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13890643 | Siegel–Tukey test | Siegel–Tukey test, named after Sidney Siegel and John Tukey, is a non-parametric test which may be applied to data measured at least on an ordinal scale. It tests for differences in scale between two groups.
The test is used to determine if one of two groups of data tends to have more widely dispersed values than the other. In other words, the test determines whether one of the two groups tends to move, sometimes to the right, sometimes to the left, but away from the center (of the ordinal scale).
The test was published in 1960 by Sidney Siegel and John Wilder Tukey in the "Journal of the American Statistical Association", in the article "A Nonparametric Sum of Ranks Procedure for Relative Spread in Unpaired Samples."
Principle.
The principle is based on the following idea:
Suppose there are two groups A and B with n observations for the first group and m observations for the second (so there are "N" = "n" + "m" total observations). If all "N" observations are arranged in ascending order, it can be expected that the values of the two groups will be mixed or sorted randomly, if there are no differences between the two groups (following the null hypothesis H0). This would mean that among the ranks of extreme (high and low) scores, there would be similar values from Group A and Group B.
If, say, Group A were more inclined to extreme values (the alternative hypothesis H1), then there will be a higher proportion of observations from group A with low or high values, and a reduced proportion of values at the center.
* Hypothesis H0: σ2A = σ2B & MeA = MeB (where σ2 and Me are the variance and the median, respectively)
* Hypothesis H1: σ2A > σ2B
Method.
Two groups, A and B, produce the following values (already sorted in ascending order):
A: 33 62 84 85 88 93 97 B: 4 16 48 51 66 98
By combining the groups, a group of 13 entries is obtained. The ranking is done by alternate extremes (rank 1 is lowest, 2 and 3 are the two highest, 4 and 5 are the two next lowest, etc.).
The sum of the ranks within each W group:
"W"A = 5 + 12 + 11 + 10 + 7 + 6 + 3 = 54
"W"B = 1 + 4 + 8 + 9 + 13 + 2 = 37
If the null hypothesis is true, it is expected that the average ranks of the two groups will be similar.
If one of the two groups is more dispersed its ranks will be lower, as extreme values receive lower ranks, while the other group will receive more of the high scores assigned to the center. To test the difference between groups for significance a Wilcoxon rank sum test is used, which also justifies the notation WA and WB in calculating the rank sums.
From the rank sums the U statistics are calculated by subtracting off the minimum possible score, "n"("n" + 1)/2 for each group:
"U"A = 54 − 7(8)/2 = 26
"U"B = 37 − 6(7)/2 = 16
According to formula_0 the minimum of these two values is distributed according to a Wilcoxon rank-sum distribution with parameters given by the two group sizes:
formula_1
Which allows the calculation of a p-value for this test according to the following formula:
formula_2
formula_3
a table of the Wilcoxon rank-sum distribution can be used to find the statistical significance of the results (see Mann–Whitney_U_test for more explanations on these tables).
For the example data, with groups of sizes m=6 and n=7 the p-value is:
formula_4
indicating little or no reason to reject the null hypothesis that the dispersion of the two groups is the same. | [
{
"math_id": 0,
"text": "H_0"
},
{
"math_id": 1,
"text": " \\min(U_A,U_B) \\sim \\text{Wilcoxon}(m,n) \\!"
},
{
"math_id": 2,
"text": "p = \\Pr\\left[X \\le \\min(U_A,U_B) \\right] \\,\\!"
},
{
"math_id": 3,
"text": "X \\sim \\text{Wilcoxon}(m,n)\\,\\!"
},
{
"math_id": 4,
"text": "p=\\Pr\\left[x \\le 16 \\right] = 0.2669.\\,\\!"
}
]
| https://en.wikipedia.org/wiki?curid=13890643 |
13890972 | HPO formalism | The history projection operator (HPO) formalism is an approach to temporal quantum logic developed by Chris Isham. It deals with the logical structure of quantum mechanical propositions asserted at different points in time.
Introduction.
In standard quantum mechanics a physical system is associated with a Hilbert space formula_0. States of the system at a fixed time are represented by normalised vectors in the space and physical observables are represented by Hermitian operators on formula_0.
A physical proposition formula_1 about the system at a fixed time can be represented by an orthogonal projection operator formula_2 on formula_0 (See quantum logic). This representation links together the lattice operations in the lattice of logical propositions and the lattice of projection operators on a Hilbert space (See quantum logic).
The HPO formalism is a natural extension of these ideas to propositions about the system that are concerned with more than one time.
History propositions.
Homogeneous histories.
A "homogeneous history proposition" formula_3 is a sequence of single-time propositions formula_4 specified at different times formula_5. These times are called the "temporal support" of the history. We shall denote the proposition formula_6 as formula_7 and read it as
"formula_8 at time formula_9 is true and then formula_10 at time formula_11 is true and then formula_12 and then formula_13 at time formula_14 is true"
Inhomogeneous histories.
Not all history propositions can be represented by a sequence of single-time propositions at different times. These are called "inhomogeneous history propositions". An example is the proposition formula_6 OR formula_15 for two homogeneous histories formula_16.
History projection operators.
The key observation of the HPO formalism is to represent history propositions by projection operators on a "history Hilbert space". This is where the name "History Projection Operator" (HPO) comes from.
For a homogeneous history formula_17 we can use the tensor product to define a projector
formula_18
where formula_19 is the projection operator on formula_0 that represents the proposition formula_4 at time formula_20.
This formula_21 is a projection operator on the tensor product "history Hilbert space" formula_22
Not all projection operators on formula_23 can be written as the sum of tensor products of the form formula_21. These other projection operators are used to represent inhomogeneous histories by applying lattice operations to homogeneous histories.
Temporal quantum logic.
Representing history propositions by projectors on the history Hilbert space naturally encodes the logical structure of history propositions. The lattice operations on the set of projection operations on the history Hilbert space formula_23 can be applied to model the lattice of logical operations on history propositions.
If two homogeneous histories formula_3 and formula_15 don't share the same temporal support they can be modified so that they do. If formula_24 is in the temporal support of formula_6 but not formula_15 (for example) then a new homogeneous history proposition which differs from formula_15 by including the "always true" proposition at each time formula_24 can be formed. In this way the temporal supports of formula_16 can always be joined. We shall therefore assume that all homogeneous histories share the same temporal support.
We now present the logical operations for homogeneous history propositions formula_3 and formula_15 such that formula_25
Conjunction (AND).
If formula_26 and formula_27 are two homogeneous histories then the history proposition "formula_6 and formula_15" is also a homogeneous history. It is represented by the projection operator
formula_28 formula_29
Disjunction (OR).
If formula_26 and formula_27 are two homogeneous histories then the history proposition "formula_6 or formula_15" is in general not a homogeneous history. It is represented by the projection operator
formula_30
Negation (NOT).
The negation operation in the lattice of projection operators takes formula_31 to
formula_32
where formula_33 is the identity operator on the Hilbert space. Thus the projector used to represent the proposition formula_34 (i.e. "not formula_26") is
formula_35
Example: Two-time history.
As an example, consider the negation of the two-time homogeneous history proposition formula_36. The projector to represent the proposition formula_34 is
formula_37
formula_38
The terms which appear in this expression:
can each be interpreted as follows:
These three homogeneous histories, joined with the OR operation, include all the possibilities for how the proposition "formula_44 and then formula_45" can be false. We therefore see that the definition of formula_46 agrees with what the proposition formula_34 should mean. | [
{
"math_id": 0,
"text": "\\mathcal{H}"
},
{
"math_id": 1,
"text": "\\,P"
},
{
"math_id": 2,
"text": "\\hat{P}"
},
{
"math_id": 3,
"text": "\\,\\alpha "
},
{
"math_id": 4,
"text": "\\alpha_{t_i}"
},
{
"math_id": 5,
"text": "t_1 < t_2 < \\ldots < t_n "
},
{
"math_id": 6,
"text": "\\,\\alpha"
},
{
"math_id": 7,
"text": "(\\alpha_1,\\alpha_2,\\ldots,\\alpha_n)"
},
{
"math_id": 8,
"text": "\\alpha_{t_1}"
},
{
"math_id": 9,
"text": "t_1"
},
{
"math_id": 10,
"text": "\\alpha_{t_2}"
},
{
"math_id": 11,
"text": "t_2"
},
{
"math_id": 12,
"text": "\\ldots"
},
{
"math_id": 13,
"text": "\\alpha_{t_n}"
},
{
"math_id": 14,
"text": "t_n"
},
{
"math_id": 15,
"text": "\\,\\beta"
},
{
"math_id": 16,
"text": "\\,\\alpha, \\beta"
},
{
"math_id": 17,
"text": "\\alpha = (\\alpha_1,\\alpha_2,\\ldots,\\alpha_n)"
},
{
"math_id": 18,
"text": "\\hat{\\alpha}:= \\hat{\\alpha}_{t_1} \\otimes \\hat{\\alpha}_{t_2} \\otimes \\ldots \\otimes \\hat{\\alpha}_{t_n}"
},
{
"math_id": 19,
"text": "\\hat{\\alpha}_{t_i}"
},
{
"math_id": 20,
"text": "t_i"
},
{
"math_id": 21,
"text": "\\hat{\\alpha}"
},
{
"math_id": 22,
"text": "H = \\mathcal{H} \\otimes \\mathcal{H} \\otimes \\ldots \\otimes \\mathcal{H} "
},
{
"math_id": 23,
"text": "H"
},
{
"math_id": 24,
"text": "\\,t_i"
},
{
"math_id": 25,
"text": "\\hat{\\alpha} \\hat{\\beta} = \\hat{\\beta}\\hat{\\alpha} "
},
{
"math_id": 26,
"text": "\\alpha"
},
{
"math_id": 27,
"text": "\\beta"
},
{
"math_id": 28,
"text": "\\widehat{\\alpha \\wedge \\beta}:= \\hat{\\alpha} \\hat{\\beta}"
},
{
"math_id": 29,
"text": "(= \\hat{\\beta} \\hat{\\alpha})"
},
{
"math_id": 30,
"text": "\\widehat{\\alpha \\vee \\beta}:= \\hat{\\alpha} + \\hat{\\beta} - \\hat{\\alpha}\\hat{\\beta}"
},
{
"math_id": 31,
"text": " \\hat{P} "
},
{
"math_id": 32,
"text": "\\neg \\hat{P} := \\mathbb{I} - \\hat{P}"
},
{
"math_id": 33,
"text": "\\mathbb{I}"
},
{
"math_id": 34,
"text": "\\neg \\alpha"
},
{
"math_id": 35,
"text": "\\widehat{\\neg \\alpha}:= \\mathbb{I} - \\hat{\\alpha}."
},
{
"math_id": 36,
"text": "\\,\\alpha = (\\alpha_1, \\alpha_2)"
},
{
"math_id": 37,
"text": "\\widehat{\\neg \\alpha} = \\mathbb{I} \\otimes \\mathbb{I} - \\hat{\\alpha}_1 \\otimes \\hat{\\alpha}_2"
},
{
"math_id": 38,
"text": "= (\\mathbb{I} - \\hat{\\alpha}_1) \\otimes \\hat{\\alpha}_2 + \\hat{\\alpha}_1 \\otimes (\\mathbb{I} - \\hat{\\alpha}_2) + (\\mathbb{I} - \\hat{\\alpha}_1) \\otimes (\\mathbb{I} - \\hat{\\alpha}_2)"
},
{
"math_id": 39,
"text": "(\\mathbb{I} - \\hat{\\alpha}_1) \\otimes \\hat{\\alpha}_2"
},
{
"math_id": 40,
"text": "\\hat{\\alpha}_1 \\otimes (\\mathbb{I} - \\hat{\\alpha}_2) "
},
{
"math_id": 41,
"text": "(\\mathbb{I} - \\hat{\\alpha}_1) \\otimes (\\mathbb{I} - \\hat{\\alpha}_2) "
},
{
"math_id": 42,
"text": "\\,\\alpha_1 "
},
{
"math_id": 43,
"text": "\\,\\alpha_2 "
},
{
"math_id": 44,
"text": "\\,\\alpha_1"
},
{
"math_id": 45,
"text": "\\,\\alpha_2"
},
{
"math_id": 46,
"text": "\\widehat{\\neg \\alpha}"
}
]
| https://en.wikipedia.org/wiki?curid=13890972 |
13891942 | Bloch spectrum | Concept in quantum mechanics
The Bloch spectrum is a concept in quantum mechanics in the field of theoretical physics; this concept addresses certain energy spectrum considerations. Let "H" be the one-dimensional Schrödinger equation operator
formula_0
where "Uα" is a periodic function of period "α". The Bloch spectrum of "H" is defined as the set of values "E" for which all the solutions of ("H" − "E")φ = 0 are bounded on the whole real axis. The Bloch spectrum consists of the half-line "E"0 < "E" from which certain closed intervals ["E"2"j"−1, "E"2"j"] ("j" = 1, 2, ...) are omitted. These are forbidden bands (or gaps) so the ("E"2"j"−2, "E"2"j"−1) are allowed bands. | [
{
"math_id": 0,
"text": " H = - \\frac{d^2}{dx^2} + U_\\alpha,"
}
]
| https://en.wikipedia.org/wiki?curid=13891942 |
13892472 | KdV hierarchy | Infinite sequence of differential equations
In mathematics, the KdV hierarchy is an infinite sequence of partial differential equations which contains the Korteweg–de Vries equation.
Details.
Let formula_0 be translation operator defined on real valued functions as formula_1. Let formula_2 be set of all analytic functions that satisfy formula_3, i.e. periodic functions of period 1. For each formula_4, define an operator
formula_5
on the space of smooth functions on formula_6. We define the Bloch spectrum formula_7 to be the set of formula_8 such that there is a nonzero function formula_9 with formula_10 and formula_11. The KdV hierarchy is a sequence of nonlinear differential operators formula_12 such that for any formula_13 we have an analytic function formula_14 and we define formula_15 to be formula_14 and
formula_16,
then formula_7 is independent of formula_17.
The KdV hierarchy arises naturally as a statement of Huygens' principle for the D'Alembertian.
Explicit equations for first three terms of hierarchy.
The first three partial differential equations of the KdV hierarchy are
formula_18
where each equation is considered as a PDE for formula_19 for the respective formula_20.
The first equation identifies formula_21 and formula_22 as in the original KdV equation. These equations arise as the equations of motion from the (countably) infinite set of independent constants of motion formula_23 by choosing them in turn to be the Hamiltonian for the system. For formula_24, the equations are called higher KdV equations and the variables formula_25 higher times.
Application to periodic solutions of KdV.
One can consider the higher KdVs as a system of overdetermined PDEs for
formula_26
Then solutions which are independent of higher times above some fixed formula_20 and with periodic boundary conditions are called finite-gap solutions. Such solutions turn out to correspond to compact Riemann surfaces, which are classified by their genus formula_27. For example, formula_28 gives the constant solution, while formula_29 corresponds to cnoidal wave solutions.
For formula_30, the Riemann surface is a hyperelliptic curve and the solution is given in terms of the theta function. In fact all solutions to the KdV equation with periodic initial data arise from this construction (Manakov, Novikov & Pitaevskii et al. 1984).
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "T"
},
{
"math_id": 1,
"text": "T(g)(x)=g(x+1)"
},
{
"math_id": 2,
"text": "\\mathcal{C}"
},
{
"math_id": 3,
"text": "T(g)(x)=g(x)"
},
{
"math_id": 4,
"text": "g \\in \\mathcal{C}"
},
{
"math_id": 5,
"text": "L_g(\\psi)(x) = \\psi''(x) + g(x) \\psi(x)"
},
{
"math_id": 6,
"text": "\\mathbb{R}"
},
{
"math_id": 7,
"text": "\\mathcal{B}_g"
},
{
"math_id": 8,
"text": "(\\lambda,\\alpha) \\in \\mathbb{C}\\times\\mathbb{C}^*"
},
{
"math_id": 9,
"text": "\\psi"
},
{
"math_id": 10,
"text": "L_g(\\psi)=\\lambda\\psi"
},
{
"math_id": 11,
"text": "T(\\psi)=\\alpha\\psi"
},
{
"math_id": 12,
"text": "D_i: \\mathcal{C} \\to \\mathcal{C}"
},
{
"math_id": 13,
"text": "i"
},
{
"math_id": 14,
"text": "g(x,t)"
},
{
"math_id": 15,
"text": "g_t(x)"
},
{
"math_id": 16,
"text": "D_i(g_t)= \\frac{d}{dt} g_t "
},
{
"math_id": 17,
"text": "t"
},
{
"math_id": 18,
"text": "\\begin{align}u_{t_0} &= u_x \\\\ u_{t_1} &= 6uu_x - u_{xxx} \\\\ u_{t_2} &= 10u u_{xxx} - 20u_x u_{xx} - 30u^2 u_x - u_{xxxxx}.\\end{align}"
},
{
"math_id": 19,
"text": "u = u(x, t_n)"
},
{
"math_id": 20,
"text": "n"
},
{
"math_id": 21,
"text": "t_0 = x"
},
{
"math_id": 22,
"text": "t_1 = t"
},
{
"math_id": 23,
"text": "I_n[u]"
},
{
"math_id": 24,
"text": "n > 1"
},
{
"math_id": 25,
"text": "t_n"
},
{
"math_id": 26,
"text": "u = u(t_0 = x, t_1 = t, t_2, t_3, \\cdots)."
},
{
"math_id": 27,
"text": "g"
},
{
"math_id": 28,
"text": "g = 0"
},
{
"math_id": 29,
"text": "g = 1"
},
{
"math_id": 30,
"text": "g > 1"
}
]
| https://en.wikipedia.org/wiki?curid=13892472 |
1389316 | Gas in a box | Basic statistical model
In quantum mechanics, the results of the quantum particle in a box can be used to look at the equilibrium situation for a quantum ideal gas in a box which is a box containing a large number of molecules which do not interact with each other except for instantaneous thermalizing collisions. This simple model can be used to describe the classical ideal gas as well as the various quantum ideal gases such as the ideal massive Fermi gas, the ideal massive Bose gas as well as black body radiation (photon gas) which may be treated as a massless Bose gas, in which thermalization is usually assumed to be facilitated by the interaction of the photons with an equilibrated mass.
Using the results from either Maxwell–Boltzmann statistics, Bose–Einstein statistics or Fermi–Dirac statistics, and considering the limit of a very large box, the Thomas–Fermi approximation (named after Enrico Fermi and Llewellyn Thomas) is used to express the degeneracy of the energy states as a differential, and summations over states as integrals. This enables thermodynamic properties of the gas to be calculated with the use of the partition function or the grand partition function. These results will be applied to both massive and massless particles. More complete calculations will be left to separate articles, but some simple examples will be given in this article.
Thomas–Fermi approximation for the degeneracy of states.
For both massive and massless particles in a box, the states of a particle are
enumerated by a set of quantum numbers ["nx", "ny", "nz"]. The magnitude of the momentum is given by
formula_0
where "h" is the Planck constant and "L" is the length of a side of the box. Each possible state of a particle can be thought of as a point on a 3-dimensional grid of positive integers. The distance from the origin to any point will be
formula_1
Suppose each set of quantum numbers specify "f" states where "f" is the number of internal degrees of freedom of the particle that can be altered by collision. For example, a spin <templatestyles src="Fraction/styles.css" />1⁄2 particle would have "f" = 2, one for each spin state. For large values of "n", the number of states with magnitude of momentum less than or equal to "p" from the above equation is approximately
formula_2
which is just "f" times the volume of a sphere of radius "n" divided by eight since only the octant with positive "ni" is considered. Using a continuum approximation, the number of states with magnitude of momentum between "p" and "p" + "dp" is therefore
formula_3
where "V" = "L"3 is the volume of the box. Notice that in using this continuum approximation, also known as Thomas−Fermi approximation, the ability to characterize the low-energy states is lost, including the ground state where "ni" = 1. For most cases this will not be a problem, but when considering Bose–Einstein condensation, in which a large portion of the gas is in or near the ground state, the ability to deal with low energy states becomes important.
Without using any approximation, the number of particles with energy "ε""i" is given by
formula_4
where formula_5 is the degeneracy of state "i" and formula_6 with "β" = 1/"k"B"T", the Boltzmann constant "k"B, temperature "T", and chemical potential "μ". (See Maxwell–Boltzmann statistics, Bose–Einstein statistics, and Fermi–Dirac statistics.)
