Cell Size Regulation Induces Sustained Oscillations in the Population Growth Rate

Abstract

We study the effect of correlations in generation times on the dynamics of population growth of microorganisms. We show that any non-zero correlation that is due to cell-size regulation, no matter how small, induces long-term oscillations in the population growth rate. The population only reaches its steady state when we include the often-neglected variability in the growth rates of individual cells. We discover that the relaxation time scale of the population to its steady state is determined by the distribution of single-cell growth rates and is surprisingly independent of details of the division process such as the noise in the timing of division and the mechanism of cell-size regulation. We validate the predictions of our model using existing experimental data and propose an experimental method to measure single-cell growth variability by observing how long it takes for the population to reach its steady state or balanced growth.

Synchronised oscillations in growing cell populations are explained by demographic noise

“…In principle, one could use this fact to study the applicability of our findings to Gaussian cell-cycle time and, hence, compare our results with other relevant studies which rely on a Gaussian approach [Jafarpour, 2019, Pirjol et al, 2017. For example, Jafarpour [2019] used a Gaussian model to study the connection between mother-daughter size regulation in bacteria and the decay of transient fluctuations. Our study focuses on synchrony emerging even in the absence of correlation of CCTs, we expect that accounting for such mechanisms will tend to amplify the amplitude of the oscillations predicted by the model, however, the analysis of this phenomenon is left for future study.…”

“…In cell biology, this approach has been supported by classic experimental studies for large populations under favourable growth conditions [Monod, 1949, Laird, 1965. However, when smaller populations are considered -for example clones of a single progenitor cell -the classical model of exponential growth fails to capture the variable per capita growth rates caused by non-exponentially distributed cell cycle times and more sophisticated models are necessary [Baker and Simpson, 2010, Yates et al, 2017, Jafarpour, 2019, Pirjol et al, 2017, Lang et al, 2009, Kuritz et al, 2018.…”

“…See Section section S.4 of Supplementary Materials for full details. transient-oscillatory regime and asymptotic-exponential regime) is a common feature of many structured growing population [Jafarpour, 2019, Jafarpour et al, 2018, Pirjol et al, 2017, Baker and Röst, 2019. It is not surprising, therefore, that these two phases play distinct but critically important roles in the dynamics of a growing cell population.…”

Quantifying phenotypic variability and fitness in finite microbial populations

“…In this paper, we have studied the relationship between growth of phenotypically heterogeneous populations in finite and exponential cultures. While a number of studies have explored the dynamics of phenotypically heterogeneous populations under exponential growth conditions and shown how to relate lineage statistics to the population growth rate (e.g., [1,20,21,22,23,19,24]), precise measurements of phenotypic variability often need to be obtained in cultures containing a fixed number of cells. Because the growth process in not ergodic (the population averages are not equivalent to single-lineage averages) it is essential to distinguish between different ways of sampling phenotypes when analyzing data from these experiments.…”

“…How does one relate this information to some measure of the population's fitness? Many previous studies have explored how population growth is related to the single-cell dynamics of an exponentially growing population in a constant environment [1,20,21,22,23,19,24,25]. In the setting of exponential growth, a proxy for fitness is the population growth rate Λ, defined by the relation N ∼ e Λt , where N is the number of cells at time t. Most notably, it was shown that the population growth rate, Λ, can be computed from the distribution of singlecell generation times taken over the entire history of the population using the Euler-Lotka equation, shown in Figure 1 (B).…”