Ation 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. doi:10.1371/journal.pone.0055042.gdynamics under steady-state conditions. Taking into account that elevation of the stimulation frequency induces beat-to-beat alternations in the cytosolic calcium transient upon elevation of the stimulation frequency [4], [7], [9], we identified modifications of the Crenolanib site gating properties of the RyR2 (such as its activation time, inactivation time, and/or the recovery time from inactivation) that were necessary for the model to reproduce these phenomena. For the present analysis activation times ranged from 0.01 to 1x the values used by Shannon et al [17]. These values were chosen to cover the range where RO5190591 Alternans could be induced, but it has also been shown that mutations in the TM10 region of the RyR2 can in fact reduce the RyR2 sensitivity to Ca2+ activation by as much as 1,000 fold less than the wild type [20]. For inactivation Table 1. Mechanisms of calcium alternans.times, we used values that ranged from 0.01 to 2x the value employed by Shannon et al [17], which is also consistent with reports showing that the failure to completely terminate Ca2+ release following channel stimulation may arise as a consequence of a loss of Ca2+-dependent inactivation (8- to 10-fold) [21]. The present RyR2 model includes inactivation processes on a fast time scale, giving rise to refractoriness in release. This is contrary to the behavior in single RyR2 dynamics, where refractoriness of gating has never been observed and inactivation processes are too slow to be significant on a beat-to-beat time scale. Thus, the RyR2 dynamics in the present model must be understood as phenomenologically modeling the collective behavior of several RyR2s orMechanism “R” Clamping protocol SR Clamping RyR2 Clamping Alternans Persists Alternans Disappears “L” Alternans Disappears Alternans Persists “R+L” Alternans Disappears Alternans Disappears “R, L” Alternans Persists Alternans Persists“R” stands for alternans due to alternation in RyR2 recovery from inactivation, “L” stands for alternans due to alternation in SR Ca load, “R+L” stands for alternans that require both oscillations in the recovery of RyR2s and in SR Ca load. Finally, “R,L” stands for alternans where both mechanisms contribute but either can sustain it. The case where both protocols were applied at the same time is not shown since, in all cases, alternans disappeared. doi:10.1371/journal.pone.0055042.tCa2+ Alternans and RyR2 RefractorinessFigure 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 24786787 in the central panels), for different pacing frequencies: 2 Hz, 3 Hz, 4 Hz (with tr = 750 ms). B) The limits for the onset of alternans for different values of the RyR2 recovery time tr: 200 ms, 750 ms, 1500 ms (at a pacing frequency of 3 Hz). doi:10.1371/journal.pone.0055042.gclusters of RyRs that generate calcium sparks, where long time refractoriness has been observed. The model used does not consider stochastic variations among calcium release units (CaRUs), and can therefore not account for asynchronous release. Indeed, the model does not present calcium waves, although complex or chaotic be.Ation 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. doi:10.1371/journal.pone.0055042.gdynamics under steady-state conditions. Taking into account that elevation of the stimulation frequency induces beat-to-beat alternations in the cytosolic calcium transient upon elevation of the stimulation frequency [4], [7], [9], we identified modifications of the gating properties of the RyR2 (such as its activation time, inactivation time, and/or the recovery time from inactivation) that were necessary for the model to reproduce these phenomena. For the present analysis activation times ranged from 0.01 to 1x the values used by Shannon et al [17]. These values were chosen to cover the range where alternans could be induced, but it has also been shown that mutations in the TM10 region of the RyR2 can in fact reduce the RyR2 sensitivity to Ca2+ activation by as much as 1,000 fold less than the wild type [20]. For inactivation Table 1. Mechanisms of calcium alternans.times, we used values that ranged from 0.01 to 2x the value employed by Shannon et al [17], which is also consistent with reports showing that the failure to completely terminate Ca2+ release following channel stimulation may arise as a consequence of a loss of Ca2+-dependent inactivation (8- to 10-fold) [21]. The present RyR2 model includes inactivation processes on a fast time scale, giving rise to refractoriness in release. This is contrary to the behavior in single RyR2 dynamics, where refractoriness of gating has never been observed and inactivation processes are too slow to be significant on a beat-to-beat time scale. Thus, the RyR2 dynamics in the present model must be understood as phenomenologically modeling the collective behavior of several RyR2s orMechanism “R” Clamping protocol SR Clamping RyR2 Clamping Alternans Persists Alternans Disappears “L” Alternans Disappears Alternans Persists “R+L” Alternans Disappears Alternans Disappears “R, L” Alternans Persists Alternans Persists“R” stands for alternans due to alternation in RyR2 recovery from inactivation, “L” stands for alternans due to alternation in SR Ca load, “R+L” stands for alternans that require both oscillations in the recovery of RyR2s and in SR Ca load. Finally, “R,L” stands for alternans where both mechanisms contribute but either can sustain it. The case where both protocols were applied at the same time is not shown since, in all cases, alternans disappeared. doi:10.1371/journal.pone.0055042.tCa2+ Alternans and RyR2 RefractorinessFigure 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 24786787 in the central panels), for different pacing frequencies: 2 Hz, 3 Hz, 4 Hz (with tr = 750 ms). B) The limits for the onset of alternans for different values of the RyR2 recovery time tr: 200 ms, 750 ms, 1500 ms (at a pacing frequency of 3 Hz). doi:10.1371/journal.pone.0055042.gclusters of RyRs that generate calcium sparks, where long time refractoriness has been observed. The model used does not consider stochastic variations among calcium release units (CaRUs), and can therefore not account for asynchronous release. Indeed, the model does not present calcium waves, although complex or chaotic be.
