Bridging the timescales of single-cell and population dynamics

Srividya Iyer-Biswas,, ∗ Herman Gudjonson, Charles S. Wright, Jedidiah Riebling, Emma Dawson,,  Klevin Lo, Aretha Fiebig, Sean Crosson, and Aaron R. Dinner Department of Physics and Astronomy, Purdue University, West Lafayette, IN  James Franck Institute and Institute for Biophysical Dynamics, University of Chicago, Chicago, IL  Department of Physics, St Olaf College, Northfield, MN,  Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, IL  Abstract It is well known that population sizes increase exponentially during balanced growth. Concomitantly, at the single-cell level, the sizes of individual cells themselves increase exponentially; the single-cell exponential growth-rate also determines the statistics of cell size and cell division time distributions. Seeking an integrated perspective of microbial growth dynamics under balanced conditions, we formulate a theoretical framework that takes into account observables at both single-cell and population scales. Our exact analytical solutions for both symmetric and asymmetric cell division reveal surprising effects of the stochastic single-cell dynamics on features of population growth. In particular, we find how the population growth rate is sensitive to the shape of the distribution of cell division times. We validate the model by quantitatively predicting the observed cell-age distributions without fitting parameters. Our model also provides a prescription for deducing the time for transitioning from the swarmer (reproductively quiescent) to stalked (reproduction able) stage of the C. crescentus lifecycle; our predictions match with previous indirect estimates. We discuss the scalings of all timescales with external parameters that control the balanced growth state. For C. crescentus cells, we show that the rate of exponential growth of single (stalked) cells governs the dynamics of the entire lifecycle, including the swarmer-to-stalked cell transition.