First-order reversible enzymatic reaction with binding of either substrate or product to enzyme and allows thermodynamic equilibrium.

Description

This model represents the enzymatic conversion of a single substrate, S, to a single product, P. First a binding of the solute to the enzyme, E, is achieved, which forms a substrate-enzyme complex, ES. The binding is followed by a reaction-release event, which yields the product and the enzyme. The entire binding-reaction-release sequence may be represented symbolically as

where k₁ is the forward binding rate of S to E, k_-1 is the backwards reaction rate of ES dissociating to E and S, k₂ is the forward reaction rate of ES forming E and P, and k_-2 is the reverse reaction rate of E and P producing ES.

Equations

This reaction is governed by a system of three ODEs which describe the concentrations of the substrate, enzyme complex and product. The fourth equation to close the system is given by specifying the total amount of enzyme present which must be conserved. The initial conditions given are that all of the substrate and no complex or product are present at time t=0. The system of equations are:

The backward reaction rates in this model are determined from the equilibrium dissociation rates of S binding to E and P binding to E and are given by:

where K_s is the equilibrium dissociation rate of S binding to E and K_p of p binding to E.