Stochastic models for evolving cellular populations of mitochondria: Disease, development, and ageing

Abstract

Mitochondria are essential cellular organelles whose dysfunction is associated with ageing, cancer, mitochondrial diseases, and many other disorders. They contain their own genomes (mtDNA), of which thousands can be present in a single cell. These genomes are repeatedly replicated and degraded over time, and are prone to mutations. If the fraction of mutated genomes (heteroplasmy) exceeds a certain threshold, cellular defects can arise. The dynamics of mtDNAs over time and the accumulation of mutant genomes form a rich and vital stochastic process, the understanding of which provides important insights into disease progression. Numerous mathematical models have been constructed to provide a better understanding of how mitochondrial dysfunctions arise and, importantly, how clinical interventions can alleviate disease symptoms. For a given mean heteroplasmy, an increased variance-and thus a wider cell-to-cell heteroplasmy distribution-implies a higher probability of exceeding a given threshold value, meaning that stochastic models are essential to describe mtDNA disease. Mitochondria can undergo fusion and fission events with each other making the mitochondrial population a dynamic network that continuously changes its morphology, and allowing for the possibility of exchange of mtDNA molecules: coupled stochastic physical and genetic dynamics thus govern cellular mtDNA populations. Here, an overview is given of the kinds of stochastic mathematical models constructed describing mitochondria, their implications, and currently existing open problems.