Simulation of association curves and 'Scatchard' plots of binding reactions where ligand and receptor are degraded or internalized.

Frequently during the course of binding to a receptor, ligand is degraded. In some preparations receptor is degraded. And with isolated cell preparations, ligand and/or receptor may be internalized. Here we present a mathematical model in which the binding and other reactions are combined. The resulting set of differential equations is solved numerically to simulate association curves and the resulting values of bound and free ligand are used to construct Scatchard plots. Where non-ideal conditions exist, the Scatchard plots are generally curvilinear. Dependence of this curvilinearity - on time of measurement of free and bound ligand, on degradation and internalization of ligand, and on degradation and internalization of receptor - is shown. Equilibrium constants derived from the Scatchard plots are generally incorrect but the derived receptor concentration is often correct. The simulations suggest experimental possibilities for distinction among the several side reactions in ligand-receptor binding systems.