Monte Carlo simulation of error propagation in the determination of binding constants from rectangular hyperbolae. 2. Effect of the maximum-response range

Many processes dictated by chemical equilibria can be described by rectangular hyperbolae. Fitting chemical responses to rectangular hyperbolas also allows the binding constants for these equilibria to be estimated. Unfortunately, the propagation of error through the different methods of estimating the binding constants is not well understood. Monte Carlo simulations are used to assess the accuracy and precision of binding constants estimated using a nonlinear regression method and three linear plotting methods. The effect of the difference between the physical response of the uncomplexed substrate and the response of the substrate-ligand complex (i.e., the maximum-response range) was demonstrated using errors typical for a capillary electrophoresis system. It was shown that binding constant estimates obtained using nonlinear regression were more accurate and more precise than estimates from when the other regression methods were used, especially when the maximum-response range was small. The precision of the nonlinear regression method correlated well with the curvature of the binding isotherm. To obtain a precise estimate for the binding constant, the maximum-response range needed to be much larger (over 70 times larger for the conditions used in this experiment) than the error present in individual data points.