12.3.6.1—
Allosteric Enzymes

Before 1956, the kinetics of numerous enzymes were shown to follow the rate law of Michaelis and Menten giving a hyperbolic plot of v against S . An examination of enzymes which were known to be subject to feedback regulation showed that in some cases the relationship between v and S was sigmoid. In other cases the addition of a feedback inhibitor led to a change from a hyperbolic to a sigmoid relationship.

Figure 12.7
Illustration of the Monod model of an allosteric enzyme.

Monod et al., (1965) proposed a simple model to account for the observed kinetics in which they took account of the observation that allosteric enzymes are composed of subunits. They assumed that the protein subunits were arranged in such a way that they occupy equivalent positions so that the enzyme must have at least one axis of symmetry. They further assumed two interconvertible states—R and T—each maintaining the symmetry principle. A simple illustration of the model is given in Fig. 12.7 based on the symbols used by Koshland (1970). The reader is referred to the original article by Monod et al., (1965) for the derivation of the rate law. However a consideration of the illustration leads to a basic understanding of the underlying causes of sigmoid kinetics. Two types of allosteric behaviour may be distinguished—one the variable K system in which the two states of the enzyme have different affinities for the substrate, the other, the variable V system in which the R state is catalytically more active (Fig. 12.8).

Figure 12.8
Relationship between v  and s.
(A) a variable K  system; (B) a variable V  system.

Variable K Systems

In the variable K system, the R form is assumed to have a higher affinity for S than the T form of the enzyme. If in the absence of ligands, the equilibrium favours the T form then increasing concentrations of S will shift the equilibrium towards the R state giving sigmoid v against S plots. Another way of looking at this situation is to imagine that the interconversion of the R and T forms can be blocked and the enzyme isolated as the R or T form. The T form would give a normal Michaelis-Menten curve with a high Km^{(T )} and the R form would also give a Michaelis-Menten curve but with a low Km^{(R )} . Allowing R and T to be interconvertible allows Km to vary.

If an activator binds preferentially to the R state it will tend to put the enzyme entirely in the R state and so remove the sigmoidicity of the v against S plot. Similarly if an inhibitor binds preferentially to the T form it will increase the sigmoidicity.

Variable V Systems

In the variable V system the R form is assumed to be catalytically more active than the T form though both forms have the same affinity for the substrate so that the v/S plot is hyperbolic in the presence or absence of activators and inhibitors. An activator is assumed to have a greater affinity for the R form than for the T form whilst the reverse holds for an inhibitor.