Mitochondrial mutations and ageing: Can mitochondrial deletion mutants accumulate via a size based replication advantage? Axel Kowald a,n , Marcus Dawson a,b , Thomas B.L. Kirkwood a a Centre for Integrated Systems Biology of Ageing and Nutrition, Institute for Ageing and Health, Newcastle University, Newcastle upon Tyne NE4 5PL, United Kingdom b University of Manchester, Manchester M13 9PT, United Kingdom HIGHLIGHTS  We modelled the accumulation of mitochondrial deletion mutants during ageing.  Can the reduced size provide a selection advantage via a shorter replication time?  We developed a delay differential equation model and a stochastic simulation.  The simulations show that the idea only works for very long lived species. article info Article history: Received 21 February 2013 Received in revised form 22 August 2013 Accepted 9 September 2013 Available online 17 September 2013 Keywords: Mitochondrial mutation Mathematical model Ageing abstract The mitochondrial theory of ageing is one of the main contenders to explain the biochemical basis of the ageing process. An important line of support comes from the observation that mtDNA deletions accumulate over the life course in post-mitotic cells of many species. A single mutant expands clonally and finally replaces the wild-type population of a whole cell. One proposal to explain the driving force behind this accumulation states that the reduced size leads to a shorter replication time, which provides a selection advantage. However, this idea has been questioned on the grounds that the mitochondrial half-life is much longer than the replication time, so that the latter cannot be a rate limiting step. To clarify this question, we modelled this process mathematically and performed extensive deterministic and stochastic computer simulations to study the effects of replication time, mitochondrial half-life and deletion size. Our study shows that the shorter size does in principle provide a selection advantage, which can lead to an accumulation of the deletion mutant. However, this selection advantage diminishes the shorter is the replication time of wt mtDNA in relation to its half-life. Using generally accepted literature values, the resulting time frame for the accumulation of mutant mtDNAs is only compatible with the ageing process in very long lived species like humans, but could not reasonably explain ageing in short lived species like mice and rats. & 2013 Elsevier Ltd. All rights reserved. 1. Introduction Ageing is an intrinsic deterioration of the homoeostatic cap- abilities of an organism, leading to a constantly increasing risk of death. Although evolutionary considerations suggest that the ageing process is in principle multifactorial (Kirkwood, 1996), a few main mechanisms have been proposed. Among these the mitochondrial theory of ageing is one of the most popular (Harman, 1972, 1983; Miquel et al., 1980; Richter, 1988; Linnane et al., 1989). The theory suggests that the accumulation of defective mitochondria is a major contributor to the ageing process. Reactive oxygen species (ROS) generated during respiration have the potential to damage all kinds of biologically relevant macromolecules such as lipids, proteins and mitochondrial DNA (mtDNA). Damage to mtDNA is quite different from damage to other macromolecules, since mitochondrial DNA represents the ultimate blueprint from which everything else fol- lows. Point mutations and deletions could impair mitochondrial ATP production with negative consequences for all aspects of cellular homoeostasis. And indeed, many studies have shown that mitochondrial deletion mutants accumulate with age in various mammalian species such as rats, monkeys and humans (Brierley et al., 1998; Khrapko et al., 1999; Cao et al., 2001; Gokey et al., 2004; Herbst et al., 2007). These single cell studies have shown that the mitochondrial population of a cell is overtaken by a single deletion mutant type via clonal expansion. Contents lists available at ScienceDirect journal homepage: www.elsevier.com/locate/yjtbi Journal of Theoretical Biology 0022-5193/$ - see front matter & 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jtbi.2013.09.009 n Corresponding author. Tel.: þ49 179 3427522. E-mail addresses: Axel.Kowald@ncl.ac.uk (A. Kowald), Marcus.Dawson@student. manchester.ac.uk (M. Dawson), Tom.Kirkwood@ncl.ac.uk (T.B.L. Kirkwood). Journal of Theoretical Biology 340 (2014) 111–118