Large Deviation Principle Linking Lineage Statistics to Fitness in Microbial Populations

Levien, Ethan; GrandPre, Trevor; Amir, Ariel

doi:10.1103/physrevlett.125.048102

Cited by 19 publications

(24 citation statements)

References 35 publications

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“…(4) and briefly summarize the main result of Ref. [13]. Assuming that δ satisfies a large deviation principle, we obtain…”

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confidence: 79%

“…Alternative approaches estimate the growth rate by comparing the outcome of sampling the population forward in time with retrospective sampling, in which individuals in the final population are traced back to their ancestors [11,12]. A recent study linked the exponential growth rate Λ to the asymptotic distribution of the number of cell divisions ∆ among lineages [13]. This approach makes use of techniques borrowed from large deviation theory and has the advantage of neither requiring the Markovian assumption, nor retrospective sampling.…”

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confidence: 99%

“…Following Refs. [13,14], we now imagine to randomly select a lineage by starting from the initial individual and picking at each divisions one of the two newborns with equal probability. With this procedure, a lineage that underwent ∆ cell divisions is chosen with probability 2 −∆ .…”

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confidence: 99%

“…We remark that, in this argument, we did not distinguish between the a priori probabilities p(∆; T ) and the empirical ones, estimated from lineage frequencies in a single tree. In fact, it can be shown that the empirical probabilities rapidly converge to the a priori ones in the large T limit [13,15], so that this distinction is not important for our aims.…”

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confidence: 99%

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Generalized Euler-Lotka equation for correlated cell divisions

Pigolotti

2021

Preprint

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Cell division times in microbial populations display significant fluctuations. These fluctuations impact the population growth rate in a non-trivial way. If fluctuations are uncorrelated among different cells, the population growth rate is predicted by the Euler-Lotka equation, which is a classic result in mathematical biology. However, cell division times can present significant correlations, due to physical properties of cells that are passed from mothers to daughters. In this paper, we derive an equation remarkably similar to the Euler-Lotka equation which is valid in the presence of correlations. Our exact result is based on large deviation theory and does not require particularly strong assumptions on the underlying dynamics. We apply our theory to a phenomenological model of bacterial cell division. We find that the discrepancy between the growth rate predicted by the Euler-Lotka equation and our generalized version is relatively small, but large enough to be measurable in experiments.

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“…(4) and briefly summarize the main result of Ref. [13]. Assuming that δ satisfies a large deviation principle, we obtain…”

mentioning

confidence: 79%

mentioning

confidence: 99%

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confidence: 99%

mentioning

confidence: 99%

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Generalized Euler-Lotka equation for correlated cell divisions

Pigolotti

2021

Preprint

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“…(4) provides an estimator for the population growth rate Λ t , which requires only mother machine data [8]. This is useful, although in practice the convergence of this estimator is a challenging issue [16], which is one motivation to look for inequalities as done below. Fluctuation-response inequality for populations of cells -Let us introduce an arbitrary function of the value s of a general trait S as g t (s).…”

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confidence: 99%

Universal constraints on selection strength in lineage trees

Genthon

Lacoste

2020

Preprint

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We obtain general inequalities constraining the difference between the average of an arbitrary function of a phenotypic trait, which includes the fitness landscape of the trait itself, in the presence or in the absence of natural selection. These inequalities imply bounds on the strength of selection, which can be measured from the statistics of traits or divisions along lineages. The upper bound is related to recent generalizations of linear response relations in Stochastic Thermodynamics, and is reminiscent of the fundamental theorem of Natural selection of R. Fisher and of its generalization by Price. The lower bound follows from recent improvements on Jensen inequality and is typically less tight than the upper bound. We illustrate our results using numerical simulations of growing cell colonies and with experimental data of time-lapse microscopy experiments of bacteria cell colonies.

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Fluctuation relations and fitness landscapes of growing cell populations

Genthon

Lacoste

2020

Sci Rep

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We construct a pathwise formulation of a growing population of cells, based on two different samplings of lineages within the population, namely the forward and backward samplings. We show that a general symmetry relation, called fluctuation relation relates these two samplings, independently of the model used to generate divisions and growth in the cell population. these relations lead to estimators of the population growth rate, which can be very efficient as we demonstrate by an analysis of a set of mother machine data. These fluctuation relations lead to general and important inequalities between the mean number of divisions and the doubling time of the population. We also study the fitness landscape, a concept based on the two samplings mentioned above, which quantifies the correlations between a phenotypic trait of interest and the number of divisions. We obtain explicit results when the trait is the age or the size, for age and size-controlled models. While the growth of cell populations appears deterministic, many processes occurring at the single cell level are stochastic. Among many possibilities, stochasticity at the single cell level can arise from stochasticity in the generation times 1 , from stochasticity in the partition at division 2,3 , or from the stochasticity of single cell growth rates, which are usually linked to stochastic gene expression 4. Ideally one would like to be able to disentangle the various sources of stochasticity present in experimental data 5. This would allow to understand and predict how the various sources of stochasticity affect macroscopic parameters of the cell population, such as the Malthusian population growth rate 6,7. Beyond this specific question, research in this field attempts to elucidate the fundamental physical constraints which control growth and divisions in cell populations. With the advances in single cell experiments, where the growth and divisions of thousand of individual cells can be tracked, robust statistics can be acquired. New theoretical methods are needed to exploit this kind of data and to relate experiments carried out at the population level with experiments carried out at the single cell level. For instance, one would like to relate single-cell time-lapse video microscopy experiments of growing cell populations 8 , which provide information on all the lineages in the branched tree, with experiments carried out with the mother machine configuration, which provide information on single lineages 9,10. Let us now review quickly how the issue was addressed theoretically. In 2015, a pathwise thermodynamic framework was built for population dynamics using large deviation theory. One important result was a variational principle for the population growth rate 11 , which was formulated in terms of two key path distributions, namely the chronological and the retrospective probability distributions. Then, in order to explain their experimental observation that populations of Escherichia coli double faster than the mean doubling time of their constituent...

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Large Deviation Principle Linking Lineage Statistics to Fitness in Microbial Populations

Cited by 19 publications

References 35 publications

Generalized Euler-Lotka equation for correlated cell divisions

Generalized Euler-Lotka equation for correlated cell divisions

Universal constraints on selection strength in lineage trees

Fluctuation relations and fitness landscapes of growing cell populations

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