Ligand-binding distributions in biopolymers

The probability distribution that a biopolymer has n ligands bound to it ca n be determined from the ligand-binding curve that gives the average number of ligands bound as a function of free-ligand concentration in solution. O ne fits the binding curve as a function of ligand concentration locally to an expansion in the ligand concentration. The expansion coefficients can be turned into moments of the ligand-binding distribution function which, usi ng the maximum-entropy method, gives an accurate construction of the entire ligand-binding distribution function. A linear expansion gives two moments of the distribution while a cubic expansion gives four. In many cases two moments are sufficient to give a very accurate distribution function. The m ethod is exactly analogous to the use of heat capacity data as a function o f temperature to construct the enthalpy probability distribution. As with t he case of the enthalpy distribution applied to proteins, knowledge of four moments of the distribution function is sufficient to resolve bimodal beha vior in the distribution function. Several examples using model systems tha t involve independent units, cooperative units, and ligand-induced conforma tional changes (illustrating bimodal behavior) are given. We then examine l iterature data for the titration of ribonuclease and, using our method of m oments, resolve all 30 average proton binding constants for the molecule. ( C) 2000 American Institute of Physics. [S0021-9606(00)50335-3].