A simple generalized equation for the analysis of multiple inhibitions of Michaelis-Menten kinetic systems

The summation of the effects of two or more reversible inhibitors of various types on the initial velocity of enzyme systems obeying Michaelis-Menten kinetics is described by the the general relation: (formula: see text) wherein v1,2,3...n is the velocity of reaction in the simultaneous presence of n inhibitors, vi is the velocity observed in the presence of each individual inhibitor, and v0 is the velocity in the absence of inhibition. The derivation is based on the assumption that each enzyme species can combine with no more than one of the inhibitors (i.e. the inhibitors are mutually exclusive). The above relationship holds irrespective of the number of inhibitors, the type of inhibition (competitive, noncompetitive, or uncompetitive), or the kinetic mechanism (sequential or ping-pong) of the enzyme reaction under consideration. Deviations from this equality define synergism or antagonism of inhibitors depending on whether the value of the left side of the above equation is greater or smaller than the right, respectively. Knowledge of the kinetic constants for substrates and inhibitors is not required. If two or more inhibitors act independently (i.e. are not mutually exclusive), their combined effects are necessarily synergistic. Under certain circumstances, described in the text, mutually nonexclusive inhibitors obey the fractional velocity product relationship: v1,2,3...n/v0 = (v1/v0) x (v2/v0) x (v3/v0)...(vn/v0).