Using the Thomas−Fermi approximation, the number of particles "dNE" with energy between "E" and "E" + "dE" is:
formula_7
where formula_8 is the number of states with energy between "E" and "E" + "dE".
Energy distribution.
Using the results derived from the previous sections of this article, some distributions for the gas in a box can now be determined. For a system of particles, the distribution formula_9 for a variable formula_10 is defined through the expression formula_11 which is the fraction of particles that have values for formula_10 between formula_10 and formula_12
formula_13
where
It follows that:
formula_18
For a momentum distribution formula_19, the fraction of particles with magnitude of momentum between formula_20 and formula_21 is:
formula_22
and for an energy distribution formula_23, the fraction of particles with energy between formula_24 and formula_25 is:
formula_26
For a particle in a box (and for a free particle as well), the relationship between energy formula_24 and momentum formula_20 is different for massive and massless particles. For massive particles,
formula_27
while for massless particles,
formula_28
where formula_29 is the mass of the particle and formula_30 is the speed of light.
Using these relationships,
Specific examples.
The following sections give an example of results for some specific cases.
Massive Maxwell–Boltzmann particles.
For this case:
formula_36
Integrating the energy distribution function and solving for "N" gives
formula_37
Substituting into the original energy distribution function gives
formula_38
which are the same results obtained classically for the Maxwell–Boltzmann distribution. Further results can be found in the classical section of the article on the ideal gas.
Massive Bose–Einstein particles.
For this case:
formula_39
where formula_40
Integrating the energy distribution function and solving for "N" gives the particle number
formula_41
where Li"s"("z") is the polylogarithm function. The polylogarithm term must always be positive and real, which means its value will go from 0 to "ζ"(3/2) as "z" goes from 0 to 1. As the temperature drops towards zero, Λ will become larger and larger, until finally Λ will reach a critical value Λc where "z" = 1 and
formula_42
where formula_43 denotes the Riemann zeta function. The temperature at which Λ = Λc is the critical temperature. For temperatures below this critical temperature, the above equation for the particle number has no solution. The critical temperature is the temperature at which a Bose–Einstein condensate begins to form. The problem is, as mentioned above, that the ground state has been ignored in the continuum approximation. It turns out, however, that the above equation for particle number expresses the number of bosons in excited states rather well, and thus:
formula_44
where the added term is the number of particles in the ground state. The ground state energy has been ignored. This equation will hold down to zero temperature. Further results can be found in the article on the ideal Bose gas.
Massless Bose–Einstein particles (e.g. black body radiation).
For the case of massless particles, the massless energy distribution function must be used. It is convenient to convert this function to a frequency distribution function:
formula_45
where Λ is the thermal wavelength for massless particles. The spectral energy density (energy per unit volume per unit frequency) is then
formula_46
Other thermodynamic parameters may be derived analogously to the case for massive particles. For example, integrating the frequency distribution function and solving for "N" gives the number of particles:
formula_47
The most common massless Bose gas is a photon gas in a black body. Taking the "box" to be a black body cavity, the photons are continually being absorbed and re-emitted by the walls. When this is the case, the number of photons is not conserved. In the derivation of Bose–Einstein statistics, when the restraint on the number of particles is removed, this is effectively the same as setting the chemical potential ("μ") to zero. Furthermore, since photons have two spin states, the value of "f" is 2. The spectral energy density is then
formula_48
which is just the spectral energy density for Planck's law of black body radiation. Note that the Wien distribution is recovered if this procedure is carried out for massless Maxwell–Boltzmann particles, which approximates a Planck's distribution for high temperatures or low densities.
In certain situations, the reactions involving photons will result in the conservation of the number of photons (e.g. light-emitting diodes, "white" cavities). In these cases, the photon distribution function will involve a non-zero chemical potential. (Hermann 2005)
Another massless Bose gas is given by the Debye model for heat capacity. This model considers a gas of phonons in a box and differs from the development for photons in that the speed of the phonons is less than light speed, and there is a maximum allowed wavelength for each axis of the box. This means that the integration over phase space cannot be carried out to infinity, and instead of results being expressed in polylogarithms, they are expressed in the related Debye functions.
Massive Fermi–Dirac particles (e.g. electrons in a metal).
For this case:
formula_49
Integrating the energy distribution function gives
formula_50
where again, Li"s"("z") is the polylogarithm function and Λ is the thermal de Broglie wavelength. Further results can be found in the article on the ideal Fermi gas. Applications of the Fermi gas are found in the free electron model, the theory of white dwarfs and in degenerate matter in general. | [
{
"math_id": 0,
"text": "p=\\frac{h}{2L}\\sqrt{n_x^2+n_y^2+n_z^2} \\qquad \\qquad n_x,n_y,n_z=1,2,3,\\ldots "
},
{
"math_id": 1,
"text": "n=\\sqrt{n_x^2+n_y^2+n_z^2}=\\frac{2Lp}{h}"
},
{
"math_id": 2,
"text": "\ng = \\left(\\frac{f}{8}\\right) \\frac{4}{3}\\pi n^3 \n = \\frac{4\\pi f}{3} \\left(\\frac{Lp}{h}\\right)^3\n"
},
{
"math_id": 3,
"text": "dg = \\frac{\\pi}{2}~f n^2\\,dn = \\frac{4\\pi fV}{h^3}~ p^2\\,dp"
},
{
"math_id": 4,
"text": " N_i = \\frac{g_i}{\\Phi(\\varepsilon_i)}"
},
{
"math_id": 5,
"text": " g_i"
},
{
"math_id": 6,
"text": " \\Phi(\\varepsilon_i) = \n\\begin{cases} \n e^{\\beta(\\varepsilon_i-\\mu)}, & \\text{for particles obeying Maxwell-Boltzmann statistics} \\\\\n e^{\\beta(\\varepsilon_i-\\mu)}-1, & \\text{for particles obeying Bose-Einstein statistics}\\\\ \n e^{\\beta(\\varepsilon_i-\\mu)}+1, & \\text{for particles obeying Fermi-Dirac statistics}\\\\\n\\end{cases}"
},
{
"math_id": 7,
"text": "dN_E= \\frac{dg_E}{\\Phi(E)} "
},
{
"math_id": 8,
"text": "dg_E"
},
{
"math_id": 9,
"text": "P_A"
},
{
"math_id": 10,
"text": "A"
},
{
"math_id": 11,
"text": "P_AdA"
},
{
"math_id": 12,
"text": "A+dA"
},
{
"math_id": 13,
"text": "P_A~dA = \\frac{dN_A}{N} = \\frac{dg_A}{N\\Phi_A}"
},
{
"math_id": 14,
"text": "dN_A"
},
{
"math_id": 15,
"text": "dg_A"
},
{
"math_id": 16,
"text": "\\Phi_A^{-1}"
},
{
"math_id": 17,
"text": "N"
},
{
"math_id": 18,
"text": "\\int_A P_A~dA = 1"
},
{
"math_id": 19,
"text": "P_p"
},
{
"math_id": 20,
"text": "p"
},
{
"math_id": 21,
"text": "p+dp"
},
{
"math_id": 22,
"text": "P_p~dp = \\frac{Vf}{N}~\\frac{4\\pi}{h^3\\Phi_p}~p^2dp"
},
{
"math_id": 23,
"text": "P_E"
},
{
"math_id": 24,
"text": "E"
},
{
"math_id": 25,
"text": "E+dE"
},
{
"math_id": 26,
"text": "P_E~dE = P_p\\frac{dp}{dE}~dE"
},
{
"math_id": 27,
"text": " E=\\frac{p^2}{2m}"
},
{
"math_id": 28,
"text": "E = pc"
},
{
"math_id": 29,
"text": "m"
},
{
"math_id": 30,
"text": "c"
},
{
"math_id": 31,
"text": "\\begin{alignat}{2}\n dg_E & = \\quad \\ \\left(\\frac{Vf}{\\Lambda^3}\\right)\n\\frac{2}{\\sqrt{\\pi}}~\\beta^{3/2}E^{1/2}~dE \\\\\n P_E~dE & = \\frac{1}{N}\\left(\\frac{Vf}{\\Lambda^3}\\right)\n\\frac{2}{\\sqrt{\\pi}}~\\frac{\\beta^{3/2}E^{1/2}}{\\Phi(E)}~dE \\\\\n\\end{alignat}"
},
{
"math_id": 32,
"text": "\\Lambda =\\sqrt{\\frac{h^2 \\beta }{2\\pi m}}"
},
{
"math_id": 33,
"text": "(V/N)^{1/3}"
},
{
"math_id": 34,
"text": "\\begin{alignat}{2}\n dg_E & = \\quad \\ \\left(\\frac{Vf}{\\Lambda^3}\\right)\n\\frac{1}{2}~\\beta^3E^2~dE \\\\\n P_E~dE & = \\frac{1}{N}\\left(\\frac{Vf}{\\Lambda^3}\\right)\n\\frac{1}{2}~\\frac{\\beta^3E^2}{\\Phi(E)}~dE \\\\\n\\end{alignat}\n"
},
{
"math_id": 35,
"text": "\\Lambda = \\frac{ch\\beta}{2\\, \\pi^{1/3}}"
},
{
"math_id": 36,
"text": "\\Phi(E)=e^{\\beta(E-\\mu)}"
},
{
"math_id": 37,
"text": "N = \\left(\\frac{Vf}{\\Lambda^3}\\right)\\,\\,e^{\\beta\\mu}"
},
{
"math_id": 38,
"text": "P_E~dE = 2 \\sqrt{\\frac{\\beta^3 E}{\\pi}}~e^{-\\beta E}~dE"
},
{
"math_id": 39,
"text": "\\Phi(E)=\\frac{e^{\\beta E}}{z}-1"
},
{
"math_id": 40,
"text": " z=e^{\\beta\\mu}."
},
{
"math_id": 41,
"text": "N = \\left(\\frac{Vf}{\\Lambda^3}\\right)\\textrm{Li}_{3/2}(z)"
},
{
"math_id": 42,
"text": "N = \\left(\\frac{Vf}{\\Lambda_{\\rm c}^3}\\right)\\zeta(3/2),"
},
{
"math_id": 43,
"text": "\\zeta(z)"
},
{
"math_id": 44,
"text": "\nN=\\frac{g_0 z}{1-z}+\\left(\\frac{Vf}{\\Lambda^3}\\right)\\operatorname{Li}_{3/2}(z)\n"
},
{
"math_id": 45,
"text": "\nP_\\nu~d\\nu = \\frac{h^3}{N}\\left(\\frac{Vf}{\\Lambda^3}\\right)\n\\frac{1}{2}~\\frac{\\beta^3\\nu^2}{e^{(h\\nu-\\mu)/k_{\\rm B}T}-1}~d\\nu\n"
},
{
"math_id": 46,
"text": "U_\\nu~d\\nu = \\left(\\frac{N\\,h\\nu}{V}\\right) P_\\nu~d\\nu = \\frac{4\\pi f h\\nu^3 }{c^3}~\\frac{1}{e^{(h\\nu-\\mu)/k_{\\rm B}T}-1}~d\\nu."
},
{
"math_id": 47,
"text": "N=\\frac{16\\,\\pi V}{c^3h^3\\beta^3}\\,\\mathrm{Li}_3\\left(e^{\\mu/k_{\\rm B}T}\\right)."
},
{
"math_id": 48,
"text": "U_\\nu~d\\nu = \\frac{8\\pi h\\nu^3 }{c^3}~\\frac{1}{e^{h\\nu/k_{\\rm B}T}-1}~d\\nu "
},
{
"math_id": 49,
"text": "\\Phi(E)=e^{\\beta(E-\\mu)}+1.\\,"
},
{
"math_id": 50,
"text": "N=\\left(\\frac{Vf}{\\Lambda^3}\\right)\\left[-\\textrm{Li}_{3/2}(-z)\\right]"
}
]
| https://en.wikipedia.org/wiki?curid=1389316 |
1389320 | Gas in a harmonic trap | Quantum mechanical model
The results of the quantum harmonic oscillator can be used to look at the equilibrium situation for a quantum ideal gas in a harmonic trap, which is a harmonic potential containing a large number of particles that do not interact with each other except for instantaneous thermalizing collisions. This situation is of great practical importance since many experimental studies of Bose gases are conducted in such harmonic traps.
Using the results from either Maxwell–Boltzmann statistics, Bose–Einstein statistics or Fermi–Dirac statistics we use the Thomas–Fermi approximation (gas in a box) and go to the limit of a very large trap, and express the degeneracy of the energy states (formula_0) as a differential, and summations over states as integrals. We will then be in a position to calculate the thermodynamic properties of the gas using the partition function or the grand partition function. Only the case of massive particles will be considered, although the results can be extended to massless particles as well, much as was done in the case of the ideal gas in a box. More complete calculations will be left to separate articles, but some simple examples will be given in this article.
Thomas–Fermi approximation for the degeneracy of states.
For massive particles in a harmonic well, the states of the particle are enumerated by a set of quantum numbers formula_1. The energy of a particular state is given by:
formula_2
Suppose each set of quantum numbers specify formula_3 states where formula_3 is the number of internal degrees of freedom of the particle that can be altered by collision. For example, a spin-1/2 particle would have formula_4, one for each spin state. We can think of each possible state of a particle as a point on a 3-dimensional grid of positive integers. The Thomas–Fermi approximation assumes that the quantum numbers are so large that they may be considered to be a continuum. For large values of formula_5, we can estimate the number of states with energy less than or equal to formula_6 from the above equation as:
formula_7
which is just formula_3 times the volume of the tetrahedron formed by the plane described by the energy equation and the bounding planes of the positive octant. The number of states with energy between formula_6 and formula_8 is therefore:
formula_9
Notice that in using this continuum approximation, we have lost the ability to characterize the low-energy states, including the ground state where formula_10. For most cases this will not be a problem, but when considering Bose–Einstein
condensation, in which a large portion of the gas is in or near the ground state, we will need to recover the ability to deal with low energy states.
Without using the continuum approximation, the number of particles with energy formula_11 is given by:
formula_12
where
with formula_13, with formula_14 being the Boltzmann constant, formula_15 being temperature, and formula_16 being the chemical potential. Using the continuum approximation, the number of particles formula_17 with energy between formula_6 and formula_8 is now written:
formula_18
Energy distribution function.
We are now in a position to determine some distribution functions for the "gas in a harmonic trap." The distribution function for any variable formula_19 is formula_20 and is equal to the fraction of particles which have values for formula_19 between formula_19 and formula_21:
formula_22
It follows that:
formula_23
Using these relationships we obtain the energy distribution function:
formula_24
Specific examples.
The following sections give an example of results for some specific cases.
Massive Maxwell–Boltzmann particles.
For this case:
formula_25
Integrating the energy distribution function and solving for formula_26 gives:
formula_27
Substituting into the original energy distribution function gives:
formula_28
Massive Bose–Einstein particles.
For this case:
formula_29
where formula_30 is defined as:
formula_31
Integrating the energy distribution function and solving for formula_26 gives:
formula_32
where formula_33 is the polylogarithm function. The polylogarithm term must always be positive and real, which means its value will go from 0 to formula_34 as formula_30 goes from 0 to 1. As the temperature goes to zero, formula_35 will become larger and larger, until finally formula_35 will reach a critical value formula_36, where formula_37 and
formula_38
The temperature at which formula_39 is the critical temperature at which a Bose–Einstein condensate begins to form. The problem is, as mentioned above, the ground state has been ignored in the continuum approximation. It turns out that the above expression expresses the number of bosons in excited states rather well, and so we may write:
formula_40
where the added term is the number of particles in the ground state. (The ground state energy has been ignored.) This equation will hold down to zero temperature. Further results can be found in the article on the ideal Bose gas.
Massive Fermi–Dirac particles (e.g. electrons in a metal).
For this case:
formula_41
Integrating the energy distribution function gives:
formula_42
where again, formula_33 is the polylogarithm function. Further results can be found in the article on the ideal Fermi gas. | [
{
"math_id": 0,
"text": "g_{i}"
},
{
"math_id": 1,
"text": "[n_x,n_y,n_z]"
},
{
"math_id": 2,
"text": "E=\\hbar\\omega\\left(n_x+n_y+n_z+3/2\\right)~~~~~~~~n_i=0,1,2,\\ldots"
},
{
"math_id": 3,
"text": "f"
},
{
"math_id": 4,
"text": "f = 2"
},
{
"math_id": 5,
"text": "n"
},
{
"math_id": 6,
"text": "E"
},
{
"math_id": 7,
"text": "g=f\\,\\frac{n^3}{6}=f\\,\\frac{(E/\\hbar\\omega)^3}{6}"
},
{
"math_id": 8,
"text": "E + dE"
},
{
"math_id": 9,
"text": "dg=\\frac{1}{2}\\,fn^2\\,dn=\\frac{f}{(\\hbar\\omega\\beta)^3}~\\frac{1}{2}~\\beta^3 E^2\\,dE"
},
{
"math_id": 10,
"text": "n_{i} = 0"
},
{
"math_id": 11,
"text": "\\epsilon_{i}"
},
{
"math_id": 12,
"text": "N_i = \\frac{g_i}{\\Phi}"
},
{
"math_id": 13,
"text": "\\beta=1/kT"
},
{
"math_id": 14,
"text": "k"
},
{
"math_id": 15,
"text": "T"
},
{
"math_id": 16,
"text": "\\mu"
},
{
"math_id": 17,
"text": "dN"
},
{
"math_id": 18,
"text": "dN= \\frac{dg}{\\Phi}"
},
{
"math_id": 19,
"text": "A"
},
{
"math_id": 20,
"text": "P_{A}dA"
},
{
"math_id": 21,
"text": "A + dA"
},
{
"math_id": 22,
"text": "P_A~dA = \\frac{dN}{N} = \\frac{dg}{N\\Phi}"
},
{
"math_id": 23,
"text": "\\int_A P_A~dA = 1"
},
{
"math_id": 24,
"text": "P_E~dE = \\frac{1}{N}\\,\\left(\\frac{f}{(\\hbar\\omega\\beta)^3}\\right)~\\frac{1}{2} \\frac{\\beta^3E^2}{\\Phi}\\,dE"
},
{
"math_id": 25,
"text": "\\Phi=e^{\\beta(E-\\mu)}"
},
{
"math_id": 26,
"text": "N"
},
{
"math_id": 27,
"text": "N = \\frac{f}{(\\hbar\\omega\\beta)^3}~e^{\\beta\\mu}"
},
{
"math_id": 28,
"text": "P_E~dE = \\frac{\\beta^3 E^2 e^{-\\beta E}}{2}\\,dE"
},
{
"math_id": 29,
"text": "\\Phi=e^{\\beta \\epsilon}/z-1"
},
{
"math_id": 30,
"text": "z"
},
{
"math_id": 31,
"text": "z=e^{\\beta\\mu}"
},
{
"math_id": 32,
"text": "N = \\frac{f}{(\\hbar\\omega\\beta)^3}~\\mathrm{Li}_3(z),"
},
{
"math_id": 33,
"text": "\\mathrm{Li}_{s}(z)"
},
{
"math_id": 34,
"text": "\\zeta(3)"
},
{
"math_id": 35,
"text": "\\beta"
},
{
"math_id": 36,
"text": "\\beta_\\text{c}"
},
{
"math_id": 37,
"text": "z = 1"
},
{
"math_id": 38,
"text": "N = \\frac{f}{(\\hbar\\omega\\beta_c)^3}~\\zeta(3) ."
},
{
"math_id": 39,
"text": "\\beta = \\beta_{c}"
},
{
"math_id": 40,
"text": "N=\\frac{g_0z}{1-z}+\\frac{f}{(\\hbar\\omega\\beta)^3}~\\mathrm{Li}_3(z)"
},
{
"math_id": 41,
"text": "\\Phi=e^{\\beta(E-\\mu)}+1"
},
{
"math_id": 42,
"text": "1=\\frac{f}{(\\hbar\\omega\\beta)^3}~\\left[-\\mathrm{Li}_3(-z)\\right]"
}
]
| https://en.wikipedia.org/wiki?curid=1389320 |
13893984 | Psychrometric constant | Relation of the partial pressure of water in air to temperature
The psychrometric constant formula_0 relates the partial pressure of water in air to the air temperature. This lets one interpolate actual vapor pressure from paired dry and wet thermometer bulb temperature readings.
formula_1
formula_2 psychrometric constant [kPa °C−1],
P = atmospheric pressure [kPa],
formula_3 latent heat of water vaporization, 2.45 [MJ kg−1],
formula_4 specific heat of air at constant pressure, [MJ kg−1 °C−1],
formula_5 ratio molecular weight of water vapor/dry air = 0.622.
Both formula_6 and formula_7 are constants.<br>
Since atmospheric pressure, P, depends upon altitude, so does formula_8.<br>
At higher altitude water evaporates and boils at lower temperature.
Although formula_9 is constant, varied air composition results in varied formula_10.
Thus on average, at a given location or altitude, the psychrometric constant is approximately constant. Still, it is worth remembering that weather impacts both atmospheric pressure and composition.
Vapor Pressure Estimation.
Saturated vapor pressure, formula_11<br>
Actual vapor pressure, formula_12
here e[T] is vapor pressure as a function of temperature, T.
Tdew = the dewpoint temperature at which water condenses.
Twet = the temperature of a wet thermometer bulb from which water can evaporate to air.
Tdry = the temperature of a dry thermometer bulb in air.
References.
<templatestyles src="Reflist/styles.css" />
<templatestyles src="Refbegin/styles.css" /> | [
{
"math_id": 0,
"text": " \\gamma "
},
{
"math_id": 1,
"text": " \\gamma =\\frac{ \\left( c_p \\right)_{air} * P }{ \\lambda_v * MW_{ratio} } "
},
{
"math_id": 2,
"text": " \\gamma = "
},
{
"math_id": 3,
"text": " \\lambda_v = "
},
{
"math_id": 4,
"text": " c_p = "
},
{
"math_id": 5,
"text": " MW_{ratio} = "
},
{
"math_id": 6,
"text": " \\lambda_v "
},
{
"math_id": 7,
"text": " MW_{ratio} "
},
{
"math_id": 8,
"text": "\\gamma"
},
{
"math_id": 9,
"text": " \\left( c_p \\right)_{H_2 O} "
},
{
"math_id": 10,
"text": " \\left( c_p \\right)_{air} "
},
{
"math_id": 11,
"text": "e_s = e \\left[ T_{wet}\\right]"
},
{
"math_id": 12,
"text": "e_a = e_s - \\gamma * \\left( T_{dry} - T_{wet} \\right) "
}
]
| https://en.wikipedia.org/wiki?curid=13893984 |
13895181 | Aleksandrov–Clark measure | In mathematics, Aleksandrov–Clark (AC) measures are specially constructed measures named after the two mathematicians, A. B. Aleksandrov and Douglas Clark, who discovered some of their deepest properties. The measures are also called either Aleksandrov measures, Clark measures, or occasionally spectral measures.
AC measures are used to extract information about self-maps of the unit disc, and have applications in a number of areas of complex analysis, most notably those related to operator theory. Systems of AC measures have also been constructed for higher dimensions, and for the half-plane.
Construction of the measures.
The original construction of Clark relates to one-dimensional perturbations of compressed shift operators on subspaces of the Hardy space:
formula_0
By virtue of Beurling's theorem, any shift-invariant subspace of this space is of the form
formula_1
where formula_2 is an inner function. As such, any invariant subspace of the adjoint of the shift is of the form
formula_3
We now define formula_4 to be the shift operator compressed to formula_5, that is
formula_6
Clark noticed that all the one-dimensional perturbations of formula_4, which were also unitary maps, were of the form
formula_7
and related each such map to a measure, formula_8 on the unit circle, via the Spectral theorem. This collection of measures, one for each formula_9 on the unit circle formula_10, is then called the collection of AC measures associated with formula_2.
An alternative construction.
The collection of measures may also be constructed for any analytic function (that is, not necessarily an inner function). Given an analytic self map, formula_11, of the unit disc, formula_12, we can construct a collection of functions, formula_13, given by
formula_14
one for each formula_15. Each of these functions is positive and harmonic, so by Herglotz' Theorem each is the Poisson integral of some positive measure formula_16 on formula_10. This collection is the set of AC measures associated with formula_17. It can be shown that the two definitions coincide for inner functions. | [
{
"math_id": 0,
"text": "H^2(\\mathbb{D},\\mathbb{C})."
},
{
"math_id": 1,
"text": "\\theta H^2(\\mathbb{D},\\mathbb{C}),"
},
{
"math_id": 2,
"text": "\\theta"
},
{
"math_id": 3,
"text": "K_\\theta = \\left(\\theta H^2(\\mathbb{D},\\mathbb{C})\\right)^\\perp."
},
{
"math_id": 4,
"text": "S_\\theta"
},
{
"math_id": 5,
"text": "K_\\theta"
},
{
"math_id": 6,
"text": "S_\\theta = P_{K_\\theta} S|_{K_\\theta}."
},
{
"math_id": 7,
"text": " U_\\alpha (f) = S_\\theta (f) + \\alpha \\left\\langle f , \\frac{\\theta}{z} \\right\\rangle, "
},
{
"math_id": 8,
"text": "\\sigma_\\alpha"
},
{
"math_id": 9,
"text": "\\alpha"
},
{
"math_id": 10,
"text": "^\\mathbb{T}"
},
{
"math_id": 11,
"text": "\\phi"
},
{
"math_id": 12,
"text": "^\\mathbb{D}"
},
{
"math_id": 13,
"text": "u_\\alpha"
},
{
"math_id": 14,
"text": " u_\\alpha(z) = \\Re \\left(\\frac{\\alpha + \\varphi(z)}{\\alpha - \\varphi(z)}\\right), "
},
{
"math_id": 15,
"text": "^{\\alpha\\in\\mathbb{T}}"
},
{
"math_id": 16,
"text": "\\mu_\\alpha"
},
{
"math_id": 17,
"text": "\\varphi"
}
]
| https://en.wikipedia.org/wiki?curid=13895181 |
13895672 | Strombine dehydrogenase | In enzymology, a strombine dehydrogenase (EC 1.5.1.22) is an enzyme that catalyzes the chemical reaction
N-(carboxymethyl)-D-alanine + NAD+ + H2O formula_0 glycine + pyruvate + NADH + H+
The 3 substrates of this enzyme are N-(carboxymethyl)-D-alanine, NAD+, and H2O, whereas its 4 products are glycine, pyruvate, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-NH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is N-(carboxymethyl)-D-alanine:NAD+ oxidoreductase (glycine-forming). Other names in common use include strombine[N-(carboxymethyl)-D-alanine]dehydrogenase, and N-(carboxymethyl)-D-alanine: NAD+ oxidoreductase.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=13895672 |
13896912 | Xanthine dehydrogenase | Protein-coding gene in the species Homo sapiens
Xanthine dehydrogenase, also known as XDH, is a protein that, in humans, is encoded by the "XDH" gene.
Function.
Xanthine dehydrogenase belongs to the group of molybdenum-containing hydroxylases involved in the oxidative metabolism of purines. The enzyme is a homodimer. Xanthine dehydrogenase can be converted to xanthine oxidase by reversible sulfhydryl oxidation or by irreversible proteolytic modification.
Xanthine dehydrogenase catalyzes the following chemical reaction:
xanthine + NAD+ + H2O formula_0 urate + NADH + H+
The three substrates of this enzyme are xanthine, NAD+, and H2O, whereas its three products are urate, NADH, and H+.
This enzyme participates in purine metabolism.
Nomenclature.
This enzyme belongs to the family of oxidoreductases, to be specific, those acting on CH or CH2 groups with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is xanthine:NAD+ oxidoreductase. Other names in common use include NAD+-xanthine dehydrogenase, xanthine-NAD+ oxidoreductase, xanthine/NAD+ oxidoreductase, and xanthine oxidoreductase.
Clinical significance.
Defects in xanthine dehydrogenase cause xanthinuria, may contribute to adult respiratory stress syndrome, and may potentiate influenza infection through an oxygen metabolite-dependent mechanism. It has been shown that patients with lung adenocarcinoma tumors which have high levels of XDH gene expression have lower survivals. Addiction to XDH protein has been used to target NSCLC tumors and cell lines in a precision oncology manner.
References.
<templatestyles src="Reflist/styles.css" />
Further reading.
<templatestyles src="Refbegin/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=13896912 |
13897128 | Xanthoxin dehydrogenase | In enzymology, a xanthoxin dehydrogenase (EC 1.1.1.288) is an enzyme that catalyzes the chemical reaction
xanthoxin + NAD+ formula_0 abscisic aldehyde + NADH + H+
Thus, the two substrates of this enzyme are xanthoxin and NAD+, whereas its 3 products are abscisic aldehyde, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is xanthoxin:NAD+ oxidoreductase. Other names in common use include xanthoxin oxidase, and ABA2. This enzyme participates in carotenoid biosynthesis.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=13897128 |
13897461 | Salicylaldehyde dehydrogenase | In enzymology, a salicylaldehyde dehydrogenase (EC 1.2.1.65) is an enzyme that catalyzes the chemical reaction
salicylaldehyde + NAD+ + H2O formula_0 salicylate + NADH + 2 H+
The 3 substrates of this enzyme are salicylaldehyde, NAD+, and H2O, whereas its 3 products are salicylate, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the aldehyde or oxo group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is salicylaldehyde:NAD+ oxidoreductase. This enzyme participates in naphthalene and anthracene degradation.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=13897461 |
13897474 | Sarcosine dehydrogenase | In enzymology, sarcosine dehydrogenase (EC 1.5.8.3) is a mitochondrial enzyme that catalyzes the chemical reaction N-demethylation of sarcosine to give glycine. This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-NH group of donor with other acceptors. The systematic name of this enzyme class is sarcosine:acceptor oxidoreductase (demethylating). Other names in common use include sarcosine N-demethylase, monomethylglycine dehydrogenase, and sarcosine:(acceptor) oxidoreductase (demethylating). Sarcosine dehydrogenase is closely related to dimethylglycine dehydrogenase, which catalyzes the demethylation reaction of dimethylglycine to sarcosine. Both sarcosine dehydrogenase and dimethylglycine dehydrogenase use FAD as a cofactor. Sarcosine dehydrogenase is linked by electron-transferring flavoprotein (ETF) to the respiratory redox chain.
The general chemical reaction catalyzed by sarcosine dehydrogenase is:
sarcosine + acceptor + H2O formula_0 glycine + formaldehyde + reduced acceptor
Structure.
There is no crystal structure available for sarcosine dehydrogenase. Sarcosine dehydrogenase contains a covalently bound FAD group " linked via the 8 alpha position of the isoalloxazine ring to an imidazole N(3) of a histidine residue". The enzyme, according to Freisell Wr. et al., also contains non-heme iron in a ratio of 1 or 2 iron per 300000g of enzyme, and 0.5 mol of acid soluble sulfur suggesting that the electron transfer during the first step in the reaction might proceed through a different pathway than that of Fe-S clusters.
Mechanism.
Sarcosine dehydrogenase, with sarcosine as its substrate, follows Michaelis–Menten kinetics and has a Km of 0.5 mM and a Vmax of 16 mmol/hr/mg protein. The enzyme is inhibited competitively by methoxyacetic acid, which has a Ki of 0.26 mM
The exact mechanism of sarcosine dehydrogenase is not available. However, according to the overall net reaction discussed in Honova.E, et al. paper:
the first step of the reaction might involve the transfer of a hydride on the N-methyl group of sarcosine onto FAD, allowing H2O to attack the carbocation in order to form intermediate 1 (See figure 1). There is no deamination step. Instead, the demethylation of the N-methyl group on sarcosine occurs directly. The reduced FADH− from the first step then is oxidized by O2 to form H2O2.
The demethylation of sarcosine catalyzed by sarcosine dehydrogenase can proceed with or without the presence of tetrahydrofolate. Under anaerobic condition and without tetrahydrofolate, however, a free formaldehyde is formed after the N-demethylation of sarcosine. The reaction with 1 mole of sarcosine and 1 mole of FAD, under this condition, yields 1 mole of glycine and 1 mole of formaldehyde (See figure 2 for mechanism).
Under the presence of tetrahydrofolate, sarcosine dehydrogenase binds to tetrahydrofolate and convert tetrahydrofolate to 5,10-methylenetetrahydrofolate. Tetrahydrofolate here serves as a 1-carbon acceptor during the demethylation process (See figure 3 for mechanism).
Function.
Sarcosine dehydrogenase is one of the enzymes in sarcosine metabolism, which catalyzes the demethylation of sarcosine to make glycine. It is preceded by dimethylglycine dehydrogenase which turns dimethylglycine into sarcosine. Glycine can also be turned into sarcosine by glycine N-methyltransferase. Since glycine is the production of sarcosine dehydrogenase catalyzed reaction, aside from sarcosine metabolism, the enzyme is also indirectly connected to the creatine cycle and the respiratory chain in the mitochondria (See figure 4 for pathway). Even so, the biological significance of sarcosine dehydrogenase beyond sarcosine metabolism is not entirely known. In a study of hereditary hemochromatosis using both wild type and HFE (gene) deficient mice fed with 2 percent carbonyl iron supplemented diet, sarcosine dehydrogenase was shown to be down-regulated in HFE deficient mice, but role sarcosine dehydrogenase in iron metabolism is unknown from the experiment conducted.
Disease relevance.
Sarcosinemia.
Sarcosinemia is an autosomal recessive disease caused by a mutation of the sarcosine dehydrogenase gene in the 9q33-q34 gene locus. This leads to a compromised sarcosine metabolism and causes the build-up of sarcosine in blood and urine, a condition known as sarcosinemia.
Prostate cancer.
In addition to sarcosinaemia, sarcosine dehydrogenase also seems to play a role in the progression process of prostate cancer. The concentration of sarcosine, along with those of uracil, kynurenine, glycerol 3-phosphate, leucine and proline increases as prostate cancer progresses. Thus, sarcosine can be used as a potential biomarker for the detection of prostate cancer and for measuring the progress of the disease. As Sreekumar, A. et al.’s paper shows, the removal of sarcosine dehydrogenase from benign prostate epithelial cells increases the concentration of sarcosine and increase cancer cell invasions while the removal of either dimethylglycine dehydrogenase or glycine N-methyltransferase in prostate cancer cells decreases cell invasions. This demonstrates that sarcosine metabolism plays a key-role in prostate cancer cell invasion and migration. Sreekumar’s study suggests that sarcosine dehydrogenase and other enzymes in the sarcosine metabolism pathways could be potential therapeutic targets for prostate cancer. However, a study done by Jentzmik F. et al. by analyzing sarcosine level in 92 patients with prostate cancer draws a different conclusion: sarcosine cannot be used as an indicator and biomarker for prostate cancer.
References.
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Further reading.
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13897482 | Sequoyitol dehydrogenase | In enzymology, a sequoyitol dehydrogenase (EC 1.1.1.143) is an enzyme that catalyzes the chemical reaction
5-O-methyl-myo-inositol + NAD+ formula_0 2D-5-O-methyl-2,3,5/4,6-pentahydroxycyclohexanone + NADH + H+
Thus, the two substrates of this enzyme are 5-O-methyl-myo-inositol and NAD+, whereas its 3 products are 2D-5-O-methyl-2,3,5/4,6-pentahydroxycyclohexanone, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 5-O-methyl-myo-inositol:NAD+ oxidoreductase. This enzyme is also called D-pinitol dehydrogenase.
References.
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13897656 | Serine 2-dehydrogenase | Enzyme
In enzymology, a serine 2-dehydrogenase (EC 1.4.1.7) is an enzyme that catalyzes the chemical reaction
L-serine + H2O + NAD+ formula_0 3-hydroxypyruvate + NH3 + NADH + H+
The 3 substrates of this enzyme are L-serine, H2O, and NAD+, whereas its 4 products are 3-hydroxypyruvate, NH3, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-NH2 group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is L-serine:NAD+ 2-oxidoreductase (deaminating). Other names in common use include L-serine:NAD+ oxidoreductase (deaminating), and serine dehydrogenase.
References.
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13897668 | Serine 3-dehydrogenase | In enzymology, a serine 3-dehydrogenase (EC 1.1.1.276) is an enzyme that catalyzes the chemical reaction
L-serine + NADP+ formula_0 2-ammoniomalonate semialdehyde + NADPH + H+
Thus, the two substrates of this enzyme are L-serine and NADP+, whereas its 3 products are 2-ammoniomalonate semialdehyde, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is L-serine:NADP+ 3-oxidoreductase.
References.
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13897682 | Shikimate dehydrogenase | Enzyme involved in amino acid biosynthesis
In enzymology, a shikimate dehydrogenase (EC 1.1.1.25) is an enzyme that catalyzes the chemical reaction
shikimate + NADP+ formula_0 3-dehydroshikimate + NADPH + H+
Thus, the two substrates of this enzyme are shikimate and NADP+, whereas its 3 products are 3-dehydroshikimate, NADPH, and H+. This enzyme participates in phenylalanine, tyrosine and tryptophan biosynthesis.
Function.
Shikimate dehydrogenase is an enzyme that catalyzes one step of the shikimate pathway. This pathway is found in bacteria, plants, fungi, algae, and parasites and is responsible for the biosynthesis of aromatic amino acids (phenylalanine, tyrosine, and tryptophan) from the metabolism of carbohydrates. In contrast, animals and humans lack this pathway hence products of this biosynthetic route are essential amino acids that must be obtained through an animal's diet.
There are seven enzymes that play a role in this pathway. Shikimate dehydrogenase (also known as 3-dehydroshikimate dehydrogenase) is the fourth step of the seven step process. This step converts 3-dehydroshikimate to shikimate as well as reduces NADP+ to NADPH.
Nomenclature.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is shikimate:NADP+ 3-oxidoreductase. Other names in common use include:
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Reaction.
Shikimate Dehydrogenase catalyzes the reversible NADPH-dependent reaction of 3-dehydroshikimate to shikimate. The enzyme reduces the carbon-oxygen double bond of a carbonyl functional group to a hydroxyl (OH) group, producing the shikimate anion. The reaction is NADPH dependent with NADPH being oxidised to NADP+.
Structure.
N terminal domain.
The Shikimate dehydrogenase substrate binding domain found at the N-terminus binds to the substrate, 3-dehydroshikimate. It is considered to be the catalytic domain. It has a structure of six beta strands forming a twisted beta sheet with four alpha helices.
C terminal domain.
The C-terminal domain binds to NADPH. It has a special structure, a Rossmann fold, whereby six-stranded twisted and parallel beta sheet with loops and alpha helices surrounding the core beta sheet.
The Structure of Shikimate dehydrogenase is characterized by two domains, two alpha helices and two beta sheets with a large cleft separating the domains of the monomer. The enzyme is symmetrical. Shikimate dehydrogenase also has an NADPH binding site that contains a Rossmann fold. This binding site normally contains a glycine P-loop. The domains of the monomer show a fair amount of flexibility suggesting that the enzyme can open in close to bind with the substrate 3-Dehydroshikimate. Hydrophobic interactions occur between the domains and the NADPH binding site. This hydrophobic core and its interactions lock the shape of the enzyme even though the enzyme is a dynamic structure. There is also evidence to support that the structure of the enzyme is conserved, meaning the structure takes sharp turns in order to take up less space.
Paralogs.
"Escherichia coli" ("E. coli") expresses two different forms of shikimate dehydrogenase, AroE and YdiB. These two forms are paralogs of each other. The two forms of shikimate dehydrogenase have different primary sequences in different organisms but catalyze the same reactions. There is about 25% similarity between the sequences of AroE and YdiB, but their two structures have similar structures with similar folds. YdiB can utilize NAD or NADP as a cofactor and also reacts with quinic acid. They both have high affinity of their ligands as shown by their similar enzyme (Km) values. Both forms of the enzyme are independently regulated.
Applications.
The shikimate pathway is a target for herbicides and other non-toxic drugs because the shikimate pathway is not present in humans. Glyphosate, a commonly used herbicide, is an inhibitor of 5-enolpyruvylshikimate 3-phosphate synthase or EPSP synthase, an enzyme in the shikimate pathway. The problem is that this herbicide has been utilized for about 20 years and now some plants have now emerged that are glyphosate-resistant. This has relevance to research on shikimate dehydrogenase because it is important to maintain diversity in the enzyme blocking process in the shikimate pathway and with more research shikimate dehydrogenase could be the next enzyme to be inhibited in the shikimate pathway. In order to design new inhibitors the structures for all the enzymes in the pathway have needed to be elucidated. The presence of two forms of the enzyme complicate the design of potential drugs because one could compensate for the inhibition of the other. Also there the TIGR data base shows that there are 14 species of bacteria with the two forms of shikimate dehydrogenase. This is a problem for drug makers because there are two enzymes that a potential drug would need to inhibit at the same time.
