Comparison between Hodgkin-Huxley and Markov formulations of cardiac ion channels

- We compare Hodgkin-Huxley (HH) vs. Markovian formalism for ionic current modeling.
- We reformulate four Markovian ionic current models using the HH formalism.
- The equivalence between formalisms was tested with action potential simulations.
- Action potential biomarkers showed no significant differences between formalisms.

When simulating the macroscopic current flowing through cardiac ion channels, two mathematical formalisms can be adopted: the Hodgkin-Huxley model (HHM) formulation, which describes openings and closings of channel 'gates', or the Markov model (MM) formulation, based on channel 'state' transitions. The latter was first used in 1995 to simulate the effects of mutations in ionic currents and, since then, its use has been extended to wild-type channels also. While the MMs better describe the actual behavior of ion channels, they are mathematically more complex than HHMs in terms of parameter estimation and identifiability and are computationally much more demanding, which can dramatically increase computational time in large-scale (e.g. whole heart) simulations. We hypothesize that a HHM formulation obtained from classical patch-clamp protocols in wild-type and mutant ion channels can be used to correctly simulate cardiac action potentials and their static and dynamic properties. To validate our hypothesis, we selected two pivotal cardiac ionic currents (the rapid delayed rectifier K+ current, IKr, and the inward Na+ current, INa) and formulated HHMs for both wild-type and mutant channels (LQT2-linked T474I mutation for IKr and LQT3-linked ΔKPQ mutation for INa). Action potentials were then simulated using the MM and HHM versions of the currents, and the action potential waveforms, biomarkers and action potential duration rate dependence properties were compared in control conditions and in the presence of physiological variability. While small differences between ionic currents were found between the two models (correlation coefficient ρ>0.92), the simulations yielded almost identical action potentials (ρ>0.99), suggesting that HHMs may also be valid to simulate the effects of mutations affecting IKr and INa on the action potential.

302