Parameters for activation and inactivation are: top panels, left: ka = 10 mM22 ms21, ki = 0.05 mM21 ms21, right: ka = 3.5 mM22 ms21, ki = 0.2 mM21 ms21; lower panels, left: ka = 1.0 mM22 ms21, ki = 0.1 mM21 ms21, right: ka = 0.6 mM22 ms21, ki = 0.5 mM21 ms21. doi:10.1371/journal.pone.0055042.gplasmic reticulum calcium fluctuations. Very low inactivation rates correspond, effectively, to situations where the inactivated state is irrelevant since the rate of RyR2 which transit to inactivation is very low. This leads to an effective two-state model of RyR2, which presents alternation due to the steep relationship between SR load and release. Alternans due to SR Ca load has also been obtained numerically by Restrepo et al [8] using different dynamics of the RyR2, with two closed and two open states. Calcium alternans is also induced by a slowing of RyR2 activation, if inactivation is non-negligible. In this case, alternans is abolished by clamping RyR2 recovery but not by clamping SR Ca load, indicating that incomplete RyR2 recovery is the underlying mechanism. The physiological relevance of this condition is emphasized by the results of the post-rest protocol, where we observe that the calcium transient increases for increasing rest times, even when SR Ca load is declining (see Figure S6 in Appendix S1). These simulations also agree with the experimental results by Picht et al [9], linking calcium alternans without fluctuation in SR Ca load with post-rest potentiation. Together, this suggests that the mechanism underlying alternans termed “R” in our simulations can explain the experimental findings of Picht et al. Alternatively, cytosolic calcium alternans at constant diastolic values of SR calcium loading has been explained by Rovetti et al [24] as a combination of effects involving RyR2 recovery, recruitment and randomness of the calcium release units (CaRUs). Their model produces calcium transients that are desynchronized in different parts of the cells, which is in accordance with results from calcium overloaded rat ventricular myocytes by Diaz et al [23]. However, it has been recently shown in human atrial myocytes with normal SR calcium load that calcium release istypically synchronized during Title Loaded From File pacing-induced calcium alternans [11], [25]. In concordance with recent experiments [11], we also show that although oscillations in SR Ca load are present, they 15857111 are not always responsible for calcium alternans. In our analysis of the model, when the SR is loaded above a certain threshold all RyR2s are activated by cSR, since all luminal calcium-binding sites in the RyR2 are filled. Oscillations in cSR can therefore not drive calcium alternans. By contrast, oscillations in RyR2 refractoriness are still able to maintain calcium alternans. Inactivation is dependent on the calcium concentration at the dyadic space, so that a larger calcium depletion produces a bigger fraction of inactivated RyR2 channels, which in turn may cause incomplete RyR2 recovery at fast pacing rates. Under such conditions, there is a steep relation between the calcium released from the SR and the fraction of the recovered RyR2s [26]. This situation is favored when both RyR2 activation and recovery from inactivation are Title Loaded From File slowed. We have shown that is indeed the case considering a situation where both the SR calcium and subsarcolemma calcium concentration remain fixed (see Section 2 in Appendix S1). Under this condition the concentration of calcium in the dyadic space incr.Parameters for activation and inactivation are: top panels, left: ka = 10 mM22 ms21, ki = 0.05 mM21 ms21, right: ka = 3.5 mM22 ms21, ki = 0.2 mM21 ms21; lower panels, left: ka = 1.0 mM22 ms21, ki = 0.1 mM21 ms21, right: ka = 0.6 mM22 ms21, ki = 0.5 mM21 ms21. doi:10.1371/journal.pone.0055042.gplasmic reticulum calcium fluctuations. Very low inactivation rates correspond, effectively, to situations where the inactivated state is irrelevant since the rate of RyR2 which transit to inactivation is very low. This leads to an effective two-state model of RyR2, which presents alternation due to the steep relationship between SR load and release. Alternans due to SR Ca load has also been obtained numerically by Restrepo et al [8] using different dynamics of the RyR2, with two closed and two open states. Calcium alternans is also induced by a slowing of RyR2 activation, if inactivation is non-negligible. In this case, alternans is abolished by clamping RyR2 recovery but not by clamping SR Ca load, indicating that incomplete RyR2 recovery is the underlying mechanism. The physiological relevance of this condition is emphasized by the results of the post-rest protocol, where we observe that the calcium transient increases for increasing rest times, even when SR Ca load is declining (see Figure S6 in Appendix S1). These simulations also agree with the experimental results by Picht et al [9], linking calcium alternans without fluctuation in SR Ca load with post-rest potentiation. Together, this suggests that the mechanism underlying alternans termed “R” in our simulations can explain the experimental findings of Picht et al. Alternatively, cytosolic calcium alternans at constant diastolic values of SR calcium loading has been explained by Rovetti et al [24] as a combination of effects involving RyR2 recovery, recruitment and randomness of the calcium release units (CaRUs). Their model produces calcium transients that are desynchronized in different parts of the cells, which is in accordance with results from calcium overloaded rat ventricular myocytes by Diaz et al [23]. However, it has been recently shown in human atrial myocytes with normal SR calcium load that calcium release istypically synchronized during pacing-induced calcium alternans [11], [25]. In concordance with recent experiments [11], we also show that although oscillations in SR Ca load are present, they 15857111 are not always responsible for calcium alternans. In our analysis of the model, when the SR is loaded above a certain threshold all RyR2s are activated by cSR, since all luminal calcium-binding sites in the RyR2 are filled. Oscillations in cSR can therefore not drive calcium alternans. By contrast, oscillations in RyR2 refractoriness are still able to maintain calcium alternans. Inactivation is dependent on the calcium concentration at the dyadic space, so that a larger calcium depletion produces a bigger fraction of inactivated RyR2 channels, which in turn may cause incomplete RyR2 recovery at fast pacing rates. Under such conditions, there is a steep relation between the calcium released from the SR and the fraction of the recovered RyR2s [26]. This situation is favored when both RyR2 activation and recovery from inactivation are slowed. We have shown that is indeed the case considering a situation where both the SR calcium and subsarcolemma calcium concentration remain fixed (see Section 2 in Appendix S1). Under this condition the concentration of calcium in the dyadic space incr.
