An explicit formulation approach for the analysis of calcium binding to EF-hand proteins using isothermal titration calorimetry.

We present an improved and extended version of a recently proposed mathematical approach for modeling isotherms of ligand-to-macromolecule binding from isothermal titration calorimetry. Our approach uses ordinary differential equations, solved implicitly and numerically as initial value problems, to provide a quantitative description of the fraction bound of each competing member of a complex mixture of macromolecules from the basis of general binding polynomials. This approach greatly simplifies the formulation of complex binding models. In addition to our generalized, model-free approach, we have introduced a mathematical treatment for the case where ligand is present before the onset of the titration, essential for data analysis when complete removal of the binding partner may disrupt the structural and functional characteristics of the macromolecule. Demonstration programs playable on a freely available software platform are provided. Our method is experimentally validated with classic calcium (Ca(2+)) ion-selective potentiometry and isotherms of Ca(2+) binding to a mixture of chelators with and without residual ligand present in the reaction vessel. Finally, we simulate and compare experimental data fits for the binding isotherms of Ca(2+) binding to its canonical binding site (EF-hand domain) of polycystin 2, a Ca(2+)-dependent channel with relevance to polycystic kidney disease.