K M, kcat, and kcat /K M

K M - The Michaelis constant, K M, is often associated with the affinity of the enzyme for substrate, but this is not always correct. A more accurate statement is that, for reactions obeying Michaelis-Menten kinetics, K M is a measure of the substrate concentration required for effective catalysis to occur. That is, an enzyme with a high K M requires a higher substrate concentration to achieve a given reaction velocity than an enzyme with a low K M. Table 11.1 lists values of K M, k cat, and k cat/K M for selected enzymes.

k cat - The Michaelis-Menten equation, V = V max[S]/(K M + [S]), can be rewritten as

> V = k cat[E]t[S] / ( K M + [S])

where V max = k cat[E]t. k cat incorporates the rate constants for all the reactions between ES and E + P in a multistep enzymatic process. For a two-step reaction, k cat = k 2. For more complex reactions, k cat depends on which steps in the process are rate-limiting.

k cat gives a direct measure of the catalytic production of product under optimum conditions (saturated enzyme). The units of k cat are seconds-1. The reciprocal of k cat can be thought of as the time required by an enzyme molecule to "turn over" one substrate molecule. Alternatively, k cat measures the number of substrate molecules turned over per enzyme molecule per second. Thus, k cat is sometimes called the turnover number. Some typical turnover numbers are shown in Table 11.1, as well.

k cat/K M - This ratio is often thought of as a measure of enzyme efficiency. Either a large value of k cat (rapid turnover) or a small value of K M (high affinity for substrate) makes k cat/K M large.

When [S] << K M (dilute solution), equation 11.27 becomes

> V (k cat/K M)[E][S]

Here, k cat/K M behaves as a second-order rate constant for the reaction between substrate and free enzyme. This ratio is important, for it shows what the enzyme and substrate can accomplish when abundant enzyme sites are available, and it allows direct comparison of the effectiveness of an enzyme toward different substrates. When an enzyme has a choice of two substrates, A or B, present at equal, dilute concentrations,

Table 11.2 shows that when an enzyme has different substrates on which it can work, the range of efficiencies may vary considerably. Note that for chymotrypsin the k cat/K M ratio varies 1-million fold.

As a second-order rate constant, k cat/K M has a maximum possible value, which is determined by the frequency with which enzyme and substrate molecules can collide. A reaction which attains such a velocity is said to be "diffusion-limited" because every encounter leads to reaction. If every collision results in formation of an enzyme-substrate complex, diffusion theory predicts that k cat/K M will attain a value of about 108 to 109 (mol/L)-1s-1. The enzymes carbonic anhydrase, fumarase, and triose phosphate isomerase actually approach this limit.

See also: Michaelis-Menten Kinetics, Analysis of Kinetic Data, Turnover Number