References.
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Further reading.
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13897698 | Sorbitol-6-phosphate 2-dehydrogenase | Enzyme
In enzymology, a sorbitol-6-phosphate dehydrogenase (EC 1.1.1.140) is an enzyme that catalyzes the chemical reaction
D-sorbitol 6-phosphate + NAD+ formula_0 D-fructose 6-phosphate + NADH + H+
Thus, the two substrates of this enzyme are D-sorbitol 6-phosphate and NAD+, whereas its 3 products are D-fructose 6-phosphate, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-sorbitol-6-phosphate:NAD+ 2-oxidoreductase. Other names in common use include ketosephosphate reductase, ketosephosphate reductase, D-sorbitol 6-phosphate dehydrogenase, D-sorbitol-6-phosphate dehydrogenase, sorbitol-6-P-dehydrogenase, and D-glucitol-6-phosphate dehydrogenase. This enzyme participates in fructose and mannose metabolism.
References.
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13897918 | Sorbose dehydrogenase | In enzymology, a sorbose dehydrogenase (EC 1.1.99.12) is an enzyme that catalyzes the chemical reaction
L-sorbose + acceptor formula_0 5-dehydro-D-fructose + reduced acceptor
Thus, the two substrates of this enzyme are L-sorbose and acceptor, whereas its two products are 5-dehydro-D-fructose and reduced acceptor.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with other acceptors. The systematic name of this enzyme class is L-sorbose:acceptor 5-oxidoreductase. This enzyme is also called L-sorbose:(acceptor) 5-oxidoreductase.
References.
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13897939 | Spermidine dehydrogenase | In enzymology, a spermidine dehydrogenase (EC 1.5.99.6) is an enzyme that catalyzes the chemical reaction
spermidine + acceptor + H2O formula_0 propane-1,3-diamine + 4-aminobutanal + reduced acceptor
The 3 substrates of this enzyme are spermidine, acceptor, and H2O, whereas its 3 products are propane-1,3-diamine, 4-aminobutanal, and reduced acceptor.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-NH group of donor with other acceptors. The systematic name of this enzyme class is spermidine:acceptor oxidoreductase. This enzyme is also called spermidine:(acceptor) oxidoreductase. This enzyme participates in urea cycle and metabolism of amino groups and beta-alanine metabolism. It has 2 cofactors: FAD, and Heme.
References.
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13897972 | Succinylglutamate-semialdehyde dehydrogenase | In enzymology, a succinylglutamate-semialdehyde dehydrogenase (EC 1.2.1.71) is an enzyme that catalyzes the chemical reaction
N-succinyl-L-glutamate 5-semialdehyde + NAD+ + H2O formula_0 N-succinyl-L-glutamate + NADH + 2 H+
The 3 substrates of this enzyme are N-succinyl-L-glutamate 5-semialdehyde, NAD+, and H2O, whereas its 3 products are N-succinyl-L-glutamate, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the aldehyde or oxo group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is N-succinyl-L-glutamate 5-semialdehyde:NAD+ oxidoreductase. Other names in common use include succinylglutamic semialdehyde dehydrogenase, N-succinylglutamate 5-semialdehyde dehydrogenase, SGSD, AruD, and AstD. This enzyme participates in arginine and proline metabolism.
References.
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13897982 | Sulfite dehydrogenase | In enzymology, a sulfite dehydrogenase (EC 1.8.2.1) is an enzyme that catalyzes the chemical reaction
sulfite + 2 ferricytochrome c + H2O formula_0 sulfate + 2 ferrocytochrome c + 2 H+
The 3 substrates of this enzyme are sulfite, ferricytochrome c, and H2O, whereas its 3 products are sulfate, ferrocytochrome c, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on a sulfur group of donor with a cytochrome as acceptor. The systematic name of this enzyme class is sulfite:ferricytochrome-c oxidoreductase. Other names in common use include sulfite cytochrome c reductase, sulfite-cytochrome c oxidoreductase, and sulfite oxidase. This enzyme participates in sulfur metabolism.
References.
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13898383 | Ephedrine dehydrogenase | In enzymology, an ephedrine dehydrogenase (EC 1.5.1.18) is an enzyme that catalyzes the chemical reaction
(-)-ephedrine + NAD+ formula_0 (R)-2-methylimino-1-phenylpropan-1-ol + NADH + H+
Thus, the two substrates of this enzyme are (-)-ephedrine and NAD+, whereas its 3 products are (R)-2-methylimino-1-phenylpropan-1-ol, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-NH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (-)-ephedrine:NAD+ 2-oxidoreductase.
References.
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13898398 | Erythrose-4-phosphate dehydrogenase | In enzymology, an erythrose-4-phosphate dehydrogenase (EC 1.2.1.72) is an enzyme that catalyzes the chemical reaction
D-erythrose 4-phosphate + NAD+ + H2O formula_0 4-phosphoerythronate + NADH + 2 H+
The 3 substrates of this enzyme are D-erythrose 4-phosphate, NAD+, and H2O, whereas its 3 products are 4-phosphoerythronat, NADH, and H+.
[explainpolicedepartment]
This enzyme belongs to the family of oxidoreductases, specifically those acting on the aldehyde or oxo group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-erythrose 4-phosphate:NAD+ oxidoreductase. Other names in common use include erythrose 4-phosphate dehydrogenase, E4PDH, GapB, Epd dehydrogenase, and E4P dehydrogenase. This enzyme participates in vitamin B6 metabolism (see DXP-dependent biosynthesis of pyridoxal phosphate).
References.
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13898437 | Estradiol 17beta-dehydrogenase | In enzymology, an estradiol 17beta-dehydrogenase (EC 1.1.1.62) is an enzyme that catalyzes the chemical reaction
estradiol-17beta + NAD(P)+ formula_0 estrone + NAD(P)H + H+
The 3 substrates of this enzyme are estradiol-17beta, NAD+, and NADP+, whereas its 4 products are estrone, NADH, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is estradiol-17beta:NAD(P)+ 17-oxidoreductase. Other names in common use include 20alpha-hydroxysteroid dehydrogenase, 17beta,20alpha-hydroxysteroid dehydrogenase, 17beta-estradiol dehydrogenase, estradiol dehydrogenase, estrogen 17-oxidoreductase, and 17beta-HSD. This enzyme participates in androgen and estrogen metabolism.
Structural studies.
As of late 2007, 29 structures have been solved for this class of enzymes, with PDB accession codes 1A27, 1BHS, 1DHT, 1EQU, 1FDS, 1FDT, 1FDU, 1FDV, 1FDW, 1GZ6, 1I5R, 1IKT, 1IOL, 1JTV, 1QYV, 1QYW, 1QYX, 1S1P, 1S1R, 1S2A, 1S2C, 1XF0, 1YB1, 1ZQ5, 2F38, 2FGB, 2HQ1, 2PD6, and 3DHE.
References.
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13898906 | Vellosimine dehydrogenase | In enzymology, a vellosimine dehydrogenase (EC 1.1.1.273) is an enzyme that catalyzes the chemical reaction
10-deoxysarpagine + NADP+ formula_0 vellosimine + NADPH + H+
Thus, the two substrates of this enzyme are 10-deoxysarpagine and NADP+, whereas its 3 products are vellosimine, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 10-deoxysarpagine:NADP+ oxidoreductase. This enzyme participates in indole and ipecac alkaloid biosynthesis.
References.
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13898915 | Vomifoliol dehydrogenase | In enzymology, a vomifoliol dehydrogenase (EC 1.1.1.221) is an enzyme that catalyzes the chemical reaction
(6S,9R)-6-hydroxy-3-oxo-alpha-ionol + NAD+ formula_0 (6R)-6-hydroxy-3-oxo-alpha-ionone + NADH + H+
Thus, the two substrates of this enzyme are (6S,9R)-6-hydroxy-3-oxo-alpha-ionol and NAD+, whereas its 3 products are (6R)-6-hydroxy-3-oxo-alpha-ionone, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is vomifoliol:NAD+ oxidoreductase. Other names in common use include vomifoliol 4'-dehydrogenase, and vomifoliol:NAD+ 4'-oxidoreductase.
References.
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13899 | Harmonic oscillator | Physical system that responds to a restoring force inversely proportional to displacement
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In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force "F" proportional to the displacement "x":
formula_0
where "k" is a positive constant.
If "F" is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude).
If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction coefficient, the system can:
The boundary solution between an underdamped oscillator and an overdamped oscillator occurs at a particular value of the friction coefficient and is called critically damped.
If an external time-dependent force is present, the harmonic oscillator is described as a "driven oscillator".
Mechanical examples include pendulums (with small angles of displacement), masses connected to springs, and acoustical systems. Other analogous systems include electrical harmonic oscillators such as RLC circuits. The harmonic oscillator model is very important in physics, because any mass subject to a force in stable equilibrium acts as a harmonic oscillator for small vibrations. Harmonic oscillators occur widely in nature and are exploited in many manmade devices, such as clocks and radio circuits. They are the source of virtually all sinusoidal vibrations and waves.
Simple harmonic oscillator.
A simple harmonic oscillator is an oscillator that is neither driven nor damped. It consists of a mass "m", which experiences a single force "F", which pulls the mass in the direction of the point "x" = 0 and depends only on the position "x" of the mass and a constant "k". Balance of forces (Newton's second law) for the system is
formula_1
Solving this differential equation, we find that the motion is described by the function
formula_2
where
formula_3
The motion is periodic, repeating itself in a sinusoidal fashion with constant amplitude "A". In addition to its amplitude, the motion of a simple harmonic oscillator is characterized by its period formula_4, the time for a single oscillation or its frequency formula_5, the number of cycles per unit time. The position at a given time "t" also depends on the phase "φ", which determines the starting point on the sine wave. The period and frequency are determined by the size of the mass "m" and the force constant "k", while the amplitude and phase are determined by the starting position and velocity.
The velocity and acceleration of a simple harmonic oscillator oscillate with the same frequency as the position, but with shifted phases. The velocity is maximal for zero displacement, while the acceleration is in the direction opposite to the displacement.
The potential energy stored in a simple harmonic oscillator at position "x" is
formula_6
Damped harmonic oscillator.
In real oscillators, friction, or damping, slows the motion of the system. Due to frictional force, the velocity decreases in proportion to the acting frictional force. While in a simple undriven harmonic oscillator the only force acting on the mass is the restoring force, in a damped harmonic oscillator there is in addition a frictional force which is always in a direction to oppose the motion. In many vibrating systems the frictional force "F"f can be modeled as being proportional to the velocity "v" of the object: "F"f = −"cv", where "c" is called the "viscous damping coefficient".
The balance of forces (Newton's second law) for damped harmonic oscillators is then
formula_7
which can be rewritten into the form
formula_8
where
The value of the damping ratio "ζ" critically determines the behavior of the system. A damped harmonic oscillator can be:
The Q factor of a damped oscillator is defined as
formula_13
"Q" is related to the damping ratio by formula_14
Driven harmonic oscillators.
Driven harmonic oscillators are damped oscillators further affected by an externally applied force "F"("t").
Newton's second law takes the form
formula_15
It is usually rewritten into the form
formula_16
This equation can be solved exactly for any driving force, using the solutions "z"("t") that satisfy the unforced equation
formula_17
and which can be expressed as damped sinusoidal oscillations:
formula_18
in the case where "ζ" ≤ 1. The amplitude "A" and phase "φ" determine the behavior needed to match the initial conditions.
Step input.
In the case "ζ" < 1 and a unit step input with "x"(0) = 0:
formula_19
the solution is
formula_20
with phase "φ" given by
formula_21
The time an oscillator needs to adapt to changed external conditions is of the order "τ" = 1/("ζω"0). In physics, the adaptation is called relaxation, and "τ" is called the relaxation time.
In electrical engineering, a multiple of "τ" is called the "settling time", i.e. the time necessary to ensure the signal is within a fixed departure from final value, typically within 10%. The term "overshoot" refers to the extent the response maximum exceeds final value, and "undershoot" refers to the extent the response falls below final value for times following the response maximum.
Sinusoidal driving force.
In the case of a sinusoidal driving force:
formula_23
where formula_24 is the driving amplitude, and formula_25 is the driving frequency for a sinusoidal driving mechanism. This type of system appears in AC-driven RLC circuits (resistor–inductor–capacitor) and driven spring systems having internal mechanical resistance or external air resistance.
The general solution is a sum of a transient solution that depends on initial conditions, and a steady state that is independent of initial conditions and depends only on the driving amplitude formula_24, driving frequency formula_25, undamped angular frequency formula_26, and the damping ratio formula_22.
The steady-state solution is proportional to the driving force with an induced phase change formula_27:
formula_28
where
formula_29
is the absolute value of the impedance or linear response function, and
formula_30
is the phase of the oscillation relative to the driving force. The phase value is usually taken to be between −180° and 0 (that is, it represents a phase lag, for both positive and negative values of the arctan argument).
For a particular driving frequency called the resonance, or resonant frequency formula_31, the amplitude (for a given formula_24) is maximal. This resonance effect only occurs when formula_32, i.e. for significantly underdamped systems. For strongly underdamped systems the value of the amplitude can become quite large near the resonant frequency.
The transient solutions are the same as the unforced (formula_33) damped harmonic oscillator and represent the systems response to other events that occurred previously. The transient solutions typically die out rapidly enough that they can be ignored.
Parametric oscillators.
A parametric oscillator is a driven harmonic oscillator in which the drive energy is provided by varying the parameters of the oscillator, such as the damping or restoring force.
A familiar example of parametric oscillation is "pumping" on a playground swing.
A person on a moving swing can increase the amplitude of the swing's oscillations without any external drive force (pushes) being applied, by changing the moment of inertia of the swing by rocking back and forth ("pumping") or alternately standing and squatting, in rhythm with the swing's oscillations. The varying of the parameters drives the system. Examples of parameters that may be varied are its resonance frequency formula_25 and damping formula_34.
Parametric oscillators are used in many applications. The classical varactor parametric oscillator oscillates when the diode's capacitance is varied periodically. The circuit that varies the diode's capacitance is called the "pump" or "driver". In microwave electronics, waveguide/YAG based parametric oscillators operate in the same fashion. The designer varies a parameter periodically to induce oscillations.
Parametric oscillators have been developed as low-noise amplifiers, especially in the radio and microwave frequency range. Thermal noise is minimal, since a reactance (not a resistance) is varied. Another common use is frequency conversion, e.g., conversion from audio to radio frequencies. For example, the Optical parametric oscillator converts an input laser wave into two output waves of lower frequency (formula_35).
Parametric resonance occurs in a mechanical system when a system is parametrically excited and oscillates at one of its resonant frequencies. Parametric excitation differs from forcing, since the action appears as a time varying modification on a system parameter. This effect is different from regular resonance because it exhibits the instability phenomenon.
Universal oscillator equation.
The equation
formula_36
is known as the universal oscillator equation, since all second-order linear oscillatory systems can be reduced to this form. This is done through nondimensionalization.
If the forcing function is "f"("t") = cos("ωt") = cos("ωtcτ") = cos("ωτ"), where "ω" = "ωt""c", the equation becomes
formula_37
The solution to this differential equation contains two parts: the "transient" and the "steady-state".
Transient solution.
The solution based on solving the ordinary differential equation is for arbitrary constants "c"1 and "c"2
formula_38
The transient solution is independent of the forcing function.
Steady-state solution.
Apply the "complex variables method" by solving the auxiliary equation below and then finding the real part of its solution:
formula_39
Supposing the solution is of the form
formula_40
Its derivatives from zeroth to second order are
formula_41
Substituting these quantities into the differential equation gives
formula_42
Dividing by the exponential term on the left results in
formula_43
Equating the real and imaginary parts results in two independent equations
formula_44
Amplitude part.
Squaring both equations and adding them together gives
formula_45
Therefore,
formula_46
Compare this result with the theory section on resonance, as well as the "magnitude part" of the RLC circuit. This amplitude function is particularly important in the analysis and understanding of the frequency response of second-order systems.
Phase part.
To solve for "φ", divide both equations to get
formula_47
This phase function is particularly important in the analysis and understanding of the frequency response of second-order systems.
Full solution.
Combining the amplitude and phase portions results in the steady-state solution
formula_48
The solution of original universal oscillator equation is a superposition (sum) of the transient and steady-state solutions:
formula_49
Equivalent systems.
Harmonic oscillators occurring in a number of areas of engineering are equivalent in the sense that their mathematical models are identical (see universal oscillator equation above). Below is a table showing analogous quantities in four harmonic oscillator systems in mechanics and electronics. If analogous parameters on the same line in the table are given numerically equal values, the behavior of the oscillators – their output waveform, resonant frequency, damping factor, etc. – are the same.
Application to a conservative force.
The problem of the simple harmonic oscillator occurs frequently in physics, because a mass at equilibrium under the influence of any conservative force, in the limit of small motions, behaves as a simple harmonic oscillator.
A conservative force is one that is associated with a potential energy. The potential-energy function of a harmonic oscillator is
formula_52
Given an arbitrary potential-energy function formula_53, one can do a Taylor expansion in terms of formula_50 around an energy minimum (formula_54) to model the behavior of small perturbations from equilibrium.
formula_55
Because formula_56 is a minimum, the first derivative evaluated at formula_57 must be zero, so the linear term drops out:
formula_58
The constant term "V"("x"0) is arbitrary and thus may be dropped, and a coordinate transformation allows the form of the simple harmonic oscillator to be retrieved:
formula_59
Thus, given an arbitrary potential-energy function formula_53 with a non-vanishing second derivative, one can use the solution to the simple harmonic oscillator to provide an approximate solution for small perturbations around the equilibrium point.
Examples.
Simple pendulum.
Assuming no damping, the differential equation governing a simple pendulum of length formula_60, where formula_61 is the local acceleration of gravity, is
formula_62
If the maximal displacement of the pendulum is small, we can use the approximation formula_63 and instead consider the equation
formula_64
The general solution to this differential equation is
formula_65
where formula_66 and formula_27 are constants that depend on the initial conditions.
Using as initial conditions formula_67 and formula_68, the solution is given by
formula_69
where formula_70 is the largest angle attained by the pendulum (that is, formula_70 is the amplitude of the pendulum). The period, the time for one complete oscillation, is given by the expression
formula_71
which is a good approximation of the actual period when formula_70 is small. Notice that in this approximation the period formula_72 is independent of the amplitude formula_70. In the above equation, formula_25 represents the angular frequency.
Spring/mass system.
When a spring is stretched or compressed by a mass, the spring develops a restoring force. Hooke's law gives the relationship of the force exerted by the spring when the spring is compressed or stretched a certain length:
formula_73
where "F" is the force, "k" is the spring constant, and "x" is the displacement of the mass with respect to the equilibrium position. The minus sign in the equation indicates that the force exerted by the spring always acts in a direction that is opposite to the displacement (i.e. the force always acts towards the zero position), and so prevents the mass from flying off to infinity.
By using either force balance or an energy method, it can be readily shown that the motion of this system is given by the following differential equation:
formula_74
the latter being Newton's second law of motion.
If the initial displacement is "A", and there is no initial velocity, the solution of this equation is given by
formula_75
Given an ideal massless spring, formula_51 is the mass on the end of the spring. If the spring itself has mass, its effective mass must be included in formula_51.
Energy variation in the spring–damping system.
In terms of energy, all systems have two types of energy: potential energy and kinetic energy. When a spring is stretched or compressed, it stores elastic potential energy, which is then transferred into kinetic energy. The potential energy within a spring is determined by the equation formula_76
When the spring is stretched or compressed, kinetic energy of the mass gets converted into potential energy of the spring. By conservation of energy, assuming the datum is defined at the equilibrium position, when the spring reaches its maximal potential energy, the kinetic energy of the mass is zero. When the spring is released, it tries to return to equilibrium, and all its potential energy converts to kinetic energy of the mass.
See also.
<templatestyles src="Div col/styles.css"/>
Notes.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": " \\vec F = -k \\vec x, "
},
{
"math_id": 1,
"text": "F = m a = m \\frac{\\mathrm{d}^2x}{\\mathrm{d}t^2} = m\\ddot{x} = -k x. "
},
{
"math_id": 2,
"text": " x(t) = A \\cos(\\omega t + \\varphi), "
},
{
"math_id": 3,
"text": "\\omega = \\sqrt{\\frac k m}."
