## MtDna Replication

To balance the loss of mtDNA molecules by degradation, mtDNA must be continually copied. This replication is independent of the cell cycle, and occurs in all cells, including postmitotic cells. The total number of mtDNA molecules replicated, ncopy, in a time span At must be equal to the mean number lost to degradation plus any additional growth, ngrow, which would be needed in dividing cells.

Little is known about the control of the mtDNA replication rate, so for the modeling we generally choose the simplest possible model, a constant replication rate. For examples of simulations with a variable mtDNA replication rate, see Chinnery and Samuels (1999) and Capps et al. (2003).

Equation 4 gives the total mtDNA replication rate. We are usually simulating conditions where the cell contains a mixture of wild-type and mutant mtDNA. The total number of replicated mtDNA molecules is split into two parts,

Wcopy = binomial(ncopy, W/N)

lvJ-copy — ncopy vvcopy

where a fraction W/N of the objects are wild-type mtDNA. The binomial function (Press et al., 1988) returns the random number of wild-type mtDNA chosen to copy, with Wc copy — ncopy y. Note that only one call to the routine binomial is needed to calculate both Wcopy and Mcopy. By using a binomial routine, the values Wcopy and Mcopy will have natural random variations that are an important driving force behind the random genetic drift in the system.

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