This model simulates the competitive binding of two different enzymes which result in a similar product.

Description

This model represents the enzymatic conversion of a single substrate, S, to a single product, P by two competing enzymes. First a binding of the solute to an enzyme, E1 or E2, is achieved, which forms a substrate-enzyme complex, ES1 or ES2. 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 k₁₁ is the forward binding rate of S to E₁, k_-11 is the backwards reaction rate of E₁S dissociating to E₁ and S, k₂₁ is the forward reaction rate of E₁S forming E₁ and P, k_-21 is the reverse reaction rate of E₁ and P producing E₁S, k₁₂ is the forward binding rate of S to E₂, k_-12 is the backwards reaction rate of E₂S dissociating to E₂ and S, k₂₂ is the forward reaction rate of E₂S forming E₂ and P, and k_-22 is the reverse reaction rate of E₂ and P producing E₂S.

Equations

This reaction is governed by a system of four ODEs which describe the concentrations of the substrate, enzyme complex for enzyme 1 and enzyme 2 and product. The fifth and sixth equations to close the system are given by specifying the total amount of enzyme 1, E_1tot, and enzyme 2, E_2tot present which must be conserved. The initial conditions specify 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 and P binding to the enzymes and are given by:

where K_s1 is the equilibrium dissociation rate of S binding to E₁, K_p1 of P binding to E₁, K_s2 of S binding to E₂ and K_p2 of P binding to E₂.