Figure 1.
Dynamic protocol for eliminating oscillations in pre-systolic SR Ca load.
Panel A) indicates the moment where the protocol is activated while panel B) shows the intervals where the SERCA dynamics are modified to pump more strongly in order to make the level of SR Ca load reach the same level on each beat. In this case, this level corresponds to 0.83 mM, which is the maximum SR Ca load obtained before the activation of the clamping-protocol. Panel C) shows that, in this case, calcium alternans persists even when oscillations in pre-systolic SR Ca load are eliminated.
Figure 2.
Dynamic protocol for eliminating oscillations in the pre-systolic level of recovered RyRs.
Panel A) indicates the moment where the protocol is activated while panel B) shows the intervals where the recovery dynamics of RyR2s is accelerated at the same time that only a fraction of them remain active. This fraction corresponds to a recovery of 37% of the total RyR2. This is the maximum level present before the clamping-protocol is started, and it is the one we aim to reach at the end of diastole. Panel C) shows that, in this case, calcium alternans is eliminated when oscillations in the level of recovered RyR2s are eliminated.
Figure 3.
Slowing of RyR2 activation or inactivation induces calcium alternans at physiological pacing rates.
A) The effect of increasing the stimulation frequency from 3 Hz to 5 Hz on trasmembrane potential (top panel), fraction of recovered RyRs (top middle panel), SR calcium load (lower middle panel) and cytosolic calcium (lower panel) for fixed activation and inactivation rates of ka = 8.5 mM−2 ms−1, ki = 0.17 mM−1 ms−1 with a recovery time from inactivation of τr = 1/kim = 750 ms. B), C), and D) Color-code graphs showing the amplitude of alternations in the calcium transient amplitude as a function of RyR2 activation and inactivation at a pacing rate of 1 Hz (B), 2 Hz (C), and 3 Hz (D). The horizontal axis represents the RyR2 inactivation rate, while the vertical axis represents the RyR2 activation rate. The alternans amplitude, defined as the difference in peak cytosolic calcium between two consecutive beats, is given in color code with blue representing no alternans and dark red corresponding to strong alternations in peak values. The gray area represents cases where a complex beat-to-beat behavior is observed, including 3∶1 or 4∶1 rhythms, or seemingly chaotic dynamics. E) Borders for the transition to cytosolic calcium alternans obtained with different pacing frequencies.
Figure 4.
Contribution of SR calcium load and recovery of RyR2 from inactivation to the induction of calcium alternans.
Figure 5.
Mechanism underlying the onset of alternans at different activation and inactivation rates.
A) Color-code graph showing the amplitude of the cytosolic alternans at 3 Hz. Blue indicates the absence of alternans and dark red the biggest alternation. B) The same simulations as in A) but with SR Ca loading clamped at presystolic values. C) The same simulations as in A) but with the fraction of recovered RyRs clamped at presystolic values. D) Lines denoting the onset of alternans under: normal (un-clamped) conditions (red line), clamped SR Ca load (green line), and clamped fraction of recovered RyRs (blue line). The gray area represents the region with irregular behavior under un-clamped conditions. These lines delimitate the regions where alternations in SR calcium load (“L”) and RyR2 recovery (“R”) are responsible for calcium alternans. “R,L” indicate the region where alternations in either recovery of RyR2s from inactivation or SR Ca load are capable of maintaining alternans, while “R+L” requires alternation in both mechanisms to sustain cytosolic calcium alternans. The four asterisks correspond to the four examples shown in Figure 4.
Table 1.
Mechanisms of calcium alternans.
Figure 6.
Mechanisms responsible for the onset of alternans for different pacing rates and RyR2 recovery times from inactivation. A)
The limits for the onset of alternans are shown as in Figure 5D (reproduced here in the central panels), for different pacing frequencies: 2 Hz, 3 Hz, 4 Hz (with τr = 750 ms). B) The limits for the onset of alternans for different values of the RyR2 recovery time τr: 200 ms, 750 ms, 1500 ms (at a pacing frequency of 3 Hz).
Figure 7.
Mechanism underlying the onset of alternans at different pacing frequencies and RyR2 recovery times
. The four panels illustrate how the mechanism underlying the induction of cytosolic calcium alternans varies with the stimulation frequency and RyR2 recovery from inactivation. Each panel has three rows of color bars, which indicates the responsible mechanism for the induction of alternans at the different stimulation frequencies. The top bar represents slow RyR2 recovery (τr = 1500 ms), the middle bar intermediate RyR2 recovery (τr = 750 ms) and the lower bar fast RyR2 recovery from inactivation (τr = 200 ms). Colors green, purple, yellow, and brown correspond, respectively, to the regimes R, L, R+L, and R,L of Table 1. Black indicates frequencies where irregular behavior is present. The parameters for activation and inactivation are: top panels, left: ka = 10 mM−2 ms−1, ki = 0.05 mM−1 ms−1, right: ka = 3.5 mM−2 ms−1, ki = 0.2 mM−1 ms−1; lower panels, left: ka = 1.0 mM−2 ms−1, ki = 0.1 mM−1 ms−1, right: ka = 0.6 mM−2 ms−1, ki = 0.5 mM−1 ms−1.