In silico optimization of atrial fibrillation-selective sodium channel blocker pharmacodynamics

Abstract

Atrial fibrillation (AF) is the most common type of clinical arrhythmia. Currently available anti-AF drugs are limited by only moderate efficacy and an unfavorable safety profile. Thus, there is a recognized need for improved antiarrhythmic agents with actions that are selective for the fibrillating atrium. State-dependent Na(+)-channel blockade potentially allows for the development of drugs with maximal actions on fibrillating atrial tissue and minimal actions on ventricular tissue at resting heart rates. In this study, we applied a mathematical model of state-dependent Na(+)-channel blocking (class I antiarrhythmic drug) action, along with mathematical models of canine atrial and ventricular cardiomyocyte action potentials, AF, and ventricular proarrhythmia, to determine the relationship between their pharmacodynamic properties and atrial-selectivity, AF-selectivity (atrial Na(+)-channel block at AF rates versus ventricular block at resting rates), AF-termination effectiveness, and ventricular proarrhythmic properties. We found that drugs that target inactivated channels are AF-selective, whereas drugs that target activated channels are not. The most AF-selective drugs were associated with minimal ventricular proarrhythmic potential and terminated AF in 33% of simulations; slightly fewer AF-selective agents achieved termination rates of 100% with low ventricular proarrhythmic potential. Our results define properties associated with AF-selective actions of class-I antiarrhythmic drugs and support the idea that it may be possible to develop class I antiarrhythmic agents with optimized pharmacodynamic properties for AF treatment.

Figure 1

Schematic representation of the guarded-receptor model of Na⁺-channel-blocking action. Transitions between the closed, activated (A), and inactivated (I) states are governed by Hodgkin-Huxley equations with rate constants α_x and β_x. Transitions between unblocked and blocked states are governed by binding-rate constants, k_A and k_I, and unbinding-rate constants, l_A and l_I.

Figure 2

(A–C) Reduction in I_Na (B_ss) for an atrial myocyte paced at 6 Hz (A) and 1 Hz (B), and a ventricular myocyte paced at 1 Hz (C) as a function of l_A and l_I for k_A = 10⁴ and k_I = 20 ms⁻¹ mol⁻¹. (D and E) Rate- and atrial-selectivities. (F) AF-selectivity. Maximum AF-selectivity is shown by the asterisk. Color scales are at the right of each panel.

Figure 3

(A–C) Rate-selectivity, atrial-selectivity, and AF-selectivity_max as a function of the binding-rate constants k_A and k_I. (D and E) Fractional block for activated (B_A) and inactivated (B_I) states. (F) Fractional block (B_A and B_I) versus AF-selectivity_max, with schematic curves (dashed lines). (G and H) Unbinding-rate constants (l_A,max and l_I,max) corresponding to k_A-k_I parameter space. An area of large AF-selectivity (at k_A = 10¹−10³ ms⁻¹ mol⁻¹ and k_I = 100 ms⁻¹ mol⁻¹) with low proarrhythmic risk and high AF-termination rates (see Figs. 5 and 6) is shown in black boxes.

Figure 4

Action potentials, Na⁺ current (I_Na), and fractional block for the optimally AF-selective Na⁺-channel blocker (k_A = 10 ms⁻¹ mol⁻¹, k_I = 500 ms⁻¹ mol⁻¹, l_A = l_I = 10⁻² ms⁻¹). (A–C) Effects on an atrial cell paced at 6 Hz, an atrial cell paced at 1 Hz, and a ventricular cell paced at 1 Hz. In all panels, the vertical red line corresponds to t_DRUG, the time at which the drug was added. (D–F) Corresponding values of I_Na. (G–I) Fractional block in the activated (B_A, green) and inactivated (B_I, lavender) states. Panels H and I illustrate the temporal dynamics of block: B_I rises sharply just after the action potential upstroke, corresponding to the onset of inactivation. It then reaches a plateau and starts to decrease at the end of the action potential, when the Na⁺ channels recover from inactivation. B_A is negligible. The atrial cell paced at 6 Hz had a much larger B_I than atrial and ventricular cells paced at 1 Hz, because of the reduced unbinding time between action potentials.

Figure 5

(A) Conduction velocity on a 1D cable as a function of k_A and k_I for Na⁺-channel blockers with l_A and l_I fixed at 10⁻³ ms⁻¹ and 10⁻² ms⁻¹, respectively. (B and C) PI and VP for the same parameters. (D and E) Fractional Na⁺-channel block for activated (B_A) and inactivated (B_I) states in a ventricular cell at 1 Hz as a function of rate constants k_A and k_I. (F) Fractional block of Na⁺ current in a ventricular cell at 1 Hz versus PI, with schematic curves showing that minimally proarrhythmic rate-constant combinations (low index) are associated with inactivated-state blockers, whereas proarrhythmic rate-constant combinations are associated with activated-state block. An area of large AF-selectivity with low proarrhythmic risk and high AF-termination rates (see Figs. 3 and 6) is shown in the black boxes in A–E.

Figure 6

(A) Time to termination after Na⁺-channel blocker addition on a 2D sheet of atrial cells for the same rate-constant combinations as in Fig. 3. (B) Percentage of successfully terminated AF episodes. The optimally AF-selective area terminated the arrhythmia quickly (average of 429 ms), although the percentage of successfully terminated simulations was lower than in the non-AF-selective region (33% vs. 100%). An area of large AF-selectivity with low proarrhythmia risk and high AF-termination rates is shown in the black boxes (k_A = 10¹−10³ ms⁻¹ mol⁻¹; k_I = 100 ms⁻¹ mol⁻¹).

Figure 7

Termination of AF after addition of maximally AF-selective Na⁺-channel blocker (AF-selectivity ratio = 23.9, k_A = 10 ms⁻¹ mol⁻¹, k_I = 500 ms⁻¹ mol⁻¹, l_A = l_I = 10⁻² ms⁻¹). (A) Top left: Position of generators from the time of drug application (t_DRUG = 1000 ms). Bottom left: Mean APD at −60 mV (APD_-60) distribution. (B) Transmembrane potential snapshots of the 2D sheet at time points indicated at the upper left of each frame; black dots denote phase singularities. (C) Number of phase singularities over time in control (black curve) and with drug (red curve). (D) Fraction of Na⁺-channels blocked at two sites (positions indicated in A); larger fractional block is in the region with longer APD. (E) Ratio of depolarized cells (R_APD) over time for control (black curve) and with Na⁺-channel blockade (red curve). (F) Transmembrane action potentials over time before and after drug addition. The time of drug addition is shown in C–F by a vertical blue line.

Figure 8

Termination of AF after addition of a slightly less AF-selective but more effective Na⁺-channel blocker (AF-selectivity ratio = 12.8, k_A = 10² ms⁻¹ mol⁻¹, k_I = 100 ms⁻¹ mol⁻¹, l_A = 10° ms⁻¹, l_I = 10^−2.5 ms⁻¹). (A) Top left: Position of generators from the time of drug application (t_DRUG = 1000 ms). Bottom left: Mean APD at −60 mV (APD_-60) distribution. (B) Transmembrane potential snapshots of the 2D sheet at time points indicated at the upper left of each frame; black dots denote phase singularities. (C) Number of phase singularities over time in control (black curve) and with drug (red curve). (D) Fraction of Na⁺-channels blocked at two sites (positions indicated in A); the larger fractional block is in the region with longer APD. (E) Ratio of depolarized cells (R_APD) over time for control (black curve) and with Na⁺-channel blocker (red curve). (F) Transmembrane action potentials over time before and after drug addition. The time of drug addition is shown in C–F by a vertical blue line.