Axel Kowald and Thomas B. L. Kirkwood
In this paper they discuss a mechanism that could be responsible for the observed "clonal expansion" of mtDNA mutations. Clonal expansion means that in individual cells, the mitochondrial population is often taken over by a single type of mutant (as opposed to many different mutants). There have been various suggestions as to how clonal expansion occurs but none of these suggestions can account for all the experimental observations. For example, the hypothesis that clonal expansion of a single mutant happens merely by chance (random drift) can explain clonal expansion in long lived, but not short lived species.
In this paper, they propose a new mechanism of clonal expansion. The idea they propose is that normally, mtDNA replication rate decreases if concentrations of some of its products are high (a negative feedback loop). Mutants that miss that part of the genome that encodes for proteins involved in this feedback loop will not be able to suppress mtDNA replication rate through this feedback mechanism. These deletion mutations therefore have a replicative advantage over wild-type mitochondria.
By studying the position in the genome of mtDNA deletions that were observed to be clonally amplified, they found that most deletions overlap a subunit of complex I of the respiratory chain. This means that it could be that this subunit is involved in the negative feedback loop, and missing this subunit gives a replicative advantage that allows for clonal expansion.
They then provide an ODE model describing the dynamics of wildtype and mutant mtDNA as well as ATP concentration. In their model they assume that mutants have a 50% higher replication rate because they lack the negative feedback loop. Because of this, the mutant population increases exponentially until the cell collapses (collapse is defined by a certain drop in ATP concentration and each extra mutant present lowers the ATP concentration by some amount). Their model predicts that, if one starts with 1000 wildtype mtDNAs and 1 mutant mtDNA, at the moment of collapse the number of mutants is 9-fold higher than the number of wildtypes. This is in agreement with experimental results.
They continue to make a stochastic version of their ODE model, which can predict clonal expansion of a single type of mutant (rather than accumulated of various mutants) in both long- and short-lived species.