Model topology determines parameter accessibility in Markov models of voltage-gated ion channels

Markov models are widely used to describe the gating kinetics of voltage-gated ion channels, but increasing model complexity can introduce parameters that are difficult to constrain from macroscopic measurements. In this study, global variance-based Sobol sensitivity analysis was used to examine how model topology, stimulation protocol, and parameter uncertainty shape the accessibility of kinetic parameters in voltage-gated ion channel models. Progressively more complex Markov schemes were analyzed, beginning with a two-state closed-open model, extending to a three-state linear closed-closed-open model, a cyclic three-state model with a direct closed-open transition, and a four-state closed-closed-open-inactivated model. Sensitivity was quantified for the open probability (P_o) under voltage-step and sinusoidal protocols. In linear models, parameter influence was concentrated in transitions directly connected to the open state, whereas distal closed-closed transitions contributed little to output variance. This weak influence was not rescued by higher-order interaction effects. Multi-frequency sinusoidal stimulation (20-200 Hz) preserved the transition-level sensitivity hierarchy observed under step protocols, indicating that dynamic stimulation does not overcome the structural limitations of serial topologies. In contrast, introducing a cyclic pathway fundamentally redistributed sensitivity, showing that distal-parameter weakness is a consequence of serial arrangement rather than a universal property of Markov gating. Adding inactivation shifted dominant variance control to the open-inactivated transition during sustained depolarization, yet distal closed-closed transitions remained weak. Finally, constraining variability at the dominant activation edge shifted variance upstream, demonstrating that low Sobol indices reflect the relative flexibility of competing bottlenecks within a given ensemble rather than the intrinsic irrelevance of a transition. Together, these results define topology-dependent limits on parameter accessibility in Markov models of voltage-gated ion channels and provide practical guidance for selecting model complexity, designing informative protocols, and favoring cyclic over extended linear topologies when constructing robust channel models.