  State-dependent Na+ channel blockers are often prescribed to treat cardiac
arrhythmias, but many Na+ channel blockers are known to have pro-arrhythmic
side effects. While the anti and proarrhythmic potential of a Na+ channel
blocker is thought to depend on the characteristics of its rate-dependent
block, the mechanisms linking these two attributes are unclear. Furthermore,
how specific properties of rate-dependent block arise from the binding kinetics
of a particular drug is poorly understood. Here, we examine the rate-dependent
effects of the Na+ channel blocker lidocaine by constructing and analyzing a
novel drug-channel interaction model. First, we identify the predominant mode
of lidocaine binding in a 24 variable Markov model for lidocaine-Na+ channel
interaction by Moreno et al. We then develop a novel 3-variable lidocaine-Na+
channel interaction model that incorporates only the predominant mode of drug
binding. Our low-dimensional model replicates the extensive voltage-clamp data
used to parameterize the Moreno et al. model. Furthermore, the effects of
lidocaine on action potential upstroke velocity and conduction velocity in our
model are similar to those predicted by the Moreno et al. model. By exploiting
the low-dimensionality of our model, we derive an algebraic expression for
level of rate-dependent block as a function of pacing frequency, restitution
properties, diastolic and plateau potentials, and drug binding rate constants.
Our model predicts that the level of rate-dependent block is sensitive to
alterations in restitution properties and increases in diastolic potential, but
it is insensitive to variations in the shape of the action potential waveform
and lidocaine binding rates.
