Optimal Segregation of Proteins: Phase Transitions and Symmetry Breaking

Lin, Jie; Min, Jiseon; Amir, Ariel

doi:10.1103/physrevlett.122.068101

Cited by 13 publications

(36 citation statements)

References 30 publications

(46 reference statements)

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“…This framework can capture any possible form of intrinsic (as opposed to environmental) generation time variability through the appropriate choices of the phenotype x and distribution f. Therefore, existing models can be derived as specific cases of this framework. These include models where division is asymmetric [21][22][23][24] and where the relationship between successive generation times is non-monotonic and nonlinear, such as the kicked cell-cycle model used to describe circadian rhythms [25].…”

Section: A General Model Of Phenotypic Variabilitymentioning

confidence: 99%

The interplay of phenotypic variability and fitness in finite microbial populations

Levien

Kondev

Amir

2020

J. R. Soc. Interface.

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In isogenic microbial populations, phenotypic variability is generated by a combination of stochastic mechanisms, such as gene expression, and deterministic factors, such as asymmetric segregation of cell volume. Here we address the question: how does phenotypic variability of a microbial population affect its fitness? While this question has previously been studied for exponentially growing populations, the situation when the population size is kept fixed has received much less attention, despite its relevance to many natural scenarios. We show that the outcome of competition between multiple microbial species can be determined from the distribution of phenotypes in the culture using a generalization of the well-known Euler–Lotka equation, which relates the steady-state distribution of phenotypes to the population growth rate. We derive a generalization of the Euler–Lotka equation for finite cultures, which relates the distribution of phenotypes among cells in the culture to the exponential growth rate. Our analysis reveals that in order to predict fitness from phenotypes, it is important to understand how distributions of phenotypes obtained from different subsets of the genealogical history of a population are related. To this end, we derive a mapping between the various ways of sampling phenotypes in a finite population and show how to obtain the equivalent distributions from an exponentially growing culture. Finally, we use this mapping to show that species with higher growth rates in exponential growth conditions will have a competitive advantage in the finite culture.

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Section: A General Model Of Phenotypic Variabilitymentioning

confidence: 99%

The interplay of phenotypic variability and fitness in finite microbial populations

Levien

Kondev

Amir

2020

J. R. Soc. Interface.

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“…exponential single cell growth rate taken to be λ ∼ N (λ 0 , σ 2 λ ). We define the parameter x as the relative difference in volume at birth between the daughter and mother cells produced from a given division event: [19], as described in Figure 1 (C). This implies 0 < x < 1.…”

Section: Models Of Size Controlmentioning

confidence: 99%

Modeling the impact of single-cell stochasticity and size control on the population growth rate in asymmetrically dividing cells

Barber

Min

Murray

et al. 2020

Preprint

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Microbial populations show striking diversity in cell growth morphology and lifecycle [1]; however, our understanding of how these factors influence the growth rate of cell populations remains limited. We use theory and simulations to predict the impact of asymmetric cell division, cell size regulation and single-cell stochasticity on the population growth rate. Our model predicts that coarse-grained noise in the single-cell growth rate λ decreases the population growth rate, as previously seen for symmetrically dividing cells [2]. However, for a given noise in λ we find that dividing asymmetrically can enhance the population growth rate for cells with strong size control (between a “sizer” and an “adder”). To reconcile this finding with the abundance of symmetrically dividing organisms in nature, we propose that additional constraints on cell growth and division must be present which are not included in our model, and we explore the effects of selected extensions thereof. Further, we find that within our model, epigenetically inherited generation times may arise due to size control in asymmetrically dividing cells, providing a possible explanation for recent experimental observations in budding yeast [3]. Taken together, our findings provide insight into the complex effects generated by non-canonical growth morphologies.

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“…those with less damage) grow faster than the "senescent" cells [3][4][5][6][7][8]. There have been a number of theoretical works [1,[9][10][11] trying to quantify the effect of asymmetric segregation of proteins to the overall growth of the population. In this paper, we strengthen the theory developed by Lin et al [1] to relate the asymmetric protein segregation and the population growth rate by implementing a more general method involving transport equations and moment expansions.…”

Section: Introductionmentioning

confidence: 99%

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mentioning

confidence: 99%

“…We provide two ways of solving the self-consistent equation: numerically by updating the solution for the self-consistent equation iteratively and analytically by expanding moments of the distribution. With these more powerful tools, we can extend the previous model by Lin et al [1] to include stochasticity to the segregation asymmetry. We show the stochastic model is equivalent to the deterministic one with a modified effective asymmetry parameter (a eff ).…”

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A transport approach to relate asymmetric protein segregation and population growth

Min,

Amir

2020

Preprint

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Many unicellular organisms allocate their key proteins asymmetrically between the mother and daughter cells, especially in a stressed environment. A recent theoretical model is able to predict when the asymmetry in segregation of key proteins enhances the population fitness, extrapolating the solution at two limits where the segregation is perfectly asymmetric (asymmetry a = 1) and when the asymmetry is small (0 ≤ a 1) [1]. We generalize the model by introducing stochasticity and use a transport equation to obtain a self-consistent equation for the population growth rate and the distribution of the amount of key proteins. We provide two ways of solving the self-consistent equation: numerically by updating the solution for the self-consistent equation iteratively and analytically by expanding moments of the distribution. With these more powerful tools, we can extend the previous model by Lin et al. [1] to include stochasticity to the segregation asymmetry. We show the stochastic model is equivalent to the deterministic one with a modified effective asymmetry parameter (a eff ). We discuss the biological implication of our models and compare with other theoretical models.

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Optimal Segregation of Proteins: Phase Transitions and Symmetry Breaking

Cited by 13 publications

References 30 publications

The interplay of phenotypic variability and fitness in finite microbial populations

The interplay of phenotypic variability and fitness in finite microbial populations

Modeling the impact of single-cell stochasticity and size control on the population growth rate in asymmetrically dividing cells

A transport approach to relate asymmetric protein segregation and population growth

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