Cooperative ligand binding on multidimensional lattices: Bethe approximation

A binding isotherm for ligands on multidimensional lattices has been calculated in the Bethe approximation. In this lattice model, a single bound ligand is assumed to occupy a contiguous sequence of lattice sites in all possible configurations; interactions between neighboring bound ligands are included. This lattice model is equivalent to one used for treating polymer solutions; a configurational entropy of athermal polymer solutions has been utilized directly to represent bound ligands. Binding isotherms are examined for their dependences on lattice coordination numbers and the number of sites occupied by a single bound ligand. Critical conditions for phase transitions in single‐ligand‐species systems are also presented. The binding isotherm reported here can be applied to a wide variety of binding phenomena; it is exact for one‐dimensional cases, i.e., it reduces to the binding isotherm of McGhee and von Hippel [(1974) J. Mol. Biol. 86, 469–489] and should serve as a good approximation for higher‐dimensional binding phenomena.