Bridging the time scales of single-cell and population dynamics

TL;DR

This paper develops a comprehensive theoretical framework linking single-cell stochastic growth and division processes to population-level dynamics, revealing how microscopic details influence macroscopic growth patterns and oscillations.

Contribution

It provides exact analytical solutions for cell-age distributions and population growth rates based on interdivision time distributions, integrating single-cell and population dynamics.

Findings

Population can spontaneously oscillate over time.

Single-cell division timescales can be inferred from population growth rates.

The framework applies to symmetric and asymmetric cell division.

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 replication-competent (stalked) stage of the {\em Caulobacter crescentus} lifecycle. Remarkably, population numbers can spontaneously oscillate with time. We elucidate the physics leading to these population oscillations. For {\em 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.