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.
Highlights
Several decades ago, the earliest quantitative microbiology experiments revealed that microbial population sizes increase exponentially under favorable growth conditions [1]
The technology that we have recently developed for C. crescentus cells has the advantage that isolated single cells in highly reproducible and unlimiting balanced-growth conditions can be observed with unprecedented statistical precision [2]
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, it yields the mean growth and division timescales, fluctuations in cell division times, the cell-age distribution, and the quiescence timescale
Summary
The earliest quantitative microbiology experiments revealed that microbial population sizes increase exponentially under favorable growth conditions [1]. We formulate a data-driven theoretical framework that takes into account observables at both single-cell and population scales, and 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. A technical challenge in developing an exact theoretical framework for predicting population level behaviors, consistent with underlying stochastic single-cell dynamics, is that the aging dynamics of individual cells are nonMarkovian or history dependent This is reflected in the nonexponential shape of typical interdivision time distributions (waiting-time distributions for duration between successive divisions). 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, it 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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