Volume 104, Issue 8, Pages 1752-1763 (April 2013) Modeling the Neuroprotective Role of Enhanced Astrocyte Mitochondrial Metabolism during Stroke  Casey O. Diekman, Christopher P. Fall, James D. Lechleiter, David Terman  Biophysical Journal  Volume 104, Issue 8, Pages 1752-1763 (April 2013) DOI: 10.1016/j.bpj.2013.02.025 Copyright © 2013 Biophysical Society Terms and Conditions

Figure 1 Diagram of neuroprotective role of enhanced astrocyte mitochondrial metabolism. (Left) P2Y1R ligands stimulate IP3-mediated calcium release from the ER of astrocytes, which increases mitochondrial calcium levels leading to the increased production of ATP and neuroprotection. (Right) Schematic of computational model of ER-mitochondrial calcium handling, ATP production, and cell swelling. Biophysical Journal 2013 104, 1752-1763DOI: (10.1016/j.bpj.2013.02.025) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 2 Simulation of ischemia. At t = 20 min, cytosolic glucose concentration is suddenly reduced by 25%. ATP production falls, leading to cell depolarization and swelling. Biophysical Journal 2013 104, 1752-1763DOI: (10.1016/j.bpj.2013.02.025) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 3 Simulation of recovery from glucose deprivation. At t = 40 min, P2Y1R receptor is stimulated, leading to an increase in mitochondrial calcium concentration, ATP production, and reversal of cell depolarization and swelling. Biophysical Journal 2013 104, 1752-1763DOI: (10.1016/j.bpj.2013.02.025) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 4 Simulation of partial recovery from oxygen deprivation. At t = 40 min, P2Y1R receptor is stimulated, leading to an increase in mitochondrial calcium concentration, ATP production, and reversal of cell depolarization and swelling. Biophysical Journal 2013 104, 1752-1763DOI: (10.1016/j.bpj.2013.02.025) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 5 Oscillations during recovery from simulated ischemia. At t = 20 min, glucose and oxygen supply are reduced simultaneously. At t = 40 min, P2Y1R receptor is stimulated, leading to oscillatory behavior and the reversal of cell depolarization and swelling. The dynamics of the model fluxes during this simulation are shown in Fig. S1 in the Supporting Material. Biophysical Journal 2013 104, 1752-1763DOI: (10.1016/j.bpj.2013.02.025) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 6 (Top) Cell membrane potential (A) and volume (B) for different values of glucose supply and MeS. (Bottom) Cell membrane potential (C) and volume (D) for different values of oxygen supply and MeS. In all cases, the cell was simulated in a control state (GLC = 4, Oout = 1, MeS = 0) for 20 min. An ischemic state was then induced by either reducing GLC or Oout or the value shown along the vertical axes for 20 min, while keeping MeS = 0. Finally, MeS was increased to the value shown along the horizontal axes for 20 min. The reported membrane potential and volume correspond to the average Va and vola values over the last 5 min of simulation. Biophysical Journal 2013 104, 1752-1763DOI: (10.1016/j.bpj.2013.02.025) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 7 (A) Increasing the maximal conductance of the KATP current leads to a smaller drop in cytosolic ATP production during stroke-like conditions and enhances the neuroprotective role of 2MeSADP application. Here, there is no PTP. (B) If MeS is sufficiently large, then the system fully recovers for all values of gKatp. (C) Addition of the PTP makes the astrocyte more vulnerable to decreases in glucose levels and weakens the neuroprotective role of 2MeSADP application. Here, gKatp. (D) Similar to panel A, except the PTP is now included. Here, ϕH = 5000. Biophysical Journal 2013 104, 1752-1763DOI: (10.1016/j.bpj.2013.02.025) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 8 (Top) Time courses of the dependent variables and the PTP flux when the PTP is (red, ϕH = 5000) and is not (blue, ϕH = 0) present. Addition of the PTP leads to lower values of ΔΨ, [ATP]m, and [NADH]m and higher values of [H]m during the recovery phase. (Bottom) Projections of the solutions shown on top onto two separate phase spaces. Very shortly after 2MeSADP is applied at t = 1000 s, there is a sharp drop followed by a fast recovery of [H]m and Ψ. Opening of the PTP, however, prevents Ψ from fully recovering, leading to lower values of mitochondrial ATP. Biophysical Journal 2013 104, 1752-1763DOI: (10.1016/j.bpj.2013.02.025) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 9 Schematic of the simplified Magnus-Keizer model. The connections represent relationships between the state variables and input parameters. (Arrowheads and solid circles) Positive and negative coupling, respectively. Biophysical Journal 2013 104, 1752-1763DOI: (10.1016/j.bpj.2013.02.025) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 10 Bifurcation diagrams of the fixed points of Eq. 22 with bifurcation parameter Caps. (A) The dependence of ΔΨ on Caps. (B) The dependence of [ADP]m on Caps. (C) Detail near the maximum in panel A. (D) The function γ defined in the text. Note that γ = −3 at the value of Caps where ΔΨ reaches its maximum. (E and F) Here, the parameter k2 = 0 and both ΔΨ(CaC) and ADPm(Caps) are monotonic. Biophysical Journal 2013 104, 1752-1763DOI: (10.1016/j.bpj.2013.02.025) Copyright © 2013 Biophysical Society Terms and Conditions

Figure 11 Bifurcation diagrams of the fixed points of Eq. 22 with bifurcation parameter O. (A) The dependence of ΔΨ on O. (B) The dependence of ADPm on O. (C) Here, k10 = 1 and k4 = 0.33. The dependence of ADPm on O is no longer monotonic. (D) The function Γ defined in the text. Note that Γ = 1 at the value of O where ADPm has its minimum value. Biophysical Journal 2013 104, 1752-1763DOI: (10.1016/j.bpj.2013.02.025) Copyright © 2013 Biophysical Society Terms and Conditions