A Thermodynamic Model of the Cardiac Sarcoplasmic/Endoplasmic Ca2+ (SERCA) Pump  Kenneth Tran, Nicolas P. Smith, Denis S. Loiselle, Edmund J. Crampin  Biophysical Journal  Volume 96, Issue 5, Pages 2029-2042 (March 2009) DOI: 10.1016/j.bpj.2008.11.045 Copyright © 2009 Biophysical Society Terms and Conditions

Figure 1 Schematic of the 12-state cardiac SERCA pump model. The binding of Ca2+ from both the cytosol and SR lumen is modeled as a partially cooperative mechanism with different Kd values for the first and second Ca2+ binding. There are five H+ binding events in the model: two for the competitive binding of H+ to the Ca2+-binding sites, two for the binding of H+ involved in the Ca2+/H+ counter-transport, and one for the release of the metabolic H+. The boxed Ps denote the probability of being in a particular state. The conformation change from E1 to E2 and back again occurs between states P5 and P6 (concomitant with ADP release), and P10 and P1 (concomitant with Pi release), respectively. For each cycle in the clockwise (forward) direction, the pump transports two Ca2+ for each ATP that is hydrolyzed. The dotted boxes indicate the partial reactions (ion binding) that are assumed to be rapid equilibrium steps (see Model Simplification: Rapid Equilibrium Assumptions). The subscripts i and sr are equivalent to 1 and 2 in the E1-E2 notation, respectively. Biophysical Journal 2009 96, 2029-2042DOI: (10.1016/j.bpj.2008.11.045) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 2 Schematic of cardiac SERCA model where the Ca2+ binding mechanism is assumed to be fully cooperative. States P3 and P3a no longer exist as they quickly evolve into P4 from the binding of the second Ca2+. Similarly in the SR lumen, state P7 has evolved into P6. Biophysical Journal 2009 96, 2029-2042DOI: (10.1016/j.bpj.2008.11.045) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 3 Schematic of the simplified three-state model. Application of the rapid equilibrium assumption to the ion-binding partial reactions (states within the two dotted boxes in Fig. 1) results in a simplified three-state model. The apparent rate constants (αi±, i = 1, 2, 3) replace the forward and backward rate constants and are a function of ion concentrations and dissociation constants. Biophysical Journal 2009 96, 2029-2042DOI: (10.1016/j.bpj.2008.11.045) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 4 The fit of the three-state model with fully cooperative Ca2+ binding (Fig. 2) to the pH-dependent Ca2+ binding data from Ji et al. (28). Biophysical Journal 2009 96, 2029-2042DOI: (10.1016/j.bpj.2008.11.045) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 5 The fit of the three-state model with fully cooperative Ca2+ binding (Fig. 2) to pH data from Ji et al. (28). Biophysical Journal 2009 96, 2029-2042DOI: (10.1016/j.bpj.2008.11.045) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 6 The fit of the three-state model with fully cooperative Ca2+ binding (Fig. 2) to Pi phosphorylation data from Dode et al. (41). Biophysical Journal 2009 96, 2029-2042DOI: (10.1016/j.bpj.2008.11.045) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 7 The fit of the three-state model with fully cooperative Ca2+ binding (Fig. 2) to ATP and ADP-dependence data from Sakamoto and Tonomura (42). Descending from the top curve, the ADP concentrations are 0 mM, 20 mM, 40 mM, 60 mM, and 100 mM. Biophysical Journal 2009 96, 2029-2042DOI: (10.1016/j.bpj.2008.11.045) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 8 The effect of changes in the net free energy on the cycle pump rate at different luminal Ca2+ concentrations. The top curve is at [Ca2+]sr = 1 mM, increasing by 0.5 mM for each curve up to 3.5 mM for the lowest curve. The free energy of ATP hydrolysis is reduced by increasing [Pi]. Other conditions in the simulation: ATP = 5 mM, ADP = 36.3 μM, pH = 7, [Ca2+]i = 1 μM. Biophysical Journal 2009 96, 2029-2042DOI: (10.1016/j.bpj.2008.11.045) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 9 The SERCA model predicts a reversal point when the net free energy is zero. However, the rate at which the pump reverses is a function of the model parameters. In the figure above, the free energy of ATP hydrolysis is reduced by increasing either [Pi] or [MgADP]. Increasing [Pi] causes the pump to reverse at an appreciable rate beyond the reversal point. However, increasing [MgADP] results in the pump slowing down considerably as it passes through the reversal point. [MgATP] = 5 mM for both curves. But when [MgADP] is increased while keeping [MgATP] low (10 μM), there is an appreciable reversal rate because the inhibitory effect of MgATP binding is reduced. Other conditions in the simulation: pH = 7, [Ca2+]i = 1 μM, [Ca2+]sr = 2 mM. Biophysical Journal 2009 96, 2029-2042DOI: (10.1016/j.bpj.2008.11.045) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 10 Application of the rapid equilibrium assumption to the ATP binding step reduces the forward and back binding constants (between states P1 and P2) to a single dissociation constant, Kd,ATP. The ATP binding step becomes lumped with the Ca2+ and H+ binding steps as outlined by the top dotted box. Biophysical Journal 2009 96, 2029-2042DOI: (10.1016/j.bpj.2008.11.045) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 11 Application of the rapid equilibrium assumption to the ATP binding step reduces the three-state model further to a two-state model. The releases of ADP and Pi are assumed to be concomitant with the conformational change of the SERCA enzyme from the E1 to E2 state and are therefore modeled as relatively slower reactions. Equations for the two-state model are given in the Appendix. Biophysical Journal 2009 96, 2029-2042DOI: (10.1016/j.bpj.2008.11.045) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 12 Simulations comparing the two- and three-state models show that they are identical when the ATP concentration is in the μM range. Conditions for simulation: pH = 7, [Ca2+]i = 1 μM, [Ca2+]sr = 1 mM, Pi = 1 mM. Biophysical Journal 2009 96, 2029-2042DOI: (10.1016/j.bpj.2008.11.045) Copyright © 2009 Biophysical Society Terms and Conditions

Figure 13 An increase in the free [Ca2+]sr leads to a decrease in the pump rate until a reversal point is reached where the pump begins to cycle in the reverse direction. The model predicts that at [MgATP] = 5 mM, the rate at which the pump cycles in reverse is almost negligible over either the physiological or the ischemic range of [Pi]. The inset shows the same set of curves but at the lower [MgATP] of 100 μM. A decrease in [MgATP] reduces the inhibitive effect of MgATP binding resulting in larger reversal rates. Other conditions in the simulation: ADP = 36.3 μM, pH = 7, [Ca2+]i = 150 nM. Biophysical Journal 2009 96, 2029-2042DOI: (10.1016/j.bpj.2008.11.045) Copyright © 2009 Biophysical Society Terms and Conditions