Most biochemical reactions involve two or more substrates, often resulting in multiple products. An example is proteolysis, which involves two substrates (the polypeptide and water) and two products (the two fragments of the cleaved polypeptide chain).

When an enzyme binds two or more substrates and releases multiple products, the order of the steps becomes an important feature of the enzyme mechanism. Several classes of mechanisms include the following:

Random substrate binding - In this mechanism, either substrate can be bound first, though in many cases one substrate will be favored for initial binding, and its binding may promote the binding of the other. The general pathway is

The phosphorylation of glucose by ATP, catalyzed by hexokinase, appears to follow this mechanism, with some tendency for glucose to bind first.

Ordered substrate binding - This mechanism occurs when one substrate must bind before a second one can bind significantly. This mechanism is

Ordered substrate binding is often observed in oxidations of substrates by the coenzyme nicotinamide adenine dinucleotide (NAD⁺).

The "ping-pong" mechanism - This occurs when a catalytic sequence of events occurs, such as one substrate is bound, one product is released, a second substrate is bound, and a second product is released. This is shown as where E* is a modified form of the enzyme, often carrying a fragment of the first substrate, S1. A good example is the cleavage of a polypeptide chain by a serine protease, such as trypsin or chymotrypsin. The polypeptide is described here as S = A^.B, where A and B designate the C-terminal and N-terminal portions of the chain from the point of cleavage:

Here E*^.B and E*^.B^.H2O indicate covalent intermediates, as in Figure 11.13.

Kinetics of a Complex Reaction - For the cleavage of a substrate by a serine protease, such as chymotrypsin, the step

E*^.B + H2O -> E*^.B^.H2O cannot be analyzed. Since the concentration of water is essentially fixed in aqueous solution and is not a variable, the reaction can be written as

Steady state measurements in this case will be insufficient. The steady state velocity is given by

The enzyme obeys Michaelis-Menten kinetics, but kcat, KM, and Ks are defined as

kcat = k2k3/(k2 + k3)

KM = Ksk3/(k2 + k3)

Ks = k-1/k1

Thus, the Michaelis-Menten equation describes the velocity correctly, but the values of kcat and KM depend on the reaction mechanism. To obtain the individual rate constsants in such a case, measurements outside the steady state range must be employed. The kinetics of the hydrolysis of esters by chymotrypsin (the enzyme also works on esters) reveals a rapid concentration increase for a few minutes until about one molecule has been produced per enzyme molecule. Steady state production begins after that point (see Figure 11.18). The initial burst is called pre-steady state production. For ester hydrolysis, k3 is much smaller than k2. Thus, the acyl intermediate forms quickly on each enzyme molecule, with accompanying release of product A. After this period, however, more A can be formed only after each acyl intermediate breaks down and the enzyme becomes available again. The dissociation of the acyl intermediate is the rate-limiting step.

Faster measurement techniques, such as stopped-flow methods, allow measurement of the rate of formation of the ES complex. Measurements of the decay of the acyl intermediates after substrate is exhausted provide k3. Combinations of these methods can be used to obtain all of the constants in equation 11.34. Example rate constants for hydrolysis of two N-acyl amino acid esters by chymotrypsin are given in Table 11.3.