Development of Markov chain models for IKr in wild-type and KCNH2 T618I mutation conditions

The Hodgkin–Huxley model (HH model) assumes that the channel gates are independent; however, experiments have shown that activation and inactivation processes are typically dependent on each other. As a result, explicit representations of ion channel states are necessary, as in the case of Markov chain models. Jæger et al. mentioned that the Markov model is able to give a more realistic representation of both the effect of mutations and the effect of drugs⁴⁶, and the superiority of the Markov model was also explicitly demonstrated in other simulation studies⁴⁷. Therefore, the Markov chain model of I_Kr developed in this study is more accurate than the HH-based I_Kr formulations. A general introduction to the use of Markov models can be found in ref. ⁴⁸.

The Markov chain model for I_Kr in this study was based on a previous I_Kr model by Clancy and Rudy⁴⁹, as illustrated in Fig. ​Fig.1B.1B. The model contained five states, including an open state (O), an inactivated state (I), and three closed states (C1, C2, C3). The model parameters were optimized by minimizing the least-squared difference between the model-generated current–voltage (I–V) curve and the experimentally recorded I–V data. The optimizing process was performed using the LMFIT package that implemented in Python. Model equations and the fitted transition rates are listed in Eqs. (1)–(25).