Chaos and control in mass-action binding of endogenous compounds

Endogenous compounds, such as hormones and neurotransmitters, interact with cellular receptors in controlled reactions governed by the mass-action law. Autoreceptors, a subset of the receptor pool, when activated by the endogenous ligand, result in a negative feedback that reduces the further release of ligand. This paper discusses and illustrates this control system when the concentrations (free and bound) are near or slightly beyond the limits of effective feedback control. Specifically, a forced periodic input function, simulating periodic release of the ligand, is used in the simulation of this controlled binding reaction in which a parameter representing the upper limit of control is varied. The solution of the system differential equations, representing free and bound ligand, is shown to pass from periodic to chaotic as the parameter is varied.