Heavy-tailed distributions in a stochastic gene autoregulation model

Bokes, Pavol

doi:10.1088/1742-5468/ac2edb

Cited by 11 publications

(4 citation statements)

References 66 publications

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“…A single-cell version of the equation without the growth term was introduced in [14] and subsequently studied by other authors (e.g. [37,38]) including us [39,40]. We and co-authors extended the model by protein-dependent growth and analysed differences between the single-cell and population models in [41,42].…”

Section: Model Formulationmentioning

confidence: 99%

Hysteresis and noise floor in gene expression optimised for persistence against lethal events

Bokes,

Singh

2024

Preprint

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Bacterial cell persistence, crucial for survival under adverse conditions like antibiotic exposure, is intrinsically linked to stochastic fluctuations in gene expression. Certain genes, while inhibiting growth under normal circumstances, confer tolerance to antibiotics at elevated expression levels. The occurrence of antibiotic events lead to instantaneous cellular responses with varied survival probabilities correlated with gene expression levels. Notably, cells with lower protein concentrations face higher mortality rates. This study aims to elucidate an optimal strategy for protein expression conducive to cellular survival. Through comprehensive mathematical analysis, we determine the optimal burst size and frequency that maximise cell proliferation. Furthermore, we explore how the optimal expression distribution changes as the cost of protein expression to growth escalates. Our model reveals a hysteresis phenomenon, characterised by discontinuous transitions between deterministic and stochastic optima. Intriguingly, stochastic optima possess a noise floor, representing the minimal level of fluctuations essential for optimal cellular resilience.

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Section: Model Formulationmentioning

confidence: 99%

Hysteresis and noise floor in gene expression optimised for persistence against lethal events

Bokes,

Singh

2024

Preprint

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“…As an example, they state that 63% of financial returns of half a century can be associated with only 10 trading days. While many authors are aware of non-negligible stochastic effects and use this to their advantage to adequately model for instance bursty gene expression (2)(3)(4), expectations remain the instrument of choice to describe stochastic processes in various scientific fields. The Chemical Master Equation (CME) is a standard approach to describe the time evolution of CRNs (see e.g.…”

Section: Introductionmentioning

confidence: 99%

The impossible challenge of estimating non-existent moments of the Chemical Master Equation

Wagner

Radde

2023

Preprint

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Motivation: The Chemical Master Equation is a set of linear differential equations that describes the evolution of the probability distribution on all possible configurations of a (bio-)chemical reaction system. Since the number of configurations and therefore the dimension of the CME rapidly increases with the number of molecules, its applicability is restricted to small systems. A widely applied remedy for this challenge are moment-based approaches which consider the evolution of the first few moments of the distribution as summary statistics for the complete distribution. Here, we investigate the performance of two moment-estimation methods for reaction systems whose equilibrium distributions encounter heavy-tailedness and hence do not possess statistical moments. Results: We show that estimation via Stochastic Simulation Algorithm trajectories lose consistency over time and estimated moment values span a wide range of values even for large sample sizes. In comparison, the Method of Moments returns smooth moment estimates but is not able to indicate the non-existence of the allegedly predicted moments. We furthermore analyze the negative effect of a CME solution's heavy-tailedness on SSA run times and explain inherent difficulties. While moment estimation techniques are a commonly applied tool in the simulation of (bio-)chemical reaction networks, we conclude that they should be used with care, as neither the system definition nor the moment estimation techniques themselves reliably indicate the potential heavy-tailedness of the CME's solution.

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“…Protein production is modelled by a compound Poisson process [12,34]. Production events are referred to as bursts and the number of protein molecules produced per event as the burst size [6,7]; these are assumed to be independent and identically geometrically distributed [35,36]. Depletion of protein can be driven by two different mechanisms: degradation or partitioning at cell division [30].…”

Section: Introductionmentioning

confidence: 99%

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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Heavy-tailed distributions in a stochastic gene autoregulation model

Cited by 11 publications

References 66 publications

Hysteresis and noise floor in gene expression optimised for persistence against lethal events

Hysteresis and noise floor in gene expression optimised for persistence against lethal events

The impossible challenge of estimating non-existent moments of the Chemical Master Equation

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

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