Bridging the Timescales of Single-Cell and Population Dynamics

Abstract

How are granular details of stochastic growth and division of individual cells reflected in smooth deterministic growth of population numbers? We provide an integrated, multiscale perspective of microbial growth dynamics by formulating a data-validated theoretical framework that accounts for observables at both single-cell and population scales. We derive exact analytical complete time-dependent solutions to cell-age distributions and population growth rates as functionals of the underlying interdivision time distributions, for symmetric and asymmetric cell division. These results provide insights into the surprising implications of stochastic single-cell dynamics for population growth. Using our results for asymmetric division, we deduce the time to transition from the reproductively quiescent (swarmer) to the replicationcompetent (stalked) stage of the Caulobacter crescentus life cycle. Remarkably, population numbers can spontaneously oscillate with time. We elucidate the physics leading to these population oscillations. For C. crescentus cells, we show that a simple measurement of the population growth rate, for a given growth condition, is sufficient to characterize the condition-specific cellular unit of time and, thus, yields the mean (single-cell) growth and division timescales, fluctuations in cell division times, the cell-age distribution, and the quiescence timescale.

Synchronised oscillations in growing cell populations are explained by demographic noise

“…Our proliferation assays are typical experimental protocols used to investigate the efficiency of cell-cycle-inhibiting drugs [Beaumont et al, 2016, Haass andGabrielli, 2017], hence our findings may impact upon the reproducibility of such experiments, the efficacy of treatment protocols [Welsh et al, 2016, Hill et al, 2009] and the findings of mathematical models of these experiments [Altinok et al, 2009, Clairambault, 2011, Lévi, 2006. Our work suggests that in-herent synchronisation will also occur in bacterial populations and consequently that studies of bacterial pathogen growth [Jafarpour et al, 2018] may be impacted. Many experimental protocols rely on the synchronisation of cell populations in order to study the structural and molecular events that occur throughout the cell cycle, providing information about gene expression patterns, post transcriptional modification and contributing to drug discovery [Banfalvi, 2017].…”

“…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

“…Therefore, existing models can be derived as specific cases of this framework. These include models where division is asymmetric [26,27,28,25] and where the relationship between successive generation times is non-monotonic and nonlinear, such as the kicked cell-cycle model used to describe circadian rhythms [29].…”

“…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).…”

Fluctuation relations and fitness landscapes of growing cell populations

“…Here, we develop a theoretical framework to relate observables measured at the single cell level and at the population level, building on a number of theoretical works [11,12,3,13] and on our own previous work on this topic [14]. Following Nozoe et al [15], we introduce two different ways to sample lineages, namely the forward (chronological) and backward (retrospective) samplings.…”