyl-1,4-beta-D- glucosylceramide
Thus, the two substrates of this enzyme are UDP-N-acetyl-D-glucosamine and D-galactosyl-1,4-beta-D-glucosylceramide, whereas its 3 products are UDP, N-acetyl-D-glucosaminyl-1,3-beta-D-galactosyl-1,4-beta-D-, and glucosylceramide.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-N-acetyl-D-glucosamine:D-galactosyl-1,4-beta-D-glucosylceramide beta-1,3-acetylglucosaminyltransferase. Other names in common use include LA2 synthase, beta1->3-N-acetylglucosaminyltransferase, uridine diphosphoacetylglucosamine-lactosylceramide, beta-acetylglucosaminyltransferase, and lactosylceramide beta-acetylglucosaminyltransferase. This enzyme participates in 3 metabolic pathways: glycosphingolipid biosynthesis - lactoseries, glycosphingolipid biosynthesis - neo-lactoseries, and glycan structures - biosynthesis 2.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660914
|
14660929
|
Lactosylceramide 4-alpha-galactosyltransferase
|
Protein family
In enzymology, a lactosylceramide 4-alpha-galactosyltransferase (EC 2.4.1.228) is an enzyme that catalyzes the chemical reaction
UDP-galactose + beta-D-galactosyl-(1->4)-D-glucosylceramide formula_0 UDP + alpha-D-galactosyl-(1->4)-beta-D-galactosyl-(1->4)-D- glucosylceramide
Thus, the two substrates of this enzyme are UDP-galactose and beta-D-galactosyl-(1->4)-D-glucosylceramide, whereas its 3 products are UDP, alpha-D-galactosyl-(1->4)-beta-D-galactosyl-(1->4)-D-, and glucosylceramide.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:lactosylceramide 4II-alpha-D-galactosyltransferase. Other names in common use include Galbeta1-4Glcbeta1-Cer alpha1,4-galactosyltransferase, globotriaosylceramide/CD77 synthase, and histo-blood group Pk UDP-galactose. This enzyme participates in glycosphingolipid biosynthesis - globoseries and glycan structures - biosynthesis 2.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660929
|
14660941
|
Lactosylceramide alpha-2,3-sialyltransferase
|
Class of enzymes
In enzymology, a lactosylceramide alpha-2,3-sialyltransferase (EC 2.4.99.9) is an enzyme that catalyzes the chemical reaction
CMP-N-acetylneuraminate + beta-D-galactosyl-1,4-beta-D-glucosylceramide formula_0 CMP + alpha-N-acetylneuraminyl-2,3-beta-D-galactosyl-1,4-beta-D- glucosylceramide
Thus, the two substrates of this enzyme are CMP-N-acetylneuraminate and beta-D-galactosyl-1,4-beta-D-glucosylceramide, whereas its 3 products are CMP, alpha-N-acetylneuraminyl-2,3-beta-D-galactosyl-1,4-beta-D-, and glucosylceramide.
This enzyme belongs to the family of transferases, specifically those glycosyltransferases that do not transfer hexosyl or pentosyl groups. The systematic name of this enzyme class is CMP-N-acetylneuraminate:lactosylceramide alpha-2,3-N-acetylneuraminyltransferase. Other names in common use include cytidine monophosphoacetylneuraminate-lactosylceramide alpha2,3-, sialyltransferase, CMP-acetylneuraminate-lactosylceramide-sialyltransferase, CMP-acetylneuraminic acid:lactosylceramide sialyltransferase, CMP-sialic acid:lactosylceramide-sialyltransferase, cytidine monophosphoacetylneuraminate-lactosylceramide, sialyltransferase, ganglioside GM3 synthetase, GM3 synthase, GM3 synthetase, and SAT 1. This enzyme participates in glycosphingolipid biosynthesis - ganglioseries and glycan structures - biosynthesis 2.
Structural studies.
As of late 2007, two structures have been solved for this class of enzymes, with PDB accession codes 2EX0 and 2EX1.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660941
|
14660964
|
Lactosylceramide alpha-2,6-N-sialyltransferase
|
Class of enzymes
In enzymology, a lactosylceramide alpha-2,6-N-sialyltransferase (EC 2.4.99.11) is an enzyme that catalyzes the chemical reaction
CMP-N-acetylneuraminate + beta-D-galactosyl-1,4-beta-D-glucosylceramide formula_0 CMP + alpha-N-acetylneuraminyl-2,6-beta-D-galactosyl-1,4-beta-D- glucosylceramide
Thus, the two substrates of this enzyme are CMP-N-acetylneuraminate and beta-D-galactosyl-1,4-beta-D-glucosylceramide, whereas its 3 products are CMP, alpha-N-acetylneuraminyl-2,6-beta-D-galactosyl-1,4-beta-D-, and glucosylceramide.
