Mitochondrial mutations, cellular instability and ageing: modelling the population dynamics of mitochondria

All eukaryotic cells rely on mitochondrial respiration as their major source of metabolic energy (ATP). However, the mitochondria are also the main cellular source of oxygen radicals and the mutation rate of mtDNA is much higher than for chromosomal DNA. Damage to mtDNA is of great importance because it will often impair cellular energy production. However, damaged mitochondria can still replicate because the enzymes for mitochondrial replication are encoded entirely in the cell nucleus. For these reasons, it has been suggested that accumulation of defective mitochondria may be an important contributor to loss of cellular homoeostasis underlying the ageing process.

We describe a mathematical model which treats the dynamics of a population of mitochondria subject to radical-induced DNA mutations. The model confirms the existence of an upper threshold level for mutations beyond which the mitochondrial population collapses. This threshold depends strongly on the division rate of the mitochondria. The model also reproduces and explains (i) the decrease in mitochondrial population with age, (ii) the increase in the fraction of damaged mitochondria in old cells, (iii) the increase in radical production per mitochondrion, and (iv) the decrease in ATP production per mitochondrion.