Fferent combinations of activation and inactivation rates, defining a boundary between uniform and alternating responses (Figures 3B, C, D), which moved depending on stimulation frequency (Figure 3E). As expected, the area of alternating responses increased as the stimulation frequency was increased (Figure 3E). For some parameters (gray area in Figures 3B, C and D) we also observed the presence of a complex beat-to-beat behavior, including 3:1 or 4:1 rhythms, or seemingly chaotic dynamics. To check that the observed alternations were due to instability in the calcium handling dynamics, with no significant effect of voltage dynamics on their generation, we repeated the previous simulations using an AP clamp protocol, obtaining the same resultsCa2+ Alternans and RyR2 RefractorinessFigure 2. PD1-PDL1 inhibitor 1 site 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 clampingprotocol 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. doi:10.1371/journal.pone.0055042.g(Figure S3 in Appendix S1). As we proceed to show, cytosolic calcium alternans appeared due to oscillations in either SR calcium loading or RyR2 dynamics.Mechanisms Underlying Cytosolic Calcium AlternansIn order to investigate how SR calcium load and fractional recovery of the RyR2s from inactivation contributed to cytosolic calcium alternans, we clamped either of these variables and determined which of the clamping procedures was able to eliminate the cytosolic calcium alternation. The simultaneous clamping of the SR Ca load and of the rate of recovered RyR2 always eliminated alternans, both with current and AP clamp. Thus, in all the cases discussed here the mechanism for calcium alternans is Oltipraz chemical information related to either SR Ca load, recovery of the RyR2 from inactivation, or both. Figure 4A shows an example where only a clamping of the SR calcium load eliminated alternans, demonstrating that, in this case, alternation in SR calcium load is necessary for the induction of alternans. Figure 4B shows an example where calcium alternans disappears only when the fraction of recovered RyR2s is clamped, and thus the responsible mechanism is alternation in the number of RyR2 that are recovered from inactivation. Figures 4C and 4D show examples where clamping of either variable eliminates calcium alternans or neither of them alone does. Thus, in Figure 4C both mechanisms are necessary to sustain alternans, while in Figure 4D either of them by itself is able to maintain it, without being necessary the presence of the other. Each of these examples was obtained with different combinations of activation and inactivation rates. To determine which mechanisms can sustain calcium alternans for any given combination of the RyR2 activation and inactivation rates, we repeated the simulations shown in Figure 3D clamping either SR calcium load (Figure 5B) or the fraction of recovered RyR2s (Figure 5C). When the SR calcium load was clamped (Figure 5B), the boundary denoting the onset of alternans moved to lower values of activation.Fferent combinations of activation and inactivation rates, defining a boundary between uniform and alternating responses (Figures 3B, C, D), which moved depending on stimulation frequency (Figure 3E). As expected, the area of alternating responses increased as the stimulation frequency was increased (Figure 3E). For some parameters (gray area in Figures 3B, C and D) we also observed the presence of a complex beat-to-beat behavior, including 3:1 or 4:1 rhythms, or seemingly chaotic dynamics. To check that the observed alternations were due to instability in the calcium handling dynamics, with no significant effect of voltage dynamics on their generation, we repeated the previous simulations using an AP clamp protocol, obtaining the same resultsCa2+ Alternans and RyR2 RefractorinessFigure 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 clampingprotocol 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. doi:10.1371/journal.pone.0055042.g(Figure S3 in Appendix S1). As we proceed to show, cytosolic calcium alternans appeared due to oscillations in either SR calcium loading or RyR2 dynamics.Mechanisms Underlying Cytosolic Calcium AlternansIn order to investigate how SR calcium load and fractional recovery of the RyR2s from inactivation contributed to cytosolic calcium alternans, we clamped either of these variables and determined which of the clamping procedures was able to eliminate the cytosolic calcium alternation. The simultaneous clamping of the SR Ca load and of the rate of recovered RyR2 always eliminated alternans, both with current and AP clamp. Thus, in all the cases discussed here the mechanism for calcium alternans is related to either SR Ca load, recovery of the RyR2 from inactivation, or both. Figure 4A shows an example where only a clamping of the SR calcium load eliminated alternans, demonstrating that, in this case, alternation in SR calcium load is necessary for the induction of alternans. Figure 4B shows an example where calcium alternans disappears only when the fraction of recovered RyR2s is clamped, and thus the responsible mechanism is alternation in the number of RyR2 that are recovered from inactivation. Figures 4C and 4D show examples where clamping of either variable eliminates calcium alternans or neither of them alone does. Thus, in Figure 4C both mechanisms are necessary to sustain alternans, while in Figure 4D either of them by itself is able to maintain it, without being necessary 
the presence of the other. Each of these examples was obtained with different combinations of activation and inactivation rates. To determine which mechanisms can sustain calcium alternans for any given combination of the RyR2 activation and inactivation rates, we repeated the simulations shown in Figure 3D clamping either SR calcium load (Figure 5B) or the fraction of recovered RyR2s (Figure 5C). When the SR calcium load was clamped (Figure 5B), the boundary denoting the onset of alternans moved to lower values of activation.
