Mitochondrial oscillations and waves in cardiac myocytes: insights from computational models

Abstract

Periodic cellwide depolarizations of mitochondrial membrane potential (PsiM) which are triggered by reactive oxygen species (ROS) and propagated by ROS-induced ROS release (RIRR) have been postulated to contribute to cardiac arrhythmogenesis and injury during ischemia/reperfusion. Two different modes of RIRR have been described: PsiM oscillations involving ROS-sensitive mitochondrial inner membrane anion channels (IMAC), and slow depolarization waves related to mitochondrial permeability transition pore (MPTP) opening. In this study, we developed a computational model of mitochondria exhibiting both IMAC-mediated RIRR and MPTP-mediated RIRR, diffusively coupled in a spatially extended network, to study the spatiotemporal dynamics of RIRR on PsiM. Our major findings are: 1), as the rate of ROS production increases, mitochondria can exhibit either oscillatory dynamics facilitated by IMAC opening, or bistable dynamics facilitated by MPTP opening; 2), in a diffusively-coupled mitochondrial network, the oscillatory dynamics of IMAC-mediated RIRR results in rapidly propagating (approximately 25 microm/s) cellwide PsiM oscillations, whereas the bistable dynamics of MPTP-mediated RIRR results in slow (0.1-2 microm/s) PsiM depolarization waves; and 3), the slow velocity of the MPTP-mediated depolarization wave is related to competition between ROS scavenging systems and ROS diffusion. Our observations provide mechanistic insights into the spatiotemporal dynamics underlying RIRR-induced PsiM oscillations and waves observed experimentally in cardiac myocytes.

Figure 1

Schematic diagrams of ROS-induced ROS release models. (A) The single mitochondrion model including both IMAC- and MPTP-mediated pathways. (B) Schematic diagram of the spatial model of mitochondrial network. (C) For computational purposes, each unit is composed of 3 × 3 voxels representing a mitochondrion with its surrounding cytoplasm: the center voxel represents both the matrix (black) and the intermembrane space (gray), and the surrounding eight lattices are the neighboring cytoplasm. The relative volumes of each type of voxel are marked proportionately to the basic unit of volume Δv, corresponding to a volume ratio among matrix, intermembrane space, and cytoplasm of 3:1:12.

Figure 2

Dynamical behaviors of the single mitochondrion model. (A) Steady-state matrix superoxide concentration ([O⁻₂]_M, black line) and IMAC open probability (P_IMAC, gray line) versus k_shunt. Dashed segments are unstable steady states. (B) Steady-state matrix H₂O₂ concentration ([H₂O₂]_M, gray line) and MPTP open probability (P_MPTP, gray line) versus k_shunt. Dashed segments are unstable steady states. Loss of stability of the steady state leads to oscillations (OSC zones in A and B) and bistability (BS zones in A and B). Dashed arrow indicates that as k_shunt increases continuously, a sudden jump occurs in H₂O₂ concentration. (C) The intermembrane superoxide concentration ([O⁻₂]_I, dashed line) and intermembrane H₂O₂ concentration ([H₂O₂]_I, solid line) versus time for k_shunt = 0.08 mM/s, which is in the oscillatory regime. (D) The intermembrane H₂O₂ concentration in the bistable regime showing two stable steady states (solid and dashed lines) resulted from two initial conditions at k_shunt = 0.2 mM/s. (E) Steady-state matrix H₂O₂ concentration ([H₂O₂]_M) versus k_shunt and RED_Total. The thick segments are the stable steady states. The thin segments are unstable steady states. “OSC” and “BS” mark the oscillatory and bistable regions, respectively.

Figure 3

Cellwide Ψ_M oscillations due to fast waves of IMAC-mediated RIRR. (A–C) Periodic cellwide Ψ_M oscillations over a long timescale are shown in the line scan in panel C, with the scanned line and laser stimulated area as marked in the left panel. For one of these cellwide oscillations (between the dashed lines), panels A and B show snapshots of cytoplasmic O⁻₂ and Ψ_M at uniform time intervals corresponding to the start (left panels) and end (right panels) of the oscillation. The mitochondrial depolarization starts from the laser stimulated area (cyan box in the left panel in C) and propagates to both ends of the whole cell. (D) The average Ψ_M and O⁻₂ of the network versus time. In this simulation, k_shunt was set to be 0.2 mM/s in the mitochondria in the center region (cyan box in the left panel in C) and 0.05 mM/s elsewhere.

Figure 4

MPTP-mediated slow Ψ_M depolarization wave. (A) Space-time plot of Ψ_M recorded along the yellow line indicated on the left, after simulated laser stimulation of the whole area. The mitochondrial depolarization wave begins from the bottom and propagates slowly to the top, taking 24 s to propagate 50 μm. (B) The wave velocity versus k_RED. k_shunt was set to 0.35 mM/s in the bottom four rows of mitochondria and 0.2 mM/s elsewhere.

Figure 5

IMAC-mediated Ψ_M oscillations triggering an MPTP-mediated final depolarization wave. (A) Space-time plot of Ψ_M recorded along the yellow line indicated at the left. O⁻₂ production rate increased progressively over time, most rapidly in the lower four rows of mitochondria (where k_shunt = 0.35[0.3 + 0.7 min (1,e^0.02t/150)]), and more slowly elsewhere (k_shunt = 0.2[0.3 + 0.7 min (1,e^0.02t/150)]). (B) Average Ψ_M versus time. (C) Mitochondrial O⁻₂ (blue) and H₂O₂ (red) concentrations versus time. k_shunt was initially zero and started to increase at the upward arrows. Black bar below the snapshot indicates the final MPTP-mediated slow wave.