How noise statistics impact models of enzyme cycles

Warmflash, Aryeh; Adamson, David N.; Dinner, Aaron R.

doi:10.1063/1.2929841

Cited by 11 publications

(8 citation statements)

References 32 publications

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“…One application of our mathematical results was to models of single or communicating "toggle switches" in bacteria, where we showed that, for suitable parameters, there are a very large number of metastable attractors. Indeed, stochastic effects have been shown before to lead to multi-stability in a population of enzymatic reactions [73].…”

Section: Discussionmentioning

confidence: 99%

Multi-modality in gene regulatory networks with slow promoter kinetics

2019

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Phenotypical variability in the absence of genetic variation often reflects complex energetic landscapes associated with underlying gene regulatory networks (GRNs). In this view, different phenotypes are associated with alternative states of complex nonlinear systems: stable attractors in deterministic models or modes of stationary distributions in stochastic descriptions. We provide theoretical and practical characterizations of these landscapes, specifically focusing on stochastic Slow Promoter Kinetics (SPK), a time scale relevant when transcription factor binding and unbinding are affected by epigenetic processes like DNA methylation and chromatin remodeling. In this case, largely unexplored except for numerical simulations, adiabatic approximations of promoter kinetics are not appropriate. In contrast to the existing literature, we provide rigorous analytic characterizations of multiple modes. A general formal approach gives insight into the influence of parameters and the prediction of how changes in GRN wiring, for example through mutations or artificial interventions, impact the possible number, location, and likelihood of alternative states. We adapt tools from the mathematical field of singular perturbation theory to represent stationary distributions of Chemical Master Equations for GRNs as mixtures of Poisson distributions and obtain explicit formulas for the locations and probabilities of metastable states as a function of the parameters describing the system. As illustrations, the theory is used to tease out the role of cooperative binding in stochastic models in comparison to deterministic models, and applications are given to various model systems, such as toggle switches in isolation or in communicating populations, a synthetic oscillator, and a trans-differentiation network.

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Section: Discussionmentioning

confidence: 99%

Multi-modality in gene regulatory networks with slow promoter kinetics

2019

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“…Theoretical studies predict that multiplicative noise can introduce bifurcations in systems that are monostable for all parameter ranges (17,(19)(20)(21)(22) (26)(27)(28)(29)(30)(31). In this paper, we refer only to one of the hypothesized sources of transcriptional pulsing; namely, the discrete random binding/ unbinding of TFs.…”

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confidence: 99%

Bimodal gene expression in noncooperative regulatory systems

Ochab-Marcinek

Tabaka

2010

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

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Bimodality of gene expression, as a mechanism contributing to phenotypic diversity, enhances the survival of cells in a fluctuating environment. To date, the bimodal response of a gene regulatory system has been attributed to the cooperativity of transcription factor binding or to feedback loops. It has remained unclear whether noncooperative binding of transcription factors can give rise to bimodality in an open-loop system. We study a theoretical model of gene expression in a two-step cascade (a deterministically monostable system) in which the regulatory gene produces transcription factors that have a nonlinear effect on the activity of the target gene. We show that a unimodal distribution of transcription factors over the cell population can generate a bimodal steadystate output without cooperative transcription factor binding. We introduce a simple method of geometric construction that allows one to predict the onset of bimodality. The construction only involves the parameters of bursting of the regulatory gene and the dose-response curve of the target gene. Using this method, we show that the gene expression may switch between unimodal and bimodal as the concentration of inducers or corepressors is varied. These findings may explain the experimentally observed bimodal response of cascades consisting of a fluorescent protein reporter controlled by the tetracycline repressor. The geometric construction provides a useful tool for designing experiments and for interpretation of their results. Our findings may have important implications for understanding the strategies adopted by cell populations to survive in changing environments.gene expression noise | gene regulation | noise filter induced bimodality | transfer function T his paper proves theoretically that bimodality of gene expression can be generated in a minimal gene regulatory system by a unimodal distribution of transcription factor (TF) combined with a nonlinear transcription rate, without cooperativity, large number of steps in gene cascade, feedback loops, or bimodal input signal. We present a method of prediction of the bimodality without using the master equation, only based on a simple geometric construction.Bimodal gene expression (the distribution of gene products that has two maxima) is a cause of phenotypic diversity in genetically identical cell populations, and it is critical for population survival in a fluctuating environment (1-4). Several mechanisms underlying the bimodality have been identified to date:1. Deterministic bistability (two deterministic stable steady states under the same external conditions) is inherent to the system even when intrinsic and extrinsic noises can be neglected. To exhibit deterministic bistability, the system must consist of a single positive feedback loop with cooperative ligand binding (5, 6) [bacteriophage λ (7), reverse tetracycline transactivator switch in Saccharomyces cerevisiae (8), lac operon in Escherichia coli (9), MAPK cascade in Xenopus oocytes (10)], multiple feedback loops with cooperativity...

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“…The enzymatic futile cycle is a simple and robust model that can, in certain parameter regimes, exhibit qualitatively different behavior due to stochastic noise [59,60]. This signaling motif can be seen in biological systems including GTPase cycles, MAPK cascades, and glucose mobilization [59,61,62].…”

Section: Modelmentioning

confidence: 99%

Efficient stochastic simulation of chemical kinetics networks using a weighted ensemble of trajectories

Donovan

Sedgewick

Faeder

et al. 2013

The Journal of Chemical Physics

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We apply the "weighted ensemble" (WE) simulation strategy, previously employed in the context of molecular dynamics simulations, to a series of systems-biology models that range in complexity from a one-dimensional system to a system with 354 species and 3680 reactions. WE is relatively easy to implement, does not require extensive hand-tuning of parameters, does not depend on the details of the simulation algorithm, and can facilitate the simulation of extremely rare events. For the coupled stochastic reaction systems we study, WE is able to produce accurate and efficient approximations of the joint probability distribution for all chemical species for all time t. WE is also able to efficiently extract mean first passage times for the systems, via the construction of a steady-state condition with feedback. In all cases studied here, WE results agree with independent "brute-force" calculations, but significantly enhance the precision with which rare or slow processes can be characterized. Speedups over "brute-force" in sampling rare events via the Gillespie direct Stochastic Simulation Algorithm range from ~10(12) to ~10(18) for characterizing rare states in a distribution, and ~10(2) to ~10(4) for finding mean first passage times.

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How noise statistics impact models of enzyme cycles

Cited by 11 publications

References 32 publications

Multi-modality in gene regulatory networks with slow promoter kinetics

Multi-modality in gene regulatory networks with slow promoter kinetics

Bimodal gene expression in noncooperative regulatory systems

Efficient stochastic simulation of chemical kinetics networks using a weighted ensemble of trajectories

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