Modifiers of enzyme-catalyzed reactions call have various types of effects oil the velocity, but the most important effect is that they provide multiple pathways to products. The rapid-equilibrium kinetic effects of modifiers ire explored for the enzyme-catalyzed reaction A -products. When a single molecule of modifier X is bound, the mechanism involves three independent equilibrium expressions and two rate constants. But when two molecules of X are bound are bound in two reactions, there are five independent equilibria and three paths to products. The advantages of using a computer to derive rapid-equilibrium rate equations are that more complicated rate equations Call be derived and the kinetic parameters can be estimated using the minimum number of velocity measurements. The mechanism with three paths to products is of special interest because the effects of cooperativity can be Studied. Thermodynamic cycles can be used to estimate additional kinetic parameters.