Cellular Properties and Population Asymptotics in the Population Balance Equation

Friedlander, Tamar; Brenner, Naama

doi:10.1103/physrevlett.101.018104

Cited by 14 publications

(41 citation statements)

References 20 publications

(30 reference statements)

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“…a result that is consistent with the analysis of symmetric cell division as performed in [28]. In the same work, it was shown that this asymptotic behavior occurs also under generic assumptions about asymmetric division.…”

Section: Binary Divisionsupporting

confidence: 77%

Stationary Size Distributions of Growing Cells with Binary and Multiple Cell Division

et al. 2011

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Populations of unicellular organisms that grow under constant environmental conditions are considered theoretically. The size distribution of these cells is calculated analytically, both for the usual process of binary division, in which one mother cell produces always two daughter cells, and for the more complex process of multiple division, in which one mother cell can produce 2 n daughter cells with n = 1, 2, 3, . . . . The latter mode of division is inspired by the unicellular algae Chlamydomonas reinhardtii. The uniform response of the whole population to different environmental conditions is encoded in the individual rates of growth and division of the cells. The analytical treatment of the problem is based on size-dependent rules for cell growth and stochastic transition processes for cell division. The comparison between binary and multiple division shows that these different division processes lead to qualitatively different results for the size distribution and the population growth rates.

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Section: Binary Divisionsupporting

confidence: 77%

Stationary Size Distributions of Growing Cells with Binary and Multiple Cell Division

et al. 2011

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“…Earlier work focused on protein accumulation and division [18][19][20][21][22], or protein accumulation and continuous dissipation [23,24]. The recent data on protein content over multiple generations [8] shows that, due to the exponential nature of protein accumulation, division or dissipation alone cannot stabilize copy numbers, and reveal a correlation between variables across generations.…”

Section: Discussionmentioning

confidence: 99%

Universal protein distributions in a model of cell growth and division

Brenner¹,

Newman²,

Osmanović³

et al. 2015

Phys. Rev. E

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Protein distributions measured under a broad set of conditions in bacteria and yeast were shown to exhibit a common skewed shape, with variances depending quadratically on means. For bacteria these properties were reproduced by temporal measurements of protein content, showing accumulation and division across generations. Here we present a stochastic growth-and-division model with feedback which captures these observed properties. The limiting copy number distribution is calculated exactly, and a single parameter is found to determine the distribution shape and the variance-to-mean relation. Estimating this parameter from bacterial temporal data reproduces the measured distribution shape with high accuracy, and leads to predictions for future experiments.

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“…In Ref. [16], the situation was just opposite: Protein partitioning was stochastic and protein production was deterministic. After combining the stochastic protein production (of Ref.…”

Section: Discussionmentioning

confidence: 99%

“…[16]. If x cannot be treated as proportional to the cell mass or volume, it is unclear how the division rate should depend on the copy number of a given protein, and various functional forms of h d (x) were used in the literature [14][15][16]. For that reason, and in order to obtain an analytically tractable model, we focus here on the simplest case of the constant cell division rate, 2h d (x) ≡ ∆ = const, which implies ∞ 0 h d (ξ)p(ξ)dξ = ∆/2.…”

Section: Modelmentioning

confidence: 99%

“…However, for small x, the half-by-half division as given by (9) is much less realistic than other continuous approximations to discrete binomial distribution, such as the 'all or none' partitioning (η(q) = η b (q) ≡ 1 2 [δ(q) + δ(1 − q)]) or even a uniform distribution of partition ratio (η(q) = η u (q) ≡ Θ(q)Θ (1 − q)), considered in Refs. [16,20].…”

Section: B Squared Coefficient Of Variation Has a Noise Floor Due Tomentioning

confidence: 99%

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Exactly solvable model of gene expression in a proliferating bacterial cell population with stochastic protein bursts and protein partitioning

2019

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Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not concentration, the decay term may also approximate the loss of protein molecules due to cell division as a continuous degradation process. The seminal model of that kind leads to gamma distributions of protein levels, whose parameters are defined by the mean frequency of protein bursts and mean burst size. However, such models (whether interpreted in terms of molecule numbers or concentrations) do not correctly account for the noise due to protein partitioning between daughter cells.We present an exactly solvable stochastic model of gene expression in cells dividing at random times, where we assume description in terms of molecule numbers with a constant mean protein burst size. The model is based on a population balance equation supplemented with protein production in random bursts.If protein molecules are partitioned equally between daughter cells, we obtain at steady state the analytical expressions for probability distributions similar in shape to gamma distribution, yet with quite different values of mean burst size and mean burst frequency than would result from fitting of the classical continuous-decay model to these distributions. For random partitioning of protein molecules between daughter cells, we obtain the moment equations for the protein number distribution and thus the analytical formulas for the squared coefficient of variation.

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Cellular Properties and Population Asymptotics in the Population Balance Equation

Cited by 14 publications

References 20 publications

Stationary Size Distributions of Growing Cells with Binary and Multiple Cell Division

Stationary Size Distributions of Growing Cells with Binary and Multiple Cell Division

Universal protein distributions in a model of cell growth and division

Exactly solvable model of gene expression in a proliferating bacterial cell population with stochastic protein bursts and protein partitioning

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