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 tree. Surprisingly, these size distributions differ significantly from observing single cells in isolation. In populations, cells seemingly grow to different sizes, typically exhibit less cell-to-cell variability and often display qualitatively different sensitivities to cell cycle noise and division errors. We demonstrate the key findings using recent single-cell data and elaborate on the implications for the ability of cells to maintain a narrow size distribution and the emergence of different power laws in these distributions.
Last. Sander J. Tans(TU Delft: Delft University of Technology)H-Index: 35
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Summary Our understanding of bacterial cell size control is based mainly on stress-free growth conditions in the laboratory [1–10]. In the real world, however, bacteria are routinely faced with stresses that produce long filamentous cell morphologies [11–28]. Escherichia coli is observed to filament in response to DNA damage [22–25], antibiotic treatment [11–14, 28], host immune systems [15, 16], temperature [17], starvation [20], and more [18, 19, 21], conditions which are relevant to clinical ...
Last. Antonio A. Alonso(CSIC: Spanish National Research Council)H-Index: 36
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A realistic description of the variability in bacterial growth and division is critical to produce reliable predictions of safety risks along the food chain. Individual-based modelling of bacteria provides the theoretical framework to deal with this variability, but it requires information about the individual behaviour of bacteria inside populations. In this work, we overcome this problem by estimating the individual behaviour of bacteria from population statistics obtained with flow cytometry....
Cells control their size through an intricate balance of cell growth, cell division, and cell death. Extensive work on unicellular model organisms revealed that cell-size-dependent cell cycle progression accounts for major aspects of cell size regulation and provided insights into the underlying molecular mechanisms. Nevertheless, elaborate live-cell imaging approaches still reveal new phenomenological observations that challenge our simplified models of size regulation and raise the question of...
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...
It is remarkable how robustly a bacterial species can maintain its preferred size. In this Review, Willis and Huang explore classic and current knowledge of the mechanisms that coordinate bacterial cell size with essential growth and cell cycle processes.
The decision to divide is the most important one that any cell must make. Recent single cell studies suggest that most bacteria follow an ``adder'' model of cell size control, incorporating a fixed amount of cell wall material before dividing. Mycobacteria, including the causative agent of tuberculosis Mycobacterium tuberculosis, are known to divide asymmetrically resulting in heterogeneity in growth rate, doubling time, and other growth characteristics in daughter cells. The interplay between a...
Last. Abhyudai Singh(UD: University of Delaware)H-Index: 34
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Abstract At the single-cell level, noise arises from multiple sources, such as inherent stochasticity of biomolecular processes, random partitioning of resources at division, and fluctuations in cellular growth rates. How these diverse noise mechanisms combine to drive variations in cell size within an isoclonal population is not well understood. Here, we investigate the contributions of different noise sources in well-known paradigms of cell-size control, such as adder (division occurs after ad...
#1Fangwei Si(UCSD: University of California, San Diego)H-Index: 10
#2Dongyang Li(UCSD: University of California, San Diego)H-Index: 4
Last. Suckjoon Jun(UCSD: University of California, San Diego)H-Index: 30
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Summary It is generally assumed that the allocation and synthesis of total cellular resources in microorganisms are uniquely determined by the growth conditions. Adaptation to a new physiological state leads to a change in cell size via reallocation of cellular resources. However, it has not been understood how cell size is coordinated with biosynthesis and robustly adapts to physiological states. We show that cell size in Escherichia coli can be predicted for any steady-state condition by proje...
#1Takashi Nozoe(UTokyo: University of Tokyo)H-Index: 2
#2Edo Kussell(NYU: New York University)H-Index: 21
Last. Yuichi Wakamoto(UTokyo: University of Tokyo)H-Index: 17
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Recent advances in single-cell time-lapse microscopy have revealed non-genetic heterogeneity and temporal fluctuations of cellular phenotypes. While different phenotypic traits such as abundance of growth-related proteins in single cells may have differential effects on the reproductive success of cells, rigorous experimental quantification of this process has remained elusive due to the complexity of single cell physiology within the context of a proliferating population. We introduce and apply...
Last. Xiongfei Fu(CAS: Chinese Academy of Sciences)
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The mechanism of bacterial cell size control has been a mystery for decades, which involves the well-coordinated growth and division in the cell cycle. The revolutionary modern techniques of microfluidics and the advanced live imaging analysis techniques allow long term observations and high-throughput analysis of bacterial growth on single cell level, promoting a new wave of quantitative investigations on this puzzle. Taking the opportunity, this theoretical study aims to clarify the stochastic...
#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...
The chemical master equation and the Gillespie algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular rea...
#2Ramon Grima(Edin.: University of Edinburgh)H-Index: 37
The stochasticity of gene expression is manifested in the fluctuations of mRNA and protein copy numbers within a cell lineage over time. While data of this type can be obtained for many generations, most mathematical models are unsuitable to interpret such data since they assume non-growing cells. Here we develop a theoretical approach that quantitatively links the frequency content of lineage data to subcellular dynamics. We elucidate how the position, height, and width of the peaks in the powe...
Last. Steffen Waldherr(Katholieke Universiteit Leuven)H-Index: 18
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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...
Last. Xiongfei Fu(CAS: Chinese Academy of Sciences)
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The mechanism of bacterial cell size control has been a mystery for decades, which involves the well-coordinated growth and division in the cell cycle. The revolutionary modern techniques of microfluidics and the advanced live imaging analysis techniques allow long term observations and high-throughput analysis of bacterial growth on single cell level, promoting a new wave of quantitative investigations on this puzzle. Taking the opportunity, this theoretical study aims to clarify the stochastic...
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...
The chemical master equation and the stochastic simulation algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled for through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any i...
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...
Last. Steffen Waldherr(Katholieke Universiteit Leuven)H-Index: 18
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Growing populations of bacteria control their growth and division reaching narrow distributions of cellsizes. In this paper we explored how different combinations of growth regimes and division mechanisms lead to different cell-size statistics in these populations. Deterministic and stochastic modeling were used to describe the size distribution of a population of cells that is observed from two different perspectives: as single cell lineages, i.e. random paths in the lineage tree, or as snapsho...