This enzyme belongs to the family of transferases, specifically those glycosyltransferases that do not transfer hexosyl or pentosyl groups. The systematic name of this enzyme class is CMP-N-acetylneuraminate:lactosylceramide alpha-2,6-N-acetylneuraminyltransferase. Other names in common use include cytidine monophosphoacetylneuraminate-lactosylceramide, sialyltransferase, CMP-acetylneuraminate-lactosylceramide-sialyltransferase, CMP-N-acetylneuraminic acid:lactosylceramide sialyltransferase, CMP-sialic acid:lactosylceramide sialyltransferase, cytidine monophosphoacetylneuraminate-lactosylceramide, and sialyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14660964
|
14661000
|
Lactosylceramide beta-1,3-galactosyltransferase
|
Class of enzymes
In enzymology, a lactosylceramide beta-1,3-galactosyltransferase (EC 2.4.1.179) is an enzyme that catalyzes the chemical reaction
UDP-galactose + D-galactosyl-1,4-beta-D-glucosyl-R formula_0 UDP + D-galactosyl-1,3-beta-D-galactosyl-1,4-beta-D-glucosyl-R
Thus, the two substrates of this enzyme are UDP-galactose and D-galactosyl-1,4-beta-D-glucosyl-R, whereas its two products are UDP and D-galactosyl-1,3-beta-D-galactosyl-1,4-beta-D-glucosyl-R.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:D-galactosyl-1,4-beta-D-glucosyl-R beta-1,3-galactosyltransferase. Other names in common use include uridine diphosphogalactose-lactosylceramide, and beta1->3-galactosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661000
|
14661016
|
Laminaribiose phosphorylase
|
Class of enzymes
In enzymology, a laminaribiose phosphorylase (EC 2.4.1.31) is an enzyme that catalyzes the chemical reaction
3-beta-D-glucosyl-D-glucose + phosphate formula_0 D-glucose + alpha-D-glucose 1-phosphate
Thus, the two substrates of this enzyme are 3-beta-D-glucosyl-D-glucose and phosphate, whereas its two products are D-glucose and alpha-D-glucose 1-phosphate.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is 3-beta-D-glucosyl-D-glucose:phosphate alpha-D-glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661016
|
14661050
|
Levansucrase
|
Enzyme used in the catalysis of sucrose
Levansucrase (EC 2.4.1.10) is an enzyme that catalyzes the chemical reaction
sucrose + (2,6-beta-D-fructosyl)n formula_0 glucose + (2,6-beta-D-fructosyl)n+1
Thus, the two substrates of this enzyme are sucrose and (2,6-beta-D-fructosyl)n, whereas its two products are glucose and (2,6-beta-D-fructosyl)n+1.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is sucrose:2,6-beta-D-fructan 6-beta-D-fructosyltransferase. Other names in common use include sucrose 6-fructosyltransferase, beta-2,6-fructosyltransferase, and beta-2,6-fructan:D-glucose 1-fructosyltransferase. This enzyme participates in starch and sucrose metabolism and two-component system - general.
Structural studies.
As of late 2007, 3 structures have been solved for this class of enzymes, with PDB accession codes 1OYG, 1PT2, and 1W18.
References.
<templatestyles src="Reflist/styles.css" />
SacB counter-selection relies on the toxic product produced by the SacB gene. sacB comes from the gram-positive bacteria Bacillus subtilis and encodes the enzyme levansucrase that converts sucrose into a toxic metabolite in gram-negative bacteria. Plating on sucrose medium will select for cells that contain constructs that have lost the sacB gene.
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661050
|
14661068
|
Limonoid glucosyltransferase
|
Enzyme that catalyzes the chemical reaction
In enzymology, a limonoid glucosyltransferase (EC 2.4.1.210) is an enzyme that catalyzes the chemical reaction.