},
{
"math_id": 4,
"text": "T = 2\\pi/\\omega"
},
{
"math_id": 5,
"text": "f=1/T"
},
{
"math_id": 6,
"text": "U = \\tfrac 1 2 kx^2."
},
{
"math_id": 7,
"text": " F = - kx - c\\frac{\\mathrm{d}x}{\\mathrm{d}t} = m \\frac{\\mathrm{d}^2x}{\\mathrm{d}t^2},"
},
{
"math_id": 8,
"text": " \\frac{\\mathrm{d}^2x}{\\mathrm{d}t^2} + 2\\zeta\\omega_0\\frac{\\mathrm{d}x}{\\mathrm{d}t} + \\omega_0^2 x = 0, "
},
{
"math_id": 9,
"text": "\\omega_0 = \\sqrt{\\frac k m}"
},
{
"math_id": 10,
"text": "\\zeta = \\frac{c}{2\\sqrt{mk}}"
},
{
"math_id": 11,
"text": "\\omega_1 = \\omega_0\\sqrt{1 - \\zeta^2},"
},
{
"math_id": 12,
"text": "\\lambda = \\omega_0\\zeta."
},
{
"math_id": 13,
"text": "Q = 2\\pi \\times \\frac{\\text{energy stored}}{\\text{energy lost per cycle}}."
},
{
"math_id": 14,
"text": "Q = \\frac{1}{2\\zeta}."
},
{
"math_id": 15,
"text": "F(t) - kx - c\\frac{\\mathrm{d}x}{\\mathrm{d}t}=m\\frac{\\mathrm{d}^2x}{\\mathrm{d}t^2}. "
},
{
"math_id": 16,
"text": " \\frac{\\mathrm{d}^2x}{\\mathrm{d}t^2} + 2\\zeta\\omega_0\\frac{\\mathrm{d}x}{\\mathrm{d}t} + \\omega_0^2 x = \\frac{F(t)}{m}. "
},
{
"math_id": 17,
"text": " \\frac{\\mathrm{d}^2z}{\\mathrm{d}t^2} + 2\\zeta\\omega_0\\frac{\\mathrm{d}z}{\\mathrm{d}t} + \\omega_0^2 z = 0,"
},
{
"math_id": 18,
"text": "z(t) = A e^{-\\zeta \\omega_0 t} \\sin \\left( \\sqrt{1 - \\zeta^2} \\omega_0 t + \\varphi \\right), "
},
{
"math_id": 19,
"text": " \\frac{F(t)}{m} = \\begin{cases} \\omega _0^2 & t \\geq 0 \\\\ 0 & t < 0 \\end{cases}"
},
{
"math_id": 20,
"text": " x(t) = 1 - e^{-\\zeta \\omega_0 t} \\frac{\\sin \\left( \\sqrt{1 - \\zeta^2} \\omega_0 t + \\varphi \\right)}{\\sin(\\varphi)},"
},
{
"math_id": 21,
"text": "\\cos \\varphi = \\zeta."
},
{
"math_id": 22,
"text": "\\zeta"
},
{
"math_id": 23,
"text": " \\frac{\\mathrm{d}^2x}{\\mathrm{d}t^2} + 2\\zeta\\omega_0\\frac{\\mathrm{d}x}{\\mathrm{d}t} + \\omega_0^2 x = \\frac{1}{m} F_0 \\sin(\\omega t),"
},
{
"math_id": 24,
"text": "F_0"
},
{
"math_id": 25,
"text": "\\omega"
},
{
"math_id": 26,
"text": "\\omega_0"
},
{
"math_id": 27,
"text": "\\varphi"
},
{
"math_id": 28,
"text": " x(t) = \\frac{F_0}{m Z_m \\omega} \\sin(\\omega t + \\varphi),"
},
{
"math_id": 29,
"text": " Z_m = \\sqrt{\\left(2\\omega_0\\zeta\\right)^2 + \\frac{1}{\\omega^2} (\\omega_0^2 - \\omega^2)^2}"
},
{
"math_id": 30,
"text": " \\varphi = \\arctan\\left(\\frac{2\\omega \\omega_0\\zeta}{\\omega^2 - \\omega_0^2} \\right) + n\\pi"
},
{
"math_id": 31,
"text": "\\omega_r = \\omega_0 \\sqrt{1 - 2\\zeta^2}"
},
{
"math_id": 32,
"text": "\\zeta < 1 / \\sqrt{2}"
},
{
"math_id": 33,
"text": "F_0 = 0"
},
{
"math_id": 34,
"text": "\\beta"
},
{
"math_id": 35,
"text": "\\omega_s, \\omega_i"
},
{
"math_id": 36,
"text": "\\frac{\\mathrm{d}^2q}{\\mathrm{d} \\tau^2} + 2 \\zeta \\frac{\\mathrm{d}q}{\\mathrm{d}\\tau} + q = 0"
},
{
"math_id": 37,
"text": "\\frac{\\mathrm{d}^2q}{\\mathrm{d} \\tau^2} + 2 \\zeta \\frac{\\mathrm{d}q}{\\mathrm{d}\\tau} + q = \\cos(\\omega \\tau)."
},
{
"math_id": 38,
"text": "q_t (\\tau) = \\begin{cases}\n e^{-\\zeta\\tau} \\left( c_1 e^{\\tau \\sqrt{\\zeta^2 - 1}} + c_2 e^{- \\tau \\sqrt{\\zeta^2 - 1}} \\right) & \\zeta > 1 \\text{ (overdamping)} \\\\\n e^{-\\zeta\\tau} (c_1+c_2 \\tau) = e^{-\\tau}(c_1+c_2 \\tau) & \\zeta = 1 \\text{ (critical damping)} \\\\\n e^{-\\zeta \\tau} \\left[ c_1 \\cos \\left(\\sqrt{1-\\zeta^2} \\tau\\right) + c_2 \\sin\\left(\\sqrt{1-\\zeta^2} \\tau\\right) \\right] & \\zeta < 1 \\text{ (underdamping)}\n\\end{cases}"
},
{
"math_id": 39,
"text": "\\frac{\\mathrm{d}^2 q}{\\mathrm{d}\\tau^2} + 2 \\zeta \\frac{\\mathrm{d}q}{\\mathrm{d}\\tau} + q = \\cos(\\omega \\tau) + i\\sin(\\omega \\tau) = e^{ i \\omega \\tau}."
},
{
"math_id": 40,
"text": "q_s(\\tau) = A e^{i (\\omega \\tau + \\varphi) }. "
},
{
"math_id": 41,
"text": "q_s = A e^{i (\\omega \\tau + \\varphi) }, \\quad\n\\frac{\\mathrm{d}q_s}{\\mathrm{d} \\tau} = i \\omega A e^{i (\\omega \\tau + \\varphi) }, \\quad\n\\frac{\\mathrm{d}^2 q_s}{\\mathrm{d} \\tau^2} = -\\omega^2 A e^{i (\\omega \\tau + \\varphi) } ."
},
{
"math_id": 42,
"text": "-\\omega^2 A e^{i (\\omega \\tau + \\varphi)} + 2 \\zeta i \\omega A e^{i(\\omega \\tau + \\varphi)} + A e^{i(\\omega \\tau + \\varphi)} = (-\\omega^2 A + 2 \\zeta i \\omega A + A) e^{i (\\omega \\tau + \\varphi)} = e^{i \\omega \\tau}."
},
{
"math_id": 43,
"text": "-\\omega^2 A + 2 \\zeta i \\omega A + A = e^{-i \\varphi} = \\cos\\varphi - i \\sin\\varphi."
},
{
"math_id": 44,
"text": "A (1 - \\omega^2) = \\cos\\varphi, \\quad 2 \\zeta \\omega A = -\\sin\\varphi."
},
{
"math_id": 45,
"text": "\\left. \\begin{aligned}\n A^2 (1-\\omega^2)^2 &= \\cos^2\\varphi \\\\\n (2 \\zeta \\omega A)^2 &= \\sin^2\\varphi\n\\end{aligned} \\right\\}\n\\Rightarrow A^2[(1 - \\omega^2)^2 + (2 \\zeta \\omega)^2] = 1."
},
{
"math_id": 46,
"text": "A = A(\\zeta, \\omega) = \\sgn \\left( \\frac{-\\sin\\varphi}{2 \\zeta \\omega} \\right) \\frac{1}{\\sqrt{(1 - \\omega^2)^2 + (2 \\zeta \\omega)^2}}."
},
{
"math_id": 47,
"text": "\\tan\\varphi = -\\frac{2 \\zeta \\omega}{1 - \\omega^2} = \\frac{2 \\zeta \\omega}{\\omega^2 - 1}~~ \\implies ~~ \\varphi \\equiv \\varphi(\\zeta, \\omega) = \\arctan \\left( \\frac{2 \\zeta \\omega}{\\omega^2 - 1} \\right ) + n\\pi."
},
{
"math_id": 48,
"text": "q_s(\\tau) = A(\\zeta,\\omega) \\cos(\\omega \\tau + \\varphi(\\zeta, \\omega)) = A\\cos(\\omega \\tau + \\varphi)."
},
{
"math_id": 49,
"text": "q(\\tau) = q_t(\\tau) + q_s(\\tau)."
},
{
"math_id": 50,
"text": "x"
},
{
"math_id": 51,
"text": "m"
},
{
"math_id": 52,
"text": "V(x) = \\tfrac{1}{2} k x^2."
},
{
"math_id": 53,
"text": "V(x)"
},
{
"math_id": 54,
"text": "x = x_0"
},
{
"math_id": 55,
"text": "V(x) = V(x_0) + V'(x_0) \\cdot (x - x_0) + \\tfrac{1}{2} V''(x_0) \\cdot (x - x_0)^2 + O(x - x_0)^3."
},
{
"math_id": 56,
"text": "V(x_0)"
},
{
"math_id": 57,
"text": "x_0"
},
{
"math_id": 58,
"text": "V(x) = V(x_0) + \\tfrac{1}{2} V''(x_0) \\cdot (x - x_0)^2 + O(x - x_0)^3."
},
{
"math_id": 59,
"text": "V(x) \\approx \\tfrac{1}{2} V''(0) \\cdot x^2 = \\tfrac{1}{2} k x^2."
},
{
"math_id": 60,
"text": "l"
},
{
"math_id": 61,
"text": "g"
},
{
"math_id": 62,
"text": "\\frac{d^2\\theta}{dt^2} + \\frac{g}{l}\\sin\\theta = 0."
},
{
"math_id": 63,
"text": "\\sin\\theta \\approx \\theta"
},
{
"math_id": 64,
"text": "\\frac{d^2\\theta}{dt^2} + \\frac{g}{l}\\theta = 0."
},
{
"math_id": 65,
"text": "\\theta(t) = A \\cos\\left(\\sqrt{\\frac{g}{l}} t + \\varphi \\right),"
},
{
"math_id": 66,
"text": "A"
},
{
"math_id": 67,
"text": "\\theta(0) = \\theta_0"
},
{
"math_id": 68,
"text": "\\dot{\\theta}(0) = 0"
},
{
"math_id": 69,
"text": "\\theta(t) = \\theta_0 \\cos\\left(\\sqrt{\\frac{g}{l}} t\\right),"
},
{
"math_id": 70,
"text": "\\theta_0"
},
{
"math_id": 71,
"text": "\\tau = 2\\pi \\sqrt\\frac{l}{g} = \\frac{2\\pi}{\\omega},"
},
{
"math_id": 72,
"text": "\\tau"
},
{
"math_id": 73,
"text": "F(t) = -kx(t),"
},
{
"math_id": 74,
"text": " F(t) = -kx(t) = m \\frac{\\mathrm{d}^2}{\\mathrm{d} t^2} x(t) = ma, "
},
{
"math_id": 75,
"text": " x(t) = A \\cos \\left( \\sqrt{\\frac{k}{m}} t \\right)."
},
{
"math_id": 76,
"text": " U = \\frac{1}{2}kx^2. "
}
]
| https://en.wikipedia.org/wiki?curid=13899 |
13899069 | Acetoacetyl-CoA reductase | InterPro Family
In enzymology, an acetoacetyl-CoA reductase (EC 1.1.1.36) is an enzyme that catalyzes the chemical reaction
(R)-3-hydroxyacyl-CoA + NADP+ formula_0 3-oxoacyl-CoA + NADPH + H+
Thus, the two substrates of this enzyme are (R)-3-hydroxyacyl-CoA and NADP+, whereas its 3 products are 3-oxoacyl-CoA, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (R)-3-hydroxyacyl-CoA:NADP+ oxidoreductase. Other names in common use include acetoacetyl coenzyme A reductase, hydroxyacyl coenzyme-A dehydrogenase, NADP+-linked acetoacetyl CoA reductase, NADPH:acetoacetyl-CoA reductase, D(−)-beta-hydroxybutyryl CoA-NADP+ oxidoreductase, short chain beta-ketoacetyl(acetoacetyl)-CoA reductase, beta-ketoacyl-CoA reductase, D-3-hydroxyacyl-CoA reductase, and (R)-3-hydroxyacyl-CoA dehydrogenase. This enzyme participates in butanoate metabolism.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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| https://en.wikipedia.org/wiki?curid=13899069 |
13899089 | Acylglycerone-phosphate reductase | Class of enzymes
In enzymology, an acylglycerone-phosphate reductase (EC 1.1.1.101) is an enzyme that catalyzes the chemical reaction
1-palmitoylglycerol 3-phosphate + NADP+ formula_0 palmitoylglycerone phosphate + NADPH + H+
Thus, the two substrates of this enzyme are 1-palmitoylglycerol 3-phosphate and NADP+, whereas its 3 products are palmitoylglycerone phosphate, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 1-palmitoylglycerol-3-phosphate:NADP+ oxidoreductase. Other names in common use include palmitoyldihydroxyacetone-phosphate reductase, palmitoyl dihydroxyacetone phosphate reductase, palmitoyl-dihydroxyacetone-phosphate reductase, acyldihydroxyacetone phosphate reductase, and palmitoyl dihydroxyacetone phosphate reductase. This enzyme participates in glycerophospholipid and ether lipid metabolism.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=13899089 |
13899139 | Aldose 1-dehydrogenase | In enzymology, an aldose 1-dehydrogenase (EC 1.1.1.121) is an enzyme that catalyzes the chemical reaction
D-aldose + NAD+ formula_0 D-aldonolactone + NADH + H+
Thus, the two substrates of this enzyme are D-aldose and NAD+, whereas its 3 products are D-aldonolactone, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-aldose:NAD+ 1-oxidoreductase. Other names in common use include aldose dehydrogenase, and dehydrogenase, D-aldohexose.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=13899139 |
13899159 | Aldose-6-phosphate reductase (NADPH) | In enzymology, an aldose-6-phosphate reductase (NADPH) (EC 1.1.1.200) is an enzyme that catalyzes the chemical reaction
D-sorbitol 6-phosphate + NADP+ formula_0 D-glucose 6-phosphate + NADPH + H+
Thus, the two substrates of this enzyme are D-sorbitol 6-phosphate and NADP+, whereas its 3 products are D-glucose 6-phosphate, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-aldose-6-phosphate:NADP+ 1-oxidoreductase. Other names in common use include aldose 6-phosphate reductase, NADP+-dependent aldose 6-phosphate reductase, A6PR, aldose-6-P reductase, aldose-6-phosphate reductase, alditol 6-phosphate:NADP+ 1-oxidoreductase, and aldose-6-phosphate reductase (NADPH).
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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| https://en.wikipedia.org/wiki?curid=13899159 |
13899178 | Allyl-alcohol dehydrogenase | Class of enzymes
In enzymology, an allyl-alcohol dehydrogenase (EC 1.1.1.54) is an enzyme that catalyzes the chemical reaction
allyl alcohol + NADP+ formula_0 acrolein + NADPH + H+
Thus, the two substrates of this enzyme are allyl alcohol and NADP+, whereas its 3 products are acrolein, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is allyl-alcohol:NADP+ oxidoreductase.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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| https://en.wikipedia.org/wiki?curid=13899178 |
13899201 | Apiose 1-reductase | In enzymology, an apiose 1-reductase (EC 1.1.1.114) is an enzyme that catalyzes the chemical reaction
D-apiitol + NAD+ formula_0 D-apiose + NADH + H+
Thus, the two substrates of this enzyme are D-apiitol and NAD+, whereas its 3 products are D-apiose, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-apiitol:NAD+ 1-oxidoreductase. Other names in common use include D-apiose reductase, and D-apiitol reductase.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
]
| https://en.wikipedia.org/wiki?curid=13899201 |
13899229 | Aryl-alcohol dehydrogenase | In enzymology, an aryl-alcohol dehydrogenase (EC 1.1.1.90) is an enzyme that catalyzes the chemical reaction
an aromatic alcohol + NAD+ formula_0 an aromatic aldehyde + NADH + H+
Thus, the two substrates of this enzyme are aromatic alcohol and NAD+, whereas its 3 products are aromatic aldehyde, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is aryl-alcohol:NAD+ oxidoreductase. Other names in common use include p-hydroxybenzyl alcohol dehydrogenase, benzyl alcohol dehydrogenase, and coniferyl alcohol dehydrogenase. This enzyme participates in 5 metabolic pathways: tyrosine metabolism, phenylalanine metabolism, biphenyl degradation, toluene and xylene degradation, and caprolactam degradation.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 1F8F.
References.
<templatestyles src="Reflist/styles.css" /> | [
{
"math_id": 0,
"text": "\\rightleftharpoons"
}
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| https://en.wikipedia.org/wiki?curid=13899229 |
13899245 | Aryl-alcohol dehydrogenase (NADP+) | In enzymology, an aryl-alcohol dehydrogenase (NADP+) (EC 1.1.1.91) is an enzyme that catalyzes the chemical reaction
an aromatic alcohol + NADP+ formula_0 an aromatic aldehyde + NADPH + H+
Thus, the two substrates of this enzyme are aromatic alcohol and NADP+, whereas its 3 products are aromatic aldehyde, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is aryl-alcohol:NADP+ oxidoreductase. Other names in common use include aryl alcohol dehydrogenase (nicotinamide adenine dinucleotide, phosphate), coniferyl alcohol dehydrogenase, NADPH-linked benzaldehyde reductase, and aryl-alcohol dehydrogenase (NADP+).
References.
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13899272 | Benzyl-2-methyl-hydroxybutyrate dehydrogenase | In enzymology, a benzyl-2-methyl-hydroxybutyrate dehydrogenase (EC 1.1.1.217) is an enzyme that catalyzes the chemical reaction
benzyl (2R,3S)-2-methyl-3-hydroxybutanoate + NADP+ formula_0 benzyl 2-methyl-3-oxobutanoate + NADPH + H+
Thus, the two substrates of this enzyme are benzyl (2R,3S)-2-methyl-3-hydroxybutanoate and NADP+, whereas its 3 products are benzyl 2-methyl-3-oxobutanoate, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is benzyl-(2R,3S)-2-methyl-3-hydroxybutanoate:NADP+ 3-oxidoreductase. This enzyme is also called benzyl 2-methyl-3-hydroxybutyrate dehydrogenase.
References.
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13899291 | Carbonyl reductase (NADPH) | Class of enzymes
In enzymology, a carbonyl reductase (NADPH) (EC 1.1.1.184) is an enzyme that catalyzes the chemical reaction
R-CO-R' + NADPH + H+ formula_0 :R-CHOH-R' + NADP+
Thus, the two products of this enzyme are R-CHOH-R' and NADP+, whereas its 3 substrates are R-CO-R', NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is secondary-alcohol:NADP+ oxidoreductase. Other names in common use include aldehyde reductase 1, prostaglandin 9-ketoreductase, xenobiotic ketone reductase, NADPH-dependent carbonyl reductase, ALR3, carbonyl reductase, nonspecific NADPH-dependent carbonyl reductase, aldehyde reductase 1, and carbonyl reductase (NADPH). This enzyme participates in arachidonic acid metabolism, and has recently been shown to catabolize S-Nitrosoglutathione, as a means to degrade NO in an NADPH-dependent manner.
Structural studies.
As of late 2007, 4 structures have been solved for this class of enzymes, with PDB accession codes 1CYD, 1WMA, 2HRB, and 2PFG.
References.
