Population Dynamics of Mitochondria in Cells: A Minimal Mathematical Model

Abstract

Mitochondria are dynamic organelles found in almost all eukaryotic cells and perform several key cellular functions such as generating energy, triggering cell differentiation, and initiating cell death. They have their own DNA (mtDNA) and often come in multiple genetic varieties within a single cell. Dynamical processes such as mitochondrial fission, fusion, autophagy, and mitotic segregation can enable a mitochondrion population to eventually dominate the mitochondria genomic pool, sometimes with devastating consequences. Therefore, understanding how changes in mtDNA accumulate over time and are correlated to changes in mitochondrial function can have a profound impact on our understanding of fundamental cell biophysics and the origins of some human diseases. Motivated by this, we develop and study a mathematical model to determine which cellular parameters have the largest impact on mtDNA population dynamics. The model consists of coupled differential equations to describe populations of healthy and dysfunctional mitochondria subject to mitochondrial fission, fusion, autophagy, and varying levels of cellular ATP. We study the time evolution of each population under specific selection biases and obtain a heat map in the parameter space of the ratio of the rates of fusion and autophagy of the healthy and dysfunctional populations. Our results may provide insights into how different mitochondrial populations survive and evolve under different selection pressures and with time.