Lecture 21. Enzyme kinetics

Friday 28 October 2016

Enzyme kinetics and the Michaelis-Menten equation. Kinetic parameters V_max and K_M. Models for bisubstrate reactions.

Reading: VVP4e - Ch.12, pp.355-367.

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Summary

Enzyme kinetics catalytic principles, reaction coordinate diagrams, mechanistic models, rate constants and kinetic parameters.

The Michaelis-Menten equation describes a hyperbolic initial rate vs substrate concentration curve. Two parameters, accessible experimentally, K_M and V_max describe the hyperbolic curve.

We note that from an experimental standpoint, k_cat and k_cat/K_M are the fundamental parameters. The turnover number, k_cat, is measured under conditions in which the enzyme is saturated with substrate (very high [S] or "V_max" conditions), while k_cat/K_M is best measured at low substrate concentrations (where [S] << K_M, which we can call "V/K" conditions).

We discuss the range of values observed for both K_M and k_cat, also noting the distinction between high turnover number (high k_cat) and relative rate enhancement (high k_cat/ k_uncat) of an enzyme-catalyzed reaction over the uncatalyzed rate for the same reaction. Recall the key concept from this chapter: Enzymes achieve such tremendous acceleration of reaction rates by lowering the free energy of activation for the reaction. Exactly how enzymes stabilize the transition state is a fascinating area of study. The quantity k_cat/K_M was then discussed as a measure of specificity (in comparing the efficiency with which an enzymes acts on a series of closely related substrates) and as a criterion for so-called "catalytic perfection" in which k_cat/K_M approaches a theoretical upper limit (the diffusion-controlled limit).

Moving beyond kinetic parameters, we spend some time considering mechanistic schemes involving reactions with multiple substrates, e.g. an enzyme catalyzing a reaction such as A + B <—> P + Q. The text discusses sequential (both the ordered sequential and random sequential mechanisms) and double-displacement ("ping-pong") schemes. We also see that in some cases enzymes display non-Michaelis-Menten kinetics and that a primary example of this is the case where the initial velocity vs. substrate concentration curve is sigmoidal rather than hyperbolic. This behavior occurs wit h multisubunit enzymes that have allosteric properties arising from cooperativity between subunits.