Ergodicity, hidden bias and the growth rate gain

Abstract

Many single-cell observables are highly heterogeneous. A part of this heterogeneity stems from age-related phenomena: the fact that there is a nonuniform distribution of cells with different ages. This has led to a renewed interest in analytic methodologies including use of the 'von Foerster equation' for predicting population growth and cell age distributions. Here we discuss how some of the most popular implementations of this machinery assume a strong condition on the ergodicity of the cell cycle duration ensemble. We show that one common definition for the term ergodicity, 'a single individual observed over many generations recapitulates the behavior of the entire ensemble' is implied by the other, 'the probability of observing any state is conserved across time and over all individuals' in an ensemble with a fixed number of individuals but that this is not true when the ensemble is growing. We further explore the impact of generational correlations between cell cycle durations on the population growth rate. Finally, we explore the 'growth rate gain'-the phenomenon that variations in the cell cycle duration leads to an improved population-level growth rate-in this context. We highlight that, fundamentally, this effect is due to asymmetric division.

Making sense of snapshot data: ergodic principle for clonal cell populations

“…In this article, we develop a framework to analyse the distribution of stochastic biochemical reactions across a growing cell population. We first note that the molecule distribution across a population snapshot sorted by cell ages disagrees with the statistics of single cells observed in isolation, similarly to what has been described for the statistics of cell-cycle durations [8,37,38]. We go on to show that a cell history, a single cell measure obtained from tree data describing typical lineages in a population [39][40][41][42][43], agrees exactly with agesorted snapshots of molecule numbers.…”

YAP and TAZ regulate cell volume

“…We did not observe growth laws of this type in the cell lines used for this article; however, we sought to examine how small variations in the growth law (e.g., comparing the exponential and linear models) may affect average volume. In previous work (Rochman et al, 2018), we discussed how some conserved quantities may be used to calculate population averages of agedependent measurements. In particular, volume and DNA distributions for an ensemble may be calculated given the growth trajectory, V(t), and DNA content progression, DNA(t) (see Materials and methods for details).…”

Prolonged culture in aerobic environments alters Escherichia coli H2 production capacity

“…It is still possible, however, that adaptations acquired in one environment, even one both constant and tightly regulated, confer a fitness advantage in unrelated environments. Features which regulate the adaptability of an organism and not a specific adaptation, likely related to the control of nongenetic heterogeneity within the population, would generalize well to many environments eliciting a stress response . It would be interesting to see how the convergence of the LTEE strains to the three distinct phenotypes under the culture conditions described here may relate to the strains' aerobic phenotypes, the discrete nature of the metabolic pathways occupied, and the underlying control of phenotypic switching.…”