A Mathematical Model for Ligand Potency in the HCN2 Channel

Binding of cAMP and cGMP to a C-terminal region shifts the activation curve of hyperpolarization-activated cyclic nucleotide-gated (HCN) channel to less negative voltages. However, how the potency of cyclic nucleotides on the HCN channel is determined at the molecular level is not known. A major challenge for understanding ligand sensitivity of the activation curve in HCN channels, as well as in ligand-gated ion channels in general, is to obtain a relevant measure of binding affinity directly by experiment. Here, we develop a mathematical model for the HCN2 channel that incorporates negative cooperativity and binding affinities obtained by isothermal titration calorimetry (ITC), and apply this model to existing gating and mutagenesis data. ITC was carried out using a region of the HCN2 C-terminus that naturally forms a tetramer at higher concentrations and, as we have found previously, results in binding affinities which suggest negative cooperativity. The mathematical model captures the relation between the shift in the activation curve and the concentration of ligand and, remarkably, predicts this relation for a subset of mutants with single-point amino acid substitutions in the binding site. Our results suggest that ligand potency for the full-length HCN2 channel in the plasma membrane s determined by negative cooperativity and asymmetric effects on structure and channel opening.