Lecture 20 Summary

Review of kinetics principles - Chemical kinetics and rate equations. (12: 363-366)

Enzyme kinetics

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 a high turnover number (high k_cat) and the large rate enhancement (high k_cat/ k_uncat - compare Table 11.1, p.323 with Table 12.1 on p.371 in VVP3e.) 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.

Learning objectives

• Distinguish between "V_max" and "V/K" conditions .

Page updated 10-30-2010

References

1. Cornish-Bowden, A. Fundamentals of Enzyme Kinetics (Revised ed. 1999, Portland Press)
2. Fersht A. Structure and Mechanism in Protein Science (1999, WH Freeman and Co.)