Role of substrate unbinding in Michaelis–Menten enzymatic reactions

Abstract

The Michaelis-Menten equation provides a hundred-year-old prediction by which any increase in the rate of substrate unbinding will decrease the rate of enzymatic turnover. Surprisingly, this prediction was never tested experimentally nor was it scrutinized using modern theoretical tools. Here we show that unbinding may also speed up enzymatic turnover-turning a spotlight to the fact that its actual role in enzymatic catalysis remains to be determined experimentally. Analytically constructing the unbinding phase space, we identify four distinct categories of unbinding: inhibitory, excitatory, superexcitatory, and restorative. A transition in which the effect of unbinding changes from inhibitory to excitatory as substrate concentrations increase, and an overlooked tradeoff between the speed and efficiency of enzymatic reactions, are naturally unveiled as a result. The theory presented herein motivates, and allows the interpretation of, groundbreaking experiments in which existing single-molecule manipulation techniques will be adapted for the purpose of measuring enzymatic turnover under a controlled variation of unbinding rates. As we hereby show, these experiments will not only shed first light on the role of unbinding but will also allow one to determine the time distribution required for the completion of the catalytic step in isolation from the rest of the enzymatic turnover cycle.single enzyme | enzyme kinetics | renewal theory E very enzymatic reaction is composed out of two basic steps:(i) the reversible binding of a substrate molecule to the enzyme and (ii) a catalytic step which gives rise to the formation of the product (1). Controlled variation of the effective binding rate to a free enzyme is attained by altering the concentration of the substrate. The rate of product formation, also known as the turnover rate, can then be measured as a function of this concentration to show a characteristic hyperbolic dependence (2-5). The Michaelis-Menten equation is used to rationalize this observation and interpret the results (2, 6).Recent advancements in single-molecule spectroscopy have gradually made it possible to follow the stochastic activity of individual enzymes over extended periods of time (7-19). Interestingly, the hyperbolic dependence of turnover on substrate concentration remains valid even at the single-molecule level (12,14). From a theoretical perspective, this result was initially puzzling but is now considered almost universal in the sense that it can be shown to hold under a wide range of modeling assumptions (20, 21). One can thus safely say that the role of binding in Michaelis-Menten enzymatic reactions is well understood. In this paper, we consider the role of unbinding.Rapid advancements in the single-molecule technological front imply that the adaptation of existing single-molecule manipulation techniques (12-14, 18, 22, 23) to allow the measurement of enzymatic turnover under a controlled variation of unbinding rates is now within reach. Single-molecule approaches to biomolecular inter...

Michaelis-Menten reaction scheme as a unified approach towards the optimal restart problem

“…arXiv:1509.05071v4 [cond-mat.stat-mech] 24 Nov 2015 [26], and the question of what can be said about it in the general case remained open. In this letter, we address the optimal restart problem within the framework of the MMRS.…”

“…Renewal theory can then be invoked to provide a generalized mathematical treatment of the MMRS [26]. A completely general analysis of the turnover-unbinding interplay is then very hard, but progress can be made if one narrows down to the case of exponentially distributed unbinding times [26,33]. Letting k of f denote the unbinding rate (assumed to be independent of the catalytic process), and f cat (t) the probability density function (PDF) of a generally distributed catalysis time T cat , it is possible to show that [26,33] (2) is the possibility of restart-facilitated-turnover, i.e., a regime in which unproductive unbinding events lead to accelerated turnover [26].…”

Reaction–diffusion with stochastic decay rates

“…This immediately yields a Michaelis-Menten scheme capable of handling heterogeneous catalysis via diffusion following unbinding events. The challenge of understanding the interplay of transport and Michaelis-Menten-like processes in cellular environments [9,59] is a particularly promising candidate for such a Michaelis-Menten-CTRW approach, given that macromolecular crowding in cells may lead to both CTRW-like subdiffusion [36,62] and modified binding dynamics [63][64][65].…”

Dependence of the Enzymatic Velocity on the Substrate Dissociation Rate

“…Arguably the simplest generalization of this scheme is to allow just the enzyme–substrate complex to have many conformations. Using the sophisticated probabilistic arguments, it has recently been shown 8–10 that if each and every conformation of the complex has the same dissociation rate constant, k off , and the conformations of free enzyme interconvert on a time scale that is much shorter than its mean lifetime, then the enzymatic velocity can be written as…”

“…Here f̂ cat ( k off ) is the Laplace transform of function $f_{\text{cat}}(t):{\hat{f}}_{\text{cat}}(k_{\text{off}})={\int }_0^{\infty }exp(-k_{\text{off}}t)f_{\text{cat}}(t)dt$, where f cat ( t ) is defined as the “probability density of the catalysis time.” 8 When f cat ( t ) = k cat exp(− k cat t ), eq 3 reduces to eq 2.…”