A reaction-diffusion model of ROS-induced ROS release in a mitochondrial network

Abstract

Loss of mitochondrial function is a fundamental determinant of cell injury and death. In heart cells under metabolic stress, we have previously described how the abrupt collapse or oscillation of the mitochondrial energy state is synchronized across the mitochondrial network by local interactions dependent upon reactive oxygen species (ROS). Here, we develop a mathematical model of ROS-induced ROS release (RIRR) based on reaction-diffusion (RD-RIRR) in one- and two-dimensional mitochondrial networks. The nodes of the RD-RIRR network are comprised of models of individual mitochondria that include a mechanism of ROS-dependent oscillation based on the interplay between ROS production, transport, and scavenging; and incorporating the tricarboxylic acid (TCA) cycle, oxidative phosphorylation, and Ca(2+) handling. Local mitochondrial interaction is mediated by superoxide (O2.-) diffusion and the O2.(-)-dependent activation of an inner membrane anion channel (IMAC). In a 2D network composed of 500 mitochondria, model simulations reveal DeltaPsi(m) depolarization waves similar to those observed when isolated guinea pig cardiomyocytes are subjected to a localized laser-flash or antioxidant depletion. The sensitivity of the propagation rate of the depolarization wave to O(2.-) diffusion, production, and scavenging in the reaction-diffusion model is similar to that observed experimentally. In addition, we present novel experimental evidence, obtained in permeabilized cardiomyocytes, confirming that DeltaPsi(m) depolarization is mediated specifically by O2.-). The present work demonstrates that the observed emergent macroscopic properties of the mitochondrial network can be reproduced in a reaction-diffusion model of RIRR. Moreover, the findings have uncovered a novel aspect of the synchronization mechanism, which is that clusters of mitochondria that are oscillating can entrain mitochondria that would otherwise display stable dynamics. The work identifies the fundamental mechanisms leading from the failure of individual organelles to the whole cell, thus it has important implications for understanding cell death during the progression of heart disease.

Figure 1. Schemes of the RD-RIRR mitochondrial network model.

In the RD-RIRR model (A: 1D and B: 2D), neighboring mitochondria are chemically coupled with each other through O₂^.− diffusion. Light and dark gray indicate polarized and depolarized mitochondria, respectively. Arrows indicate release of superoxide anion, O₂ ^.−, and its effect on mitochondrial neighbors. D stands for O₂ ^.− _i diffusion, and S for O₂ ^.− _i scavenging by Cu,Zn SOD and catalase.

Figure 2. Spatial propagation of ΔΨ_m depolarization in the oscillating mitochondrial network: computer simulations using the 1D RD-RIRR model and experimental evidence.

A network consisting of a linear array of 13 mitochondria was analyzed. The mitochondrion in the center (mito_7) was initially depolarized whereas the others on both sides were polarized. A and B) The dynamics of ΔΨ_m and O₂ ^.− _i without O₂^.− coupling through diffusion between mitochondria (i.e., D _O2 ^.− _i = 0). Mitochondria in the row are differentiated by colors, and only one side of the row is shown (i.e., from mito_7 to mito_13). C) ΔΨ_m dynamics in the presence of O₂ ^.− _i diffusion (D _O2 ^.− _i = 4×10⁻⁹ cm² s⁻¹). D and E) Expanded records of the first and second depolarization waves propagating from mito_7 (depolarized in D) through mito_8 (red line) until mito_13. F) Expanded record of the second repolarization wave. G) Montage of the experimental evidence of ΔΨ_m depolarization (left) and repolarization (right) wave propagation obtained in a single cardiomyocyte during laser flash-induced whole cell mitochondrial oscillations. Notice that the mitochondria in the network that depolarized last were the first to repolarize. Mitochondrial oscillations were triggered with a laser flash in cardiomyocytes labeled with 100 nM TMRE. Frame acquisition was every 500 msec. Other imaging conditions were as described in Materials and Methods and . The main parameters changed in the simulations in order to obtain mitochondrial oscillations were the shunt ( = 0.14), and etSOD ( = 1.45 µM) whereas all other parameters were as described in and also listed in the Supplemental Materials (Table S2).

Figure 3. Spatial propagation of ΔΨ_m depolarization in non-oscillating mitochondrial networks using the 1D RD-RIRR model.

A network consisting of a row of 17 mitochondria was analyzed. The mitochondrion in the center (mito_9) was initialized with parameters within the oscillatory domain (shunt = 0.14) whereas the other mitochondria were within the nonoscillatory stable range of parameters (shunt = 0.02). etSOD was 1.45 µM for all mitochondria in the network. A and B) The dynamics of ΔΨ_m and O₂ ^.− _i without O₂^.− coupling through diffusion between mitochondria (i.e., D _O2 ^.− _i = 0). Mitochondria in the row are differentiated by colors, and only part of one side of the row is shown (i.e., from mito_9 to mito_17). C) ΔΨ_m dynamics in the presence of O₂^.− diffusion (D _O2 ^.− _i = 4×10⁻⁹ cm² s⁻¹). D and E) Expanded records of the third depolarization (D) and repolarization (E) waves spanning mito_9 through mito_17. F) Expanded record of O₂^.− during a repolarization wave showing the dynamics of O₂ ^.− _i in each mitochondrion (color coded) with mito_9 showing the highest amount of cytoplasmic O₂ ^.−. G and H) The rate of O₂^.− release from mitochondria to the periplasmic space (Vt _O2 ^.− _i) in the network (G) or in an isolated mitochondrion (H). All other parameters were as described in and also listed in the Supplemental Materials (Table S2).