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13899306 | Carnitine 3-dehydrogenase | Class of enzymes
In enzymology, a carnitine 3-dehydrogenase (EC 1.1.1.108) is an enzyme that catalyzes the chemical reaction
carnitine + NAD+ formula_0 3-dehydrocarnitine + NADH + H+
Thus, the two substrates of this enzyme are carnitine and NAD+, whereas its 3 products are 3-dehydrocarnitine, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is carnitine:NAD+ 3-oxidoreductase.
References.
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13899324 | Carveol dehydrogenase | Enzyme
In enzymology, a carveol dehydrogenase (EC 1.1.1.243) is an enzyme that catalyzes the chemical reaction
(-)-trans-carveol + NADP+ formula_0 (-)-carvone + NADPH + H+
Thus, the two substrates of this enzyme are (-)-trans-carveol and NADP+, whereas its 3 products are (-)-carvone, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (-)-trans-carveol:NADP+ oxidoreductase. This enzyme is also called (-)-trans-carveol dehydrogenase. This enzyme participates in monoterpenoid biosynthesis and limonene and pinene degradation.
References.
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13899342 | Chlordecone reductase | In enzymology, a chlordecone reductase (EC 1.1.1.225) is an enzyme that catalyzes the chemical reaction
chlordecone alcohol + NADP+ formula_0 chlordecone + NADPH + H+
Thus, the two substrates of this enzyme are chlordecone alcohol and NADP+, whereas its 3 products are chlordecone, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is chlordecone-alcohol:NADP+ 2-oxidoreductase. This enzyme is also called CDR.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 2FVL.
References.
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13899361 | Cholest-5-ene-3beta,7alpha-diol 3beta-dehydrogenase | Class of enzymes
In enzymology, a cholest-5-ene-3β,7α-diol 3β-dehydrogenase (EC 1.1.1.181) is an enzyme that catalyzes the chemical reaction
cholest-5-ene-3β,7α-diol + NAD+ formula_0 7α-hydroxycholest-4-en-3-one + NADH + H+
Thus, the two substrates of this enzyme are cholest-5-ene-3β,7α-diol and NAD+, whereas its 3 products are 7α-hydroxycholest-4-en-3-one, NADH, and H+.
The systematic name of this enzyme class is cholest-5-ene-3β,7α-diol:NAD+ 3-oxidoreductase. This enzyme is also called 3β-hydroxy-Δ5-C27-steroid oxidoreductase. The human version of this enzyme is known as hydroxy-Δ-5-steroid dehydrogenase, 3 β- and steroid delta-isomerase 7 or HSD3B7 which is encoded by the "HSD3B7" gene.
Function.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. This enzyme is involved in the initial stages of the synthesis of bile acids from cholesterol and a member of the short-chain dehydrogenase/reductase superfamily. This enzyme is a membrane-associated endoplasmic reticulum protein which is active against 7-alpha hydrosylated sterol substrates.
Clinical significance.
Mutations in the HSD3B7 gene are associated with a congenital bile acid synthesis defect which leads to neonatal cholestasis, a form of progressive liver disease.
References.
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13899374 | Cholestanetetraol 26-dehydrogenase | In enzymology, a cholestanetetraol 26-dehydrogenase (EC 1.1.1.161) is an enzyme that catalyzes the chemical reaction
(25R)-5beta-cholestane-3alpha,7alpha,12alpha,26-tetraol + NAD+ formula_0 (25R)-3alpha,7alpha,12alpha-trihydroxy-5beta-cholestan-26-al + NADH + H+
Thus, the two substrates of this enzyme are (25R)-5beta-cholestane-3alpha,7alpha,12alpha,26-tetraol and NAD+, whereas its 3 products are (25R)-3alpha,7alpha,12alpha-trihydroxy-5beta-cholestan-26-al, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (25R)-5beta-cholestane-3alpha,7alpha,12alpha,26-tetraol:NAD+ 26-oxidoreductase. Other names in common use include cholestanetetraol 26-dehydrogenase, 5beta-cholestane-3alpha,7alpha,12alpha,26-tetrol dehydrogenase, TEHC-NAD oxidoreductase, 5beta-cholestane-3alpha,7alpha,12alpha,26-tetraol:NAD+, and 26-oxidoreductase. This enzyme participates in bile acid biosynthesis.
References.
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13899391 | Cinnamyl-alcohol dehydrogenase | In enzymology, a cinnamyl-alcohol dehydrogenase (EC 1.1.1.195) is an enzyme that catalyzes the chemical reaction
cinnamyl alcohol + NADP+ formula_0 cinnamaldehyde + NADPH + H+
Thus, the two substrates of this enzyme are cinnamyl alcohol and NADP+, whereas its 3 products are cinnamaldehyde, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is cinnamyl-alcohol:NADP+ oxidoreductase. Other names in common use include cinnamyl alcohol dehydrogenase, and CAD. This enzyme participates in phenylpropanoid biosynthesis.
Structural studies.
As of late 2007, 4 structures have been solved for this class of enzymes, with PDB accession codes 1YQD, 1YQX, 2CF5, and 2CF6.
References.
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13899409 | Codeinone reductase (NADPH) | Enzyme
In enzymology, a codeinone reductase (NADPH) (EC 1.1.1.247) is an enzyme that catalyzes the chemical reaction
codeine + NADP+ formula_0 codeinone + NADPH + H+
Thus, the two substrates of this enzyme are codeine and NADP+, whereas its 3 products are codeinone, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is codeine:NADP+ oxidoreductase. This enzyme participates in alkaloid biosynthesis i.
References.
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13899423 | Coniferyl-alcohol dehydrogenase | Enzyme
In enzymology, a coniferyl-alcohol dehydrogenase (EC 1.1.1.194) is an enzyme that catalyzes the chemical reaction
coniferyl alcohol + NADP+ formula_0 coniferyl aldehyde + NADPH + H+
Thus, the two substrates of this enzyme are coniferyl alcohol and NADP+, whereas its 3 products are coniferyl aldehyde, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is coniferyl-alcohol:NADP+ oxidoreductase. This enzyme is also called CAD.
References.
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13899439 | Cyclohexane-1,2-diol dehydrogenase | In enzymology, a cyclohexane-1,2-diol dehydrogenase (EC 1.1.1.174) is an enzyme that catalyzes the chemical reaction
trans-cyclohexane-1,2-diol + NAD+ formula_0 2-hydroxycyclohexan-1-one + NADH + H+
Thus, the two substrates of this enzyme are trans-cyclohexane-1,2-diol and NAD+, whereas its 3 products are 2-hydroxycyclohexan-1-one, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is trans-cyclohexane-1,2-diol:NAD+ 1-oxidoreductase. This enzyme participates in caprolactam degradation.
References.
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13899457 | Cyclohexanol dehydrogenase | In enzymology, a cyclohexanol dehydrogenase (EC 1.1.1.245) is an enzyme that catalyzes the chemical reaction
cyclohexanol + NAD+ formula_0 cyclohexanone + NADH + H+
Thus, the two substrates of this enzyme are cyclohexanol and NAD+, whereas its 3 products are cyclohexanone, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is cyclohexanol:NAD+ oxidoreductase. This enzyme participates in caprolactam degradation.
References.
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13899505 | Cyclopentanol dehydrogenase | In enzymology, a cyclopentanol dehydrogenase (EC 1.1.1.163) is an enzyme that catalyzes the chemical reaction
cyclopentanol + NAD+ formula_0 cyclopentanone + NADH + H+
Thus, the two substrates of this enzyme are cyclopentanol and NAD+, whereas its 3 products are cyclopentanone, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is cyclopentanol:NAD+ oxidoreductase.
References.
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13899581 | D-arabinitol 4-dehydrogenase | In enzymology, a D-arabinitol 4-dehydrogenase (EC 1.1.1.11) is an enzyme that catalyzes the chemical reaction
D-arabinitol + NAD+ formula_0 D-xylulose + NADH + H+
Thus, the two substrates of this enzyme are D-arabinitol and NAD+, whereas its 3 products are D-xylulose, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-arabinitol:NAD+ 4-oxidoreductase. Other names in common use include D-arabitol dehydrogenase and arabitol dehydrogenase. This enzyme participates in pentose and glucuronate interconversions and fructose and mannose metabolism.
References.
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13899601 | D-arabinose 1-dehydrogenase | Class of enzymes
In enzymology, a D-arabinose 1-dehydrogenase (EC 1.1.1.116) is an enzyme that catalyzes the chemical reaction
D-arabinose + NAD+ formula_0 D-arabinono-1,4-lactone + NADH + H+
Thus, the two substrates of this enzyme are D-arabinose and NAD+, whereas its 3 products are D-arabinono-1,4-lactone, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-arabinose:NAD+ 1-oxidoreductase. Other names in common use include NAD+-pentose-dehydrogenase, and arabinose(fucose)dehydrogenase.
References.
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13899634 | D-iditol 2-dehydrogenase | In enzymology, a d-iditol 2-dehydrogenase (EC 1.1.1.15) is an enzyme that catalyzes the chemical reaction
d-iditol + NAD+ formula_0 d-sorbose + NADH + H+
Thus, the two substrates of this enzyme are d-iditol and NAD+, whereas its 3 products are d-sorbose, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is d-iditol:NAD+ 2-oxidoreductase. This enzyme is also called d-sorbitol dehydrogenase. This enzyme participates in pentose and glucuronate interconversions and fructose and mannose metabolism.
References.
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13899665 | Diethyl 2-methyl-3-oxosuccinate reductase | In enzymology, a diethyl 2-methyl-3-oxosuccinate reductase (EC 1.1.1.229) is an enzyme that catalyzes the chemical reaction
diethyl (2R,3R)-2-methyl-3-hydroxysuccinate + NADP+ formula_0 diethyl 2-methyl-3-oxosuccinate + NADPH + H+
Thus, the two substrates of this enzyme are diethyl (2R,3R)-2-methyl-3-hydroxysuccinate and NADP+, whereas its 3 products are diethyl 2-methyl-3-oxosuccinate, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is diethyl-(2R,3R)-2-methyl-3-hydroxysuccinate:NADP+ 3-oxidoreductase.
References.
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13899687 | Dihydrobunolol dehydrogenase | In enzymology, a dihydrobunolol dehydrogenase (EC 1.1.1.160) is an enzyme that catalyzes the chemical reaction
(+/−)-5-[(tert-butylamino)-2'-hydroxypropoxy]-1,2,3,4-tetrahydro-1- naphthol + NADP+ formula_0 (+/−)-5-[(tert-butylamino)-2'-hydroxypropoxy]-3,4-dihydro-1(2H)- naphthalenone + NADPH + H+
The three substrates of this enzyme are (+/−)-5-[(tert-butylamino)-2'-hydroxypropoxy]-1,2,3,4-tetrahydro-1-naphthol, and NADP+, whereas its 4 products are (+/−)-5-[(tert-butylamino)-2'-hydroxypropoxy]-3,4-dihydro-1(2H)-, naphthalenone, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (+/−)-5-[(tert-butylamino)-2'-hydroxypropoxy]-1,2,3,4-tetrahydro-1-naphthol:NADP+ oxidoreductase. This enzyme is also termed bunolol reductase.
References.
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13899704 | Dihydrokaempferol 4-reductase | In enzymology, a dihydrokaempferol 4-reductase (EC 1.1.1.219) is an enzyme that catalyzes the chemical reaction
cis-3,4-leucopelargonidin + NADP+ formula_0 (+)-dihydrokaempferol + NADPH + H+
Thus, the two substrates of this enzyme are cis-3,4-leucopelargonidin and NADP+, whereas its 3 products are (+)-dihydrokaempferol, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is cis-3,4-leucopelargonidin:NADP+ 4-oxidoreductase. Other names in common use include dihydroflavanol 4-reductase (DFR), dihydromyricetin reductase, NADPH-dihydromyricetin reductase, and dihydroquercetin reductase. This enzyme participates in flavonoid biosynthesis.
Function.
Anthocyanidins, common plant pigments, are further reduced by the enzyme dihydroflavonol 4-reductase (DFR) to the corresponding colorless leucoanthocyanidins.
DFR uses dihydromyricetin (ampelopsin) NADPH and 2 H+ to produce leucodelphinidin and NADP.
A cDNA for DFR has been cloned from the orchid "Bromheadia finlaysoniana".
Researchers in Japan have genetically manipulated roses by using RNA interference to knock out endogenous DFR, adding a gene DFR from an iris, and adding a gene for the blue pigment, delphinidin, in an effort to create a blue rose, which is being sold worldwide.
Dihydroflavonol 4-reductase is an enzyme part of the lignin biosynthesis pathway. In "Arabidopsis thaliana", the enzyme uses sinapaldehyde or coniferyl aldehyde or coumaraldehyde and NADPH to produce sinapyl alcohol or coniferyl alcohol or coumaryl alcohol respectively and NADP+.
Structural studies.
As of late 2007, two structures have been solved for this class of enzymes, with PDB accession codes 2C29 and 2IOD.
References.
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Further reading.
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13899722 | Diiodophenylpyruvate reductase | In enzymology, a diiodophenylpyruvate reductase (EC 1.1.1.96) is an enzyme that catalyzes the chemical reaction
3-(3,5-diiodo-4-hydroxyphenyl)lactate + NAD+ formula_0 3-(3,5-diiodo-4-hydroxyphenyl)pyruvate + NADH + H+
Thus, the two substrates of this enzyme are 3-(3,5-diiodo-4-hydroxyphenyl)lactate and NAD+, whereas its 3 products are 3-(3,5-diiodo-4-hydroxyphenyl)pyruvate, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 3-(3,5-diiodo-4-hydroxyphenyl)lactate:NAD+ oxidoreductase. Other names in common use include aromatic alpha-keto acid, KAR, and 2-oxo acid reductase.
References.
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13899738 | Dimethylmalate dehydrogenase | Class of enzymes
In enzymology, a dimethylmalate dehydrogenase (EC 1.1.1.84) is an enzyme that catalyzes the chemical reaction
(R)-3,3-dimethylmalate + NAD+ formula_0 3-methyl-2-oxobutanoate + CO2 + NADH
Thus, the two substrates of this enzyme are (R)-3,3-dimethylmalate and NAD+, whereas its 3 products are 3-methyl-2-oxobutanoate, CO2, and NADH.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (R)-3,3-dimethylmalate:NAD+ oxidoreductase (decarboxylating). This enzyme is also called beta,beta-dimethylmalate dehydrogenase. This enzyme participates in pantothenate and coa biosynthesis. It has 5 cofactors: ammonia, manganese, cobalt, potassium, and NH4+.
References.
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13899756 | D-malate dehydrogenase (decarboxylating) | Enzyme
In enzymology, a D-malate dehydrogenase (decarboxylating) (EC 1.1.1.83) is an enzyme that catalyzes the chemical reaction
(R)-malate + NAD+ formula_0 pyruvate + CO2 + NADH
Thus, the two substrates of this enzyme are (R)-malate and NAD+, whereas its 3 products are pyruvate, CO2, and NADH.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of a donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (R)-malate:NAD+ oxidoreductase (decarboxylating). Other names in common use include D-malate dehydrogenase, D-malic enzyme, bifunctional L(+)-tartrate dehydrogenase-D(+)-malate (decarboxylating). This enzyme participates in butanoate metabolism.
References.
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13899769 | D-pinitol dehydrogenase | In enzymology, a D-pinitol dehydrogenase (EC 1.1.1.142) is an enzyme that catalyzes the chemical reaction
1D-3-O-methyl-chiro-inositol + NADP+ formula_0 2D-5-O-methyl-2,3,5/4,6-pentahydroxycyclohexanone + NADPH + H+
Thus, the two substrates of this enzyme are 1D-3-O-methyl-chiro-inositol and NADP+, whereas its 3 products are 2D-5-O-methyl-2,3,5/4,6-pentahydroxycyclohexanone, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 1D-3-O-methyl-chiro-inositol:NADP+ oxidoreductase. This enzyme is also called 5D-5-O-methyl-chiro-inositol:NADP+ oxidoreductase.
References.
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13899785 | DTDP-4-dehydro-6-deoxyglucose reductase | In enzymology, a dTDP-4-dehydro-6-deoxyglucose reductase (EC 1.1.1.266) is an enzyme that catalyzes the chemical reaction
dTDP-D-fucose + NADP+ formula_0 dTDP-4-dehydro-6-deoxy-D-glucose + NADPH + H+
Thus, the two substrates of this enzyme are dTDP-D-fucose and NADP+, whereas its 3 products are dTDP-4-dehydro-6-deoxy-D-glucose, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is dTDP-D-fucose:NADP+ oxidoreductase. This enzyme is also called dTDP-4-keto-6-deoxyglucose reductase. This enzyme participates in polyketide sugar unit biosynthesis.
References.
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13899801 | DTDP-4-dehydrorhamnose reductase | In enzymology, a dTDP-4-dehydrorhamnose reductase (EC 1.1.1.133) is an enzyme that catalyzes the chemical reaction
dTDP-6-deoxy-L-mannose + NADP+ formula_0 dTDP-4-dehydro-6-deoxy-L-mannose + NADPH + H+
Thus, the two substrates of this enzyme are dTDP-6-deoxy-L-mannose and NADP+, whereas its 3 products are dTDP-4-dehydro-6-deoxy-L-mannose, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is dTDP-6-deoxy-L-mannose:NADP+ 4-oxidoreductase. Other names in common use include dTDP-4-keto-L-rhamnose reductase, reductase, thymidine diphospho-4-ketorhamnose, dTDP-4-ketorhamnose reductase, TDP-4-keto-rhamnose reductase, and thymidine diphospho-4-ketorhamnose reductase. This enzyme participates in 3 metabolic pathways: nucleotide sugars metabolism, streptomycin biosynthesis, and polyketide sugar unit biosynthesis.
Structural studies.
As of late 2007, 5 structures have been solved for this class of enzymes, with PDB accession codes 1KBZ, 1KC1, 1KC3, 1N2S, and 2GGS.
References.
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| https://en.wikipedia.org/wiki?curid=13899801 |
13899814 | DTDP-6-deoxy-L-talose 4-dehydrogenase | In enzymology, a dTDP-6-deoxy-L-talose 4-dehydrogenase (EC 1.1.1.134) is an enzyme that catalyzes the chemical reaction
dTDP-6-deoxy-L-talose + NADP+ formula_0 dTDP-4-dehydro-6-deoxy-L-mannose + NADPH + H+
Thus, the two substrates of this enzyme are dTDP-6-deoxy-L-talose and NADP+, whereas its 3 products are dTDP-4-dehydro-6-deoxy-L-mannose, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is dTDP-6-deoxy-L-talose:NADP+ 4-oxidoreductase. Other names in common use include thymidine diphospho-6-deoxy-L-talose dehydrogenase, TDP-6-deoxy-L-talose dehydrogenase, thymidine diphospho-6-deoxy-L-talose dehydrogenase, and dTDP-6-deoxy-L-talose dehydrogenase (4-reductase). This enzyme participates in nucleotide sugars metabolism.
References.
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| https://en.wikipedia.org/wiki?curid=13899814 |
13899823 | DTDP-galactose 6-dehydrogenase | Class of enzymes
In enzymology, a dTDP-galactose 6-dehydrogenase (EC 1.1.1.186) is an enzyme that catalyzes the chemical reaction
dTDP-D-galactose + 2 NADP+ + H2O formula_0 dTDP-D-galacturonate + 2 NADPH + 2 H+
The 3 substrates of this enzyme are dTDP-D-galactose, NADP+, and H2O, whereas its 3 products are dTDP-D-galacturonate, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is dTDP-D-galactose:NADP+ 6-oxidoreductase. This enzyme is also called thymidine-diphosphate-galactose dehydrogenase. This enzyme participates in nucleotide sugars metabolism.
References.
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| https://en.wikipedia.org/wiki?curid=13899823 |
13899836 | D-threo-aldose 1-dehydrogenase | In enzymology, a D-threo-aldose 1-dehydrogenase (EC 1.1.1.122) is an enzyme that catalyzes the chemical reaction
a D-threo-aldose + NAD+ formula_0 a D-threo-aldono-1,5-lactone + NADH + H+
Thus, the two substrates of this enzyme are D-threo-aldose and NAD+, whereas its 3 products are D-threo-aldono-1,5-lactone, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-threo-aldose:NAD+ 1-oxidoreductase. Other names in common use include L-fucose dehydrogenase, (2S,3R)-aldose dehydrogenase, dehydrogenase, L-fucose, and L-fucose (D-arabinose) dehydrogenase. This enzyme participates in ascorbate and aldarate metabolism.
