Nathalie Krell

Division in Escherichia coli is triggered by a size-sensing rather than a timing mechanism

BackgroundMany organisms coordinate cell growth and division through size control mechanisms: cells must reach a critical size to trigger a cell cycle event. Bacterial division is often assumed to be controlled in this way, but experimental evidence to support this assumption is still lacking. Theoretical arguments show that size control is required to maintain size homeostasis in the case of exponential growth of individual cells. Nevertheless, if the growth law deviates slightly from exponential for very small cells, homeostasis can be maintained with a simple ‘timer’ triggering division. Therefore, deciding whether division control in bacteria relies on a ‘timer’ or ‘sizer’ mechanism requires quantitative comparisons between models and data.ResultsThe timer and sizer hypotheses find a natural expression in models based on partial differential equations. Here we test these models with recent data on single-cell growth of Escherichia coli. We demonstrate that a size-independent timer mechanism for division control, though theoretically possible, is quantitatively incompatible with the data and extremely sensitive to slight variations in the growth law. In contrast, a sizer model is robust and fits the data well. In addition, we tested the effect of variability in individual growth rates and noise in septum positioning and found that size control is robust to this phenotypic noise.ConclusionsConfrontations between cell cycle models and data usually suffer from a lack of high-quality data and suitable statistical estimation techniques. Here we overcome these limitations by using high precision measurements of tens of thousands of single bacterial cells combined with recent statistical inference methods to estimate the division rate within the models. We therefore provide the first precise quantitative assessment of different cell cycle models.

Statistical estimation of a growth-fragmentation model observed on a genealogical tree

We model the growth of a cell population by a piecewise deterministic Markov branching tree. Each cell splits into two offsprings at a division rate

Self-Similar Branching Markov Chains

B(x)

PIECEWISE DETERMINISTIC MARKOV PROCESS — RECENT RESULTS

that depends on its size

Multifractal spectra and precise rates of decay in homogeneous fragmentations

x

Non-parametric estimation of the spiking rate in systems of interacting neurons

. The size of each cell grows exponentially in time, at a rate that varies for each individual. We show that the mean empirical measure of the model satisfies a growth-fragmentation type equation if structured in both size and growth rate as state variables. We construct a nonparametric estimator of the division rate

Statistical estimation of jump rates for a specific class of Piecewise Deterministic Markov Processes.

B(x)

Investigation of asymmetry in E. coli growth rate

based on the observation of the population over different sampling schemes of size

Martingales and rates of presence in homogeneous fragmentations

n

Energy efficiency of consecutive fragmentation processes

on the genealogical tree. Our estimator nearly achieves the rate