Mitochondrial DNA (mtDNA) mutations cause severe congenital diseases but may also be associated with healthy aging. mtDNA is stochastically replicated and degraded, and exists within organelles which undergo dynamic fusion and fission. The role of the resulting mitochondrial networks in the time evolution of the cellular proportion of mutated mtDNA molecules (heteroplasmy), and cell-to-cell variability in heteroplasmy (heteroplasmy variance), remains incompletely understood. Heteroplasmy variance is particularly important since it modulates the number of pathological cells in a tissue. Here, we provide the first wide-reaching theoretical framework which bridges mitochondrial network and genetic states. We show that, under a range of conditions, the (genetic) rate of increase in heteroplasmy variance and de novo mutation are proportionally modulated by the (physical) fraction of unfused mitochondria, independently of the absolute fission-fusion rate. In the context of selective fusion, we show that intermediate fusion:fission ratios are optimal for the clearance of mtDNA mutants. Our findings imply that modulating network state, mitophagy rate, and copy number to slow down heteroplasmy dynamics when mean heteroplasmy is low could have therapeutic advantages for mitochondrial disease and healthy aging. KEYWORDS mitochondrial DNA; mitochondrial networks; heteroplasmy variance; cellular noise M ITOCHONDRIAL DNA (mtDNA) encodes elements of the respiratory system vital for cellular function. Mutation of mtDNA is one of several leading hypotheses for the cause of normal aging (López-Otín et al. 2013; Kauppila et al. 2017), as well as underlying a number of heritable mtDNArelated diseases (Schon et al. 2012). Cells typically contain hundreds, or thousands, of copies of mtDNA per cell: each molecule encodes crucial components of the electron transport chain, which generates energy for the cell in the form of ATP. Consequently, the mitochondrial phenotype of a single cell is determined, in part, by its fluctuating population of mtDNA molecules (Wallace and Chalkia 2013; Stewart and Chinnery 2015; Aryaman et al. 2019; Johnston 2019). The broad biomedical implications of mtDNA mutation, combined with the countable nature of mtDNAs and the stochastic nature of their dynamics, offer the opportunity for mathematical understanding to provide important insights into human health and disease (Aryaman et al. 2019). An important observation in mitochondrial physiology is the threshold effect, whereby cells may often tolerate relatively high levels of mtDNA mutation until the fraction of mutated mtDNAs (termed heteroplasmy) exceeds a certain critical value where a pathological phenotype occurs (Rossignol et al. 2003; Picard et al. 2014; Stewart and Chinnery 2015; Aryaman et al. 2017). Fluctuations within individual cells mean that the fraction of mutant mtDNAs per cell is not constant within a tissue (Figure 1A), but follows a probability distribution which changes with time