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.

To maintain a constant cell size, dividing cells have to coordinate cell-cycle events with cell growth. This coordination has long been supposed to rely on the existence of size thresholds determining cell-cycle progression [1]. In budding yeast, size is controlled at the G1/S transition [2]. In agreement with this hypothesis, the size at birth influences the time spent in G1: smaller cells have a longer G1 period [3]. Nevertheless, even though cells born smaller have a longer G1, the compensation is imperfect and they still bud at smaller cell sizes. In bacteria, several recent studies have shown that the incremental model of size control, in which size is controlled by addition of a constant volume (in contrast to a size threshold), is able to quantitatively explain the experimental data on four different bacterial species [4-7]. Here, we report on experimental results for the budding yeast Saccharomyces cerevisiae, finding, surprisingly, that cell size control in this organism is very well described by the incremental model, suggesting a common strategy for cell size control with bacteria. Additionally, we argue that for S. cerevisiae the "volume increment" is not added from birth to division, but rather between two budding events.

MreB is essential for rod shape in many bacteria. Membrane-associated MreB filaments move around the rod circumference, helping to insert cell wall in the radial direction to reinforce rod shape. To understand how oriented MreB motion arises, we altered the shape of Bacillus subtilis. MreB motion is isotropic in round cells, and orientation is restored when rod shape is externally imposed. Stationary filaments orient within protoplasts, and purified MreB tubulates liposomes in vitro, orienting within tubes. Together, this demonstrates MreB orients along the greatest principal membrane curvature, a conclusion supported with biophysical modeling. We observed that spherical cells regenerate into rods in a local, self-reinforcing manner: rapidly propagating rods emerge from small bulges, exhibiting oriented MreB motion. We propose that the coupling of MreB filament alignment to shape-reinforcing peptidoglycan synthesis creates a locally-acting, self-organizing mechanism allowing the rapid establishment and stable maintenance of emergent rod shape.

Bacteria are able to maintain a narrow distribution of cell sizes by regulating the timing of cell divisions. In rich nutrient conditions, cells divide much faster than their chromosomes replicate. This implies that cells maintain multiple rounds of chromosome replication per cell division by regulating the timing of chromosome replications. Here, we show that both cell size and chromosome replication may be simultaneously regulated by the long-standing initiator accumulation strategy. The strategy proposes that initiators are produced in proportion to the volume increase and is accumulated at each origin of replication, and chromosome replication is initiated when a critical amount per origin has accumulated. We show that this model maps to the incremental model of size control, which was previously shown to reproduce experimentally observed correlations between various events in the cell cycle and explains the exponential dependence of cell size on the growth rate of the cell. Furthermore, we show that this model also leads to the efficient regulation of the timing of initiation and the number of origins consistent with existing experimental results.

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...