Enzymes are proteins that catalyze organic reactions occurring in biological systems. Most of them are "globular" proteins, meaning they are folded into tightly packed conformations.

Typical characteristics ascribed to enzymes:

• Substantial rate enhancements compared to chemical systems

• Substrate specificity for either
  • single substrates, or

  • closely related groups of substrates

• Stereospecificity: action upon a single stereoisomer or production of a single stereoisomer, or both

• Reaction specificity: catalysis of only the intended reaction with no wasteful by-products

We now know that not all of these are valid descriptors of all enzymes.

To determine rate enhancements, we need two things:

• a description of the rates of enzyme catalyzed reactions;

• estimates of rates for the uncatalyzed reactions.

Enzyme reaction rates typically are described with the following model:

The enzyme and its substrate associate, reaction occurs, and the product is released.

The second step is shown as irreversible because most kinetic measurements with enzymes are made in the very early stages of reaction, before significant quantities of product are present.

The equation describing the kinetics of this system can be derived in a variety of ways; we will simply present it, since your text has all the details:

The expression in this form was first derived by Leonor Michaelis and Maud Menten, and therefore is known as the Michaelis-Menten equation.

• The rate of reaction measured as described, in the early stages of reaction, is n_o

• V_max is the rate achieved when the enzyme is saturated with substrate
  • That is, each molecule of enzyme has a substrate bound, and the addition of more substrate therefore cannot increase the rate.

  • Under these saturating conditions, k_cat = V_max/[E]_total, and represents the number of catalytic events per second per active site. It is sometimes called the "turnover number".

• K_m, the Michaelis constant (why not the Menten constant?) can be shown to be k_-1 + k_cat / k₁

• If k_cat is much smaller than either k₁ or k_-1, it can be ignored, and K_m then becomes the equilibrium constant for complex formation

• Depending upon the stage of reaction, either k_cat or k_cat/K_m is used to describe the rate of reaction of a particular enzyme-substrate pair.

Judging the rate acceleration provided by enzymatic catalysis is not an easy game, since many biochemical reactions do not proceed at measureable rates under physiological conditions in the absence of enzymes.

Richard Wolfenden and his group at UNC Chapel Hill have devoted much effort in recent years to measuring experimentally rates that can be extrapolated to those expected at physiological pH and temperature

• For example, J. Am. Chem. Soc, 1998, 120, 6814; 1999, 121, 7419; 2000, 122, 11507; Science, 1995, 267, 90; Chem. Rev., 2006, 106, 3379; Proc. Nat. Acad. Sci., 2006, 103, 4052.

Some of his results on the rates of uncatalyzed reactions are summarized in the Figure below: