Figure 4.

Copy number statistics for the relaxed replication model of mtDNA. Lines are analytic results; points are from stochastic simulation. (a) $\mathbb{E}(m)$ and (b) $\mathbb{V}(m)$ for binomial partitioning, modelling dividing cells, with m₀=m_opt=1000, $\beta =\frac{1}{2}$. $\mathbb{V}(m)$ and $\mathbb{E}(m)$ converge to the same trajectory; the grey line gives the analytic result for $\mathbb{E}(m)$ at the end of a cell cycle. (c) $\mathbb{E}(m)$ and (d) $\mathbb{V}(m)$ for random subtractive partitioning, modelling budding cells, with m₀=100=m_opt=100, $\beta =\frac{1}{2}$, η=15. Grey lines give analytic results for $\mathbb{E}(m)$ at the end of a cell cycle, and $\mathbb{V}(m)$ at the start, end and minimum point (blue crosses) in the cell cycle. (e) Comparison of theory and stochastic simulation in illustrative snapshots of probability distribution functions at given times in the binomial case using equation (3.8).