Stochastic Simulation of Ligand–Receptor Interaction

We have developed an algorithm for the stochastic simulation of ligand–receptor interactions based on 10⁴–10⁵fictitious binding sites. Reversible receptor binding was simulated by alternate random selection of sites, the first selection resulting in “occupation” if the selected site was “free,” the second selection resulting in “dissociation” if the selected site was “occupied.” We show that the mathematical formalism of mass action kinetics is predicted on purely statistical grounds. The model was extended by the introduction of two further selections, simulating a conformational change in the ligand–receptor complex (“receptor isomerization model”). All random selections were gauged separately by “probability barriers,” taking the place of macroscopic kinetic rate constants. Simulation of gradual increases and gradual decreases of the fraction of occupied fictitious binding sites in the receptor isomerization model, using various combinations of “rate constants,” resulted in biexponential time dependencies, in agreement with predictions from the integrated rate equations. Stochastic simulation of molecular processes is a powerful and versatile technique, providing the researcher with a means of studying mechanisms of increasing complexity.