Cardiac Alternans Occurs through the Synergy of Voltage- and Calcium-Dependent Mechanisms

Figure A1. Calcium in the subspaces during (A) Ca2+ sparks and (B) Ca2+ quarks, (C) Dynamics of jSR Ca2+ release, (D) Number of RyR openings, (E) Ca2+-bound calmodulin complex.

Figure A2. A single action potential at 1 Hz pacing. To emulate the excitation-contraction of the cell, a stimulus current Istim = −6.5189 µA/cm2 was given during 5.0 ms second [40]. (A) [Ca2+]myo, (B) Membrane potential (Vm); (C) Network SR Ca2+ concentration ([Ca]nsr); (D) RyR2 open probability (PO,RyR); (E) L-type Ca2+ channel open probability (PO,LCC); (F) subspace free Ca2+ concentration ([Ca2+]ds); (G) L-type Ca2+ current (ILCC); (H) NCX current (Incx); (I) PMCA current (IPMCA); (J) Ca2+ current (INa); (K) Na/K exchanger current; (L) K1 current; (M) slow component of transient-outward K+ current; (N) fast-component of transient-outward K+ current; (O) Na+ current; (P) Na+-K+ ATPase current; (Q) Background Na+ current.

Figure A3. The amount of Ca2+/CaM complex in the subspace is greater during pacing at 8 Hz compared to acing at 1 Hz pacing leading to increased Ca-dependent inactivation of the L-type channel.

Figure A4. Pacing at 8 Hz pacing produces alternans and a diastolic [Na+]i of 10.2 mM. To emulate the excitation-contraction of the cell, a stimulus current Istim = −6.5189 µA/cm2 was given during 5.0 ms second [40]. (A) [Ca2+]myo; (B) Membrane potential (Vm); (C) Network SR Ca2+ concentration ([Ca2+]nsr); (D) RyR2 open probability (PO,RyR); (E) L-type Ca2+ channel open probability (PO,LCC); (F) subspace free Ca2+ concentration ([Ca2+]ds); (G) L-type Ca2+ current (ILCC); (H) NCX current (Incx); (I) Plasmalemmal Ca2+-ATPase current (IPMCA); (J) background Ca2+ current (ICab); (K) slow transient outward current (Itos); (L) fast transient outward current (Itof); (M) K1 current (M) slow component of transient-outward K+ current; (N) Background K+ current; (O) Na+ current; (P) Na+-K+ ATPase current; (Q) Background Na+ current.

Figure A5. Pacing at 8 Hz pacing produces alternans with diastolic [Na+]I = 20 mM. To emulate the excitation-contraction of the cell, a stimulus current Istim = −6.5189 µA/cm2 was given during 5.0 ms second [40]. (A) [Ca2+]myo; (B) Membrane potential (Vm); (C) Network SR Ca2+ concentration ([Ca2+]nsr); (D) RyR2 open probability (PO,RyR); (E) L-type Ca2+ channel open probability (PO,LCC); (F)subspace free Ca2+ concentration ([Ca2+]ds); (G) L-type Ca2+ current (ILCC); (H) NCX current (Incx); (I) PMCA current (IPMCA); (J) Ca2+ current (INa); (K) Na/K exchanger current; (L) K1 current; (M) slow component of transient-outward K+ current; (N) fast-component of transient-outward K+ current; (O) Na+ current; (P) Na+-K+ ATPase current; (Q) Background Na+ current.

Figure A6. Ca2+-dependent inactivation of the L-type channel occurs at different rates in large and small beats during alternans. (A) The decay in the L-type Ca2+ current for large (red) and small (blue) beats. (B) Fitting an monoexponential curve (f(x) = a × exp(−x/b)) to the decay yielded a = −9.37 pA and b = 0.21 s for the large beat with a R2 = 0.977. (C) Fitting an monoexponential curve (f(x) = a × exp(−x/b)) to the decay yielded a = −55.8 pA and b = 0.46 s for the small beat with a R2 = 0.980, respectively.

Figure 1. Schematic diagram of a ventricular cell that shows only 2 T-tubule branches with 4 or the 20,000 Ca2+ release units. Abbreviations: jSR—junctional sarcoplasmic reticulum; nSR—network sarcoplasmic reticulum; ryr—ryanodine receptor; T-tubule—transverse tubule; NCX—sodium-calcium exchanger; Na/K—sodium-potassium ATP ase; PMCA—plasmalemmal calcium ATPase; SERCA—sarcoplasmic and endoplasmic reticulum calcium ATPase; INa—sodium current; IKss—steady-state (sustained) potassium current; IKtof—fast transient outward potassium current; Itos—slow transient outward potassium current; IK1—inward rectifier potassium current; IbCa = background calcium current; IbK—background potassium current; IbNa—background sodium current.

Figure 2. Schematic diagram of the model (top) for the L-type calcium channel (DHPR channel) from [29]. C1 and C6 are closed states with C6 the resting state. O2 and O3 are the open states that conduct Ca2+ ions with equal conductance. C4 is Ca2+-dependent inactivated state. C5 is the voltage-dependent inactivated state. The fraction of LCC channels in different states during the voltage-clamp of Vstim = +10 mV for 200 ms (bottom).

Figure 3. (A) steady-state inactivation curve (B) steady-state activation curve; (C) voltage dependence of slow inactivation gate time constant (D) voltage dependence of activation gate time constants at different voltages. (E) I-V curve, (F) dynamics of gating variables of the proposed model during an AP—activation gate m (red), inactivation gate h (blue), and slow inactivation gate j (green).

Figure 4. A long trace of calcium dynamics in the (A) myoplasmic [Ca2+], (B) network SR [Ca2+], and (C) Action Potential, (D) L-type current density, and (E) Sodium current density.

Figure 5. Calcium alternans at 8 Hz: (A) Cytosolic calcium, (B) RyR open probability Po (RyR2), (C) membrane potential Vm, (D) L-type Ca2+ current ICaL, (E) Sodium current INa.

Figure 6. Alternans occurs at 8 Hz pacing rate. (A) An example that show a CRU that fires at two contiguous beats, e.g., (X) marks an individual release site that is Act-Act. (B) Alternans in the calcium release seen by the changing amplitude and duration of the [Ca2+]myo. Beat-to-beat variation in CRU’s states where we examine act-act—the fraction of CRU that activate in beat (i) (red) and continue to activate in beat (i + 1), similarly with act-inact (blue), inact-inact (yellow), and inact-act (dark green). (C) The probability of RyR opening at each beat (red = open, black = closed). (D) The fraction of LCC open (states O2-blue and O3-green) during each beat.