Figure 4. Simulation of the effect of increasing the ROS shunt in one mitochondrion on row oscillatory behavior using the 1D model.

(A) represents ΔΨ_m without the presence of ROS diffusion (D _O2 ^.− _i = 0); (B) represents ΔΨ_m with the presence of ROS diffusion (D _O2 ^.− _i = 4×10⁻⁹ cm² s⁻¹); (C) enlarged ΔΨ_m depolarization wave; (D) enlarged ΔΨ_m depolarization wave; etSOD = 1.43×10⁻³ mM and all other parameters are as listed in Supplemental Materials Tables S2.1, S2.2, S2.3, S2.4.

Figure 5. Mitochondrial O₂^.− and ΔΨ_m in response to increased exogenous O₂^.− in saponin-permeabilized cardiomyocytes.

Myocytes were loaded with TMRM (100 nM) and CM-H₂DCFDA (2 µM) for at least 20min and imaged using two-photon laser scanning fluorescence microscopy (see Materials and Methods). After loading, the excess dye was washed out and the cells were briefly superfused with a permeabilizing solution (saponin) as previously described . After permeabilization, the myocytes were continuously perfused with an intracellular solution containing GSH∶GSSG at a ratio of 300∶1. The TMRM was included in the medium to avoid depletion of the probe during depolarization-repolarization cycles. A) The TMRM and CM-DCF images of a permeabilized cardiomyocyte at time zero after loading and before (top row image) or after permeabilization and 5min imaging under control conditions (Control, second row) or the presence of KO₂ (10 µM, third row; 20 µM, fourth row; 30 µM, fifth row) after 3min equilibration in each case. RIRR-mediated ΔΨ_m depolarization without a permeability transition occurs at the two lower concentrations, while loss of the CM-DCF probe (∼500MW) from the mitochondrial matrix due to PTP opening occurs at 30 µM KO₂. B) The rates of O₂^.− accumulation as a function of KO₂ concentration. Slopes were calculated when the linear rate of change of the CM-DCF signal stabilized under each condition.

Figure 6. Plot of membrane potential of selected mitochondrial groups that display limited cycle oscillations.

Guinea-pig ventricular myocyte was loaded with TMRM and CM-DCF and then partially permeabilized with 25µg ml⁻¹ saponin as described in Materials and Methods. Image frames were collected every 3.5 seconds using a two-photon laser scanning fluorescence microscope. See also the supplemental materials Video S1.

Figure 7. Simulation of ΔΨ_m depolarization wave propagation in the 2D RD-RIRR model.

In a network consisting of 500 mitochondria (10×50), 6 of which were initially depolarized while the others stayed polarized. A) Spatial propagation of ΔΨ_m depolarization (left) and O₂ ^.− _i (right) with a rate of 200 µm s⁻¹; B) ΔΨ_m dynamics, and (C, D) expanded views of ΔΨ_m depolarization in the x and y directions, respectively, corresponding to the 500 mitochondria in the network. Shunt = 0.14; etSOD = 1.43 µM; D _O2 ^.− _i = 2×10⁻¹⁰ cm² s⁻¹. All other parameters were as described in and also listed in the Supplemental Materials (Table S2).

Figure 8. Increasing the fraction of O₂^.− production from 0.02 to 0.14 in ∼1% of 500 mitochondria induces propagation of membrane potential depolarization wave and elicits whole network oscillations.

A) ΔΨ_m; B) enlarged ΔΨ_m depolarization wave in the x direction; and (C) enlarged ΔΨ_m depolarization wave in the y direction. For mito(j,k) (j = 4 or 5; k = 5 or 6), shunt = 0.14; for all other mitochondria, shunt = 0.02. Other parameters and initial conditions were same for all mitochondria and listed in Supplemental Materials Tables S2.1, S2.2, S2.3, S2.4. D_O2^.−_i = 4×10⁻¹¹ cm² s⁻¹. D) Selected images of a pair of TMRM-loaded canine ventricular myocytes (cell-cell junction indicated by the white arrow in left panel) which displayed 22 consecutive oscillations (see time series in Supplemental Materials, Video S3) that originated at the end of the righthand cell. Images within each panel were acquired at a 1 second frame rate and depict the 1st (left panel), 11th (center panel), and 14th cycle of ΔΨ_m oscillation (right panel). Entrainment was indicated by an increase in the area of the oscillating cluster after a number of cycles until the whole cell (up to the border of the neighboring cell) was included.

Figure 9. Effect of D _O2 ^.− _i or etSOD on the propagation rate of ΔΨ_m depolarization wave.

A and B) Increasing D _O2 ^.− _i by two orders of magnitude (from 4×10⁻¹¹ to 4×10⁻⁹ cm² s⁻¹) accelerated wave propagation from 155 to 486 µm s⁻¹. C and D) decreasing etSOD from 1.43 to 1.33 mM decreased the propagation time from 126 to 110 ms. shunt = 0.14, etSOD = 1.43 µM and D _O2 ^.− _i = 4×10⁻⁹ cm² s⁻¹ except where specifically indicated. Other parameters and initial conditions were the same for all mitochondria (Supplemental Materials, Tables S2 and S3).

Figure 10. Depolarization of even a single mitochondrion can evoke ΔΨ_m collapse of almost the entire network when a cell is at the edge of criticality.

Mitochondrial depolarization was triggered with a laser flash (1×1 pixel) in cardiomyocytes labeled with 100 nM TMRE. Frame acquisition was every 500 msec. Other imaging conditions were as described in Materials and Methods.