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 replication-competent (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.

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Plain Language Summary

Exponential growth processes are ubiquitous in both natural and everyday phenomena. Familiar examples include population growth of microorganisms, compounding of interest, nuclear fission, the inflation of the Universe, Moore’s law for the increase of computer processor power, and viral posts on social media. Despite the prevalence of exponential growth, there are still fundamental open questions concerning these phenomena. In particular, the earliest microbiology experiments revealed that population sizes of microorganisms increase exponentially. Yet this smooth growth masks the noisiness and randomness of the underlying growth and division of individual cells. How are the two perspectives to be reconciled? What signatures of the underlying probabilistic events remain in the coarse-grained exponential growth of populations?

Here, we take advantage of high-quality single-cell and bulk-population growth data to build a fundamental theory that is applicable at both scales and yields testable predictions. By combining data with our theoretical framework, we show that an emergent cellular unit of time governs growth phenomena at both scales. Owing to unexpected universality in growth dynamics under different growth conditions, a simple measurement of this timescale reveals a wealth of information about underlying probabilistic phenomena.

Our results serve as a starting point for future lines of inquiry involving time-dependent growth phenomena, such as the aging of cells and organisms.