Comment on “Thermodynamic Trajectory of Enzyme Evolution”

Bulletin of Mathematical Biology, 2012

Biochemical and Biophysical Research Communications, 1977

Frieden [Biochem. Biophys. Res. Commun. (1976) 68, 914-917] recently identified limitations on using initial velocity data to distinguish certain ordered and random mechanisms. He found that the rapid equilibrium ordered mechanism with EB and EP abortive complexes cannot be distinguished from the random addition case, except by equilibrium exchange measurements. Reexamination of the rapid equilibrium assumption clearly demonstrates, however, that isotope exchange methods are also ineffective. Nonetheless, it is demonstrated that the rapid equilibrium assumption does not hold when the kca t exceeds 30-50 sec-l. Thus combined use of initial rates and isotope exchange approaches offer reliable tests for rigorously defining the mechanism of many, and possibly most, enzymes.

2008

We develop a uniform theory for the many-particle diffusion-control effects on the Michaelis-Menten scheme in solution, based on the Gopich-Szabo relaxation-time approximation (Gopich, I. V.; Szabo, A. J. Chem. Phys. 2002, 117, 507). We extend the many-particle simulation algorithm to the Michaelis-Menten case by utilizing the Green function previously derived for excited-state reversible geminate recombination with different lifetimes (Gopich, I. V.; Agmon, N. J. Chem. . Running the simulation for representative parameter sets in the time domain and under steady-state conditions, we find poor agreement with classical kinetics but excellent agreement with some of the modern theories for bimolecular diffusion-influenced reactions. Our simulation algorithm can be readily extended to the biologically interesting case of dense patches of membrane-bound enzymes. † Part of the "Attila Szabo Festschrift".

Michaelis and Menten's mechanism for enzymatic catalysis is remarkable both in its simplicity and its wide applicability. The extension for reversible processes, as done by Haldane, makes it even more relevant as most enzymes catalyze reactions that are reversible in nature and carry in vivo flux in both directions. Here, we decompose the reversible Michaelis-Menten equation into three terms, each with a clear physical meaning: catalytic capacity, substrate saturation and thermodynamic driving force. This decomposition facilitates a better understanding of enzyme kinetics and highlights the relationship between thermodynamics and kinetics, a relationship which is often neglected. We further demonstrate how our separable rate law can be understood from different points of view, shedding light on factors shaping enzyme catalysis.

Physical Chemistry Chemical Physics, 2014

Simulations of the enzymatic dynamics of a model enzyme containing multiple substrate binding sites indicate the existence of diffusional correlations in the chemical reactivity of the active sites. A coarsegrain, particle-based, mesoscopic description of the system, comprising the enzyme, the substrate, the product and solvent, is constructed to study these effects. The reactive and non-reactive dynamics is followed using a hybrid scheme that combines molecular dynamics for the enzyme, substrate and product molecules with multiparticle collision dynamics for the solvent. It is found that the reactivity of an individual active site in the multiple-active-site enzyme is reduced substantially, and this effect is analyzed and attributed to diffusive competition for the substrate among the different active sites in the enzyme. 2 Model for the enzymatic system Mesoscopic models of an enzymatic system, where the enzyme was represented as a network of beads, the substrate and product molecules were structureless particles that interact with the enzyme through intermolecular potentials, and the substrate, product and chemically inert solvent molecules interacted among themselves by multiparticle collision (MPC) dynamics, 18,19 have been described earlier. 14,15 In this investigation we employ a variant of such models where the substrate

Biochemical Journal, 2006

Biochimica et Biophysica Acta (BBA) - Enzymology, 1978

As the kinetic behavior of bound enzymes is frequently affected by substrate diffusion between the bulk solution and the catalytic sites, a fast and simple method is proposed to detect and, subsequently, to remove diffusion effects on measured enzymic activities. The procedure makes use of the effectiveness factor concept and essentially involves the direct determination on two diagrams of the magnitude of both external and internal diffusion limitations. It requires a prior estimation of the volume and external surface area of the matrix, of the substrate external transport coefficient and internal diffusivity, and of the intrinsic Michaelis constant of the bound enzyme. However, it does not necessitate the knowledge of the quantity of bound enzyme. The two basic graphs have been calculated for Michaelis-Menten kinetics. They can also be used to evaluate diffusional effects on two-substrate reactions, as illustrated with previously published data.

Journal of Histochemistry & Cytochemistry, 1982

2012

The basis of enzyme kinetic modelling was established during the early 1900’s when the work of Leonor Michaelis and Maud Menten produced a pseudo-steady state equation linking enzymatic catalytic rate to substrate concentration (Michaelis & Menten, 1913). Building from the Michaelis-Menten equation, other equations used to describe the effects of modifiers of enzymatic activity were developed based on their effect on the catalytic parameters of the Michaelis-Menten equation. Initially, inhibitors affecting the substrate affinity were deemed competitive and inhibitors affecting the reaction rate were labelled non-competitive (McElroy 1947). These equations have persisted as the basis for inhibition studies and can be found in most basic textbooks dealing with the subject of enzyme inhibition. Here the functionality of the competitive and non-competitive equations are examined to support the development of a unified equation for enzymatic activity modulation. From this, a modular appr...