UDP-glucose + limonin formula_0 glucosyl-limonin + UDP
Thus, the two substrates of this enzyme are UDP-glucose and limonin, whereas its two products are glucosyl-limonin and UDP.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is uridine diphosphoglucose-limonoid glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661068
|
14661090
|
Linamarin synthase
|
Class of enzymes
In enzymology, a linamarin synthase (EC 2.4.1.63) is an enzyme that catalyzes the chemical reaction
UDP-glucose + 2-hydroxy-2-methylpropanenitrile formula_0 UDP + linamarin
Thus, the two substrates of this enzyme are UDP-glucose and 2-hydroxy-2-methylpropanenitrile, whereas its two products are UDP and linamarin.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:2-hydroxy-2-methylpropanenitrile beta-D-glucosyltransferase. Other names in common use include uridine diphosphoglucose-ketone glucosyltransferase, uridine diphosphate-glucose-ketone cyanohydrin, beta-glucosyltransferase, UDP glucose ketone cyanohydrin glucosyltransferase, UDP-glucose:ketone cyanohydrin beta-glucosyltransferase, and uridine diphosphoglucose-ketone cyanohydrin glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661090
|
14661096
|
Lipid-A-disaccharide synthase
|
Class of enzymes
In enzymology, a lipid-A-disaccharide synthase (EC 2.4.1.182) is an enzyme that catalyzes the chemical reaction
UDP-2,3-bis(3-hydroxytetradecanoyl)glucosamine + 2,3-bis(3-hydroxytetradecanoyl)-beta-D-glucosaminyl 1-phosphate formula_0 UDP + 2,3-bis(3-hydroxytetradecanoyl)-D-glucosaminyl-1,6-beta-D-2,3-bis(3-hydroxytetradecanoyl)-beta-D-glucosaminyl 1-phosphate
Thus, the two substrates of this enzyme are UDP-2,3-bis(3-hydroxytetradecanoyl)glucosamine and 2,3-bis(3-hydroxytetradecanoyl)-beta-D-glucosaminyl 1-phosphate, whereas its 2 products are UDP and 2,3-bis(3-hydroxytetradecanoyl)-D-glucosaminyl-1,6-beta-D-2,3-bis(3-hydroxytetradecanoyl)-beta-D-glucosaminyl 1-phosphate.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-2,3-bis(3-hydroxytetradecanoyl)glucosamine:2,3-bis(3-hydroxytet radecanoyl)-beta-D-glucosaminyl-1-phosphate 2,3-bis(3-hydroxytetradecanoyl)-glucosaminyltransferase. This enzyme participates in lipopolysaccharide biosynthesis.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661096
|
146611
|
History of large numbers
|
Different cultures used different traditional numeral systems for naming large numbers. The extent of large numbers used varied in each culture. Two interesting points in using large numbers are the confusion on the term billion and milliard in many countries, and the use of "zillion" to denote a very large number where precision is not required.
Indian mathematics.
The Shukla Yajurveda has a list of names for powers of ten up to 1012.
The list given in the Yajurveda text is:
"eka" (1), "daśa" (10), "mesochi" (100), "sahasra" (1,000), "ayuta" (10,000), "niyuta" (100,000), "prayuta" (1,000,000), "arbuda" (10,000,000), "nyarbuda" (100,000,000), "saguran" (1,000,000,000), "madhya" (10,000,000,000), "anta" (100,000,000,000), "parârdha" (1,000,000,000,000).
Later Hindu and Buddhist texts have extended this list, but these lists are no longer mutually consistent and names of numbers larger than 108 differ between texts.
For example, the Panchavimsha Brahmana lists 109 as "nikharva", 1010 "vâdava", 1011 "akṣiti", while Śâṅkhyâyana Śrauta Sûtra has 109 "nikharva", 1010 "samudra", 1011 "salila", 1012 "antya", 1013 "ananta". Such lists of names for powers of ten are called "daśaguṇottarra saṁjñâ". There area also analogous lists of Sanskrit names for fractional numbers, that is, powers of one tenth.
The Mahayana "Lalitavistara Sutra" is notable for giving a very extensive such list, with terms going up to 10421. The context is an account of a contest including writing, arithmetic, wrestling and archery, in which the Buddha was pitted against the great mathematician Arjuna and showed off his numerical skills by citing the names of the powers of ten up to 1 'tallakshana', which equals 1053, but then going on to explain that this is just one of a series of counting systems that can be expanded geometrically.
