Cell Size Regulation in Bacteria

Abstract

Various rod-shaped bacteria such as the canonical gram negative Escherichia coli or the wellstudied gram positive Bacillus subtilis divide symmetrically after they approximately double their volume. Their size at division is not constant, but is typically distributed over a narrow range. Here, we propose an analytically tractable model for cell size control, and calculate the cell size and interdivision time distributions. We suggest ways of extracting the model parameters from experimental data. Existing data for E. coli supports partial size control, and a particular explanation: a cell attempts to add a constant volume from the time of initiation of DNA replication to the next initiation event. This hypothesis explains how bacteria control their tight size distributions and accounts for the experimentally observed correlations between parents and daughters as well as the exponential dependence of size on growth rate.PACS numbers: 87.17. Ee, 87.17.Aa, 87.10.Mn, 87.18.Tt Microorganisms such as bacteria come in a diverse set of shapes and sizes. Nonetheless, individual strains have remarkably reproducible shapes, and a narrow distribution of sizes [1][2][3][4]. Many bacteria, such as E. coli, are rod-shaped, and during their exponential growth phase they elongate while maintaining a constant diameter. After approximately doubling their length (as well as mass and volume), and completing DNA replication for their offspring, they divide symmetrically into two approximately identical daughter cells. In spite of decades of research, we still do not have a good understanding of how cells regulate their shape, both mechanically (i.e., what is the biophysical feedback necessary to achieve a rod-shape cell? [5]) and dimensionally: the coefficient of variation (standard deviation:mean, CV) can be as low as 0.1 for bacteria [2]. Bacteria are also remarkable in their ability to have a generation time that is shorter than the time it takes them to replicate DNA: doubling time τ d for E. coli in rich media at 37• C is about 20 mins, while T r ≈ 60 mins are needed from initiation of DNA replication to cell division. This apparent paradox is explained by the existence of multiple replication forks: in these situations, a cell will already start replicating DNA for its 4 granddaughters (or 8 great-granddaughters), in order for the replication to complete in time.Many models for cell size regulation exist in the literature [1, 2,[6][7][8][9][10][11][12]. Different strategies will yield particular cell size and inter-division time distributions, as well as distinct correlations. Hence, it is important to understand the connection between different regulation models and the resulting distributions and correlations. Moreover, there are two seemingly contradictory results in the literature: the first is the model by Donachie [13], which shows that the measured exponential dependence of bacterial size on growth rate [14] is consistent with initiation of DNA replication at a constant, growth-rateindependent volume per replication f...

Analysis of Cell Size Homeostasis at the Single-Cell and Population Level

“…For a = 0 division size is independent of birth size, called the sizer mechanism. For a = 1 the size added from birth to division varies independently of birth size, an adder mechanism that is commonly observed in bacteria [3,10,13]. For a = 2 division size is directly proportional to birth size, which resembles cell-size control based on division timing.…”

“…A possible strategy for such a control, called a sizer, is to set a stochastic threshold. Many microbes, however, rather grow by a constant size from birth to division, called the adder control [3,[13][14][15]. Other mixed strategies may be described by sizer-or timer-like controls [9,15,16].…”

“…These initial studies formulated sizer models based on the population balance equation, an integro-differential equation that is notoriously difficult to solve in practice [21][22][23][24]. With the advent of single-cell traps such as the mother machine [2], the theoretical focus moved toward describing single cells over many divisions [13,[25][26][27]. This path is more amenable to analysis because it considers only a single individual described by a discrete-time stochastic process or stochastic map [28].…”

Universal protein distributions in a model of cell growth and division

“…In this appendix, we detail the differences between our model and a mathematically similar model of cell size regulation recently proposed by Amir [12,28]. However, before describing those differences, we first discuss some nontrivial consequences following from the similarity between the models.…”

“…Both our model and that of [12,28] are also easily modified to handle asymmetric division, as in yeast. However, until data are available that relate temporal to population statistics, it remains to be seen to what extent the dynamics of proteins across generations in yeast can be described by the approach outlined in the main text.…”