A chemical kinetic model for ligand binding to identical and independent binding sites in vivo

In living systems, hormones bind to receptor proteins that are continuously synthesized and degraded. Since these systems cannot be described by equilibrium binding equations, we present a chemical kinetic model for the binding of a hormone to a receptor with identical and independent binding sites in which synthesis and degradation occur. We have derived, from the model, equations that can be used to calculate the bound ligand concentration and the total protein concentration as a function of the free ligand concentration and time. These results show that the methods for experimental measurements, parameter estimation, interpretation of the parameters, and error analysis that are commonly used for equilibrium binding to identical and independent binding sites can be adapted for the analysis of steady-state binding data. The equations we derived for the steady-state ligand binding permit determination of the total receptor protein concentration and the binding affinity from experimental data. In contrast, if an equilibrium model were used, the values of these parameters would not necessarily approximate the true values. A useful approximation to the total receptor concentration as a function of time was found that requires only three of the five rate constants required for exact description by the model. This approximation is shown to be accurate in the biologically relevant range by using previously published parameters estimated from steroid binding data, and adding perturbations to include experimental error and variations among biological systems. When complexities exist, such that the model does not describe the data, these analyses aid in assessing the types of additional components and interactions that may exist.