The Avataṃsaka Sūtra, a text associated with the Lokottaravāda school of Buddhism, has an even more extensive list of names for numbers, and it goes beyond listing mere powers of ten introducing concatenation of exponentiation, the largest number mentioned being "nirabhilapya nirabhilapya parivarta" (Bukeshuo bukeshuo zhuan 不可說不可說轉), corresponding to formula_0. though chapter 30 (the Asamkyeyas) in Thomas Cleary's translation of it we find the definition of the number "untold" as exactly 1010*2122, expanded in the 2nd verses to 104*5*2121 and continuing a similar expansion indeterminately.
Examples for other names given in the Avatamsaka Sutra include: "asaṃkhyeya" (असंख्येय) 10140.
The Jain mathematical text Surya Prajnapti (c. 4th–3rd century BCE) classifies all numbers into three sets: enumerable, innumerable, and infinite. Each of these was further subdivided into three orders: enumerable (lowest, intermediate, and highest), innumerable (nearly innumerable, truly innumerable, and innumerably innumerable), and infinite (nearly infinite, truly infinite, infinitely infinite).
In modern India, the terms lakh for 105 and crore for 107 are in common use. Both are vernacular (Hindustani) forms derived from a list of names for powers of ten in Yājñavalkya Smṛti, where 105 and 107 named "lakṣa" and "koṭi", respectively.
Classical antiquity.
In the Western world, specific number names for larger numbers did not come into common use until quite recently. The Ancient Greeks used a system based on the myriad, that is, ten thousand, and their largest named number was a myriad myriad, or one hundred million.
In "The Sand Reckoner", Archimedes (c. 287–212 BC) devised a system of naming large numbers reaching up to
formula_1,
essentially by naming powers of a myriad myriad. This largest number appears because it equals a myriad myriad to the myriad myriadth power, all taken to the myriad myriadth power. This gives a good indication of the notational difficulties encountered by Archimedes, and one can propose that he stopped at this number because he did not devise any new ordinal numbers (larger than 'myriad myriadth') to match his new cardinal numbers. Archimedes only used his system up to 1064.
Archimedes' goal was presumably to name large powers of 10 in order to give rough estimates, but shortly thereafter, Apollonius of Perga invented a more practical system of naming large numbers which were not powers of 10, based on naming powers of a myriad, for example, βΜ would be a myriad squared.
Much later, but still in antiquity, the Hellenistic mathematician Diophantus (3rd century) used a similar notation to represent large numbers.
The Romans, who were less interested in theoretical issues, expressed 1,000,000 as "decies centena milia", that is, 'ten hundred thousand'; it was only in the 13th century that the (originally French) word 'million' was introduced.
Modern use of large finite numbers.
Far larger finite numbers than any of these occur in modern mathematics. For instance, Graham's number is too large to reasonably express using exponentiation or even tetration. For more about modern usage for large numbers, see Large numbers. To handle these numbers, new notations are created and used. There is a large community of mathematicians dedicated to naming large numbers. Rayo's number has been claimed to be the largest named number.
Infinity.
The ultimate in large numbers was, until recently, the concept of infinity, a number defined by being greater than any finite number, and used in the mathematical theory of limits.
However, since the 19th century, mathematicians have studied transfinite numbers, numbers which are not only greater than any finite number, but also, from the viewpoint of set theory, larger than the traditional concept of infinity. Of these transfinite numbers, perhaps the most extraordinary, and arguably, if they exist, "largest", are the large cardinals.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "10^{7\\times 2^{122}}"
},
{
"math_id": 1,
"text": "10^{8 \\times 10^{16}}"
}
] |
https://en.wikipedia.org/wiki?curid=146611
|
14661107
|
Lipopolysaccharide 3-alpha-galactosyltransferase
|
Class of enzymes
In enzymology, a lipopolysaccharide 3-alpha-galactosyltransferase (EC 2.4.1.44) is an enzyme that catalyzes the chemical reaction
UDP-galactose + lipopolysaccharide formula_0 UDP + 3-alpha-D-galactosyl-[lipopolysaccharide glucose]
Thus, the two substrates of this enzyme are UDP-galactose and lipopolysaccharide, whereas its two products are UDP and 3-alpha-D-galactosyl-[lipopolysaccharide glucose].
