A generalized McGhee–von Hippel method for the cooperative binding of different competing ligands to an infinite one-dimensional lattice

Two novel algorithms have been derived for competitive binding of different ligands to an infinite lattice of binding sites. The algorithms are general with no limitation regarding the number of possible interacting ligand species or to lattice or ligand polarity. The first algorithm provides a generalization of the equations of McGhee and von Hippel for the calculation of free ligand concentrations as a function of binding densities. The second algorithm, a Newton–Raphson procedure with analytical derivatives, calculates the binding isotherm as a function of the total concentrations of ligands and binding sites. These new methods, based on efficient matrix power iterations, should in many cases eliminate the need for Monte Carlo simulations in the treatment of complex binding systems.