Location of critical points in the reaction velocity/concentration relationships predicted by the exponential model for a two substrate regulatory enzyme.

The two substrate exponential model for a regulatory enzyme (Ainsworth and Gregory, J. Theor. Biol., 75 (1978) 97-114) can be employed to describe non-hyperbolic relationships between the initial velocity of the catalysed reaction and the concentration of one substrate when the concentration of the second substrate is kept constant, v = f(A)B. The model equation for v = f(A)B predicts the possibility of a maximum, catastrophe and inflections but, because the equation is transcendental, it is not possible to locate the critical points by algebraic analysis. The paper describes an iterative computer program that has been devised to solve this problem.