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-galactose:lipopolysaccharide 3-alpha-D-galactosyltransferase. Other names in common use include UDP-galactose:lipopolysaccharide alpha,3-galactosyltransferase, UDP-galactose:polysaccharide galactosyltransferase, uridine diphosphate galactose:lipopolysaccharide, alpha-3-galactosyltransferase, uridine diphosphogalactose-lipopolysaccharide, and alpha,3-galactosyltransferase. This enzyme participates in lipopolysaccharide biosynthesis and glycan structures - biosynthesis 2.
Structural studies.
As of late 2007, two structures have been solved for this class of enzymes, with PDB accession codes 1GA8 and 1SS9.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661107
|
14661126
|
Lipopolysaccharide glucosyltransferase I
|
Class of enzymes
In enzymology, a lipopolysaccharide glucosyltransferase I (EC 2.4.1.58) is an enzyme that catalyzes the chemical reaction
UDP-glucose + lipopolysaccharide formula_0 UDP + D-glucosyl-lipopolysaccharide
Thus, the two substrates of this enzyme are UDP-glucose and lipopolysaccharide, whereas its two products are UDP and D-glucosyl-lipopolysaccharide.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:lipopolysaccharide glucosyltransferase. Other names in common use include UDP-glucose:lipopolysaccharide glucosyltransferase I, lipopolysaccharide glucosyltransferase, uridine diphosphate glucose:lipopolysaccharide glucosyltransferase, I, and uridine diphosphoglucose-lipopolysaccharide glucosyltransferase. This enzyme participates in lipopolysaccharide biosynthesis and glycan structures - biosynthesis 2.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661126
|
14661142
|
Lipopolysaccharide glucosyltransferase II
|
Class of enzymes
In enzymology, a lipopolysaccharide glucosyltransferase II (EC 2.4.1.73) is an enzyme that catalyzes the chemical reaction
UDP-glucose + lipopolysaccharide formula_0 UDP + alpha-D-glucosyl-lipopolysaccharide
Thus, the two substrates of this enzyme are UDP-glucose and lipopolysaccharide, whereas its two products are UDP and alpha-D-glucosyl-lipopolysaccharide.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucose:galactosyl-lipopolysaccharide alpha-D-glucosyltransferase. Other names in common use include uridine diphosphoglucose-galactosylpolysaccharide, and glucosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661142
|
14661159
|
Lipopolysaccharide N-acetylglucosaminyltransferase
|
Class of enzymes
In enzymology, a lipopolysaccharide N-acetylglucosaminyltransferase (EC 2.4.1.56) is an enzyme that catalyzes the chemical reaction
UDP-N-acetyl-D-glucosamine + lipopolysaccharide formula_0 UDP + N-acetyl-D-glucosaminyllipopolysaccharide
Thus, the two substrates of this enzyme are UDP-N-acetyl-D-glucosamine and lipopolysaccharide, whereas its two products are UDP and N-acetyl-D-glucosaminyllipopolysaccharide.
This enzyme participates in lipopolysaccharide biosynthesis and glycan structures - biosynthesis 2.
Nomenclature.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-N-acetyl-D-glucosamine:lipopolysaccharide N-acetyl-D-glucosaminyltransferase. Other names in common use include UDP-N-acetylglucosamine-lipopolysaccharide, N-acetylglucosaminyltransferase, uridine diphosphoacetylglucosamine-lipopolysaccharide, and acetylglucosaminyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661159
|
14661175
|
Lipopolysaccharide N-acetylmannosaminouronosyltransferase
|
Class of enzymes
In enzymology, a lipopolysaccharide N-acetylmannosaminouronosyltransferase (EC 2.4.1.180) is an enzyme that catalyzes the chemical reaction
UDP-N-acetyl-beta-D-mannosaminouronate + lipopolysaccharide formula_0 UDP + N-acetyl-beta-D-mannosaminouronosyl-1,4-lipopolysaccharide
Thus, the two substrates of this enzyme are UDP-N-acetyl-beta-D-mannosaminouronate and lipopolysaccharide, whereas its two products are UDP and N-acetyl-beta-D-mannosaminouronosyl-1,4-lipopolysaccharide.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-N-acetyl-beta-D-mannosaminouronate:lipopolysaccharide N-acetyl-beta-D-mannosaminouronosyltransferase. Other names in common use include ManNAcA transferase, uridine-diphosphoacetylmannosaminuronatetranferase, N-acetylglucosaminylpyrophosphorylundecaprenol glucosyltransferase, and acetylmannosaminuronosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661175
