Inhibition of enzyme-catalysed reactions by excess substrate. A theoretical and Monte Carlo study of turning points in v(S) graphs.

Some difficulties associated with observing and defining substrate inhibition curves are discussed. Then a new method for measuring the steepness of substrate inhibition curves is derived and a parameter, lambda, is defined to measure the steepness of descent from a maximum or steepness of ascent from a minimum in v(S) plots. A mathematical theorem is presented to show how the magnitude of lambda is limited by the degree of the rate equation. Conditions for satisfactory Monte Carlo simulations of enzyme mechanisms are explored and the constraints necessary to generate v(S) curves with profiles in physiological ranges of substrate concentrations are investigated using 16 enzyme mechanisms. The probability of detecting substrate inhibition is estimated. It is shown that there exists a lower limit to the substrate concentration at which maxima can occur in v(S) plots but no upper limit and also that enzyme mechanisms can approach but never achieve the maximum steepness of descent possible for arbitrary rational functions with non-negative coefficients.