Rate-dependent effects of state-specific sodium channel blockers in cardiac tissue: Insights from idealized models

A common side effect of pharmaceutical drugs is an increased propensity for cardiac arrhythmias. Many drugs bind to cardiac ion-channels in a state-specific manner, which alters the ionic conductances in complicated ways, making it difficult to identify the mechanisms underlying pro-arrhythmic drug effects. To better understand the fundamental mechanisms underlying the diverse effects of state-dependent sodium (Na⁺) channel blockers on cellular excitability, we consider two canonical motifs of drug-ion-channel interactions and compare the effects of Na⁺ channel blockers on the rate-dependence of peak upstroke velocity, conduction velocity, and vulnerable window size. In the literature, both motifs are referred to as "guarded receptor," but here we distinguish between state-specific binding that does not alter channel gating (referred to here as "guarded receptor") and state-specific binding that blocks certain gating transitions ("gate immobilization"). For each drug binding motif, we consider drugs that bind to the inactivated state and drugs that bind to the non-inactivated state of the Na⁺ channel. Exploiting the idealized nature of the canonical binding motifs, we identify the fundamental mechanisms underlying the effects on excitability of the various binding interactions. Specifically, we derive the voltage-dependence of the drug binding time constants and the equilibrium fractions of channels bound to drug, and we then derive a formula that incorporates these time constants and equilibrium fractions to elucidate the fundamental mechanisms. In the case of charged drug, we find that drugs that bind to inactivated channels exhibit greater rate-dependence than drugs that bind to non-inactivated channels. For neutral drugs, the effects of guarded receptor interactions are rate-independent, and we describe a novel mechanism for reverse rate-dependence resulting from neutral drug binding to non-inactivated channels via the gate immobilization motif.