Properties and ionic mechanisms of action potential adaptation, restitution, and accommodation in canine epicardium

Abstract

Computational models of cardiac myocytes are important tools for understanding ionic mechanisms of arrhythmia. This work presents a new model of the canine epicardial myocyte that reproduces a wide range of experimentally observed rate-dependent behaviors in cardiac cell and tissue, including action potential (AP) duration (APD) adaptation, restitution, and accommodation. Model behavior depends on updated formulations for the 4-aminopyridine-sensitive transient outward current (I(to1)), the slow component of the delayed rectifier K(+) current (I(Ks)), the L-type Ca(2+) channel current (I(Ca,L)), and the Na(+)-K(+) pump current (I(NaK)) fit to data from canine ventricular myocytes. We found that I(to1) plays a limited role in potentiating peak I(Ca,L) and sarcoplasmic reticulum Ca(2+) release for propagated APs but modulates the time course of APD restitution. I(Ks) plays an important role in APD shortening at short diastolic intervals, despite a limited role in AP repolarization at longer cycle lengths. In addition, we found that I(Ca,L) plays a critical role in APD accommodation and rate dependence of APD restitution. Ca(2+) entry via I(Ca,L) at fast rate drives increased Na(+)-Ca(2+) exchanger Ca(2+) extrusion and Na(+) entry, which in turn increases Na(+) extrusion via outward I(NaK). APD accommodation results from this increased outward I(NaK). Our simulation results provide valuable insight into the mechanistic basis of rate-dependent phenomena important for determining the heart's response to rapid and irregular pacing rates (e.g., arrhythmia). Accurate simulation of rate-dependent phenomena and increased understanding of their mechanistic basis will lead to more realistic multicellular simulations of arrhythmia and identification of molecular therapeutic targets.

Fig. 1.

Hund-Rudy dynamic model of the canine epicardial myocyte. SR, sarcoplasmic reticulum, SS, steady state; CT_KCl, K⁺-Cl⁻ cotransporter; CT_NaCl, Na⁺-Cl⁻ cotransporter; I_NaL, slowly activating late Na⁺ current; I_Na, Na⁺ current; I_Nab, background Na⁺ current; I_NaCa,i, Na⁺/Ca²⁺ exchanger (localized to myoplasm); I_Cab, background Ca²⁺ current; I_pca, sarcolemmal Ca²⁺ pump; I_to1, 4-aminopyridine-sensitive transient outward current; I_Kr, fast component of delayed rectifier K⁺ current; I_Ks, slow component of delayed rectifier K⁺ current; I_K1, time-dependent K⁺ current; I_NaK, Na⁺-K⁺ pump current; I_leak, NSR leak current; I_diff, ion diffusion, myoplasm-to-SR subspace; I_tr, Ca²⁺ transfer, NSR to JSR; I_rel, JSR release current; I_diff,ss, ion diffusion, subspace-to-local I_CaL subspace; I_NaCa,ss, Na⁺/Ca²⁺ exchanger (localized to SR subspace); I_Ca,L, L-type Ca²⁺ current; I_to2, Ca²⁺-dependent transient outward Cl⁻ current; SS(CaL), I_CaL subspace; SS(SR), SR subspace; PLB, phospholamban; SERCA, sarco(endo)plasmic reticulum Ca²⁺-ATPase; CSQN, calsequestrin; CaMKII, Ca²⁺/calmodulin-dependent kinase; NSR, network SR; JSR, junctional SR. (For additional model details, see Refs. and , supplemental information in the online version of this article, and http://rudylab.wustl.edu/.)

Fig. 2.

A and B: model I_Ca,L current-voltage (I-V) relationship and steady-state inactivation fit to experimental data from canine epicardial myocytes (36, 48). C and D: model I_to1 I-V curve and time to peak fit to data from canine epicardial myocytes (27). E and F: model I_Ks activation and accumulation fit to data from canine ventricular myocytes (47, 53). G and H: model I_NaK density and steady-state intracellular Na⁺ concentration ([Na⁺]_i) fit to data from canine ventricular myocytes (13). V_test, test potential; CL, cycle length.

Fig. 3.

