Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels open more easily when cAMP or cGMP bind to a domain in the intracellular C-terminus in each of four identical subunits. How sensitivity of the channels to these ligands is determined is not well understood. Here, we apply a mathematical model, which incorporates negative cooperativity, to gating and mutagenesis data available in the literature and combine the results with binding data collected using isothermal titration calorimetry. This model recapitulates the concentration–response data for the effects of cAMP and cGMP on wild-type HCN2 channel opening and, remarkably, predicts the concentration–response data for a subset of mutants with single-point amino acid substitutions in the binding site. Our results suggest that ligand sensitivity is determined by negative cooperativity and asymmetric effects on structure and channel opening, which are tuned by ligand-specific interactions and residues within the binding site.