Modeling complex equilibria in isothermal titration calorimetry experiments: thermodynamic parameters estimation for a three-binding-site model.

Isothermal titration calorimetry (ITC) is a powerful technique that can be used to estimate a complete set of thermodynamic parameters (e.g., K(eq) (or ΔG), ΔH, ΔS, and n) for a ligand-binding interaction described by a thermodynamic model. Thermodynamic models are constructed by combining equilibrium constant, mass balance, and charge balance equations for the system under study. Commercial ITC instruments are supplied with software that includes a number of simple interaction models, for example, one binding site, two binding sites, sequential sites, and n-independent binding sites. More complex models, for example, three or more binding sites, one site with multiple binding mechanisms, linked equilibria, or equilibria involving macromolecular conformational selection through ligand binding, need to be developed on a case-by-case basis by the ITC user. In this paper we provide an algorithm (and a link to our MATLAB program) for the nonlinear regression analysis of a multiple-binding-site model with up to four overlapping binding equilibria. Error analysis demonstrates that fitting ITC data for multiple parameters (e.g., up to nine parameters in the three-binding-site model) yields thermodynamic parameters with acceptable accuracy.