References.
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| https://en.wikipedia.org/wiki?curid=13899836 |
13899849 | D-xylose 1-dehydrogenase | In enzymology, a D-xylose 1-dehydrogenase (EC 1.1.1.175) is an enzyme that catalyzes the chemical reaction
D-xylose + NAD+ formula_0 D-xylonolactone + NADH + H+
Thus, the two substrates of this enzyme are D-xylose and NAD+, whereas its 3 products are D-xylonolactone, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-xylose:NAD+ 1-oxidoreductase. Other names in common use include NAD+-D-xylose dehydrogenase, D-xylose dehydrogenase, and (NAD+)-linked D-xylose dehydrogenase. This enzyme participates in pentose and glucuronate interconversions.
References.
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| https://en.wikipedia.org/wiki?curid=13899849 |
13899865 | D-xylose 1-dehydrogenase (NADP+) | In enzymology, a D-xylose 1-dehydrogenase (NADP+) (EC 1.1.1.179) is an enzyme that catalyzes the chemical reaction
D-xylose + NADP+ formula_0 D-xylono-1,5-lactone + NADPH + H+
Thus, the two substrates of this enzyme are D-xylose and NADP+, whereas its 3 products are D-xylono-1,5-lactone, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-xylose:NADP+ 1-oxidoreductase. Other names in common use include D-xylose (nicotinamide adenine dinucleotide phosphate), dehydrogenase, D-xylose-NADP+ dehydrogenase, D-xylose:NADP+ oxidoreductase, and D-xylose 1-dehydrogenase (NADP+).
References.
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| https://en.wikipedia.org/wiki?curid=13899865 |
13899894 | Erythrulose reductase | In enzymology, an erythrulose reductase (EC 1.1.1.162) is an enzyme that catalyzes the chemical reaction
erythritol + NADP+ formula_0 D-erythrulose + NADPH + H+
Thus, the two substrates of this enzyme are erythritol and NADP+, whereas its 3 products are D-erythrulose, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is erythritol:NADP+ oxidoreductase. This enzyme is also called D-erythrulose reductase.
References.
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| https://en.wikipedia.org/wiki?curid=13899894 |
13899915 | Farnesol dehydrogenase | In enzymology, a farnesol dehydrogenase (EC 1.1.1.216) is an enzyme that catalyzes the chemical reaction
2-trans,6-trans-farnesol + NADP+ formula_0 2-trans,6-trans-farnesal + NADPH + H+
Thus, the two substrates of this enzyme are 2-trans,6-trans-farnesol and NADP+, whereas its 3 products are 2-trans,6-trans-farnesal, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is 2-trans,6-trans-farnesol:NADP+ 1-oxidoreductase. Other names in common use include NADP+-farnesol dehydrogenase, and farnesol (nicotinamide adenine dinucleotide phosphate) dehydrogenase.
References.
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| https://en.wikipedia.org/wiki?curid=13899915 |
13899930 | Flavanone 4-reductase | In enzymology, a flavanone 4-reductase (EC 1.1.1.234) is an enzyme that catalyzes the chemical reaction
(2S)-flavan-4-ol + NADP+ formula_0 (2S)-flavanone + NADPH + H+
Thus, the two substrates of this enzyme are (2S)-flavan-4-ol and NADP+, whereas its 3 products are (2S)-flavanone, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (2S)-flavan-4-ol:NADP+ 4-oxidoreductase. This enzyme participates in flavonoid biosynthesis.
References.
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| https://en.wikipedia.org/wiki?curid=13899930 |
13899954 | Fluoren-9-ol dehydrogenase | In enzymology, a fluoren-9-ol dehydrogenase (EC 1.1.1.256) is an enzyme that catalyzes the chemical reaction
fluoren-9-ol + 2 NAD(P)+ formula_0 fluoren-9-one + 2 NAD(P)H + 2 H+
The 3 substrates of this enzyme are fluoren-9-ol, NAD+, and NADP+, whereas its 4 products are fluoren-9-one, NADH, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is fluoren-9-ol:NAD(P)+ oxidoreductase. This enzyme participates in fluorene degradation.
References.
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| https://en.wikipedia.org/wiki?curid=13899954 |
13899977 | Fructose 5-dehydrogenase (NADP+) | In enzymology, a fructose 5-dehydrogenase (NADP+) (EC 1.1.1.124) is an enzyme that catalyzes the chemical reaction
D-fructose + NADP+ formula_0 5-dehydro-D-fructose + NADPH + H+
Thus, the two substrates of this enzyme are D-fructose and NADP+, whereas its 3 products are 5-dehydro-D-fructose, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-fructose:NADP+ 5-oxidoreductase. Other names in common use include 5-ketofructose reductase (NADP+), 5-keto-D-fructose reductase (NADP+), fructose 5-(nicotinamide adenine dinucleotide phosphate), dehydrogenase, D-(-)fructose:(NADP+) 5-oxidoreductase, and fructose 5-dehydrogenase (NADP+).
References.
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| https://en.wikipedia.org/wiki?curid=13899977 |
13899993 | D-arabinose 1-dehydrogenase (NAD(P)+) | In enzymology, a D-arabinose 1-dehydrogenase [NAD(P)+] (EC 1.1.1.117) is an enzyme that catalyzes the chemical reaction
D-arabinose + NAD(P)+ formula_0 D-arabinono-1,4-lactone + NAD(P)H + H+
The 3 substrates of this enzyme are D-arabinose, NAD+, and NADP+, whereas its 4 products are D-arabinono-1,4-lactone, NADH, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-arabinose:NAD(P)+ 1-oxidoreductase. This enzyme is also called D-arabinose 1-dehydrogenase [NAD(P)+].
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 2H6E.
References.
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| https://en.wikipedia.org/wiki?curid=13899993 |
13899994 | Coomber's relationship | Coomber's relationship can be used to describe how the internal pressure and dielectric constant of a non-polar liquid are related.
As formula_0, which defines the internal pressure of a liquid, it can be found that:
formula_1
where
where for most non-polar liquids formula_7 | [
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"math_id": 1,
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},
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"math_id": 2,
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"math_id": 7,
"text": "n=1"
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| https://en.wikipedia.org/wiki?curid=13899994 |
13900005 | Fructuronate reductase | In enzymology, a fructuronate reductase (EC 1.1.1.57) is an enzyme that catalyzes the chemical reaction
D-mannonate + NAD+ formula_0 D-fructuronate + NADH + H+
Thus, the two substrates of this enzyme are D-mannonate and NAD+, whereas its 3 products are D-fructuronate, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-mannonate:NAD+ 5-oxidoreductase. Other names in common use include mannonate oxidoreductase, mannonic dehydrogenase, D-mannonate dehydrogenase, and D-mannonate:NAD+ oxidoreductase. This enzyme participates in pentose and glucuronate interconversions. | [
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| https://en.wikipedia.org/wiki?curid=13900005 |
13900015 | Galactitol-1-phosphate 5-dehydrogenase | In enzymology, a galactitol-1-phosphate 5-dehydrogenase (EC 1.1.1.251) is an enzyme that catalyzes the chemical reaction
galactitol-1-phosphate + NAD+ formula_0 L-tagatose 6-phosphate + NADH + H+
Thus, the two substrates of this enzyme are galactitol-1-phosphate and NAD+, whereas its 3 products are L-tagatose 6-phosphate, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is galactitol-1-phosphate:NAD+ oxidoreductase. This enzyme participates in galactose metabolism. It employs one cofactor, zinc.
References.
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| https://en.wikipedia.org/wiki?curid=13900015 |
13900027 | Galactitol 2-dehydrogenase | In enzymology, a galactitol 2-dehydrogenase (EC 1.1.1.16) is an enzyme that catalyzes the chemical reaction
galactitol + NAD+ formula_0 D-tagatose + NADH + H+
Thus, the two substrates of this enzyme are galactitol and NAD+, whereas its 3 products are D-tagatose, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is galactitol:NAD+ 2-oxidoreductase. This enzyme is also called dulcitol dehydrogenase. This enzyme participates in galactose metabolism.
References.
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| https://en.wikipedia.org/wiki?curid=13900027 |
13900047 | D-galactose 1-dehydrogenase | In enzymology, a d-galactose 1-dehydrogenase (EC 1.1.1.48) is an enzyme that catalyzes the chemical reaction
d-galactose + NAD+ formula_0 d-galactono-1,4-lactone + NADH + H+
Thus, the two substrates of this enzyme are d-galactose and NAD+, whereas its 3 products are d-galactono-1,4-lactone, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is d-galactose:NAD+ 1-oxidoreductase. Other names in common use include d-galactose dehydrogenase, beta-galactose dehydrogenase, and NAD+-dependent d-galactose dehydrogenase. This enzyme participates in galactose metabolism.
References.
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| https://en.wikipedia.org/wiki?curid=13900047 |
13900060 | Galactose 1-dehydrogenase (NADP+) | Enzyme class
In enzymology, a galactose 1-dehydrogenase (NADP+) (EC 1.1.1.120) is an enzyme that catalyzes the chemical reaction
D-galactose + NADP+ formula_0 D-galactono-1,5-lactone + NADPH + H+
Thus, the two substrates of this enzyme are D-galactose and NADP+, whereas its 3 products are D-galactono-1,5-lactone, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-galactose:NADP+ 1-oxidoreductase. Other names in common use include D-galactose dehydrogenase (NADP+), and galactose 1-dehydrogenase (NADP+). This enzyme participates in galactose metabolism.
References.
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| https://en.wikipedia.org/wiki?curid=13900060 |
13900076 | GDP-4-dehydro-6-deoxy-D-mannose reductase | In enzymology, a GDP-4-dehydro-6-deoxy-D-mannose reductase (EC 1.1.1.281) is an enzyme that catalyzes the chemical reaction
GDP-6-deoxy-D-mannose + NAD(P)+ formula_0 GDP-4-dehydro-6-deoxy-D-mannose + NAD(P)H + H+
The 3 substrates of this enzyme are GDP-6-deoxy-D-mannose, NAD+, and NADP+, whereas its 4 products are GDP-4-dehydro-6-deoxy-D-mannose, NADH, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is GDP-6-deoxy-D-mannose:NAD(P)+ 4-oxidoreductase (D-rhamnose-forming). Other names in common use include GDP-4-keto-6-deoxy-D-mannose reductase [ambiguous], GDP-6-deoxy-D-lyxo-4-hexulose reductase, and Rmd. This enzyme participates in fructose and mannose metabolism.
References.
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| https://en.wikipedia.org/wiki?curid=13900076 |
13900080 | Alcohol dehydrogenase (NAD(P)+) | In enzymology, an alcohol dehydrogenase [NAD(P)+] (EC 1.1.1.71) is an enzyme that catalyzes the chemical reaction
an alcohol + NAD(P)+ formula_0 an aldehyde + NAD(P)H + H+
The 3 substrates of this enzyme are alcohol, NAD+, and NADP+, whereas its 4 products are aldehyde, NADH, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is alcohol:NAD(P)+ oxidoreductase. Other names in common use include retinal reductase, aldehyde reductase (NADPH/NADH), and alcohol dehydrogenase [NAD(P)]. This enzyme participates in glycolysis and gluconeogenesis.
References.
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| https://en.wikipedia.org/wiki?curid=13900080 |
13900091 | GDP-4-dehydro-D-rhamnose reductase | In enzymology, a GDP-4-dehydro-D-rhamnose reductase (EC 1.1.1.187) is an enzyme that catalyzes the chemical reaction
GDP-6-deoxy-D-mannose + NAD(P)+ formula_0 GDP-4-dehydro-6-deoxy-D-mannose + NAD(P)H + H+
The 3 substrates of this enzyme are GDP-6-deoxy-D-mannose, NAD+, and NADP+, whereas its 4 products are GDP-4-dehydro-6-deoxy-D-mannose, NADH, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is GDP-6-deoxy-D-mannose:NAD(P)+ 4-oxidoreductase. Other names in common use include GDP-4-keto-6-deoxy-D-mannose reductase, GDP-4-keto-D-rhamnose reductase, and guanosine diphosphate-4-keto-D-rhamnose reductase. This enzyme participates in fructose and mannose metabolism.
References.
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| https://en.wikipedia.org/wiki?curid=13900091 |
13900110 | GDP-6-deoxy-D-talose 4-dehydrogenase | In enzymology, a GDP-6-deoxy-D-talose 4-dehydrogenase (EC 1.1.1.135) is an enzyme that catalyzes the chemical reaction
GDP-6-deoxy-D-talose + NAD(P)+ formula_0 GDP-4-dehydro-6-deoxy-D-mannose + NAD(P)H + H+
The 3 substrates of this enzyme are GDP-6-deoxy-D-talose, NAD+, and NADP+, whereas its 4 products are GDP-4-dehydro-6-deoxy-D-mannose, NADH, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is GDP-6-deoxy-D-talose:NAD(P)+ 4-oxidoreductase. This enzyme is also called guanosine diphospho-6-deoxy-D-talose dehydrogenase. This enzyme participates in fructose and mannose metabolism.
References.
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| https://en.wikipedia.org/wiki?curid=13900110 |
13900116 | Homoserine dehydrogenase | Enzyme
In enzymology, a homoserine dehydrogenase (EC 1.1.1.3) is an enzyme that catalyzes the chemical reaction
L-homoserine + NAD(P)+ formula_0 L-aspartate 4-semialdehyde + NAD(P)H + H+
The 2 substrates of this enzyme are L-homoserine and NAD+ (or NADP+), whereas its 3 products are L-aspartate 4-semialdehyde, NADH (or NADPH), and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is L-homoserine:NAD(P)+ oxidoreductase. Other names in common use include HSDH, and HSD.
Homoserine dehydrogenase catalyses the third step in the aspartate pathway; the NAD(P)-dependent reduction of aspartate beta-semialdehyde into homoserine. Homoserine is an intermediate in the biosynthesis of threonine, isoleucine, and methionine.
Enzyme structure.
The enzyme can be found in a monofunctional form, in some bacteria and yeast. Structural analysis of the yeast monofunctional enzyme indicates that the enzyme is a dimer composed of three distinct regions; an N-terminal nucleotide-binding domain, a short central dimerisation region, and a C-terminal catalytic domain. The N-terminal domain forms a modified Rossmann fold, while the catalytic domain forms a novel alpha-beta mixed sheet.
The enzyme can also be found in a bifunctional form consisting of an N-terminal aspartokinase domain and a C-terminal homoserine dehydrogenase domain, as found in bacteria such as "Escherichia coli" and in plants.
The bifunctional aspartokinase-homoserine dehydrogenase (AK-HSD) enzyme has a regulatory domain that consists of two subdomains with a common loop-alpha helix-loop-beta strand loop-beta strand motif. Each subdomain contains an ACT domain that allows for complex regulation of several different protein functions. The AK-HSD gene codes for aspartate kinase, an intermediate domain (coding for the linker region between the two enzymes in the bifunctional form), and finally the coding sequence for homoserine dehydrogenase.
As of late 2007, 4 structures have been solved for this class of enzymes, with PDB accession codes 1EBF, 1EBU, 1Q7G, and 1TVE.
Enzyme mechanism.
Homoserine dehydrogenase catalyzes the reaction of aspartate-semialdehyde (ASA) to homoserine. The overall reaction reduces the C4 carboxylic acid functional group of ASA to a primary alcohol and oxidizes the C1 aldehyde to a carboxylic acid. Residues Glu 208 and Lys 117 are thought to be involved in the active catalytic site of the enzyme. Asp 214 and Lys 223 have been shown to be important for hydride transfer in the catalyzed reaction.
Once the C4 carboxylic acid is reduced to an aldehyde and the C1 aldehyde is oxidized to a carboxylic acid, experiments suggest that Asp 219, Glu 208 and a water molecule bind ASA in the active site while Lys 223 donates a proton to the aspartate-semialdehyde C4 oxygen. Homoserine dehydrogenase has an NAD(P)H cofactor, which then donates a hydrogen to the same carbon, effectively reducing the aldehyde to an alcohol. (Refer to figures 1 and 2).
However, the precise mechanism of complete homoserine dehydrogenase catalysis remains unknown.
The homoserine dehydrogenase-catalyzed reaction has been postulated to proceed through a bi-bi kinetic mechanism, where the NAD(P)H cofactor binds the enzyme first and is the last to dissociate from the enzyme once the reaction is complete. Additionally, while both NADH and NADPH are adequate cofactors for the reaction, NADH is preferred. The Km of the reaction is four-times smaller with NADH and the Kcat/Km is three-times greater, indicating a more efficient reaction.
Homoserine dehydrogenase also exhibits multi-order kinetics at subsaturating levels of substrate. Additionally, the variable kinetics for homoserine dehydrogenase is an artifact of the faster dissociation of the amino acid substrate from the enzyme complex as compared to cofactor dissociation.
Biological function.
The aspartate metabolic pathway is involved in both storage of asparagine and in synthesis of aspartate-family amino acids. Homoserine dehydrogenase catalyzes an intermediate step in this nitrogen and carbon storage and utilization pathway. (Refer to figure 3).
In photosynthetic organisms, glutamine, glutamate, and aspartate accumulate during the day and are used to synthesize other amino acids. At night, aspartate is converted to asparagine for storage. Additionally, the aspartate kinase-homoserine dehydrogenase gene is primarily expressed in actively growing, young plant tissues, particularly in the apical and lateral meristems.
Mammals lack the enzymes involved in the aspartate metabolic pathway, including homoserine dehydrogenase. As lysine, threonine, methionine, and isoleucine are made in this pathway, they are considered essential amino acids for mammals.
Biological regulation.
Homoserine dehydrogenase and aspartate kinase are both subject to significant regulation (refer to figure 3). HSD is inhibited by downstream products of the aspartate metabolic pathway, mainly threonine. Threonine acts as a competitive inhibitor for both HSD and aspartate kinase. In AK-HSD expressing organisms, one of the threonine binding sites is found in the linker region between AK and HSD, suggesting potential allosteric inhibition of both enzymes.
However, some threonine-resistant HSD forms exist that require concentrations of threonine much greater than physiologically present for inhibition. These threonine-insensitive forms of HSD are used in genetically engineered plants to increase both threonine and methionine production for higher nutritional value.
Homoserine dehydrogenase is also subject to transcriptional regulation. Its promoter sequence contains a cis-regulatory element TGACTC sequence, which is known to be involved in other amino acid biosynthetic pathways. The Opaque2 regulatory element has also been implicated in homoserine dehydrogenase regulation, but its effects are still not well defined.
In plants, there is also environmental regulation of AK-HSD gene expression. Light exposure has been demonstrated to increase expression of the AK-HSD gene, presumably related to photosynthesis.
Disease relevance.
In humans, there has been a significant increase in disease from pathogenic fungi, so developing anti-fungal drugs is an important biochemical task. As homoserine dehydrogenase is found mainly in plants, bacteria, and yeast, but not mammals, it is a strong target for antifungal drug development. Recently, 5-hydroxy-4-oxonorvaline (HON) was discovered to target and inhibit HSD activity irreversibly. HON is structurally similar to aspartate semialdehyde, so it is postulated that it serves as a competitive inhibitor for HSD. Likewise, (S) 2-amino-4-oxo-5-hydroxypentanoic acid (RI-331), another amino acid analog, has also been shown to inhibit HSD. Both of these compounds are effective against "Cryptococcus neoformans" and "Cladosporium fulvum", among others.
In addition to amino acid analogs, several phenolic compounds have been shown to inhibit HSD activity. Like HON and RI-331, these molecules are competitive inhibitors that bind to the enzyme active site. Specifically, the phenolic hydroxyl group interacts with the amino acid binding site.
References.
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13900125 | GDP-L-fucose synthase | In enzymology, a GDP-L-fucose synthase (EC 1.1.1.271) is an enzyme that catalyzes the chemical reaction
GDP-4-dehydro-6-deoxy-D-mannose + NADPH + H+ formula_0 GDP-L-fucose + NADP+
Thus, the three substrates of this enzyme are GDP-4-dehydro-6-deoxy-D-mannose, NADPH, and H+, whereas its two products are GDP-L-fucose and NADP+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is GDP-L-fucose:NADP+ 4-oxidoreductase (3,5-epimerizing). This enzyme is also called GDP-4-keto-6-deoxy-D-mannose-3,5-epimerase-4-reductase. This enzyme participates in fructose and mannose metabolism.
Relevance in diseases.
