Probability Fluxes and Transition Paths in a Markovian Model Describing Complex Subunit Cooperativity in HCN2 Channels

Hyperpolarization-activated cyclic nucleotide-modulated (HCN) channels are voltage-gated tetrameric cation channels that generate electrical rhythmicity in neurons and cardiomyocytes. Activation can be enhanced by the binding of adenosine-3′,5′-cyclic monophosphate (cAMP) to an intracellular cyclic nucleotide binding domain. Based on previously determined rate constants for a complex Markovian model describing the gating of homotetrameric HCN2 channels, we analyzed probability fluxes within this model, including unidirectional probability fluxes and the probability flux along transition paths. The time-dependent probability fluxes quantify the contributions of all 13 transitions of the model to channel activation. The binding of the first, third and fourth ligand evoked robust channel opening whereas the binding of the second ligand obstructed channel opening similar to the empty channel. Analysis of the net probability fluxes in terms of the transition path theory revealed pronounced hysteresis for channel activation and deactivation. These results provide quantitative insight into the complex interaction of the four structurally equal subunits, leading to non-equality in their function. Author Summary: The activation of a receptor protein by a small molecule (ligand) can be quantified by Markovian models. These models, which are widely used in natural sciences, consist of distinct states and transitions between them. In nature receptor proteins are often formed by the assembly of more than one subunit and each subunit can bind a ligand on its own. In such a multimeric receptor protein the translation of the ligand binding into receptor activation is more complex because the subunits interact. This usually limits the application of Markovian models. HCN2 pacemaker channels are tetrameric ion channels that mediate electrical rhythmicity in multiple brain and peripheral neurons and in specialized heart cells. The channels are modulated by cAMP binding to each subunit. We were recently successful to quantify ligand-induced activation for these channels by a complex Markovian model and a full set of rate constants. Herein we applied the transition path theory to further analyze the identified Markovian model, and we quantified time-dependent probability fluxes within the model. Our results provide unprecedented insight into the complex interaction of the four structurally equal subunits of a presumably fourfold symmetric channel that leads to pronounced non-equality of the subunit function.