Cell size control in bacteria is modulated through extrinsic noise, single-cell- and population-growth

TL;DR

The paper tackles how extrinsic noise, single-cell growth fluctuations, and population dynamics shape bacterial cell-size control. It develops a generalised noisy linear map for forward lineages and a tilted linear map for lineage trees, coupled with an extrinsic-noise framework that yields a universal quadratic relation for division-size fluctuations and data collapse. Across diverse data, extrinsic noise dominates, and population dynamics can shift observed size-control from adder toward sizer or timer modes depending on noise, with a pronounced lineage-population bias and a growth-rate–size-control trade-off. The work provides a cohesive analytical framework linking single-cell measurements to population-level statistics, suggesting bacteria prioritize robust division-size distributions over maximal growth rate and offering a path to reconcile different experimental setups.

Abstract

Living cells maintain size homeostasis by actively compensating for size fluctuations. Here, we present two stochastic maps that unify phenomenological models by integrating fluctuating single-cell growth rates and size-dependent noise mechanisms with cell size control. One map is applicable to mother machine lineages and the other to lineage trees of exponentially-growing cell populations, which reveals that population dynamics alter size control measured in mother machine experiments. For example, an adder can become more sizer-like or more timer-like at the population level depending on the noise statistics. Our analysis of bacterial data identifies extrinsic noise as the dominant mechanism of size variability, characterized by a quadratic conditional variance-mean relationship for division size across growth conditions. This finding contradicts the reported independence of added size relative to birth size but is consistent with the adder property in terms of the independence of the mean added size. Finally, we derive a trade-off between population-growth-rate gain and division-size noise. Correlations between size control quantifiers and single-cell growth rates inferred from data indicate that bacteria prioritize a narrow division-size distribution over growth rate maximisation.

Figures (6)

• Figure 1: Modulation of cell size control by noise, growth rate and experimental setup. (a) Experimental setups: growing population and mother machine. (b) Cell size trajectory along a single lineage in a mother machine. (c) The tree statistics is obtained by sampling with uniform weights all cell divisions in the population, shown in black, but excluding leaf cells, shown in light blue, that have not yet divided at the end of the experiment (dotted line). The forward statistics can be obtained in mother machines or with a non-uniform sampling of lineages in the population nozoe_inferring_2017. (d) The tree and forward conditional distributions of division sizes are different. (e,f) Cell size control can be modulated at the average and variance levels by (e) single cell growth rates $\alpha$ and (f) noise in division sizes.
• Figure 2: Noise changes the mode of cell size control in populations. In each of the first three columns only one type of noise is considered: additive, intrinsic or extrinsic. (a-c) Different types of noise impact differently the mean and variance of conditional distributions of division sizes. (d-f) The conditional average added size in the tree statistics depends on the size at birth and on the noise levels (boxed legend) for a reference forward adder ($a=1$, black). Predictions of the population linear map (slope $\hat{a}$ from \ref{['eq_pop_lin_a']}, offset for readability) shown for sizes in an interval of two standard deviations below and above the mean birth size (circles) agree with exact solutions computed with \ref{['powell_cond_sd']}. Insets show average birth sizes in the tree statistics against noise levels, compared to the forward value (black). (h-j) Modulation of the population variance of division sizes. Variance (h) and CV (i,j) on the y-axis are rescaled by their values in the forward statistics to highlight the modulation of the birth-size dependence. Extrinsic noise remains extrinsic while extra size-dependence arise for forward additive and intrinsic noises. (g,k) The last column illustrates the forward-to-population changes in (g) linear map slope $\hat{a}-a$ and in (k) mean birth size $\langle s_b \rangle_\mathrm{tree}/\langle s_b \rangle_\mathrm{fw}$, as a function of the forward slope $a$ and for the three types of noise with the same standard deviation $\sigma=0.3$.
• Figure 3: Single-cell data of medium and temperature perturbations in E. coli and M. smegmatis collapse on extrinsic noise model predictions. First column: data of E. coli in mother machine in different media from taheri-araghi_cell-size_2015, second column: data of E. coli in mother machine in LB medium at different temperatures from tanouchi_noisy_2015, third column: data of M. smegmatis in growing population in different media from priestman_mycobacteria_2017. (a-c) Collapse of conditional variance $\sigma^2[s_d|s_b]$ vs conditional mean $\langle s_d |s_b \rangle$, rescaled by marginal variance $\sigma^2[s_d]$ and mean $\langle s_d \rangle$, on extrinsic master curve $y=0.75 x^2$ for most conditions. The best extrinsic fits for each condition are shown as light-coloured curves, and the master curve is shown in red. Insets: conditions which do not follow the extrinsic noise model, with the same axis labels as the main plots, and the best noise model (TSB: correlated, pyruvate: additive) shown with light colour curves. Error bars denote the $95\%$ confidence interval of the estimate determined by bootstrapping. (d-f) Conditional distributions of added sizes for different birth sizes do not collapse. Inset: added size variance vs birth size follows the extrinsic model prediction shown in grey. (g-i) Likelihoods of different noise models were computed as Akaike weights $p(m)=\text{softmax}(-\mathrm{AIC}(m)/2)$.
• Figure 4: Predictions for cell size control using data from a different experimental setup. (a,b) Mean added size against birth size for E. coli in mother machines (blue) vs prediction of \ref{['powell_cond_sd']} for the same quantity in growing population experiments (orange). Error bars denote the $95\%$ confidence interval of the estimate determined by bootstrapping. The linear fits of the original data are shown in black, and the predictions of the tilted linear map, \ref{['eq_pop_lin_map']}, with fitted parameters are shown in green. (c) For M. smegmatis, population-level data are used to compute forward predictions using \ref{['powell_cond_sd']}, and using \ref{['eq_pop_lin_map']} with fitted parameters. Because population datasets are much smaller, error bars denote the $80\%$ confidence interval of the bootstrap. To reduce noise, averages were computed with sliding size windows of width (a) 1, (b) 0.3, and (c) 1.
• Figure 5: Growth rate modulation affects cell size control both in lineages and populations. (a-c) Modes of growth rate modulation of cell size control occur through slope, intercept, and variance. (d-f) Data suggest all cell size control variables are modulated for E. coli in glucose. Slopes $a(\alpha)$ and intercepts $b(\alpha)$ were obtained with linear fits of $s_d$ against $s_b$ for single-cell growth rates $\alpha$ in the interquantile interval $[2.5\%,97.5\%]$ divided into eight bins, and extrinsic variances $\sigma_e^2(\alpha)$ by fitting $\sigma^2[s_d|s_b,\alpha]$ against $\langle s_d|s_b,\alpha \rangle$ when varying $s_b$, for $\alpha$ in the same interval divided into three bins. Error bars represent the standard errors on the estimated parameters. (g-i) The model predicts how the lineage-population biases in sensitivities and in slope depend on cell size control variables and added size sensitivity. $\mathrm{CV}_\alpha=0.4$, $\sigma_e=0.3$. (g) $S_\sigma=-0.5$. (h) $a=1$, $\mathrm{CV}_p=0$. (i) $a=1$. (j,k) Even without growth rate modulation of a forward adder (black, $a=1$), population size control variables depend on single-cell growth rate. (j) $S_a=S_b=S_\sigma=0$, $\sigma_e=0.3$. (k) $\mathrm{CV}_p=0$, $S_\Delta=0$, $\sigma_e=0.3$. (l) Lineage-population bias in size control mechanisms differs between the adder (red), sizer (blue) and timer-like (grey). $\mathrm{CV}_\alpha=0.4$, $\sigma_e=0.3$.