Pathwise thermodynamic structure in population dynamics

Sughiyama, Yuki; Kobayashi, Tetsuya; Tsumura, Koji; Aihara, Kazuyuki

doi:10.1103/physreve.91.032120

Cited by 28 publications

(44 citation statements)

References 21 publications

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“…This fluctuation relation depends only on the structure of the branched tree but not on the class of dynamical models defined on it. This relation has analogies with the fluctuation relations well known in Stochastic Thermodynamics [18], as first noted in [19,20], which we further discuss here.…”

Section: Introductionsupporting

confidence: 72%

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Fluctuation relations and fitness landscapes of growing cell populations

Genthon

Lacoste

2020

Preprint

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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. Known models of cell size control are studied with a formalism based on path integrals or on operators. We investigate some consequences of this fluctuation relation, which constrains the distributions of the number of cell divisions and leads to inequalities between the mean number of divisions and the doubling time of the population. We finally study the concept of fitness landscape, 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.

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Section: Introductionsupporting

confidence: 72%

“…19). Let us examine the particular case of uncontrolled models, for which the division rate is constant: B = ν.…”

mentioning

confidence: 99%

Fluctuation relations and fitness landscapes of growing cell populations

Genthon

Lacoste

2020

Preprint

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“…Noting that g * ðτÞ is the typical lineage generation time distribution within a population, we can understand from the above relations that growth rate differences are linked with the different statistics along cell lineages in isolation and within a population. The advantage of the lineage viewpoint in analyzing population dynamics has been explored theoretically (12,(25)(26)(27)(28); our study provides an experimental foundation behind this powerful concept.…”

Section: Age Distributions Along Long Single-cell Lineages In Populatmentioning

confidence: 99%

Noise-driven growth rate gain in clonal cellular populations

Hashimoto

Nozoe

Nakaoka

et al. 2016

Proc. Natl. Acad. Sci. U.S.A.

165

205

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Cellular populations in both nature and the laboratory are composed of phenotypically heterogeneous individuals that compete with each other resulting in complex population dynamics. Predicting population growth characteristics based on knowledge of heterogeneous single-cell dynamics remains challenging. By observing groups of cells for hundreds of generations at single-cell resolution, we reveal that growth noise causes clonal populations of Escherichia coli to double faster than the mean doubling time of their constituent single cells across a broad set of balanced-growth conditions. We show that the population-level growth rate gain as well as age structures of populations and of cell lineages in competition are predictable. Furthermore, we theoretically reveal that the growth rate gain can be linked with the relative entropy of lineage generation time distributions. Unexpectedly, we find an empirical linear relation between the means and the variances of generation times across conditions, which provides a general constraint on maximal growth rates. Together, these results demonstrate a fundamental benefit of noise for population growth, and identify a growth law that sets a "speed limit" for proliferation.growth noise | age-structured population model | cell lineage analysis | growth law | microfluidics C ell growth is an important physiological process that underlies the fitness of organisms. In exponentially growing cell populations, proliferation is usually quantified using the bulk population growth rate, which is assumed to represent the average growth rate of single cells within a population. In addition, basic growth laws exist that relate ribosome function and metabolic efficiency, macromolecular composition, and cell size of the culture as a whole to the bulk population growth rate (1-3). Population growth rate is therefore a quantity of primary importance that reports cellular physiological states and fitness.However, at the single-cell level, growth-related parameters such as the division time interval and division cell size are heterogeneous even in a clonal population growing at a constant rate (4-9). Such "growth noise" causes concurrently living cells to compete within the population for representation among its future descendants. For example, if two sibling cells born from the same mother cell had different division intervals, the faster dividing sibling is likely to have more descendants in the future population compared with its slower dividing sister, despite the fact that progenies of both siblings may proliferate equally well (Fig. 1). Intrapopulation competition complicates single-cell analysis because any growth-correlated quantities measured over the population deviate from intrinsic single-cell properties (10-12). In the case of the toy model described in Fig. 1, cells are assumed to determine their generation times (division interval) randomly by roll of a dice. The mean of intrinsic cellular generation time is thus ð1 + 2 + ⋯ + 6Þ=6 = 3.5 h, but population doubling time, which is...

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“…See (45) for the derivation. This is also an extension of our previous work (46) in which the division 137 time was not considered. T B (x |x) and π B together define a semi-Markov process of x, which, by 138 construction, asymptotically generates the retrospective cell lineage.…”

mentioning

confidence: 70%

Lineage EM Algorithm for Inferring Latent States from Cellular Lineage Trees

Nakashima

Sughiyama

Kobayashi

2018

Preprint

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Phenotypic variability in a population of cells can work as the bet-hedging of the cells under an unpredictably changing environment, the typical example of which is the bacterial persistence. To understand the strategy to control such phenomena, it is indispensable to identify the phenotype of each cell and its inheritance. Although recent advancements in microfluidic technology offer us useful lineage data, they are insufficient to directly identify the phenotypes of the cells. An alternative approach is to infer the phenotype from the lineage data by latent-variable estimation. To this end, however, we must resolve the bias problem in the inference from lineage called survivorship bias. In this work, we clarify how the survivor bias distorts statistical estimations. We then propose a latent-variable estimation algorithm without the survivorship bias from lineage trees based on an expectation-maximization (EM) algorithm, which we call Lineage EM algorithm (LEM). LEM provides a statistical method to identify the traits of the cells applicable to various kinds of lineage data. 1 2 3 4 5 6 7 8 2generations (1-3). Such phenotypic variety leads to behavioral individuality of each cell, which, in turn, generates complicated 3 population phenomena. One example is bacterial persistence in which a fraction of cells in a population survives when the 4 population experiences an antibiotic exposure even though the other fraction dies out (4-8). Persistence is also recently 5 recognized relevant to the drug-resistance of cancers (9, 10). While the survivors, which are also called persisters, were originally 6 conjectured as dormant and thereby drug-insensitive cells in a population, recent bioimaging analysis revealed that persistence 7 is a more intricate phenomenon, which involves resistant but still growing cells (5, 6). Because drug-resistance is tightly related 8 to the manner how the drug is incorporated into a cell and interferes with the self-replicating process, quantitative analysis 9 of persistence requires a characterization of growth states of individual cells and their competition in a population. More 10 generally, the heterogeneities in the growth speed and the death rate as well as their inheritance from a mother to daughter 11 cells constitute Darwinian natural selection among the cells. Such natural selection at the cellular level is also highly relevant 12 to drug-resistances of pathogens and cancers, immunological memories, cell competitions in tissues, and induction of iPS cells 13 (9-13). Moreover, the population dynamics under selection is integratively determined by the growth states of cells, their 14 statistical property, and their inheritance dynamics over generations. Therefore, identification of growth states of cells from 15 data is crucial for predicting and controlling those selection-driven phenomena (14, 15). 16To determine the growth states and their dynamics, we can take advantage of recent bioimaging and microfluidic technology, 17 which provide abundant but incomplete data of the popul...

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Pathwise thermodynamic structure in population dynamics

Cited by 28 publications

References 21 publications

Fluctuation relations and fitness landscapes of growing cell populations

Fluctuation relations and fitness landscapes of growing cell populations

Noise-driven growth rate gain in clonal cellular populations

Lineage EM Algorithm for Inferring Latent States from Cellular Lineage Trees

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