Theory and Simulation of Diffusion-Controlled Michaelis−Menten Kinetics for a Static Enzyme in Solution

Park, Soohyung; Agmon, Noam

doi:10.1021/jp075941d

Cited by 42 publications

(44 citation statements)

References 60 publications

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“…It is possible to extend this theory by using the self-consistent relaxation time formalism that we developed and applied to simple reactions such as A + B ⇌ C and A + B ⇌ C + D (17), where it is exact at both short and long times. For a substrate with a single catalytic site, this formalism predicts that, as a result of diffusion, the Lineweaver-Burk plot becomes nonlinear at high concentrations (18,19). When there are multiple sites, the complexity of the theory increases dramatically, and thus there must be compelling reasons for carrying out such a generalization.…”

Section: Discussionmentioning

confidence: 99%

Diffusion modifies the connectivity of kinetic schemes for multisite binding and catalysis

Gopich

Szabó

2013

Proc. Natl. Acad. Sci. U.S.A.

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The simplest way to describe the influence of the relative diffusion of the reactants on the time course of bimolecular reactions is to modify or renormalize the phenomenological rate constants that enter into the rate equations of conventional chemical kinetics. However, for macromolecules with multiple inequivalent reactive sites, this is no longer sufficient, even in the low concentration limit. The physical reason is that an enzyme (or a ligand) that has just modified (or dissociated from) one site can bind to a neighboring site rather than diffuse away. This process is not described by the conventional chemical kinetics, which is only valid in the limit that diffusion is fast compared with reaction. Using an exactly solvable many-particle reaction-diffusion model, we show that the influence of diffusion on the kinetics of multisite binding and catalysis can be accounted for by not only scaling the rates, but also by introducing new connections into the kinetic scheme. The rate constants that describe these new transitions or reaction channels turn out to have a transparent physical interpretation: The chemical rates are scaled by the appropriate probabilities that a pair of reactants, which are initially in contact, bind rather than diffuse apart. The theory is illustrated by application to phosphorylation of a multisite substrate.multisite phosphorylation | escape and capture probabilities | splitting probability | diffusion-influenced rate constants | ultrasensitivity F or bimolecular reactions in solution, the formalism of chemical kinetics is valid only in the limit that the reactants come together many times before reacting. This means that the intrinsic reaction rate must be slower than the rate at which the partners diffuse together. Starting with the seminal work of Smoluchowski (1), it has been shown that the relative diffusion of the reactants, even in a macroscopically homogeneous solution, can lead to deviations from the predictions of conventional chemical kinetics. For example, for reversible reactions, the concentrations decay to their equilibrium values not exponentially, but rather as a power law (2, 3). However, for biochemically relevant concentrations, such effects are small. Even in the crowded environment of a cell, although the total concentration of all macromolecules is of course high, the concentrations of specific molecules that can react with each other are typically low. Although it is interesting and challenging to develop a theory of reversible diffusion-influenced reactions that is accurate at all times and concentrations, in many cases the concentrations are so low that all one has to do is to replace the phenomenological rate constants by their diffusioninfluenced values.In this paper we consider a class of reactions involving macromolecules with multiple sites where, even at low concentrations, it is not enough to replace the rate constants with diffusion-influenced ones. Our interest in such problems was stimulated by the important work of Takahashi et al. (4) on the role...

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Section: Discussionmentioning

confidence: 99%

Diffusion modifies the connectivity of kinetic schemes for multisite binding and catalysis

Gopich

Szabó

2013

Proc. Natl. Acad. Sci. U.S.A.

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“…For instance, the present results can be directly applied to investigate the field effect on Michaelis-Menten enzyme kinetics, where the reaction mechanism is given by E + S ES→ E+P. [39][40][41] For the case where the reaction mechanism has more complicated unimolecular conversion steps than Eqs. ͑2.1c͒ and ͑2.1d͒, we can utilize the present results with slight modifications.…”

Section: Discussionmentioning

confidence: 99%

Effect of an external field on the reversible reaction of a neutral particle and a charged particle in three dimensions. II. Excited-state reaction

Reigh

Shin

Kim

2010

The Journal of Chemical Physics

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Articles you may be interested inEffect of an external electric field on the diffusion-influenced geminate reversible reaction of a neutral particle and a charged particle in three dimensions. IV. Excited-state ABCD reaction J. Chem. Phys. 140, 064502 (2014); 10.1063/1.4864202Effect of an external electric field on the diffusion-influenced geminate reversible reaction of a neutral particle and a charged particle in three dimensions. III. Ground-state ABCD reaction J. Chem. Phys. 139, 194107 (2013) The excited-state reversible reaction of a neutral particle and a charged particle in an external electric field is studied in three dimensions. This work extends the previous investigation for the ground-state reaction ͓S. Y. Reigh et al., J. Chem. Phys. 129, 234501 ͑2008͔͒ to the excited-state reaction with two different lifetimes and quenching. The analytic series solutions for all the fundamental probability density functions are obtained with the help of the diagonal approximation. They are found to be in excellent agreement with the exact numerical solutions of anisotropic diffusion-reaction equations. The analytical solutions for reaction rates and survival probabilities are also obtained. We find that the long-time kinetic transition from a power-law decrease to an exponential increase can be controlled by the external field strength or excited-state decay rates or both.

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“…The units of k 1 and k 2 are [length] 3 [time] −1 . As it is well known [8,9], the probability distribution function of a pair of particles such as p(x A , x B , t | x A 0 , x B 0 ) where x A , x B , x A 0 and x B 0 are the position vectors of the particles at time t and t = 0, respectively, can be factored as p(x, t | x 0 )p(X, t | X 0 ), by using the transformation…”

Section: General Considerationsmentioning

confidence: 93%

“…Simulations based on the Green's functions of the diffusion equation (GFDE) have been widely used to study chemical reactions in solutions [1][2][3][4][5][6][7][8][9][10][11][12][13]. More recently, this approach has been used in radiation chemistry codes to simulate the radiolysis of water and aqueous solutions [14,15], chemical dosimeters [16] and to study of interaction of ligand molecules with receptors [17].…”

Section: Introductionmentioning

confidence: 99%

On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

Plante

Devroye

2015

Journal of Computational Physics

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Theory and Simulation of Diffusion-Controlled Michaelis−Menten Kinetics for a Static Enzyme in Solution

Cited by 42 publications

References 60 publications

Diffusion modifies the connectivity of kinetic schemes for multisite binding and catalysis

Diffusion modifies the connectivity of kinetic schemes for multisite binding and catalysis

Effect of an external field on the reversible reaction of a neutral particle and a charged particle in three dimensions. II. Excited-state reaction

On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

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