The dynamics of the size distribution in growing and dividing rod-shaped bacteria can change depending on the perspective through which the cell population is observed. From the perspective of single-cell lineages, only one descendant is followed after each division, while in population snapshots all of the offspring is considered. In this letter, we propose an analytical derivation of Population Balance Equations (PBEs) that can be used to compute the dynamics of the main statistics of the cell size distribution. We then explore how the dynamics are affected by different division strategies and by the two different perspectives of observation. To assess the accuracy of our derivations, we compare the analytical results with those obtained numerically and through stochastic simulations. The comparison allows us to establish mathematical relationships between the two perspectives of observation, thus improving our knowledge of how cells control their growth and proliferation.

Classical models of gene expression consider this process as a first order chemical reaction with rates dependent of the concentration of the reactants (typically, DNA loci, plasmids, RNA, enzymes, etc). By this, cell size is not usually considered to describe protein synthesis. However, due to the low number of these reactants and not perfectly symmetric cell division and molecule segregation, cell size dynamics may reveal hidden properties of the protein synthesis process. Here, we implement a...

Recent experiments support the adder model for E. coli division control. This model posits that bacteria grow, on average, a fixed size before division. It also predicts decorrelation between the noise in the added size and the size at birth. Here we develop a theory based on stochastic hybrid systems which could explain the main division strategies, including not only the adder strategy but the whole range from sizer to timer. We use experiments to explore the division control of E. coli growin...

Single-cell experiments have revealed cell-to-cell variability in generation times and growth rates for genetically identical cells. Theoretical models relating the fluctuating generation times of single cells to the population growth rate are usually based on the assumption that the generation times of mother and daughter cells are uncorrelated. This assumption, however, is inconsistent with the exponential growth of cell volume in time observed for many cell types. Here we develop a more gener...

How small, fast-growing bacteria ensure tight cell-size distributions remains elusive. High-throughput measurement techniques have propelled efforts to build modeling tools that help to shed light on the relationships between cell size, growth and cycle progression. Most proposed models describe cell division as a discrete map between size at birth and size at division with stochastic fluctuations assumed. However, such models underestimate the role of cell size transient dynamics by excluding t...

Last. Eugenio Cinquemani(IRIA: French Institute for Research in Computer Science and Automation)H-Index: 16

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MOTIVATION: Modern experimental technologies enable monitoring of gene expression dynamics in individual cells and quantification of its variability in isogenic microbial populations. Among the sources of this variability is the randomness that affects inheritance of gene expression factors at cell division. Known parental relationships among individually observed cells provide invaluable information for the characterization of this extrinsic source of gene expression noise. Despite this fact, m...

Last. David Lacoste(PSL Research University)H-Index: 21

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Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels are derived. One of these relations implies inequalities comparing the population doubling time with the mean generation time at the lineage or population levels. We argue that testing these inequalities provides useful insights into the underlying mechanism controlling the division rate in such branching processes.

It is outstanding and intriguing how robustly bacteria can maintain its preferred size despite recurrent rounds of growth and divisions. We model cell size using the stochastic hybrid system framework (SHS), where a cell grows either linearly or exponentially in size over time and random division events are fired at discrete time intervals. We ask for growth and division rates that reproduce the uncorrelated behavior of the added size at division and the newborn cell size in experiments. We prov...

Growth pervades all areas of life from single cells to cell populations to tissues. However, cell size often fluctuates significantly from cell to cell and from generation to generation. Here we present a unified framework to predict the statistics of cell size variations within a lineage tree of a proliferating population. We analytically characterise (i) the distributions of cell size snapshots, (ii) the distribution within a population tree, and (iii) the distribution of lineages across the t...

Population growth is often ignored when quantifying gene expression levels across clonal cell populations. We develop a framework for obtaining the molecule number distributions in an exponentially...

Last. Abhyudai Singh(UD: University of Delaware)H-Index: 34

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How isogenic cell populations maintain size homeostasis, i.e., a narrow distribution of cell size, is an intriguing fundamental problem. We model cell size using a stochastic hybrid system, where a cell grows exponentially in size (volume) over time and probabilistic division events are triggered at discrete-time intervals. Moreover, whenever division occurs, size is randomly partitioned among daughter cells. We first consider a scenario where a timer (cell-cycle clock) that measures the time el...

#2Archana Singh(UD: University of Delaware)H-Index: 13

Last. Ramon Grima(Edin.: University of Edinburgh)H-Index: 37

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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 l...

#1Marius Wiggert(University of California, Berkeley)H-Index: 1

#2Megan A. Turnidge(OHSU: Oregon Health & Science University)H-Index: 1

Last. Claire J. Tomlin(University of California, Berkeley)H-Index: 73

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Sequences of different drugs have shown potential to improve treatment strategies for cancer. Typical switched system approaches model the population dynamics of each drug independently, not rigorously considering the effects of pretreatment or drug-drug interactions. In this paper, a general model family incorporating pre-treatment effects and biological domain knowledge is proposed, and a model from this family is identified by using a novel experimental data set of two-drug sequences. Leverag...

Last. Ramon Grima(Edin.: University of Edinburgh)H-Index: 37

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Summary Recent advances in single-cell technologies have enabled time-resolved measurements of the cell size over several cell cycles. This data encodes information on how cells correct size aberrations so that they do not grow abnormally large or small. Here we formulate a piecewise deterministic Markov model describing the evolution of the cell size over many generations, for all three cell size homeostasis strategies (timer, sizer, and adder). The model is solved to obtain an analytical expre...

Recent studies describe bacterial division as a jump process triggered when it reaches a fixed number of stochastic discrete events at a rate depending on the cell-size. This theoretical approach enabled the computation of stochastic cell-size transient dynamics with arbitrary precision, with the possibility of being coupled to other continuous processes as gene expression. Here we synthesize most of this theory in the tool PyEcoLib, a python-based library to estimate bacterial cell size stochas...

Abstract Bacterial division is an inherently stochastic process. However, theoretical tools to simulate and study the stochastic transient dynamics of cell-size are scarce. Here, we present a general theoretical approach based on the Chapman-Kolmogorov formalism to describe these stochastic dynamics including continuous growth and division events as jump processes. Using this approach, we analyze the effect of different sources of noise on the dynamics of the size distribution. Oscillations in t...