## Effect of Substrate Concentration on Initial Velocity

Let us consider a series of experiments designed to see how the initial velocity of an enzyme reaction varies with the concentration of substrate (which is always much greater than that of the enzyme). Each of the smaller graphs in Figure 11.6 shows the result of one of these experiments. As we increase the substrate concentration, we find that at first the velocity increases with each increase in substrate concentration but that, as the substrate Figure 11.6. v0 measured in a number of reaction tubes (with [E] constant and always less than [S]) forms a hyperbolic curve when plotted as a function of substrate concentration.

concentration becomes larger, the increases in rate produced get smaller and smaller. We have already met the name of a curve of this type: it is a hyperbola. The initial velocity approaches a maximum value that is never exceeded. Reactions that show this sort of dependence on substrate concentration are said to show saturation kinetics.

How can we explain this? The reaction sequence can be simplified to

(we are using initial velocities so we can ignore any back reaction). The enzyme and substrate must collide in solution, and the substrate must bind at the enzyme's active site to form the ES complex. The chemical reaction then takes place within the ES complex, and finally the product is released. In experiments with higher and higher substrate concentrations, there is ever more ES present, and this increasing ES gives an increasing rate of product release. At very high substrate concentrations virtually all of the enzyme is present as ES, and the observed rate is limited by the ES ^ E + P step. Thus, as the substrate concentration increases, the reaction rate levels off as it approaches a maximal velocity called Vm or Vmax. We can define Vm as the limiting initial velocity obtained as the substrate concentration approaches infinity. It is the product of the catalytic rate constant kcat and the amount of enzyme present, that is, Vm = kcat [Etotal]. Having defined Vm, we now define the Michaelis constant, KM, as that substrate concentration that gives an initial velocity equal to half Vm.

The plot of v0 against [S] gives a hyperbolic curve that is described by the equation

where [S] is the substrate concentration. This is called the Michaelis-Menten equation after Maud Menten and Leonor Michaelis who propounded a general theory of enzyme action in 1913. The Michaelis constant KM is the substrate concentration that gives an initial velocity numerically equal to half of Vm. Another way of looking at this is to say that if the enzyme is saturated with substrate, then the rate of reaction will be Vm, while at a substrate concentration giving an initial velocity of 72 Vm the enzyme is half saturated with substrate. A small value of KM means that the enzyme has a high affinity for the substrate.