The Importance of the Dissociation Rate in Ion Channel Blocking

Abstract

Understanding the relationships between the rates and dynamics of current wave forms under voltage clamp conditions is essential for understanding phenomena such as state-dependence and use-dependence, which are fundamental for the action of drugs used as anti-epileptics, anti-arrhythmics, and anesthetics. In the present study, we mathematically analyze models of blocking mechanisms. In previous experimental studies of potassium channels we have shown that the effect of local anesthetics can be explained by binding to channels in the open state. We therefore here examine models that describe the effect of a blocking drug that binds to a non-inactivating channel in its open state. Such binding induces an inactivation-like current decay at higher potential steps. The amplitude of the induced peak depends on voltage and concentration of blocking drug. In the present study, using analytical methods, we (i) derive a criterion for the existence of a peak in the open probability time evolution for a model with an arbitrary number of closed states, (ii) derive formula for the relative height of the peak amplitude, and (iii) determine the voltage dependence of the relative peak height. Two findings are apparent: (1) the dissociation (unbinding) rate constant is important for the existence of a peak in the current waveform, while the association (binding) rate constant is not, and (2) for a peak to exist it suffices that the dissociation rate must be smaller than the absolute value of all eigenvalues to the kinetic matrix describing the model.

Keywords: Markov chain model; Monte Carlo simulation; dissociation rate constant; ion channel block; peak current; voltage-clamp.

Figure 1

Regions associated with a peak in the β−δ plane (α = 1). The existence of a peak was independent of the value of γ, as long as γ > 0, for all cases. (A) One closed state (α > δ). (B) Two closed states. (C) Three closed states. (D) Four closed states.

Figure 2

Topologically equivalent regions in the rate-potential plane. The three-state model (Equation 1) at K_d-concentration of the blocking drug (i.e., γ = δ). A1 represents an area in which there is no open probability peak and the steady state value decreases with potential approaching a value of a half, A2 represents an area in which there is a peak and the relative amplitude decreases with potential and A3 represents an area in which there is a peak, but the relative amplitude increases with potential, approaching a value of one.