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.

Physical bioenergetics: Energy fluxes, budgets, and constraints in cells

“…Techniques have also been developed to coarse-grain detailed microscopic models to obtain hydrodynamic models for these systems (146)(147)(148)(149). This coarse-grained modeling approach has started seeing applications in modeling cellular energy flows (30,89,91,(150)(151)(152)(153)(154). Such coarse-grained, phenomenological laws can potentially be used to interpret the changes of global energy fluxes as measured by OCR (28,43) and heat production rate (23,24) and provide insights into the energy usage of cells.…”

Power Failure of Mitochondria and Oxidative Stress in Neurodegeneration and Its Computational Models

“…The mitochondrial population can also respond to stresses, such as hypoxia and calcium flux, by changing its spatial distribution [ 131 ]. Computational studies can explain how these pathways are related to the maintenance of mitochondrial functions against internal and external stressors [ 132 , 133 , 134 , 135 , 136 , 137 , 138 , 139 , 140 ].…”

Metabolic Regulation of Mitochondrial Morphologies in Pancreatic Beta Cells: Bioenergetics-Mitochondrial Dynamics Coupling

“…What bridges cellular bioenergetics and mitochondrial dynamics together is the choice of fission/fusion rates. For simplicity, we fixed the mitochondrial fission rate according to previous studies [16,44,47] and scaled the fusion rate to the ratio of the ATP synthesis (J ANT ) rate and the proton leak rate (J HL ). Choosing these two rates alone enabled us to simulate the mitochondrial network architectures in bioimages under different modes of energy supply and expenditure [5].…”

“…One of the few examples is Kornick's population-based model [47], which is a minimalistic ODEbased model simulating the dynamics of fragmented/fused and healthy/unhealthy mitochondrial populations and is dependent on the generation and consumption of ATP. However, the mathematical descriptors for bioenergetics and fission/fusion rates were set based on constant ratios of healthy compared with unhealthy mitochondria without considering any mechanistic details of OXPHOS and the associated effects on mitochondrial dynamics.…”