A Markov Model for the Human Cardiac Sodium Channel

Abstract

Voltage-gated sodium channels play an important role in the function of the human heart. Different voltage-clamp protocols were employed to determine kinetic and steady state voltage dependences that characterize channel gating. They include activation, deactivation, inactivation, and recovery from inactivation kinetics, current-voltage relationships, steady-state inactivation, and voltage dependence of normalized channel conductance (G/Gmax). Several attempts were made to develop comprehensive mathematical model for sodium channel, however, most of them have noticeable limitations. We developed a new Markov model for the human sodium channel that includes three closed states (C1, C2, and C3), three closed-inactivated states (IC1, IC2, and IC3), one open state (O), one fast open-inactivated state (IF), and one slow open-inactivated state (IS). This final model was chosen from the several Markov models that had been analyzed. The aim was to develop a Markov model with minimum number of states which gives the best description of the several sets of experimental data. We started from the model with three closed states, one open state, and one open-inactivated state (connected only to open state). This minimal model reproduced the current-voltage relationship, the voltage dependence of normalized channel conductance, the time constant of deactivation, and gave reasonable approximation to the time-to-peak current. However, the model did not simulate well the steady-state inactivation relationship, voltage dependence of the inactivation kinetics and recovery from inactivation. We have modified this model by adding three closed-inactivated states parallel to the existing activation pathway. This model gave good description for the kinetics and steady-state properties of the fast inactivation of the channel. As the experimental data shows bi-exponential inactivation and recovery, we included additional slow inactivated state connected to the open state. The resulting model reproduced well both the inactivation-recovery and the activation-deactivation data.