Individual and population approaches for calibrating division rates in population dynamics: Application to the bacterial cell cycle

Doumic, Marie; Hoffmann, Marc

doi:10.48550/arxiv.2108.13155

Cited by 2 publications

(3 citation statements)

References 94 publications

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“…gives the total number of cells existing at time t and is finite. The empirical population density ( 6) is an example of a measure-valued Markov process [14,18]. Let us consider the expected value of the empirical population density…”

Section: Population Model: a Measure-valued Markov Processmentioning

confidence: 99%

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Joint Distribution of Protein Concentration and Cell Volume Coupled by Feedback in Dilution

Zabaikina

Bokes

Singh

2023

Preprint

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We consider a protein that negatively regulates the rate with which a cell grows. Since less growth means less protein dilution, this mechanism forms a positive feedback loop on the protein concentration. We couple the feedback model with a simple description of the cell cycle, in which a division event is triggered when the cell volume reaches a critical threshold. Following the division we either track only one of the daughter cells (single cell framework) or both cells (population framework). For both frameworks, we find an exact time-independent distribution of protein concentration and cell volume. We explore the consequences of dilution feedback on ergodicity, population growth rate, and the bias of the population distribution towards faster growing cells with less protein.

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Section: Population Model: a Measure-valued Markov Processmentioning

confidence: 99%

“…Since both sides are independent from one another, each side must be equal to a constant, which we denoted as ξ. We rewrite (18) and add the boundary condition on g(v):…”

Section: Chapman-kolmogorov Equationmentioning

confidence: 99%

Joint Distribution of Protein Concentration and Cell Volume Coupled by Feedback in Dilution

Zabaikina

Bokes

Singh

2023

Preprint

View full text Add to dashboard Cite

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“…Note that this is not true for deterministic asymmetric partitioning. In addition, if there is no noise on the growth, that is when D = 0, then we recover φ(x) = Kxψ(x) [30].…”

Section: A Model and Definitionsmentioning

confidence: 99%

Analytical cell size distribution: lineage-population bias and parameter inference

Genthon¹

2022

Preprint

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Solving population balance equations, we derive analytical steady-state cell size distributions for single-lineage experiments, such as the mother machine. These experiments are fundamentally different from batch cultures where populations of cells grow freely, and the statistical bias between them is obtained by comparing our results to cell size distributions measured in population. For exponential single-cell growth, characterizing most bacteria, the lineage-population bias is obtained explicitly. In addition, if volume is evenly split between the daughter cells at division, we show that cells are on average smaller in populations. For more general power-law growth rates and deterministic volume partitioning, both symmetric and asymmetric, we derive the exact lineage distribution. This solution is in good agreement with E. Coli mother machine data, and can be used to infer cell cycle parameters, such as the strength of the size control and the asymmetry of the division. When introducing stochastic volume partitioning, we derive the large-size and smallsize tails of the lineage size distributions, and show that they respectively do not depend on the partitioning of volume and on the size control strength. Finally, we show that introducing noise, either on the volume partitioning or on the single cell growth rate, can cancel the lineage-population bias.

show abstract

Individual and population approaches for calibrating division rates in population dynamics: Application to the bacterial cell cycle

Cited by 2 publications

References 94 publications

Joint Distribution of Protein Concentration and Cell Volume Coupled by Feedback in Dilution

Joint Distribution of Protein Concentration and Cell Volume Coupled by Feedback in Dilution

Analytical cell size distribution: lineage-population bias and parameter inference

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