E value c?SRClamp before each external excitation (see Figure 1B). The value of c?SRClamp is taken to be equal to the maximum presystolic SR calcium load during the non-clamped dynamics. During the external excitation and SR calcium release, the original SERCA current is used. In this way we do not affect the dynamics of calcium release and 298690-60-5 web re-uptake. More importantly, the dynamics is only affected when all the variables are close to their equilibrium values. As seen in Figure 1B the result is a clamped dynamics where the SR Ca load before each calcium release is constant and where the evolution of the cytosolic calcium transient (Figure 1C) indicates if calcium alternans is affected or not by this clamping. The procedure can be summarized as testing whether calcium alternans disappears when the SERCA current is set 23115181 as 3PO follows: JSERCA Q10{SERCA Vmaxi KmfHc 1z K imfSR H { Kmr H SR H z Kmr??fornTvtv(nz1)T{t0 msJSERCA 10Vmax ( ?SRClamp { SR ) for (nz1)T{t0 vtv(nz1)T ms??Dynamic Clamping ProtocolsDuring alternans, the intracellular cytosolic calcium transient alternates from beat to beat. Whenever this happens there is a corresponding alternation in both the pre-systolic SR calcium load and the level of RyR2 ready to open (not inactivated, i.e. in state R of Figure S1 in Appendix S1). These two types of oscillations are directly related with two mechanisms proposed to account for calcium alternans in the literature. One states that a change in the calcium loading process leads to cytosolic calcium alternans (calcium alternans due to SR calcium load). The other states that the level of RyR2s recovered from inactivation oscillates. An ideal experiment to discern the underlying mechanism would require eliminating the alternation in one of thewhere typically t0 = 150 ms (we use t0 = 75?00 ms for T,240 ms). Equation (1) is the original SERCA uptake, with the parameters given in [17] active during the external excitation, calcium release and first stages of the reuptake. During the last t0 before each beat we substitute the SERCA uptake for a stronger current, which keeps pumping calcium from the cytosol until SR ?SRClamp .Clamping of RyR2 RecoveryFollowing the same idea of the previous clamping protocol, the clamping of RyR2 recovery is achieved changing its dynamics during the 150 ms before each calcium release (see Figure 2). These changes in the RyR2 are 15857111 applied to eliminate dynamically the oscillation in the pre-systolic ratio of recovered RyR2 (R state)Ca2+ Alternans and RyR2 RefractorinessFigure 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. doi:10.1371/journal.pone.0055042.gwithout affecting calcium release and uptake. In this clamping protocol a number of RyR2 channels are disabled at a time t0 before the following beat, with an acceleration of the recovery rate of the remaining RyR2s, so that the final recovery level of receptors before the calcium release is set to a given value Rclamp. The equations for th.E value c?SRClamp before each external excitation (see Figure 1B). The value of c?SRClamp is taken to be equal to the maximum presystolic SR calcium load during the non-clamped dynamics. During the external excitation and SR calcium release, the original SERCA current is used. In this way we do not affect the dynamics of calcium release and re-uptake. More importantly, the dynamics is only affected when all the variables are close to their equilibrium values. As seen in Figure 1B the result is a clamped dynamics where the SR Ca load before each calcium release is constant and where the evolution of the cytosolic calcium transient (Figure 1C) indicates if calcium alternans is affected or not by this clamping. The procedure can be summarized as testing whether calcium alternans disappears when the SERCA current is set 23115181 as follows: JSERCA Q10{SERCA Vmaxi KmfHc 1z K imfSR H { Kmr H SR H z Kmr??fornTvtv(nz1)T{t0 msJSERCA 10Vmax ( ?SRClamp { SR ) for (nz1)T{t0 vtv(nz1)T ms??Dynamic Clamping ProtocolsDuring alternans, the intracellular cytosolic calcium transient alternates from beat to beat. Whenever this happens there is a corresponding alternation in both the pre-systolic SR calcium load and the level of RyR2 ready to open (not inactivated, i.e. in state R of Figure S1 in Appendix S1). These two types of oscillations are directly related with two mechanisms proposed to account for calcium alternans in the literature. One states that a change in the calcium loading process leads to cytosolic calcium alternans (calcium alternans due to SR calcium load). The other states that the level of RyR2s recovered from inactivation oscillates. An ideal experiment to discern the underlying mechanism would require eliminating the alternation in one of thewhere typically t0 = 150 ms (we use t0 = 75?00 ms for T,240 ms). Equation (1) is the original SERCA uptake, with the parameters given in [17] active during the external excitation, calcium release and first stages of the reuptake. During the last t0 before each beat we substitute the SERCA uptake for a stronger current, which keeps pumping calcium from the cytosol until SR ?SRClamp .Clamping of RyR2 RecoveryFollowing the same idea of the previous clamping protocol, the clamping of RyR2 recovery is achieved changing its dynamics during the 150 ms before each calcium release (see Figure 2). These changes in the RyR2 are 15857111 applied to eliminate dynamically the oscillation in the pre-systolic ratio of recovered RyR2 (R state)Ca2+ Alternans and RyR2 RefractorinessFigure 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. doi:10.1371/journal.pone.0055042.gwithout affecting calcium release and uptake. In this clamping protocol a number of RyR2 channels are disabled at a time t0 before the following beat, with an acceleration of the recovery rate of the remaining RyR2s, so that the final recovery level of receptors before the calcium release is set to a given value Rclamp. The equations for th.
