Analysis of ligand-binding data without knowledge of bound or free ligand molar concentration

A method is proposed to set the parameters in a nonlinear regression procedure to determine the equilibrium dissociation constant (Kd) and the high affinity receptor concentration (Bmax) of systems consisting of one ligand, one high affinity receptor, and n low affinity binding sites. This method is suitable when neither bound or free ligand formal concentrations nor the maximum of the binding signal can be deduced from the experimental data. The method makes use of (i) the abscissa of the first inflection point of the plot of any signal proportional to the binding of ligand to receptors versus the logarithm of the total ligand concentration, and (ii) the initial slope of the saturation curve plotted in direct coordinates. We first demonstrate that when such an inflection point exists, its abscissa lies between Bmax/2 + Kd(1 + d) and Bmax + 2Kd(1 + d), where d is a parameter representative of the binding to the low affinity sites. Second, we demonstrate that the initial slopes of two saturation curves in direct coordinates, where Bmax varies by a known factor, allows an estimation of the Bmax/Kd ratio, within certain limits. From these two sets of data it is subsequently possible to define a precise window for the values of both Bmax and Kd. The performance of the method has been evaluated in representative cases using Monte Carlo studies. The results establish conditions for the existence of an inflection point as well as the influence of low affinity binding, whether or not proportional to Bmax.