Modeling of stochastic biological processes with non-polynomial propensities using non-central conditional moment equation

Kazeroonian, Atefeh; Theis, Fabian J.; Hasenauer, Jan

doi:10.3182/20140824-6-za-1003.02298

Cited by 9 publications

(7 citation statements)

References 23 publications

(27 reference statements)

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“…This problem has been previously addressed by either assuming rational functions [35] or Taylor expanding nonlinear functions [2,5,13,19,22,24]. However, we show that, in many practical scenarios, these previous approaches are either infeasible or may produce less robust optimisation convergence.…”

Section: Introductionmentioning

confidence: 84%

Revisiting moment-closure methods with heterogeneous multiscale population models

Lunz

Bonnans

Ruess

2022

Mathematical Biosciences

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Section: Introductionmentioning

confidence: 84%

Revisiting moment-closure methods with heterogeneous multiscale population models

Lunz

Bonnans

Ruess

2022

Mathematical Biosciences

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“…A well-known problem that often arises when dealing with nonlinear stochastic systems is unclosed moment dynamics -time evolution of lower order moments depends on higher order moments [37]. While a number of closure methods have been developed to tackle this issue [38][39][40][41][42][43][44][45][46][47][48][49][50][51], we circumvent this problem by exploiting the Linear Noise Approximation (LNA) [52]. Assuming small fluctuations in x(t) and z(t)…”

Section: Probabilistic Event Change In Population Counts Propensity Fmentioning

confidence: 99%

Optimal feedback mechanisms for regulating cell numbers

Modi

Singh

2018

Preprint

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How living cells employ counting mechanisms to regulate their numbers or density is a long-standing problem in developmental biology that ties directly with organism or tissue size. Diverse cells types have been shown to regulate their numbers via secretion of factors in the extracellular space. These factors act as a proxy for the number of cells and function to reduce cellular proliferation rates creating a negative feedback. It is desirable that the production rate of such factors be kept as low as possible to minimize energy costs and detection by predators. Here we formulate a stochastic model of cell proliferation with feedback control via a secreted extracellular factor. Our results show that while low levels of feedback minimizes random fluctuations in cell numbers around a given set point, high levels of feedback amplify Poisson fluctuations in secreted-factor copy numbers. This trade-off results in an optimal feedback strength, and sets a fundamental limit to noise suppression in cell numbers. Intriguingly, this fundamental limit depends additively on two variables: relative half-life of the secreted factor with respect to the cell proliferation rate, and the average number of factors secreted in a cell's lifespan. We further expand the model to consider external disturbances in key physiological parameters, such as, proliferation and factor synthesis rates. Intriguingly, while negative feedback effectively mitigates disturbances in the proliferation rate, it amplifies disturbances in the synthesis rate. In summary, these results provide unique insights into the functioning of feedback-based counting mechanisms, and apply to organisms ranging from unicellular prokaryotes and eukaryotes to human cells.

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“…Conditional derivative-matching works based upon conditioning higher order moments on the state of the gene. However, only conditioning cannot solve the problem of moment closure [24], [25] because of nonlinearity in biochemical reactions. Thus conditioning is combined with derivative-matching closure method.…”

Section: Introductionmentioning

confidence: 99%

Approximate statistical dynamics of a genetic feedback circuit

Soltani

Vargas

Kumar

et al. 2015

2015 American Control Conference (ACC)

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Auto-regulation, a process wherein a protein negatively regulates its own production, is a common motif in gene expression networks. Negative feedback in gene expression plays a critical role in buffering intracellular fluctuations in protein concentrations around optimal value. Due to the nonlinearities present in these feedbacks, moment dynamics are typically not closed, in the sense that the time derivative of the lower-order statistical moments of the protein copy number depends on high-order moments. Moment equations are closed by expressing higher-order moments as nonlinear functions of lower-order moments, a technique commonly referred to as moment closure. Here, we compare the performance of different moment closure techniques. Our results show that the commonly used closure method, which assumes a priori that the protein population counts are normally distributed, performs poorly. In contrast, conditional derivative-matching, a novel closure scheme proposed here provides a good approximation to the exact moments across different parameter regimes. In summary our study provides a new moment closure method for studying stochastic dynamics of genetic negative feedback circuits, and can be extended to probe noise in more complex gene networks.

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Modeling of stochastic biological processes with non-polynomial propensities using non-central conditional moment equation

Cited by 9 publications

References 23 publications

Revisiting moment-closure methods with heterogeneous multiscale population models

Revisiting moment-closure methods with heterogeneous multiscale population models

Optimal feedback mechanisms for regulating cell numbers

Approximate statistical dynamics of a genetic feedback circuit

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