Non-Markovian memory and emergent simplicities in the stochastic and plastic adaptation of individual cells to dynamic environments

Abstract

Do individual bacterial cells retain memories of the history of environmental conditions experienced in previous generations? Here we directly address this question through a synthesis of physics theory and high-precision experiments on statistically identical, non-interacting individual bacterial cells, which grow and divide with intrinsic stochasticity in precisely controlled conditions. From these data, we extract "emergent simplicities" in the seemingly complex interplay between history dependence, persistence, and transience in the stochastic memories of the dynamic environments experienced by individuals over multiple generations. First, we find that the instantaneous single-cell growth rate is the key physiologically relevant quantity where intergenerational memory is stored. In contrast, the cell size dynamics are memory free, or Markovian, over intergenerational timescales. Next, we find that the effect of experiencing dynamic environments can be captured quantitatively by recal-ibrating the cellular unit of time by the measured mean instantaneous growth rate; the dynamically rescaled cell age distributions undergo a scaling collapse. Moreover, in a given condition, an individual bacterial cell retains history-dependent, or non-Markovian, memory of its growth rate over tens of generations. We derive from first principles a physically-motivated metric to quantify the degree of non-Markovianity. Furthermore, when conditions change, the instantaneous single-cell growth distribution becomes bimodal, as the bacteriums memory of past environment encountered is reset stochastically and plastically, prior to achieving a new homeostasis.