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. 2008 Jan 15;94(2):392-410.
doi: 10.1529/biophysj.106.98160.

A rabbit ventricular action potential model replicating cardiac dynamics at rapid heart rates

Aman Mahajan  1 , Yohannes Shiferaw, Daisuke Sato, Ali Baher, Riccardo Olcese, Lai-Hua Xie, Ming-Jim Yang, Peng-Sheng Chen, Juan G Restrepo, Alain Karma, Alan Garfinkel, Zhilin Qu, James N Weiss
Affiliations

A rabbit ventricular action potential model replicating cardiac dynamics at rapid heart rates

Aman Mahajan et al. Biophys J. .

Abstract

Mathematical modeling of the cardiac action potential has proven to be a powerful tool for illuminating various aspects of cardiac function, including cardiac arrhythmias. However, no currently available detailed action potential model accurately reproduces the dynamics of the cardiac action potential and intracellular calcium (Ca(i)) cycling at rapid heart rates relevant to ventricular tachycardia and fibrillation. The aim of this study was to develop such a model. Using an existing rabbit ventricular action potential model, we modified the L-type calcium (Ca) current (I(Ca,L)) and Ca(i) cycling formulations based on new experimental patch-clamp data obtained in isolated rabbit ventricular myocytes, using the perforated patch configuration at 35-37 degrees C. Incorporating a minimal seven-state Markovian model of I(Ca,L) that reproduced Ca- and voltage-dependent kinetics in combination with our previously published dynamic Ca(i) cycling model, the new model replicates experimentally observed action potential duration and Ca(i) transient alternans at rapid heart rates, and accurately reproduces experimental action potential duration restitution curves obtained by either dynamic or S1S2 pacing.

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Figures

FIGURE 1
FIGURE 1
Schematic representation of Markovian model and Cai cycling machinery: (A) Seven-state Markovian model of the L-type Ca channel. The red lines denote Ca-dependent transitions to inactivated states. (B) Schematic illustration of the different conformational states corresponding to the VDI and CDI pathways. Domains III and IV of the L-type Ca channel are shown, with the pore in the middle. The I-II cytoplasmic linker connecting domains I and II (not shown) acts as the voltage-dependent inactivation gate (VDI), whose ability to inactivate the channel is inhibited by CaM tethered to the COOH terminus. The braking effect is removed when Ca binds to CaM, allowing the I-II linker to inactivate the channel more rapidly. (C) Demonstration that CDI can be minimally represented using a direct Ca-dependent transition to the inactivated state (see text for explanation). The single open state in panel B corresponds to a reduction of two physical states O1 and O2.
FIGURE 2
FIGURE 2
(A) Sketch of spatially distributed dyadic junctions where L-type Ca channels are in close proximity to RyR receptors which gate Ca flux from the JSR. (B) Reduced whole-cell model showing basic elements of Ca cycling machinery and membrane ion currents. Ca release is modeled phenomenologically by taking into account recruitment of discrete release events (Ca sparks). See text for further details.
FIGURE 3
FIGURE 3
ICa,L traces along with model fits using Ba and Ca as charge carriers, and for intact and depleted SR. The black line represents a typical experimentally measured current trace. The red lines represent the best fit of that current trace to the Markovian model. The gray line represents the largest deviations from a sample of eight cells, where the peak has been normalized to the typical case. Dashed lines indicate zero current levels.
FIGURE 4
FIGURE 4
The kinetics of recovery of ICa,L. (A) Plot of the time constant of recovery from inactivation as a function of membrane voltage with either Ca or Ba as the charge carrier, obtained with a double pulse protocol (see Methods). The recovery time constant was estimated by fitting the recovery curve to a monoexponential function. Symbols represent the experimental measurements and lines correspond to the model fits. (B) Pedestal current remaining after 300-ms voltage-clamps to the potentials indicated, expressed as fraction of the peak current at that potential, illustrating the classic U-shaped relationship with Ca as the charge carrier and SR Ca release intact. Symbols show experimental data, lines show model fits. (C) Voltage dependence of activation (red) and quasi-steady-state inactivation after 300 ms (black) in the model, illustrating the region of ICa,L window currents between −30 and −10 mV.
FIGURE 5
FIGURE 5
Experimental validation of Markovian model. (A) IV curve showing the peak ICa,L versus membrane voltage for experimental data (black) versus the model (red). (B) Comparison of nicardipine-sensitive current during an AP clamp in myocytes (black and gray) versus the model (red). Black trace is from a representative myocyte, and the gray zone indicates the range of nicardipine-sensitive currents recorded from eight myocytes, normalized to the same peak. The AP clamp was applied from −40 mV to inactivate the Na current. For the model, the solid red line shows the simulated nicardipine-sensitive current and the dashed red line shows ICa,L during the AP clamp in the model.
FIGURE 6
FIGURE 6
Ionic currents and Ca concentrations in the model after steady-state pacing at 400 ms for 200 beats. (A) Action potential. The red line represents the AP after Ito,f was reduced by 50%, keeping all other model parameters the same. As expected the AP notch is reduced, and the APD increases slightly. (B) K currents during the AP. (C) Plots of ICa,L, INaCa, Ito,f, and INa. Note that INa has been truncated. (D) Ca concentrations in the various compartments. The black and red lines show the Cai transient with normal and reduced Ito,f. Other Ca concentrations correspond to the normal (control) Ito,f case. (E) Profile of Ca fluxes in the various compartments. (F) The voltage dependence of the peak ICa,L and peak SR Ca release flux (Jrel) (both normalized). The peak SR Ca release flux mirrors the voltage dependence of ICa,L, as required for graded release, and Ca-induced Ca release gain is higher at negative than positive voltages.
FIGURE 7
FIGURE 7
Rate-dependent features: dynamic pacing. (A) APs and Cai transients from a representative myocyte (left traces) and the model (right traces) at pacing cycle lengths (PCL) above (upper) and below (lower) the threshold for alternans. (B) APD versus heart rate during the dynamic pacing protocol in a representative myocyte (black points) versus the model (red line). Alternans developed at a PCL of 190 ms and 210 ms for the myocyte and model experiment, respectively. (C) The dynamic APD restitution curve. Same data as in panel B, but with APD plotted versus DI = PCL-APD. Inset compares the average maximum APD restitution slope in myocytes to that in the model. (D) Systolic and diastolic Cai versus PCL in the model. (E) Peak JSR Ca concentration versus PCL in the model. (F) Intracellular Na versus PCL in the model.
FIGURE 8
FIGURE 8
Rate-dependent features: S1S2 pacing. (A) Superimposed APs from a representative myocyte (upper black traces) and the model (lower red traces) during the last paced S1 beat at 400 ms, and the S2 beats at progressively shorted S1S2 intervals. (B) The S1S2 APD restitution curve, showing the APD of the S2 beat versus the S1S2 interval in a representative myocyte (black points) versus the model (red line). (C) Peak systolic, diastolic and Cai transient amplitude (ΔCa) versus the S1S2 interval in the model. Black circles show ΔCa data points from a myocyte subjected to the same protocol, replotted from Goldhaber et al. (14).
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