It has been reported that some cases of multiple sclerosis that present the HLA variant DRB3, present also autoimmunity against GDP-L-fucose synthase. The same report points out that the autoimmune problem could derive from the gut microbiota.
References.
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13900148 | GDP-mannose 6-dehydrogenase | In enzymology, a GDP-mannose 6-dehydrogenase (EC 1.1.1.132) is an enzyme that catalyzes the chemical reaction
GDP-D-mannose + 2 NAD+ + H2O formula_0 GDP-D-mannuronate + 2 NADH + 2 H+
The 3 substrates of this enzyme are GDP-D-mannose, NAD+, and H2O, whereas its 3 products are GDP-D-mannuronate, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is GDP-D-mannose:NAD+ 6-oxidoreductase. Other names in common use include guanosine diphosphomannose dehydrogenase, GDP-mannose dehydrogenase, guanosine diphosphomannose dehydrogenase, and guanosine diphospho-D-mannose dehydrogenase. This enzyme participates in fructose and mannose metabolism.
This protein may use the morpheein model of allosteric regulation.
Structural studies.
As of late 2007, 3 structures have been solved for this class of enzymes, with PDB accession codes 1MFZ, 1MUU, and 1MV8.
References.
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Further reading.
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13900157 | (R,R)-butanediol dehydrogenase | Class of enzymes
In enzymology, a (R,R)-butanediol dehydrogenase (EC 1.1.1.4) is an enzyme that catalyzes the chemical reaction
(R,R)-butane-2,3-diol + NAD+ formula_0 (R)-acetoin + NADH + H+
Thus, the two substrates of this enzyme are (R,R)-butane-2,3-diol and NAD+, whereas its 3 products are (R)-acetoin, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (R,R)-butane-2,3-diol:NAD+ oxidoreductase. Other names in common use include butyleneglycol dehydrogenase, D-butanediol dehydrogenase, D-(−)-butanediol dehydrogenase, butylene glycol dehydrogenase, diacetyl (acetoin) reductase, D-aminopropanol dehydrogenase, D-aminopropanol dehydrogenase, 1-amino-2-propanol dehydrogenase, 2,3-butanediol dehydrogenase, D-1-amino-2-propanol dehydrogenase, (R)-diacetyl reductase, (R)-2,3-butanediol dehydrogenase, D-1-amino-2-propanol:NAD+ oxidoreductase, 1-amino-2-propanol oxidoreductase, and aminopropanol oxidoreductase. This enzyme participates in butanoic acid metabolism.
References.
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13900171 | Geraniol dehydrogenase | In enzymology, a geraniol dehydrogenase (EC 1.1.1.183) is an enzyme that catalyzes the chemical reaction
geraniol + NADP+ formula_0 geranial + NADPH + H+
Thus, the two substrates of this enzyme are geraniol and NADP+, whereas its 3 products are geranial, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is geraniol:NADP+ oxidoreductase.
References.
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13900176 | Glycerol dehydrogenase | Glycerol dehydrogenase (EC 1.1.1.6, also known as NAD+-linked glycerol dehydrogenase, glycerol: NAD+ 2-oxidoreductase, GDH, GlDH, GlyDH) is an enzyme in the oxidoreductase family that utilizes the NAD+ to catalyze the oxidation of glycerol to form glycerone (dihydroxyacetone). This enzyme is an oxidoreductase, specifically a metal-dependent alcohol dehydrogenase that plays a role in anaerobic glycerol metabolism and has been isolated from a number of bacteria, including "Enterobacter aerogenes," "Klebsiella aerogenes," "Streptococcus faecalis," "Erwinia aeroidea," "Bacillus megaterium," and "Bacillus stearothermophilus." However, most studies of glycerol dehydrogenase have been performed in "Bacillus stearothermophilus," "(B. stearothermophilus)" due to its thermostability and the following structural and functional information will, therefore, refer primarily to the characterization of the enzyme in this bacterium.
Structure.
Glycerol dehydrogenase is a homooctamer composed of eight identical monomer subunits made up of a single polypeptide chain of 370 amino acids (molecular weight 42,000 Da). Each subunit contains 9 beta sheets and 14 alpha helices within two distinct domains (N-terminal, residues 1-162 and C-terminal, residues 163–370). The deep cleft formed between these two domains serves as the enzyme's active site. This active site consists of one bound metal ion, one NAD+ nicotinamide ring binding site, and a substrate binding site.
Research into the structure of "B. stearothermophilus" shows that the active site contains a divalent cation—zinc ion, Zn2+. This zinc ion forms tetrahedral dipole interactions between the amino acid residues Asp173, His256, and His274 as well as a water molecule.
The NAD+ binding site, resembling the Rossmann fold within the N-terminal domain, extends from the surface of the enzyme to the cleft containing the active site. The nicotinamide ring (the active region of NAD+) binds in a pocket of the cleft consisting of the residues Asp100, Asp123, Ala124, Ser127, Leu129, Val131, Asp173, His174, and Phe247.
Finally, the substrate binding site consists of the residues Asp123, His256, His274 as well as a water molecule.
Function.
Encoded by the gene gldA, the enzyme glycerol dehydrogenase, GlyDH catalyzes the oxidation of glycerol to glycerone. Unlike more common pathways utilizing glycerol, GlyDH effectively oxidizes glycerol in anaerobic metabolic pathways under ATP-independent conditions (a useful mechanism in the breakdown of glycerol in bacteria). In addition, GlyDH selectively oxidizes the C2 hydroxyl group to form a ketone rather than a terminal hydroxyl group to form an aldehyde.
Mechanism.
While the precise mechanism of this specific enzyme has not yet been characterized, kinetic studies support that GlyDH catalysis of the chemical reaction
glycerol + NAD+ formula_0 glycerone + NADH + H+
is comparable to those of other alcohol dehydrogenases. Therefore, the following mechanism offers a reasonable representation of glycerol oxidation by NAD+.
After NAD+ is bound to the enzyme, glycerol substrate binds to the active site in such a way as to have two coordinated interactions between two adjacent hydroxyl groups and the neighboring zinc ion. GlyDH then catalyzes the base-assisted deprotonation of the C2 hydroxyl group, forming an alkoxide. The zinc atom further serves to stabilize the negative charge on the alkoxide intermediate before the excess electron density around the charged oxygen atom shifts to form a double bond with the C2 carbon atom. Hydride is subsequently removed from the secondary carbon and acts as a nucleophile in electron transfer to the NAD+ nicotinamide ring. As a result, the H+ removed by the base is released as a proton into the surrounding solution; followed by the release of the product glycerone, then NADH by GlyDH.
Industrial implications.
As a result of increasing biodiesel production, formation of the byproduct, crude glycerol, has also increased. While glycerol is commonly used in food, pharmaceuticals, cosmetics, and other industries, increased production of crude glycerol has become very expensive to purify and utilize in these industries. Because of this, researchers are interested in finding new economical ways to utilize low-grade glycerol products. Biotechnology is one such technique: using particular enzymes to break down crude glycerol to form products such as 1,3-propanediol, 1,2-propanediol, succinic acid, dihydroxyacetone (glycerone), hydrogen, polyglycerols, and polyesters. As a catalyst for the conversion of glycerol to glycerone, glycerol dehydrogenase is one such enzyme being investigated for this industrial purpose.
References.
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13900189 | Gluconate 2-dehydrogenase | In enzymology, a gluconate 2-dehydrogenase (EC 1.1.1.215) is an enzyme that catalyzes the chemical reaction
D-gluconate + NADP+ formula_0 2-dehydro-D-gluconate + NADPH + H+
Thus, the two substrates of this enzyme are D-gluconate and NADP+, whereas its 3 products are 2-dehydro-D-gluconate, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-gluconate:NADP+ oxidoreductase. Other names in common use include 2-keto-D-gluconate reductase, and 2-ketogluconate reductase.
References.
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13900198 | Propanediol-phosphate dehydrogenase | In enzymology, a propanediol-phosphate dehydrogenase (EC 1.1.1.7) is an enzyme that catalyzes the chemical reaction
propane-1,2-diol 1-phosphate + NAD+ formula_0 hydroxyacetone phosphate + NADH + H+
Thus, the two substrates of this enzyme are propane-1,2-diol 1-phosphate and NAD+, whereas its 3 products are hydroxyacetone phosphate, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is propane-1,2-diol-1-phosphate:NAD+ oxidoreductase. Other names in common use include PDP dehydrogenase, 1,2-propanediol-1-phosphate:NAD+ oxidoreductase, and propanediol phosphate dehydrogenase.
References.
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13900216 | Gluconate 5-dehydrogenase | In enzymology, a gluconate 5-dehydrogenase (EC 1.1.1.69) is an enzyme that catalyzes the chemical reaction
D-gluconate + NAD(P)+ formula_0 5-dehydro-D-gluconate + NAD(P)H + H+
The 3 substrates of this enzyme are D-gluconate, NAD+, and NADP+, whereas its 4 products are 5-dehydro-D-gluconate, NADH, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-gluconate:NAD(P)+ 5-oxidoreductase. Other names in common use include 5-keto-D-gluconate 5-reductase, 5-keto-D-gluconate 5-reductase, 5-ketogluconate 5-reductase, 5-ketogluconate reductase, and 5-keto-D-gluconate reductase.
Structural studies.
As of late 2007, only one structure has been solved for this class of enzymes, with the PDB accession code 1VL8.
References.
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13900229 | Glucose 1-dehydrogenase | In enzymology, a glucose 1-dehydrogenase (EC 1.1.1.47) is an enzyme that catalyzes the chemical reaction
beta-D-glucose + NAD(P)+ formula_0 D-glucono-1,5-lactone + NAD(P)H + H+
The 3 substrates of this enzyme are beta-D-glucose, NAD+, and NADP+, whereas its 4 products are D-glucono-1,5-lactone, NADH, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is beta-D-glucose:NAD(P)+ 1-oxidoreductase. Another name in common use is D-glucose dehydrogenase (NAD(P)+).
Structural studies.
As of late 2007, 9 structures have been solved for this class of enzymes, with PDB accession codes 1G6K, 1GCO, 1GEE, 1RWB, 1SPX, 2B5V, 2B5W, 2CD9, and 2CDA.
References.
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13900237 | Glucose 1-dehydrogenase (NAD+) | In enzymology, a glucose 1-dehydrogenase (NAD+) (EC 1.1.1.118) is an enzyme that catalyzes the chemical reaction
D-glucose + NAD+ formula_0 D-glucono-1,5-lactone + NADH + H+
Thus, the two substrates of this enzyme are D-glucose and NAD+, whereas its 3 products are D-glucono-1,5-lactone, NADH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-glucose:NAD+ 1-oxidoreductase. Other names in common use include D-glucose:NAD+ oxidoreductase, D-aldohexose dehydrogenase, and glucose 1-dehydrogenase (NAD+).
Structural studies.
As of late 2007, 3 structures have been solved for this class of enzymes, with PDB accession codes 2DTD, 2DTE, and 2DTX.
References.
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13900248 | Glucose 1-dehydrogenase (NADP+) | In enzymology, a glucose 1-dehydrogenase (NADP+) (EC 1.1.1.119) is an enzyme that catalyzes the chemical reaction
D-glucose + NADP+ formula_0 D-glucono-1,5-lactone + NADPH + H+
Thus, the two substrates of this enzyme are D-glucose and NADP+, whereas its 3 products are D-glucono-1,5-lactone, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is D-glucose:NADP+ 1-oxidoreductase. Other names in common use include nicotinamide adenine dinucleotide phosphate-linked aldohexose, dehydrogenase, NADP+-linked aldohexose dehydrogenase, NADP+-dependent glucose dehydrogenase, and glucose 1-dehydrogenase (NADP+).
References.
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13900270 | Glucuronate reductase | In enzymology, a glucuronate reductase (EC 1.1.1.19) is an enzyme that catalyzes the chemical reaction
L-gulonate + NADP+ formula_0 D-glucuronate + NADPH + H+
Thus, the two substrates of this enzyme are L-gulonate and NADP+, whereas its 3 products are D-glucuronate, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is L-gulonate:NADP+ 6-oxidoreductase. Other names in common use include aldehyde reductase, L-hexonate:NADP dehydrogenase, TPN-L-gulonate dehydrogenase, aldehyde reductase II, NADP-L-gulonate dehydrogenase, D-glucuronate dehydrogenase, D-glucuronate reductase, and L-glucuronate reductase (incorrect). This enzyme participates in pentose and glucuronate interconversions and ascorbate and aldarate metabolism.
References.
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13900287 | Glucuronolactone reductase | In enzymology, a glucuronolactone reductase (EC 1.1.1.20) is an enzyme that catalyzes the chemical reaction
L-gulono-1,4-lactone + NADP+ formula_0 D-glucurono-3,6-lactone + NADPH + H+
Thus, the two substrates of this enzyme are L-gulono-1,4-lactone and NADP+, whereas its 3 products are D-glucurono-3,6-lactone, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is L-gulono-1,4-lactone:NADP+ 1-oxidoreductase. Other names in common use include GRase, and gulonolactone dehydrogenase. This enzyme participates in ascorbate and aldarate metabolism.
References.
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13900300 | Glycerate dehydrogenase | In enzymology, a glycerate dehydrogenase (EC 1.1.1.29) is an enzyme that catalyzes the chemical reaction
(D)-glycerate + NAD+ formula_0 hydroxypyruvate + NADH + H+
Thus, the two substrates of this enzyme are (R)-glycerate and NAD+, whereas its 3 products are hydroxypyruvate, NADH, and H+. However, in nature these enzymes have the ability to catalyze the reverse reaction as well. That is, hydroxypyruvate, NADH, and H+ can act as the substrates while (R)-glycerate and NAD+ are formed as products. Additionally, NADPH can take the place of NADH in this reaction.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is (R)-glycerate:NAD+ oxidoreductase. Other names in common use include D-glycerate dehydrogenase, and hydroxypyruvate reductase (due to the reversibility of the reaction). This enzyme participates in glycine, serine and threonine metabolism and glyoxylate and dicarboxylate metabolism.
Enzyme structure.
This class of enzyme is part of a larger superfamily of enzymes known as D-2-hydroxy-acid dehydrogenases.
Many organisms from "Hyphomicrobium methylovorum" to humans have some form of the glycerate dehydrogenase protein. There are currently several structures that have been solved for this class of enzyme including those for the two mentioned above with PDB access code 1GDH, D-glycerate dehydrogenase, and the human homolog Glyoxylate reductase/Hydroxypyruvate reductase (GRHPR), 2WWR.
These studies have yielded a better understanding of the structure and function of these enzymes. It has been shown that these proteins are homodimeric enzymes. This means that 2 identical proteins are linked forming one larger complex. The active site is found in each subunit between the two distinct α/β/α globular domains, the substrate binding domain and the coenzyme binding domain. This coenzyme binding domain is slightly larger than the substrate binding domain and contains a NAD(P) Rossmann fold along with the "dimerisation loop" which holds the two subunits of the homodimer together. In addition to linking the two proteins together, the "dimerisation loop" of each subunit protrudes into the active site of the other subunit increasing the specificity of the enzyme, by preventing the binding of pyruvate as a substrate. Hydroxypyruvate is still able to bind to the active site due to extra stabilization from hydrogen bonds with neighboring amino-acid residues.
Glyoxylate reductase/Hydroxypyruvate reductase.
Biological relevance.
Glyoxylate reductase/Hydroxypyruvate reductase (GRHPR) is the glycerate dehydrogenase found, predominantly in the liver, of humans encoded by the gene GRHPR. Under physiological conditions, the production of D-glycerate is favored over its consumption as a substrate. It can then be converted to 2-phosphoglycerate, which can then enter into glycolysis, gluconeogenesis, or the serine pathway.
As the name suggests, in addition to the glycerate dehydrogenase and hydroxypyruvate reductase activity, the protein also exhibits glyoxylate reductase activity. The ability of GRHPR to reduce glyoxylate to glycolate is found in other glycerate dehydrogenase homologs as well. This is important for the intracellular regulation of glyoxylate levels, which has important medical ramifications. As mentioned earlier, these enzymes have the ability to use either NADH or NADPH as the coenzyme. This gives them an advantage over other enzymes that can only use a single form of the coenzyme. Lactate dehydrogenase(LDH) is one such enzyme that directly competes with GRHPR for substrates and converts glyoxylate to oxalate. However, due to the relatively large concentration of NADPH compared to NADH under normal cellular concentration, the GRHPR activity is greater than that of LDH so the production of glycolate is dominant.
Medical relevance.
Primary hyperoxaluria is a condition that results in the overproduction of oxalate which combines with calcium to generate calcium oxalate, the main component of kidney stones. Primary Hyperoxaluria type 2 is caused by any one of several mutations to the GRHPR gene and results in the accumulation of calcium oxalate in the kidneys, bones, and many other organs. The mutations to GRHPR prevent it from converting glyoxylate to glycolate, leading to a build-up of glyoxylate. This excess glyoxylate is then oxidized by lactate dehydrogenase to produce the oxalate that is characteristic of hyperoxaluria.
References.
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13900325 | Sn-glycerol-1-phosphate dehydrogenase | Class of enzymes
In enzymology, a "sn"-glycerol-1-phosphate dehydrogenase (EC 1.1.1.261) is an enzyme that catalyzes the chemical reaction
sn-glycerol 1-phosphate + NAD(P)+ formula_0 glycerone phosphate + NAD(P)H + H+
The 3 substrates of this enzyme are sn-glycerol 1-phosphate, NAD+, and NADP+, whereas its 4 products are glycerone phosphate, NADH, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is sn-glycerol-1-phosphate:NAD(P)+ 2-oxidoreductase. This enzyme is also called glycerol-1-phosphate dehydrogenase [NAD(P)+].
G-1-P dehydrogenase is responsible for the formation of "sn"-glycerol 1-phosphate, the backbone of the membrane phospholipids of Archaea. The gene encoding glycerol-1-phosphate dehydrogenase has been detected in all the archaeal species and has not been found in any bacterial or eukaryal species. "sn"-glycerol 1-phosphate produced by this enzyme is the most fundamental difference by which Archaea and bacteria are discriminated.
The enzyme sn-glycerol-1-phosphate dehydrogenase, usually having 394 amino acids, was also identified in bacteria. More than 5700 sequences have been published in GenBank (September 2023) in a different bacteria, including such well-known ones as Bacillus subtilis (GenBank: AOR99168.1).
References.
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13900326 | Glycerol 2-dehydrogenase (NADP+) | Class of enzymes
In enzymology, a glycerol 2-dehydrogenase (NADP+) (EC 1.1.1.156) is an enzyme that catalyzes the chemical reaction
glycerol + NADP+ formula_0 glycerone + NADPH + H+
Thus, the two substrates of this enzyme are glycerol and NADP+, whereas its 3 products are glycerone, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is glycerol:NADP+ 2-oxidoreductase (glycerone-forming). Other names in common use include dihydroxyacetone reductase, dihydroxyacetone (reduced nicotinamide adenine dinucleotide, phosphate) reductase, dihydroxyacetone reductase (NADPH), DHA oxidoreductase, and glycerol 2-dehydrogenase (NADP+). This enzyme participates in glycerolipid metabolism.
References.
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13900345 | Glycerol-3-phosphate 1-dehydrogenase (NADP+) | In enzymology, a glycerol-3-phosphate 1-dehydrogenase (NADP+) (EC 1.1.1.177) is an enzyme that catalyzes the chemical reaction
sn-glycerol 3-phosphate + NADP+ formula_0 D-glyceraldehyde 3-phosphate + NADPH + H+
Thus, the two substrates of this enzyme are sn-glycerol 3-phosphate and NADP+, whereas its 3 products are D-glyceraldehyde 3-phosphate, NADPH, and H+.
This enzyme belongs to the family of oxidoreductases, specifically those acting on the CH-OH group of donor with NAD+ or NADP+ as acceptor. The systematic name of this enzyme class is sn-glycerol-3-phosphate:NADP+ 1-oxidoreductase. Other names in common use include glycerol phosphate (nicotinamide adenine dinucleotide phosphate), dehydrogenase, L-glycerol 3-phosphate:NADP+ oxidoreductase, glycerin-3-phosphate dehydrogenase, NADPH-dependent glycerin-3-phosphate dehydrogenase, and glycerol-3-phosphate 1-dehydrogenase (NADP+).
References.
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| https://en.wikipedia.org/wiki?curid=13900345 |
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