Comparing Hodgkin-Huxley and Markovian Formulations for the Rapid Potassium Current in Cardiac Myocytes: A Simulation Study

Two mathematical approaches have been used to describe ion channel kinetics in cardiac action potential simulations: the classical Hodgkin & Huxley (HH) gating model formalism and state transitions Markov models (MMs). This last approach is more flexible and it is capable of characterizing state transitions dependent on the state of the channel, consequently being able to match experimental observations on gating currents more accurately and mechanistically. However, the high number of differential equations associated to MMs makes multi-cellular whole-organ simulations very costly from a computational point of view. Moreover, the large number of transition rates implicit in the model also adds difficulties in parameter estimation.

The aim of this study is to compare the results obtained with both formalisms when simulating the effects of the delayed rectifier K+ current (I

Kr

) in the action potential in isolated cardiac cells. For this purpose, a new mathematical model for I

Kr

based on the HH formalism (I

Kr,HH

) using the Clancy – Rudy (I

Kr

,

CR

) dynamics for guinea pig ventricular cells was developed. The dynamic characteristics of the CR model were fitted to the HH formalism to obtain the parameters for the new HH current. This new model was incorporated to the Clancy – Rudy action potential model to simulate the steady state action potential and ionic currents under physiological cycle lengths, and the action potential duration (APD) restitution curve.

Our results show similar action potential and ionic current waveforms and APD values with both I

Kr

models, although some differences are observed on the I

Kr

time course. We conclude that the HH formalism is appropriate and more efficient than the MM formalism to simulate I

Kr

current behavior during the AP under the normal physiological conditions considered in this study.