Analysis of protein ligand equilibria

The thermodynamics of calcium binding to thermolysin

Calcium binding isotherms were determined for thermolysin in the range pH 5.6-10.5, and from 5 to 45 degrees C. An extensive statistical analysis of the binding data suggests that at least two of the four binding sites bind Ca2+ with complete positive cooperativity and independently of the other two. Nonlinear regression analysis of the binding data was used to calculate cooperative (K1) and independent (K2) binding constants for the four calcium sites. Thermodynamic parameters obtained from a van't Hoff analysis indicate that calcium binding to both cooperative and independent sites is an entropy-driven process. At pH 7.0, delta H1 = 90.4 kJ/mol; delta H2 = 97.5 kJ/mol; delta S1 = 456 J K-1 mol-1; delta S2 = 262 J K-1 mol-1. These results are compared to those obtained for other calcium-binding proteins. An analysis of the pH dependence of the calcium binding constants indicates that the binding of four protons at the cooperative site and one to two protons at the independent sites, modulates the calcium affinity. This confirms an earlier structural assignment of the double-site as the locus of the two cooperatively binding Ca2+. Calcium binding to thermolysin is enhanced in the presence of an active site directed inhibitor, suggesting that there may be positive cooperativity between substrate and calcium binding.

Ligand binding and self-association of proteins

This review deals with the quantitative analysis of protein self-association and ligand binding when there is a signficant mutual influence of the two processes. The particular points of interest are the evaluation of the pertinent equilibrium constants and the prediction and interpretation of concentration profiles in transport experiments, including gel elution and sedimentation velocity. The case of dimertetramer equilibrium with four binding sites for ligand is considered in detail. Three representative experimental studies are described which deal with hemoglobin, phosphorylase b, and tubulin.

Ligand binding and self-association of phosphorylase b

The mutual influence of ligand binding and self-association has been examined for phosphorylase b in the presence of a series of small ligands. The stepwise equilibrium constants describing the mutual dependence have been evaluated and discussed in terms of possible molecular mechanisms.

A simple algorithm for the solution of the 'n X m' case of a binding equilibrium

Accurate estimates of the equilibrium concentrations in the non-interactive reaction of several ligands with several classes of binding sites with univalent stoichiometry can be rapidly obtained by a simple method of successive approximations on a programmable desk calculator.