Quantum Mechanical Methods for Enzyme Kinetics

This review discusses methods for the incorporation of quantum mechanical effects into enzyme kinetics simulations in which the enzyme is an explicit part of the model. We emphasize three aspects: (a) use of quantum mechanical electronic structure methods such as molecular orbital theory and density functional theory, usually in conjunction with molecular mechanics; (b) treating vibrational motions quantum mechanically, either in an instantaneous harmonic approximation, or by path integrals, or by a three-dimensional wave function coupled to classical nuclear motion; (c) incorporation of multidimensional tunneling approximations into reaction rate calculations.[1]

The origins of enzyme kinetics

The equation commonly called the Michaelis–Menten equation is sometimes attributed to other authors. However, although Victor Henri had derived the equation from the correct mechanism, and Adrian Brown before him had proposed the idea of enzyme saturation, it was Leonor Michaelis and Maud Menten who showed that this mechanism could also be deduced on the basis of an experimental approach that paid proper attention to pH and spontaneous changes in the product after formation in the enzyme-catalysed reaction. By using initial rates of reaction they avoided the complications due to substrate depletion, product accumulation and progressive inactivation of the enzyme that had made attempts to analyse complete time courses very difficult. Their methodology has remained the standard approach to steady-state enzyme kinetics ever since.[2]

Enzyme kinetics at high enzyme concentration

We re-visit previous analyses of the classical Michaelis-Menten substrate-enzyme reaction and, with the aid of the reverse quasi-steady-state assumption, we challenge the approximation d[C]/dt ≈ 0 for the basic enzyme reaction at high enzyme concentration. For the first time, an approximate solution for the concentrations of the reactants uniformly valid in time is reported. Numerical simulations are presented to verify this solution. We show that an analytical approximation can be found for the reactants for each initial condition using the appropriate quasi-steady-state assumption. An advantage of the present formalism is that it provides a new procedure for fitting experimental data to determine reaction constants. Finally, a new necessary criterion is found that ensures the validity of the reverse quasi-steady-state assumption. This is verified numerically.[3]

Enzyme Kinetics, Past and Present

Enzymes catalyze biochemical reactions, speeding up the conversion from substrate to product molecules. One hundred years ago, Leonor Michaelis and Maud Leonora Menten studied the equation characterizing enzymatic rates (1). This landmark development in the quantitative description of enzymes has stood the test of time, and the Michaelis-Menten equation remains the fundamental equation in enzyme kinetics (2). Today, the quest for fundamental understanding of the working of enzymes continues with vigor at the single-molecule level as new experiments and theories emerge.[4]


On the Meaning of Km and V/K in Enzyme Kinetics

Most biochemistry textbooks describe V/K, or kcat/Km, as one of the fundamental kinetic constants for catalysis in enzymatic reactions and associate it with some measure of the rate of the chemical transformation of substrate into product. However, in the reactions of all enzymes except isomerases and mutases, V/K fails to encompass a complete turnover. Instead, it can be shown that V/K actually provides a measure of the rate of capture of substrate by free enzyme into a productive complex or complexes destined to form products and complete a turnover at some later time. Similarly, V or kcat provides a measure of the rate of release of product from the productive enzyme complexes that constitute capture. It is here suggested that the symbols V/K and kcat be replaced by kcap and krel, respectively, at least in the teaching of enzyme kinetics. Capture and release are equally necessary to generate a complete catalytic turnover, but they are determined by different things, and the proposed symbolism is less abstract than older alternatives. Used together, they provide a more accurate definition of the Michaelis constant, as Km = krel/kcap, which is the kinetic equivalent of the thermodynamic dissociation constant, Kd = koff /kon.[5]


Reference

[1] Gao, J. and Truhlar, D.G., 2002. Quantum mechanical methods for enzyme kinetics. Annual Review of Physical Chemistry, 53(1), pp.467-505.

[2] Cornish-Bowden, A., 2013. The origins of enzyme kinetics. FEBS letters, 587(17), pp.2725-2730.

[3] Schnell, S. and Maini, P.K., 2000. Enzyme kinetics at high enzyme concentration. Bulletin of mathematical biology, 62(3), pp.483-499.

[4] Xie, X.S., 2013. Enzyme kinetics, past and present. Science, 342(6165), pp.1457-1459.

[5] Northrop, D.B., 1998. On the meaning of Km and V/K in enzyme kinetics. Journal of Chemical Education, 75(9), p.1153.