Figure 4: Cell size dynamics qualitatively impact the stochastic dynamics of clonal population size.

(A) Plot of the squared coefficient of variation of clonal size ($C{V}_N^2$) over time for cell size dynamics following exponential and non-exponential growth laws as described in Figure 3. In all cases, cell size homeostasis occurs according to the adder model, with ${\mathrm{\Delta }}_d$ following a gamma distribution with $⟨{\mathrm{\Delta }}_d⟩=1$ and two values of $C{V}_{{\mathrm{\Delta }}_d}^2$ corresponding to high noise $\left(C{V}_{{\mathrm{\Delta }}_d}^2=1\right)$ and low noise $\left(C{V}_{{\mathrm{\Delta }}_d}^2=0.1\right)$. For exponential cell size dynamics, $C{V}_N$ exhibits a transient peak and then approaches zero as $t\to \mathrm{\infty }$. In stark contrast, $C{V}_N^2$ increases over time to asymptotically approach a non-zero value for non-exponential cell size dynamics. Lowering the noise in the added size $\left(C{V}_{{\mathrm{\Delta }}_d}^2\right)$ results in lower values of $C{V}_N$. (B) Plot of the squared coefficient of variation $\left(C{V}_B^2\right)$ of total biomass, i.e., the aggregated size of all cells in a colony. For the exponential case, $C{V}_B=0$ due to (13), while $C{V}_B$ monotonically increases over time in the non-exponential case, exhibiting similar asymptotic values to $C{V}_N$. All coefficients of variation are computed based on 5000 colony replicas, with colored regions representing the 95% confidence interval obtained using bootstrapping.