Emergent simplicities in an individual cell's stochastic response to disruptive change

Abstract

Here we seek and find recurring patterns of behaviors in the stochastic response of an individual bacterial cell to a disruptive change in growth conditions. Building on the known scaling law that a single timescale, a cellular unit of time, governs stochastic growth and division of individual bacterial cells under constant growth conditions, here we show using experimental data that a dynamic rescaling of the cellular unit of time captures the predominant effect of temporal variations in environmental conditions. Furthermore, we identify the instantaneous exponential growth rate as the scaling factor that scales the internal clocks of the cells to the laboratory time. Our results reveal the natural representation for these time-dependent dynamics. When recast in its terms the cell age distribution for suitable initial conditions evolves under time-invariant rules even as growth conditions remain dynamic! Through the experimental realization at different temperatures of otherwise identical disruptive changes, we not only substantiate the general applicability of the cellular frame of reference but also uncover more emergent simplicities. Motivated by this representation, when time and instantaneous growth rate are expressed in terms of their naturally dimensionless counterparts, remarkably consistent patterns are revealed. These include a unimodal-bimodal-unimodal transition in the shape of the instantaneous growth rate distribution as cells initially in homeostasis experience a disruptive change in nutrient quality and subsequently recover and attain a new homeostasis. The remarkable scaling of the pattern of responses across temperatures suggests that the organizational rules and processes governing the response to disruptive change in nutrient quality remain the same at different temperatures. While the progression of the response appears to proceed at different tempos at different temperatures, upon shifting from the laboratory to the cellular frame of reference these changes progress at the same pace even at different temperatures.