Markov models of use-dependence and reverse use-dependence during the mouse cardiac action potential

Abstract

The fast component of the cardiac transient outward current, I(Ktof), is blocked by a number of drugs. The major molecular bases of I(Ktof) are Kv4.2/Kv4.3 voltage-gated potassium channels. Drugs with similar potencies but different blocking mechanisms have differing effects on action potential duration (APD). We used in silico analysis to determine the effect of I(Ktof)-blocking drugs with different blocking mechanisms on mouse ventricular myocytes. We used our existing mouse model of the action potential, and developed 4 new Markov formulations for I(Ktof), I(Ktos), I(Kur), I(Ks). We compared effects of theoretical I(Ktof)-specific channel blockers: (1) a closed state, and (2) an open channel blocker. At concentrations lower or close to IC(50), the drug which bound to the open state always had a much greater effect on APD than the drug which bound to the closed state. At concentrations much higher than IC(50), both mechanisms had similar effects at very low pacing rates. However, an open state binding drug had a greater effect on APD at faster pacing rates, particularly around 10 Hz. In summary, our data indicate that drug effects on APD are strongly dependent not only on IC(50), but also on the drug binding state.

Figure 1. Dose dependent blockade of I_Ktof.

The effect of various concentrations of drug on the action potential for A: open state block, and B: closed state block. The degree of block was determined by holding at −70 mV, the applying a test pulse to +50 mV for 500 ms. C: Open state binding of Drug O. D: Closed state binding of Drug C. Change in peak (▪), change in total current flow (○). Solid lines are Boltzmann fits to the data .

Figure 2. Effect of drugs O and C on APD prolongation.

A: simulated action potentials of the mouse ventricular model for the epicardial and endocardial cells. Pacing rate was 1 Hz. Relative APD prolongation normalized to the maximum prolongation with I_Ktof completely blocked was determined at various drug concentrations for drug O (○) and drug C (▪) on B: endocardium and C: Epicardium. Pacing rate was 1 Hz.

Figure 3. APD-BCL relationships.

A: endocardium and B: epicardium. (i) APD 30; (ii) APD75; (iii) APD90. Control in the absence of drug (▪), 0.1 mM drug C (•), 1 mM drug C (▴), 0.1 mM drug O (○), 1 mM drug O (Δ).

Figure 4. Comparison of action potentials from endocardium and epicardium at fast and slow pacing rates.

Endocardium: A: 200 ms B: 2s. Epicardium: C: 200 ms D: 2 s. Control is solid black line. Drug O is red, drug C blue.

Figure 5. Relative APD-BCL relationships.

A: endocardium and B: epicardium. (i) APD 30; (ii) APD75; (iii) APD90. Simulations are with 0.1 mM drug C (•), 1 mM drug C (▴), 0.1 mM drug O (○), 1 mM drug O (Δ). All APDs are normalized for control in the absence of drug.

Figure 6. Example of APs recorded with different S1–S2 intervals.

The first AP (control) represents the last beat of the pacing train at a cycle length of 1s (S1) on endocardial cells. APs are shown for S1–S2 intervals of 60, 100, 200, and 300 ms. Peak amplitudes are shown above the AP. APD30 is 4.89 ms, 8.17 ms, 6.11 ms, 5.58 ms, and 5.56 ms; APD75 is 18.11 ms, 22.07 ms, 18.65 ms, 17.81 ms, and 17.81 ms; and APD90 is 29.82 ms, 32.73 ms, 30.13 ms, 29.54 ms, and 29.47 ms for control, 60, 100, 200, and 300 ms S1–S2 intervals respectively.

Figure 7. Restitution curves for endocardial cells.

A: 1 Hz pacing; B: 2 Hz pacing; C: 10 Hz pacing. Top: APD30; Middle: APD75; Bottom: APD30. Control in the absence of drug (▪), 0.1 mM drug C (•), 1 mM drug C (▴), 0.1 mM drug O (○), 1 mM drug O (Δ).

Figure 8. Restitution curves for epicardial cells.

A: 1 Hz pacing; B: 2 Hz pacing; C: 10 Hz pacing. Top: APD30; Middle: APD75; Bottom: APD30. Control in the absence of drug (▪), 0.1 mM drug C (•), 1 mM drug C (▴), 0.1 mM drug O (○), 1 mM drug O (Δ).

Figure 9. Comparison of action potentials at with S1S2 interval at 40 ms.

Endocardium was stimulated at A: 1 Hz B: 10 Hz. Epicardium was stimulated at C: 1 Hz D: 10 Hz. Control, in the absence of drug is indicated by solid black line. Drug C is shown in blue, and drug O in red.