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 Ca2+ 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 ΔΨm 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 O2.− 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 ΔΨm 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.

We present computational methods for simulating electrical conduction in cardiac ventricles on parallel machines. We used the network model approach to describe the tissue geometry and biophysically detailed models of ion currents and membrane transporters in cardiac ventricular myocytes. Simulations of biophysically detailed ionic models with anatomically detailed tissue geometries are computationally very expensive. We investigated the use of high performance computers to reduce execution time. Experiments have shown that we can adapt and optimize our existing models of electrical activity in heart tissue for the High Performance Computers. The solution was implemented on the IBM R p690, a shared memory machine and on a cluster of workstations, a distributed memory machine. An efficient algorithm was designed to partition the data and to pass messages between processors using Message Passing Interface (MPI). The algorithm was highly scalable to the problem size as well as the number of processors used, and could easily be ported to other parallel architectures. We were able to achieve speedup of up to 13.5 on the p690 and 27 on the cluster of workstations. Using the method developed, the simulated pattern of electrical activation agreed with the experimental data.