Lecture 20. Enzyme kinetics

Wednesday 26 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

Review of chemical kinetics principles.

The hyperbolic initial rate vs. substrate concentration curve characteristic of the great majority of enzyme-catalyzed reactions can be modeled by the Michaelis-Menten equation, an equation with two parameters that we can determine experimentally, K_M and V_max. Bisubstrate reactions. (12: 366-376)

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).

See the enzyme kinetics page for full exposition, including reaction coordinate diagrams, mechanistic models, rate constants and kinetic parameters.

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 with multisubunit enzymes that have allosteric properties arising from cooperativity between subunits.