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

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.

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IntroductionSince the vaccine roll out, research has focused on vaccine safety and efficacy, with large clinical trials confirming that vaccines are generally effective against symptomatic COVID-19 infection. However, breakthrough infections can still occur, and the effectiveness of vaccines against transmission from infected vaccinated people to susceptible contacts is unclear.Health Technology Wales (HTW) collaborated with the Wales COVID-19 Evidence Centre to identify and examine evidence on the transmission risk of SARS-CoV-2 from vaccinated people to unvaccinated or vaccinated people.MethodsWe conducted a systematic literature search for evidence on vaccinated people exposed to SARS-CoV-2 in any setting. Outcome measures included transmission rate, cycle threshold (Ct) values and viral load. We identified a rapid review by the University of Calgary that was the main source of our outcome data. Nine studies published following the rapid review were also identified and included.ResultsIn total, 35 studies were included in this review: one randomized controlled trial (RCT), one post-hoc analysis of an RCT, 13 prospective cohort studies, 16 retrospective cohort studies and four case control studies.All studies reported a reduction in transmission of the B.1.1.7 (Alpha) variant from partial and fully vaccinated individuals. More recent evidence is uncertain on the effects of vaccination on transmission of the B.1.617.2 (Delta) variant. Overall, vaccine effectiveness in reducing transmission appears to increase with full vaccination, compared with partial vaccination. Most of the direct evidence is limited to transmission in household settings therefore, there is a gap in the evidence on risk of transmission in other settings. One UK study found protection against onward transmission waned within 3 months post second vaccination.ConclusionsEarly findings that focused on the alpha variant, showed a reduction in transmission from vaccinated people. There is limited evidence on the effectiveness of vaccination on transmission of the Delta variant, therefore alternative preventative measures to reduce transmission may still be required.