FIGURE 8.

Stability and bifurcations of intracellular Ca²⁺ dynamics in voltage-clamped mTP06b model cell. (A) Dynamics of intracellular Ca²⁺ concentrations as well as Ca²⁺-dependent sarcolemmal currents in the Na_i-fixed voltage-clamped model cell under the control condition (P_up = 1) and the conditions of β-AS (P_up = 1.41, 1.67, and 2.00). Temporal behaviors of the voltage-clamped model cell during a train of 1-s step depolarization from −85 mV to −10 mV at 0.5 Hz were computed for 10 min; Ca_i, Ca_ss, Ca_SR, I_CaL and I_NCX for the last 12 s (6 pulses) are shown as steady-state dynamics. Spontaneous SR Ca²⁺ releases, as evidenced by abrupt falls of Ca_SR and increases in Ca_i, Ca_ss and inward I_NCX with attenuated I_CaL, occurred at higher P_up (indicated by the dots). (B) One-parameter bifurcation diagrams of the equilibrium point (EP) and extrema of limit cycles (LC_min/max) and spontaneous Ca_i oscillations (CaO_min/max) as functions of V_m for the voltage-clamped model cell (left and middle). The middle panel shows an enlarged diagram of the rectangular area in the left panel. The periods of spontaneous Ca²⁺ oscillations (CaO) and limit cycles (LC) are also plotted against V_m (right). H_1–2, Hopf bifurcations of the EP; NS_1–2, Neimark-Sacker bifurcations of the LC. (C) Two-parameter diagrams on the V_m–P_up (left), V_m–I_NCX (middle) and V_m–g_CaL (right) planes, indicating how the unstable V_m range changed depending on P_up, I_NCX and I_CaL. HB values, i.e., the critical V_m at which an EP is (de)stabilized are plotted as functions of P_up, I_NCX and I_CaL for the Na_i-fixed mTP06b model; the HB points were very close to the Neimark-Sacker bifurcation points at which LCs were destabilized with the emergence of CaOs.