Quantitative Examination of Five Stochastic Cell-Cycle and Cell-Size Control Models for Escherichia coli and Bacillus subtilis

We examine five quantitative models of the cell-cycle and cell-size control in Escherichia coli and Bacillus subtilis that have been proposed over the last decade to explain single-cell experimental data generated with high-throughput methods. After presenting the statistical properties of these models, we test their predictions against experimental data. Based on simple calculations of the defining correlations in each model, we first dismiss the stochastic Helmstetter-Cooper model and the Initiation Adder model, and show that both the Replication Double Adder (RDA) and the Independent Double Adder (IDA) model are more consistent with the data than the other models. We then apply a recently proposed statistical analysis method and obtain that the IDA model is the most likely model of the cell cycle. By showing that the RDA model is fundamentally inconsistent with size convergence by the adder principle, we conclude that the IDA model is most consistent with the data and the biology of bacterial cell-cycle and cell-size control. Mechanistically, the Independent Adder Model is equivalent to two biological principles: (i) balanced biosynthesis of the cell-cycle proteins, and (ii) their accumulation to a respective threshold number to trigger initiation and division.

Characterizing non-exponential growth and bimodal cell size distributions in Schizosaccharomyces pombe: an analytical approach

Unlike many single-celled organisms, the growth of fission yeast cells within a cell cycle is not exponential. It is rather characterized by three distinct phases (elongation, septation and fission), each with a different growth rate. Experiments also show that the distribution of cell size in a lineage is often bimodal, unlike the unimodal distributions measured for the bacterium Escherichia coli. Here we construct a detailed stochastic model of cell size dynamics in fission yeast. The theory leads to analytic expressions for the cell size and the birth size distributions, and explains the origin of bimodality seen in experiments. In particular our theory shows that the left peak in the bimodal distribution is associated with cells in the elongation phase while the right peak is due to cells in the septation and fission phases. We show that the size control strategy, the variability in the added size during a cell cycle and the fraction of time spent in each of the three cell growth phases have a strong bearing on the shape of the cell size distribution. Furthermore we infer all the parameters of our model by matching the theoretical cell size and birth size distributions to those from experimental single cell time-course data for seven different growth conditions. Our method provides a much more accurate means of determining the cell size control strategy (timer, adder or sizer) than the standard method based on the slope of the best linear fit between the birth and division sizes. We also show that the variability in added size and the strength of cell size control of fission yeast depend weakly on the temperature but strongly on the culture medium.

Quantitative examination of five stochastic cell-cycle and cell-size control models for Escherichia coli and Bacillus subtilis

We examine five quantitative models of the cell-cycle and cell-size control in Escherichia coli and Bacillus subtilis that have been proposed over the last decade to explain single-cell experimental data generated with high-throughput methods. After presenting the statistical properties of these models, we test their predictions against experimental data. Based on simple calculations of the defining correlations in each model, we first dismiss the stochastic Helmstetter-Cooper model and the Initiation Adder model, and show that both the Replication Double Adder and the Independent Double Adder model are more consistent with the data than the other models. We then apply a recently proposed statistical analysis method and obtain that the Independent Double Adder model is the most likely model of the cell cycle. By showing that the Replication Double Adder model is fundamentally inconsistent with size convergence by the adder principle, we conclude that the Independent Double Adder model is most consistent with the data and the biology of bacterial cell-cycle and cell-size control. Mechanistically, the Independent Adder Model is equivalent to two biological principles: (i) balanced biosynthesis of the cell-cycle proteins, and (ii) their accumulation to a respective threshold number to trigger initiation and division.

Direct and indirect regulation of Pom1 cell size pathway by the protein phosphatase 2C Ptc1

The fission yeast cells Schizosaccharomyces pombe divide at constant cell size regulated by environmental stimuli. An important pathway of cell size control involves the membrane-associated DYRK-family kinase Pom1, which forms decreasing concentration gradients from cell poles and inhibits mitotic inducers at mid-cell. Here, we identify the phosphatase 2C Ptc1 as negative regulator of Pom1. Ptc1 localizes to cell poles in a manner dependent on polarity and cell-wall integrity factors. We show that Ptc1 directly binds Pom1 and can dephosphorylate it in vitro but modulates Pom1 localization indirectly upon growth in low glucose conditions by influencing microtubule stability. Thus, Ptc1 phosphatase plays both direct and indirect roles in the Pom1 cell size control pathway. [Media: see text]

Direct and indirect regulation of Pom1 cell size pathway by the protein phosphatase 2C Ptc1

The fission yeast cells Schizosaccharomyces pombe divide at constant cell size regulated by environmental stimuli. An important pathway of cell size control involves the membrane-associated DYRK-family kinase Pom1, which forms decreasing concentration gradients from cell poles and inhibits mitotic inducers at mid-cell. Here, we identify the phosphatase 2C Ptc1 as negative regulator of Pom1. Ptc1 localizes to cell poles in a manner dependent on polarity and cell-wall integrity factors. We show that Ptc1 directly binds Pom1 and can dephosphorylate it in vitro but modulates Pom1 localization indirectly upon growth in low glucose conditions by influencing microtubule stability. Thus, Ptc1 phosphatase plays both direct and indirect roles in the Pom1 cell size control pathway.

Comment on ‘Initiation of chromosome replication controls both division and replication cycles in E. coli through a double-adder mechanism’

Witz et al. recently performed single-cell mother machine experiments to track growth and the replication cycle in E. coli. They analyzed the correlation structure of selected parameters using both their data and published data, and concluded that E. coli cell-size control is implemented at replication initiation, which challenged the newly emerged division-centric mechanism of cell-size control in bacteria. We repeated Witz et al.’s analysis, and performed additional experiments and analytical calculations. These results explain Witz et al.’s observation and in fact support the division-centric model.