Differential Binding Models for Isothermal TitrationCalorimetry: Moving beyond the Wiseman Isotherm.

We present a set of model-independent differential equations toanalyze isothermal titration calorimetry (ITC) experiments. In contrastwith previous approaches that begin with specific assumptions aboutthe number of binding sites and the interactions among them (e.g.,sequential, independent, cooperative), our derivation makes more generalassumptions, such that a receptor with multiple sites for one typeof ligand species (homotropic binding) can be studied with the sameanalytical expression. Our approach is based on the binding polynomialformalism, and the resulting analytical expressions can be extendedto account for any number of binding sites and any type of bindinginteraction among them. We refer to the set of model-independent differentialequations to study ITC experiments as a differential binding model(DBM). To demonstrate the flexibility of our DBM, we present the analyticalexpressions to study receptors with one or two binding sites. TheDBM for a receptor with one site is equivalent to the Wiseman isothermbut with a more intuitive representation that depends on the bindingpolynomial and the dimensionless parameter c= K·MT, where Kis the bindingconstant and MTthe total receptor concentration.In addition, we show how to constrain the general DBM for a receptorwith two sites to represent sequential, independent, or cooperativebinding interactions between the sites. We use the sequential bindingmodel to study the binding interaction between Gd(III) and citrateanions. In addition, we simulate calorimetry titrations of receptorswith positive, negative, and noncooperative interactions between thetwo binding sites. Finally, we derive a DBM for titrations of receptorswith n-independent binding sites. [ABSTRACT FROM AUTHOR]