Mechanisms Underlying Rate-Dependent Effects of State-Specific Binding of Sodium Channel Blockers in Cardiac Tissue: Insights from Idealized Models

Abstract

Increased propensity for arrhythmias is a well-documented but poorly understood side-effect of drugs. Many arrhythmogenic drugs bind to and block ion-channels in a conformational state-specific manner, making it difficult to discern the fundamental mechanisms underlying pro-arrhythmic drug effects. We have developed mathematical models to examine the effects of state-specific Na+ channel blockers with various binding mechanisms on the rate-dependence of peak upstroke velocity, conduction velocity, and the vulnerable window of cardiac tissue. Specifically, we compared the effects of drugs that bind via the guarded receptor and gate immobilization models, which are idealized models consisting of motifs commonly found in modulated receptor models of drug binding. For both the guarded receptor and gate immobilization models, we considered drugs that bind to either inactivated or non-inactivated Na-channels. Our results suggest that drugs that bind to inactivated Na+ channels give rise to greater rate-dependent effects on peak upstroke velocity and conduction velocity than drugs that bind to non-inactivated Na+ channels. Additionally, we find drugs that bind to non-inactivated Na+ channels via the gate immobilization motif induce a reversal of the rate-dependence of peak upstroke velocity. By exploiting the idealized nature of guarded receptor and gate immobilization models and utilizing singular perturbation analysis, we provide an explanation of the fundamental mechanisms of rate-dependent drug effects. Finally, we show that a gate immobilization model with inactivated state binding captures the rate-dependent effects of lidocaine, demonstrating that idealized models can be useful models to study mechanisms of action of real drugs.