Kinetics of Growth of Individual Cells of<i>Escherichia coli</i>and<i>Azotobacter agilis</i>

Harvey, Richard J.; Marr, Allen G.; Painter, Page R.

doi:10.1128/jb.93.2.605-617.1967

Cited by 121 publications

(55 citation statements)

References 20 publications

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“…The generation-time distribution, τ(t), that we measured ( Fig. 2A) can be accurately approximated by a normal distribution, which has also been observed by others 5,[32][33][34][35] . The coefficient of variation of the generation time is 27%, which indicates that 16% of the cells have a generation time below 53 min and the generation time of the same percentage of cells exceeds 92 min.…”

Section: The Population Growth Rate Calculated From Single-cell Genersupporting

confidence: 86%

Statistics and simulation of growth of single bacterial cells: illustrations withB. subtilisandE. coli

Heerden

Kempe

Doerr

et al. 2017

Preprint

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The inherent stochasticity of molecular reactions prevents us from predicting the exact state of singlecells in a population. However, when a population grows at steady-state, the probability to observe a cell with particular combinations of properties is fixed. Here we validate and exploit existing theory on the statistics of single-cell growth in order to predict the probability of phenotypic characteristics such as cell-cycle times, volumes, accuracy of division and cell-age distributions, using real-time imaging data for Bacillus subtilis and Escherichia coli. Our results show that single-cell growth-statistics can accurately be predicted from a few basic measurements. These equations relate different phenotypic characteristics, and can therefore be used in consistency tests of experimental single-cell growth data and prediction of single-cell statistics. We also exploit these statistical relations in the development of a fast stochastic-simulation algorithm of single-cell growth and protein expression. This algorithm greatly reduces computational burden, by recovering the statistics of growing cell-populations from the simulation of only one of its lineages. Our approach is validated by comparison of simulations and experimental data. This work illustrates a methodology for the prediction, analysis and tests of consistency of single-cell growth and protein expression data from a few basic statistical principles.Thousands of biochemical reactions are required for bacterial growth and division. Some of them operate in a regime where they are susceptible to stochastic fluctuations in the concentrations of their reactants and regulators 1,2 . These fluctuations can be amplified by molecular networks , where fluctuations at a cellular level can in turn cause cell-to-cell variations at the level of molecules and reaction activities. For instance, uneven cell division causes size differences between cells such that their protein content and reaction rates vary 4,6,7 . The fluctuating copy number of a particular molecule in a cell, over a time period of several bacterial cell cycles, is therefore the outcome of (stochastic) biochemical and cell-growth processes [8][9][10] . Coupled molecular and cellular fluctuations are associated with many surprising phenomena in single-cell biology [10][11][12][13][14] . This complex feedback circuitry generates cell-to-cell variability in a population of isogenic cells, which may result in individual cells transiting to different phenotypic states when conditions change [11][12][13]15,16 . Examples include adaptive phenotypic-diversification of populations of cells, e.g. the emergence of antibiotics-tolerant persister cells 2 and bacterial-cell differentiation 16 . Acquiring a predictive understanding of these phenomena is one of the current challenges in single-cell physiology 17 , with direct applications in biotechnology 18 and medical microbiology 19,20 . Disentangling causes and effects, using a stochastic framework, is a major challenge for single-cell physiology 21,22 an...

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Section: The Population Growth Rate Calculated From Single-cell Genersupporting

confidence: 86%

Statistics and simulation of growth of single bacterial cells: illustrations withB. subtilisandE. coli

Heerden

Kempe

Doerr

et al. 2017

Preprint

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“…Such data form the basis for a statistical description of population behavior. The theoretical framework of statistical population models was established over two decades ago (Collins and Richmond, 1962;Bell and Anderson, 1967;Harvey et al, 1967;Ramkrishna, 1979). However, their application has been limited by the lack of accessibility to critical experimental data needed to make them useful.…”

Section: Discussionmentioning

confidence: 99%

Slit Scanning of Saccharomyces cerevisiae Cells: Quantification of Asymmetric Cell Division and Cell Cycle Progression in Asynchronous Culture

Block

Eitzman

Wangensteen

et al. 1990

Biotechnology Progress

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Slit scanning flow cytometry has been applied to the analysis of the cell cycle and cell-cycle-dependent events in Saccharomyces cerevisiae, yielding information on the low-resolution spatial distribution of cellular components in single cells of unperturbed cell populations. Because this process is rapid, large numbers of cells can be analyzed to give distributions of parameters in a given population. To study asymmetric cell division and cell cycle progression, forward-angle light scattering (FALS) signals together with fluorescence signals from acriflavine-stained nuclei have been measured in cells from exponentially growing yeast populations. An algorithm has been developed that assigns the position of the bud neck in the FALS signals so that both FALS and DNA signals can be analyzed in terms of the contributions from the mother cell and the cell bud. The data indicate that mother cell FALS, on average, remains constant while FALS due to the cell bud increases as a cell progresses through the cell cycle. By identifying mitotic cells and measuring their properties, we have found that the coefficient of variation for the distribution of FALS is smallest within the dividing cell population and largest within the newborn cell population, in accordance with the critical size control mechanism of yeast cell growth. The use of this experimental approach to provide data for statistical population models is discussed.

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“…There is also some variability in the bacterial volume at birth or at division [60, [68][69][70][71][72], and of the cell volume or age at the time of DNA initiation [64,70,[72][73][74]. The coefficient of variation of the cell size at division time seems to be around 10% [60].…”

Section: Variability Of Cyclic Eventsmentioning

confidence: 99%

The cell cycle ofEscherichia coliand some of its regulatory systems

Képès¹

1986

FEMS Microbiology Letters

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Kinetics of Growth of Individual Cells ofEscherichia coliandAzotobacter agilis

Cited by 121 publications

References 20 publications

Statistics and simulation of growth of single bacterial cells: illustrations withB. subtilisandE. coli

Statistics and simulation of growth of single bacterial cells: illustrations withB. subtilisandE. coli

Slit Scanning of Saccharomyces cerevisiae Cells: Quantification of Asymmetric Cell Division and Cell Cycle Progression in Asynchronous Culture

The cell cycle ofEscherichia coliand some of its regulatory systems

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