Pharmacological management of cardiac arrhythmias has been a long and widely sought goal. One of the difficulties in treating arrhythmia stems, in part, from incomplete understanding of the mechanisms of drug block, and how intrinsic properties of channel gating affect drug access, binding affinity and unblock. In the last decade, a plethora of genetic information has revealed that genetics may play a critical role in determining arrhythmia susceptibility, and in efficacy of pharmacologic therapy. In this context, we present a theoretical approach for investigating effects of drug-channel interaction. We use as an example open-channel or inactivated-channel block by the local anesthetics mexiletine and lidocaine, respectively, of normal and KPQ mutant Na⁺ channels associated with the long-QT syndrome type 3. Results show how kinetic properties of channel gating, which are affected by mutations, are important determinants of drug efficacy. Investigations of Na⁺channel blockade are conducted at multiple scales: single channel, macroscopic current and, importantly, during the cardiac action potential (AP). Our findings suggest that channel mean open time is a primary determinant of open state blocker efficacy. Channels that remain in the open state longer, such as the KPQ mutant channels in the abnormal burst mode, are blocked preferentially by low mexiletine concentrations. AP simulations confirm that a low dose of mexiletine can remove early afterdepolarizations and restore normal repolarization without affecting the AP upstroke. The simulations also suggest that inactivation state block by lidocaine is less effective in restoring normal repolarization and adversely suppresses peak Na⁺ current.