Exponential function of chymotrypsin action.

Enzyme kinetics are usually described by the hyperbolic Michaelis-Menten equation, but they can also be described by the following exponential function: -dS/dt = Vm [1 - exp (-S/Km)]. The time-dependent decrease of the substrate (-dS/dt) is an exponential function of maximal velocity (Vm), the Michaelis constant (Km) and the actual substrate value (S). This exponential function is based on the assumption that the association of the substrate-enzyme complex is a concentration-dependent process, whereas the transformation of the substrate-enzyme complex is time-dependent. It can be shown that this exponential function is a more general solution of which the hyperbolic Michaelis-Menten equation is a special derivative under the conditions of low substrate (S) and high constant (Km) values. If the association process is time-dependent, the decline in substrate values will show a more concave curve. However, exponential functions in general are more concave than hyperbolic functions. Probably, therefore, the enzyme action of chymotrypsin could be described more appropriately by the present exponential function than by the conventional hyperbolic function.