Extreme properties of the initial rate of the four-stage reaction of enzyme catalyzed ATP hydrolysis

Zhuk, P. F.; Karakhim, S. O.

doi:10.1007/s10910-021-01262-2

Cited by 2 publications

(10 citation statements)

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“…We have previously shown [19,45] that for other partial mechanisms through which enzyme catalysed hydrolysis of ATP can occur, the initial rate can increase monotonously with increasing initial reactant concentration until it reaches the maximum limiting level. In such cases, as will be shown later, the initial rate may increase hyperbolically (i.e., slower than the concentration) or sigmoidally (i.e., faster than the concentration) (over the entire reactant concentration range).…”

Section: Logarithmic Coordinatesmentioning

confidence: 99%

“…Since reactions proceeding by the mechanism (1.4) are characterized by kinetics with maxima rather than saturation, it is impossible to apply the Hill equation to such kinetic data. Earlier, we published an article [45] where we investigated the kinetics of the ATP hydrolysis reaction, which proceeds according to the following mechanism: The concentration of the activator varied in the range x 2 = 1 . 10 -7 -1 .…”

Section: Linearization Of Sigmoid Kinetic Curves Using Hill's Equationmentioning

confidence: 99%

“…Conversely, the condition K 2 < K m holds for R5, but in this case there is a kinetics of the N = +1 has a solution with respect to x i , i = 1,2,3. As an example, consider the simplest casethe dependence v vs x 2 for the mechanism (7.2) that we investigated earlier [45].…”

Section: The Criterion For Sigmoiditymentioning

confidence: 99%

“…This happened in the study of mechanisms N 13, 15 and 17 (see the table in [19]), when in the course of computational experiments only hyperbolic dependencies of the initial rate on the concentrations of the substrate and activator were observed. After some time, it was discovered [45] that these mechanisms can also demonstrate kinetic dependencies of another kind -with a maximum point after which the initial rate decreases and goes to a plateau. Therefore, the results 8 obtained in the course of computational experiments can only be considered to be a plausible hypothesis, and not as a strictly proven statement.…”

Section: Introductionmentioning

confidence: 99%

“…= is one of the nine roots of the equation(8.1). Knowing 3 y = , it is possible to calculate 2 y = (see equation(3.6) in[45]), 4 y = and 6 y = (see equations (B.13) in Appendix B), the sum of which is 2 x = . Usually, in the case of sigmoid kinetics, there are two real, positive roots that make it possible to calculate the initial activator concentration at the point where2 v x N = +1: one of them leads to zero concentration, and the other to 2 x = .…”

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Two different types of kinetics, where the initial rate increases faster or slower than the reactant concentration, can coexist on bell-shaped kinetic dependencies

Zhuk

Karakhim

2022

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We have shown the possibility of mathematical analysis of complex biochemical reactions without simplifying assumptions regarding their parameters by investigating the mechanism of adenosine triphosphate (ATP) hydrolysis by the “basal” Mg2+-ATPase in which ATP (substrate), Mg2+ (essential activator) and MgATP (true substrate) compete for binding with the enzyme catalytic site. For this mechanism, we proved, using the quasi-steady state principle by Bodenstein, the existence and uniqueness of a quasi-steady state at any fixed parameters (initial reactant concentrations, positive reaction rate constants). On this basis, the definition of the initial reaction rate v as a function of the initial concentrations of ATP (x1), Mg2+ (x2), ATPase (x3) is given and the dependencies v vs xi are investigated. We proved that at fixed initial concentrations of any two reactants, the kinetic curve v vs xi has a unique maximum point. In different regions of the kinetic curve located before and after the maximum point, the initial rate may vary in different ways: in one region it can change more slowly than the reactant concentration, as in the case of hyperbolic dependencies, and in the other it can change much faster than the reactant concentration, as in the case of sigmoid dependencies, which is typical for regulatory enzymes. This initial rate behaviour causes the existence of four different types of bell-shaped kinetic curves. To quantify the degree of sigmoidity of kinetics, we used derivatives (d ln v)/(d ln xi) which allowed us to estimate the maximal velocity of the initial rate change. MSC codes: 92C45, 65H10

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Section: Logarithmic Coordinatesmentioning

confidence: 99%

Section: Linearization Of Sigmoid Kinetic Curves Using Hill's Equationmentioning

confidence: 99%

Section: The Criterion For Sigmoiditymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

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