A cell contains many copies of mitochondrial DNA. The distribution of a mitochondrial gene mutation in a cell culture is governed by the way in which the mtDNA molecules of a cell are replicated and partitioned between the two daughter cells during mitosis. Assuming that this partition process is random, we describe the evolution of the mitochondrial genetic state of a cell culture. The mutated mtDNA is ultimately segregated and the rate of the trend to segregation is relatively slow. It is nevertheless greatly accelerated if the model takes into account the spatial mtDNA partition by the mitochondrial compartments.