Quantitative modelling of interaction of propafenone with sodium channels in cardiac cells

A mathematical model of the interaction of propafenone with cardiac sodium channels is based on experimental data that demonstrate use-dependent effects of the drug. The Clancy-Rudy model is applied to describe Na-channels in absence of the drug. The values of rate constants of the drug-receptor reaction are fitted to experimental data by iterative computer simulations using a genetic algorithm. The model suggests the following interpretation of available experimental results: First, drug molecules have access to the binding sites predominantly in the inactivated states. Secondly, the biphasic development of the block during depolarisation is consistent with a rapid increase due to drug binding in the fast inactivated state (rate constants k(on) = 645 mumol(-1)/s(-1), k(off) = 16.21 s(-1)) and a slow increase due to binding in the intermediate inactivated state (rate constants similar to100-fold lower), followed by transition to the drug-occupied slow inactivated state (rate constants 0.784 and 0.921 s(-1)). Thirdly, the observed biphasic time course of recovery of I-Na from block following restoration of the resting voltage results from simultaneous relief of block from the channels residing in the intermediate and slow inactivated states. Fourthly, the accumulation of blocked channels in the slow inactivated state is responsible for the observed use-dependent effects. Fifthly, when incorporated into a quantitative description of the electrical activity of a ventricular cell, the model predicts that propafenone (0.2 mumol l(-1)) effectively suppresses premature excitations, leaving the regular action potentials nearly unaffected.