Regulation of Ca2+ and electrical alternans in cardiac myocytes: role of CAMKII and repolarizing currents

Abstract

Alternans of cardiac repolarization is associated with arrhythmias and sudden death. At the cellular level, alternans involves beat-to-beat oscillation of the action potential (AP) and possibly Ca(2+) transient (CaT). Because of experimental difficulty in independently controlling the Ca(2+) and electrical subsystems, mathematical modeling provides additional insights into mechanisms and causality. Pacing protocols were conducted in a canine ventricular myocyte model with the following results: 1) CaT alternans results from refractoriness of the sarcoplasmic reticulum Ca(2+) release system; alternation of the L-type calcium current has a negligible effect; 2) CaT-AP coupling during late AP occurs through the sodium-calcium exchanger and underlies AP duration (APD) alternans; 3) increased Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) activity extends the range of CaT and APD alternans to slower frequencies and increases alternans magnitude; its decrease suppresses CaT and APD alternans, exerting an antiarrhythmic effect; and 4) increase of the rapid delayed rectifier current (I(Kr)) also suppresses APD alternans but without suppressing CaT alternans. Thus CaMKII inhibition eliminates APD alternans by eliminating its cause (CaT alternans) while I(Kr) enhancement does so by weakening CaT-APD coupling. The simulations identify combined CaMKII inhibition and I(Kr) enhancement as a possible antiarrhythmic intervention.

FIG. 1

(A) Ventricular myocyte model. Symbols are defined in Appendix Table I. Model equations are provided (including code) in research section of http://rudylab.wustl.edu. (B) SR Ca²⁺ release model. (C) Variable gain. Measured (grey) ([63], reproduced with permission) and simulated (black) excitation-contraction coupling (ECC) gain as function of membrane voltage. (D) Graded release. Ca²⁺ released by RyR (∫_CL I_Reldt, CL=1000 ms) as function of peak I_Ca(L). (E) Fractional SR Ca²⁺ release. Ca²⁺ released by RyR (∫_CL=1000 I_Reldt) as function of JSR end-diastolic loading ([Ca²⁺]_JSR,t) in percentage of [Ca²⁺]_JSR,t.

FIG. 2

(A) Simulated and (B) experimental ([10], reproduced with permission) time course of CaMKII activity at stimulation rates of 1 Hz, 2.5 Hz and 4 Hz; CaT duration and amplitude are held constant at 200 ms and 20 μmol/L. Different time scales reflect different isoforms in model and experiment (see text). (C) Simulated and (D) measured [10] frequency dependence of CaMKII activity for indicated CaT durations (CaTd). (E) Time course of AP, CaT, CaMKII ctivity and [Ca²⁺]_JSR at 1 Hz stimulation rate. Black: control; grey: AP-clamp pacing with wice APD. (F) CaMKII activity as function of pacing rate for different AP-clamp APDs; control (black), 1.5xAPD (dashed-dotted grey), 2xAPD (dashed grey).

FIG. 3

Simulated (top) and measured (bottom)([60], reproduced with permission) CaT during pacing at 0.25-,0.5-,1-, and 2-Hz. Descending limb of CaT is fit by a single exponential with time constant τ. (B) Simulated and (C) measured (mouse, force)([12], reproduced with permission) effect of CaMKII inhibition (by KN-93) on rate of CaT decline and mechanical relaxation. (D) Simulated effect of CaMKII inhibition on force-frequency (CaT-frequency) relation. (E) Corresponding experimental data ([69], reproduced with permission) (rabbit, time-derivative of ventricular pressure, dP/dt).

FIG. 4

APD and CaT rate-adaptation curves. Insets show bifurcation portions on enlarged scale. (A) and (B) Guinea pig (C) and (D) Canine. Inset in (C) shows experimental data ([23], reproduced with permission).

FIG. 5

AP and CaT clamp protocols. (A) AP (top), CaT (middle) and I_Ca(L)(bottom), during alternans at 4Hz. (B) AP clamp with short (grey) or long (black) AP. In spite of AP clamping (top), calcium subsystem oscillates (bottom). (C) Clamping CaT (bottom) to its small (grey) or large (black) waveform eliminates AP alternans (top). (D) Clamping I_Ca(L) (bottom) to its small (grey) or large (black) waveform does not eliminate AP (top) or CaT (middle) alternans.

FIG. 6

(A) Superimposed AP, CaT, I_NaCa and I_Kr of consecutive beats during alternans at CL=250 ms. (B) Measured (canine) ([24], reproduced with permission) AP and I_Kr during alternans.

FIG. 7

Steady state SR Ca²⁺ flux balance during alternans. (A) Dependence of ΔCa²⁺=max(CaT)-min (CaT) on JSR Ca²⁺ content during alternans at 5 Hz. Simulation (top) is compared to experiment (rat)([13], reproduced with permission) (bottom). Only 40% change in [Ca²⁺]_JSR leads to 4-fold change in ΔCa²⁺. [Ca²⁺]_JSR,t= free and buffered Ca²⁺ concentration in JSR before release; black (grey) bars correspond to larger (smaller) [Ca²⁺]_JSR,t, respectively. Data are normalized to small [Ca²⁺]_JSR,t. (B) Total end-diastolic SR Ca²⁺ content ([Ca²⁺]_JSR,t and [Ca²⁺]_NSR) as function of rate. (C) Free Ca²⁺ in JSR ([Ca²⁺]_JSR) as function of frequency. (D) Total Ca²⁺ released by RyR (∫_CL I_Reldt, black thick line), reloaded into NSR [∫_CL(I_up − I_leak)dt, grey] and translocated from NSR to JSR (∫_CL I_trdt, black thin line) over one cycle, as function of frequency.

FIG. 8

(A) APD (top) and ΔCa²⁺ (bottom) adaptation curves for three different levels of CaMKII activity: control (100 %), 25 % elevation (125 %) or complete block (0 %). (B) Effect of I_Kr on APD and CaT alternans. APD (top) and CaT (bottom) adaptation curves for three different levels of I_Kr conductance: control (100%), 300% elevation and 50 % reduction. Inset: superimposed consecutive APs at 5 Hz for I_Kr increase of 300%.