Decomposing complex cooperative ligand binding into simple components: Connections between microscopic and macroscopic models

Cooperative ligand-binding curves may often appear deceptively featureless, yet the underlying microscopic models may be rather complex, and the connection between them is not intuitive. To address some of these issues, we have extended the framework of the decoupled sites representation (DSR), previously developed in the context of pH titration, to include cooperative ligand binding as well as multiple conformations and multiple ligands. The extended framework is based on general thermodynamic arguments and is applicable to both anti-cooperative and cooperative binding. It can be used to elucidate the connection between the experimentally observed binding curves and parameters of underlying microscopic models. It is demonstrated that any binding curve can be decomposed into simple standard components that permit a model-independent physical interpretation in terms of noninteracting (quasi) groups. A simple mathematical form of the DSR is proposed, that is well-suited for use in least-squares fitting of experimental binding curves; the fitting procedure produces an integer parameter indicative of the degrees of cooperativity possible in the system. A two-site example is worked out in detail. We demonstrate that the same macroscopic binding behavior observed experimentally can have qualitatively different origins at the level of the underlying microscopic mechanism. We also show that, in the absence of the microscopic model, it is not possible to draw a meaningful distinction between non-cooperative and anti-cooperative scenarios. We define a new measure of cooperativity and show that it is in many cases more adequate than the Hill coefficient when used to characterize complex binding curves. The extended DSR is applied to experimental data sets on oxygen binding to carp hemoglobin at different pHs, where the framework is used to interpret the degree of cooperativity in the system and provides an indication as to whether specific microscopic models are applicable.