Control and stability of ligand receptor interaction in the presence of a competitive compound

The law of mass action is almost universally applied to both endogenous ligands and drugs that interact with specific cellular receptors. The concentration, and hence the receptor binding, of a foreign drug molecule will depend on its pharmacokinetic properties, whereas an endogenous ligand is subject to intrinsic control since the concentration (z) remains within limits around an equilibrium level. We have previously examined this control for ligand-receptor interactions proceeding according to mass action in which the ligand is produced (rate F), eliminated exponentially (rate constant E) and controlled by a feedback function of receptor occupancy, phi (y), where y is the bound concentration. The current study examines the control of an endogenous ligand in the presence of a second compound (agonist or antagonist) that interacts with the same receptor. From a computer solution of the set of differential equations, illustrated in both time-plots and phase plane (y-z) plots, it is shown that if the second agent is a pure competitive antagonist the bound concentration of the endogenous agonist ligand may not decrease appreciably, even for large doses of the antagonist. Instead the level of binding depends on certain parameters of the control function. Further, the computer simulation shows how these parameters affect the time course of released ligand resulting from administration of an antagonist and the suppression of such release when the second compound is an agonist.