Comprehensive analyses of ventricular myocyte models identify targets exhibiting favorable rate dependence

Abstract

Reverse rate dependence is a problematic property of antiarrhythmic drugs that prolong the cardiac action potential (AP). The prolongation caused by reverse rate dependent agents is greater at slow heart rates, resulting in both reduced arrhythmia suppression at fast rates and increased arrhythmia risk at slow rates. The opposite property, forward rate dependence, would theoretically overcome these parallel problems, yet forward rate dependent (FRD) antiarrhythmics remain elusive. Moreover, there is evidence that reverse rate dependence is an intrinsic property of perturbations to the AP. We have addressed the possibility of forward rate dependence by performing a comprehensive analysis of 13 ventricular myocyte models. By simulating populations of myocytes with varying properties and analyzing population results statistically, we simultaneously predicted the rate-dependent effects of changes in multiple model parameters. An average of 40 parameters were tested in each model, and effects on AP duration were assessed at slow (0.2 Hz) and fast (2 Hz) rates. The analysis identified a variety of FRD ionic current perturbations and generated specific predictions regarding their mechanisms. For instance, an increase in L-type calcium current is FRD when this is accompanied by indirect, rate-dependent changes in slow delayed rectifier potassium current. A comparison of predictions across models identified inward rectifier potassium current and the sodium-potassium pump as the two targets most likely to produce FRD AP prolongation. Finally, a statistical analysis of results from the 13 models demonstrated that models displaying minimal rate-dependent changes in AP shape have little capacity for FRD perturbations, whereas models with large shape changes have considerable FRD potential. This can explain differences between species and between ventricular cell types. Overall, this study provides new insights, both specific and general, into the determinants of AP duration rate dependence, and illustrates a strategy for the design of potentially beneficial antiarrhythmic drugs.

Figure 1. Reverse rate dependence of action potential prolongation.

Reverse rate dependence is observed with perturbations to ionic current properties in a ventricular cell model, LR09. (A) Slow delayed rectifier K⁺ current (I_Ks) block through decreased maximal conductance (parameter G_Ks) at fast (2 Hz) and slow (0.2 Hz) pacing. (B) L-type Ca²⁺ current (I_CaL) enhancement through increased channel permeability (parameter G_CaL) at fast (2 Hz) and slow (0.2 Hz) pacing.

Figure 2. Rate dependence action potential duration across a population of models.

APD distributions for models paced at 2(colored histograms) and 0.2 Hz (black histograms). Shaded regions represent experimental ranges estimated from the following sources: canine , , guinea pig , –, and human , –. Colored shading indicates the range at 2 Hz, gray shading the range at 0.2 Hz, and an intermediate color the range overlap.

Figure 3. Action potential parameter sensitivity rate dependence.

(A) Sensitivities (B) for hypothetical parameters a–d indicate how much each parameter influences the APD. Black bars represent that parameter's influence at slow pacing, and blue bars its influence at fast pacing. (B) B_RD is calculated from sensitivities B for each parameter in (A) as described in Methods . Positive B_RD indicates a parameter that lengthens the APD with reverse-rate dependence (parameter c), negative B_RD indicates a parameter that lengthens the APD with forward rate dependence (parameters a and d), and near-zero B_RD indicates neutral rate dependence (parameter b). (C) B_RD for parameters in the TP06 model, derived from parameter sensitivities calculated from a population of 600 virtual myocytes. (D) Single perturbation simulation results for parameters G_Ks and G_CaL (slow delayed rectifier K⁺ channel and L-type Ca²⁺ channel conductance, respectively). Decreasing G_Ks increases the APD with reverse rate dependence, and increasing G_CaL increases the APD with forward rate dependence, as predicted by each parameter's B_RD (C).

Figure 4. Inter-model comparison of APD parameter sensitivity rate dependence.

Ventricular cell models were found to vary greatly in rate dependencies, which is apparent from variations in B_RD plot structure. (A) B_RD for the LR09 guinea pig model, showing largely RRD parameters. (B) B_RD for the HR canine model, showing a majority of FRD parameters. B_RD plots for all models studied can be found in Figures S1–S13 in Text S2.

Figure 5. Rate-dependent change in AP contour corresponds to capacity for forward rate-dependence.

(A) AP traces for a model with mostly RRD parameters (LR09) and a model with mostly FRD parameters (HR). Each trace was calculated after pacing to steady state at each rate. For each model, the fast AP was rescaled with respect to time such that APD_slow = APD_fast, to isolate AP contour changes independent of APD changes. Rate-dependent contour change is quantified by the root mean square deviation (RMSD) between the rescaled AP traces at fast and slow pacing. (B) A strong correlation (R² = 0.8366) was observed between the RMSD and the percentage of model parameters that are FRD.

Figure 6. APD parameter sensitivity rate dependence in 13 ventricular myocyte models.

For 14 selected parameters that were common to most myocyte models, the heat map shows the rate dependence of these parameters (B_RD) across the various models. B_RD≥0.03 is considered reverse rate dependent (red), B_RD≤−0.03 forward rate dependent (blue), and −0.03<B_RD<0.03 non-rate dependent (white). Epi = epicardial, mid = midmyocardial, and endo = endocardial.

Figure 7. Quantitative contributions of individual ionic currents to AP rate dependence.

(A) Hypothetical APs before (solid) and after a perturbation that causes RRD prolongation of the AP. (B) A specific hypothetical ionic current under the conditions shown in (A). This inward (i.e. depolarizing) current increases with the perturbation at the slow rate (gray shaded area) but barely changes at the fast rate (blue shaded area). (C) ΔQ is the integral of the difference in current between control and perturbation (shaded areas in (B)) in units of pC/nF. The large, negative ΔQ at slow pacing (gray bar) indicates that this current will prolong the AP at this rate, whereas the small, negative ΔQ at fast pacing (blue bar) indicates a minimal alteration of the AP at this rate. This current will therefore contribute to RRD AP prolongation. Figure S4 shows additional hypothetical examples of ΔQ that can contribute to either RRD or FRD behavior.

Figure 8. Ionic current changes underlying rate dependence of perturbations in the TP06 epicardial model.

(A) ΔQ analysis of major ionic currents under 3 perturbations: increase in L-type Ca²⁺ channel maximal conductance, G_CaL (271% of baseline, a FRD perturbation), slowed activation of the slow delayed rectifier K⁺ channel (38% of baseline p_xs, a RRD perturbation), and a negative shift in the voltage dependence of L-type Ca²⁺ activation (5 mV decrease in V_d, a NRD perturbation). ΔQ quantifies the change in current flux with the perturbation, and is calculated at fast and slow pacing. (B) Slow delayed rectifier current (I_Ks) under each perturbation, at fast and slow pacing. (C) APD under increased G_CaL (271% baseline) and varying degrees of I_Ks block. The APD rate dependence of I_CaL enhancement is reversed by simultaneous block of I_Ks, as predicted by ΔQ analysis (A).