From single-cell statistics to population: Interactions and ergodicity-breaking

Biological cells vary in many measurable properties; this variability was extensively studied in recent years, as single-cell experimental methods advanced. However, integrating the statistical properties of single cells into those of a population is not straightforward. We will discuss two aspects of this integration in bacterial cells: First, cells interact and communicate with one another through their shared environment; Second, the dynamics of single cells across time can break ergodicity (time- and population-averages are not the same).

Interactions between bacteria in a shared environment are illustrated in the context of “lag times” – waking-up and initiating growth following a dormant state. Statistics of wake-up times are shown to follow Extreme Value Theory, indicating that the first cell to wake-up rapidly signals and triggers growth in the rest of the population.

Quantifying ergodicity reveals a heterogenous landscape where some variables break ergodicity more than others, making up a “sloppy” dynamical system.

Interestingly, these aspects of the complex transformation from single cells to population are revealed by a purely phenomenological statistical approach, without reference to specific molecular mechanisms.

References:

A. Stawsky, H. Vashistha, H. Salman and N. Brenner, “Multiple timescales in bacterial growth homeostasis”. iScience 25, 103678 (2022).

A leader cell triggers end of lag phase in populations of P. fluorescens. M. Ardré, G. Doulcier, N. Brenner, P.B. Rainey, microLife 3, 1-9 (2022).