A, left: model steady-state action potentials (APs) at CL = 0.3, 0.5, 1, and 2 s in single-cell and strand simulations. V_m, membrane potential. Inset: peak upstroke voltage and rate dependence of notch depth. A, right: experimental steady-state APs in a single cell and 3 tissue preparations. Experimental data for a single cell are from Ref. (cell CL = 0.3, 0.5, 0.8, 2, and 8 s); experimental data for tissue are from Ref. (tissue CL = 0.3, 1, 2, and 5 s), Ref. (tissue CL = 0.3, 0.5, 0.8, and 2 s), and Ref. (tissue CL = 0.3, 1, and 5 s). B, left: model CL_S1 dependence of AP duration (APD) restitution in single cell and strand. Gray traces denote adaptation (S2 coupling interval = CL_S1). B, right: experimental results from study of CL_S1 dependence of APD restitution in right ventricle of open-chest dogs (9). C, left: model accommodation of APD after change from CL = 1 s to CL = 0.5 s in single cell and strand. C, right: APD accommodation in canine ventricular muscle fiber experiments (39).

Fig. 4.

A: isolated single-cell stimulus (black trace, I_stim) and strand axial current (gray trace, I_axial). Inset: sustained repolarizing axial current. B–E: CL_S1 dependence of maximum upstroke velocity (dV/dt_max), APD, Ca²⁺ transient amplitude (CaT_AMP), and maximal intracellular Na⁺ concentration ([Na⁺]_i,max) in single-cell and strand simulations.

Fig. 5.

CaT_AMP (A), V_m (B), I_to1 (C), I_Ca,L (D), and I_rel (E) in control and after 100% I_to1 block in single-cell (top) and strand (bottom) simulations. In B–E, CL_S1 = 1 s. Arrows in B denote time and V_m at peak I_Ca,L.

Fig. 6.

A: APD (normalized to maximum) as a function of diastolic interval (DI) during restitution at CL_S1 = 2 s in control and after 100% I_to1 block in strand simulations. Results are compared with data from canine epicardial (42) and endocardial (23) tissue experiments. B–D: V_m, I_to1, and I_Kr during APD restitution at S2 coupling intervals (CI_S2) of 0.3 and 2 s in control and after I_to1 block in the strand. Inset in B shows very similar AP after I_to1 block at short CI_S2 (thick gray trace) and long CI_S2 (thin gray trace).

Fig. 7.

A: percent increase in steady-state APD after 100% I_Ks block as a function of CL_S1. B–E: I_Ks current density and state occupancy of zone 2, zone 1, and open state at steady-state for CL_S1 = 0.25, 0.5, and 1 s.

Fig. 8.

A: premature APs at S2 coupling intervals (CI_S2) of 0.26, 0.3, and 0.4 s for CL_S1 = 2 s. B: percent increase after 100% I_Ks block as a function of coupling interval. C–F: I_Ks activation and occupancy of open state, zone 2, and zone 1 for restitution protocol in A.

Fig. 9.

A and B: accommodation of APD and [Na⁺]_i,max after a change from CL = 1 s to CL = 0.5 s in control, after I_Ca,L block, after block of SR Ca²⁺ release (I_Rel) and uptake (I_up), and with [Na⁺]_i clamped to its steady-state value at CL = 0.5 s. C: I_NaK for the 1st beat and a steady-state (SS) beat after change from CL = 1 s to CL = 0.5 s.

Fig. 10.

Integrated Ca²⁺ (A) and Na⁺ (C) fluxes and maximum [Ca²⁺]_i (B) calculated for each beat during transition from steady state at CL = 1 s to steady state at CL = 0.5 s. Integrated sarcolemmal Ca²⁺ influx was calculated as I_Ca,L + I_Cab and efflux as I_NaCa + I_pca. Integrated Na⁺ influx was calculated as I_NaCa + I_Na + I_NaL + I_Nab + CT_NaCl and Na⁺ efflux as I_NaK.

Fig. 11.

A and B: dependence of APD restitution and [Na⁺]_i,max on pacing rate (CL_S1). C: dependence of I_NaK on pacing rate (CL_S1) at constant S2 coupling interval (CI_S2 = 2 s).