An analytic solution to the Monod-Wyman-Changeux model and all parameters in this model

Starting from the Monod-Wyman-Changeux (MWC) model (Monod, J., J. Wyman, and J. P. Changeux. 1965. J. Mol. Biol. 12:88–118), we obtain an analytical expression for the slope of the Hill plot at any ligand concentration. Furthermore, we derive an equation satisfied by the ligand concentration at the position of maximum slope. From these results, we derive a set of formulas which allow determination of the parameters of the MWC model (kR, C, and L) from the value of the Hill coefficient, nH, the ligand concentration at the position of maximum slope [( A]0), and the value of nu/(n-nu) at this point. We then outline procedures for utilizing these equations to provide a "best fit" of the MWC model to the experimental data, and to obtain a refined set of the parameters. Finally, we demonstrate the applicability of the technique by analysis of oxygen binding data for Octopus hemocyanin.