|
14661193
|
Luteolin-7-O-diglucuronide 4'-O-glucuronosyltransferase
|
Class of enzymes
In enzymology, a luteolin-7-O-diglucuronide 4'-O-glucuronosyltransferase (EC 2.4.1.191) is an enzyme that catalyzes the chemical reaction
UDP-glucuronate + luteolin 7-O-beta-D-diglucuronide formula_0 UDP + luteolin 7-O-[beta-D-glucuronosyl-(1->2)-beta-D-glucuronide]-4'-O-beta-D- glucuronide
Thus, the two substrates of this enzyme are UDP-glucuronate and luteolin 7-O-beta-D-diglucuronide, whereas its 4 products are UDP, luteolin, 7-O-[beta-D-glucuronosyl-(1->2)-beta-D-glucuronide]-4'-O-beta-D-, and glucuronide.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucuronate:luteolin-7-O-beta-D-diglucuronide 4'-O-glucuronosyltransferase. Other names in common use include uridine diphosphoglucuronate-luteolin 7-O-diglucuronide, glucuronosyltransferase, UDP-glucuronate:luteolin 7-O-diglucuronide-glucuronosyltransferase, UDPglucuronate:luteolin, 7-O-diglucuronide-4'-O-glucuronosyl-transferase, and LDT.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661193
|
14661219
|
Luteolin-7-O-glucuronide 2"-O-glucuronosyltransferase
|
Class of enzymes
In enzymology, a luteolin-7-O-glucuronide 2"-O-glucuronosyltransferase (EC 2.4.1.190) is an enzyme that catalyzes the chemical reaction
UDP-glucuronate + luteolin 7-O-beta-D-glucuronide formula_0 UDP + luteolin 7-O-[beta-D-glucuronosyl-(1→2)-beta-D-glucuronide]
Thus, the two substrates of this enzyme are UDP-glucuronate and luteolin 7-O-beta-D-glucuronide, whereas its two products are UDP and luteolin 7-O-(beta-D-glucuronosyl-(1→2)-beta-D-glucuronide).
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucuronate:luteolin-7-O-beta-D-glucuronide 2"-O-glucuronosyltransferase. Other names in common use include uridine diphosphoglucuronate-luteolin 7-O-glucuronide, glucuronosyltransferase, LMT, and UDP-glucuronate:luteolin 7-O-glucuronide-glucuronosyltransferase.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661219
|
14661249
|
Luteolin 7-O-glucuronosyltransferase
|
Class of enzymes
In enzymology, a luteolin 7-O-glucuronosyltransferase (EC 2.4.1.189) is an enzyme that catalyzes the chemical reaction
UDP-glucuronate + luteolin formula_0 UDP + luteolin 7-O-beta-D-glucuronide
Thus, the two substrates of this enzyme are UDP-glucuronate and luteolin, whereas its two products are UDP and luteolin 7-O-beta-D-glucuronide.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is UDP-glucuronate:luteolin 7-O-glucuronosyltransferase. Other names in common use include uridine diphosphoglucuronate-luteolin 7-O-glucuronosyltransferase, and LGT.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661249
|
14661273
|
Maltose phosphorylase
|
Class of enzymes
In enzymology, a maltose phosphorylase (EC 2.4.1.8) is an enzyme that catalyzes the chemical reaction
maltose + phosphate formula_0 D-glucose + beta-D-glucose 1-phosphate
Thus, the two substrates of this enzyme are maltose and phosphate, whereas its two products are D-glucose and beta-D-glucose 1-phosphate.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is maltose:phosphate 1-beta-D-glucosyltransferase. This enzyme participates in starch and sucrose metabolism.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 1H54.
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661273
|
14661292
|
Maltose synthase
|
Class of enzymes
In enzymology, a maltose synthase (EC 2.4.1.139) is an enzyme that catalyzes the chemical reaction
2 alpha-D-glucose 1-phosphate + H2O formula_0 maltose + 2 phosphate
Thus, the two substrates of this enzyme are alpha-D-glucose 1-phosphate and H2O, whereas its two products are maltose and phosphate.
This enzyme belongs to the family of glycosyltransferases, specifically the hexosyltransferases. The systematic name of this enzyme class is alpha-D-glucose-1-phosphate:alpha-D-glucose-1-phosphate 4-alpha-D-glucosyltransferase (dephosphorylating).
References.
<templatestyles src="Reflist/styles.css" />
|
[
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
] |
https://en.wikipedia.org/wiki?curid=14661292
|
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.