Parameter estimation for a two-site cooperative binding model. (A) Diagram of a model that assumes two binding sites with microscopic association constants K_I and K_II, and cooperativity factor F. (B) Two parameter sets with very different values yield identical simulated binding curves. Parameter set A: {K_I, K_II, F } = {500 µM⁻¹, 500 µM⁻¹, 1}; parameter set B: {K_I, K_II, F } = {997.5 µM⁻¹, 2.5 µM⁻¹, 100}. For parameters A, the binding sites have identical affinity and weak cooperativity, whereas for parameters B, the binding sites have distinct affinities and strong positive cooperativity. (C) Log-error surface of a region of the F-K_II parameter space. The curve generated from parameters A was used as a reference curve. Binding curves were calculated for various points in the parameter space, and the total error between the two curves was computed. Areas of lighter shading correspond to areas of less error. The minimum error estimate of the parameters defines a curve through the parameter space and not a point estimate. (D) MCMC samples drawn from the joint posterior distribution of K_I and F. The curved structure of the posterior distribution indicates that the model’s parameters are not identifiable using this binding data.