Small-Number Effects: A Third Stable State in a Genetic Bistable Toggle Switch

Ma, Rui; Wang, Jichao; Hou, Zhonghuai

doi:10.1103/physrevlett.109.248107

Cited by 31 publications

(43 citation statements)

References 23 publications

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“…This small molecule number leads to non-negligible fluctuations and a discrete nature of molecular concentrations, which may in turn alter the frequencies of each chemical reaction event; indeed, several salient phenomena induced by the smallness in molecule numbers have been studied, both theoretically [3][4][5][6][7][8][9][10][11][12][13][14][15][16] and experimentally. [17][18][19] Moreover, how such microscopic molecular discreteness can contribute to cellular functions at a larger scale has gathered much interest, and the effect induced by the discreteness is expected to provide a novel concept to understand cellular behaviors and function. 17,18,[20][21][22] In a macroscopic system, i.e., when the volume size of a system and the number of contained molecules are large, the overall behaviors of the system can be described by the deterministic rate equation of reaction dynamics for the average concentration of chemicals or a Langevin equation that takes into account small Gaussian fluctuation around it.…”

Section: Introductionmentioning

confidence: 99%

“…[17][18][19] Moreover, how such microscopic molecular discreteness can contribute to cellular functions at a larger scale has gathered much interest, and the effect induced by the discreteness is expected to provide a novel concept to understand cellular behaviors and function. 17,18,[20][21][22] In a macroscopic system, i.e., when the volume size of a system and the number of contained molecules are large, the overall behaviors of the system can be described by the deterministic rate equation of reaction dynamics for the average concentration of chemicals or a Langevin equation that takes into account small Gaussian fluctuation around it.…”

Section: Introductionmentioning

confidence: 99%

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Motif analysis for small-number effects in chemical reaction dynamics

Saito

Sughiyama

Kaneko

2016

The Journal of Chemical Physics

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The number of molecules involved in a cell or subcellular structure is sometimes rather small. In this situation, ordinary macroscopic-level fluctuations can be overwhelmed by non-negligible large fluctuations, which results in drastic changes in chemical-reaction dynamics and statistics compared to those observed under a macroscopic system (i.e., with a large number of molecules). In order to understand how salient changes emerge from fluctuations in molecular number, we here quantitatively define small-number effect by focusing on a 'mesoscopic' level, in which the concentration distribution is distinguishable both from micro-and macroscopic ones, and propose a criterion for determining whether or not such an effect can emerge in a given chemical reaction network. Using the proposed criterion, we systematically derive a list of motifs of chemical reaction networks that can show small-number effects, which includes motifs showing emergence of the power law and the bimodal distribution observable in a mesoscopic regime with respect to molecule number. The list of motifs provided herein is helpful in the search for candidates of biochemical reactions with a small-number effect for possible biological functions, as well as for designing a reaction system whose behavior can change drastically depending on molecule number, rather than concentration.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Motif analysis for small-number effects in chemical reaction dynamics

Saito

Sughiyama

Kaneko

2016

The Journal of Chemical Physics

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“…The dramatic failure of this prediction (the black areas are highly asymmetrical and extend around the bistable zone (Fig. 3c)) signals that either convergence to the local steady state(s) is drastically slowed down (for example, by a catastrophic slowdown 37 ) or even arrested (for example, by small number effects 38 ), or that an alternative stable state emerges from an unsuspected mechanism 39 . In any case, these trapped states could provide alternative options for memories on practical time scales.…”

Section: Resultsmentioning

confidence: 96%

High-resolution mapping of bifurcations in nonlinear biochemical circuits

et al. 2016

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Analog molecular circuits can exploit the nonlinear nature of biochemical reaction networks to compute low-precision outputs with fewer resources than digital circuits. This analog computation is similar to that employed by gene-regulation networks. Although digital systems have a tractable link between structure and function, the nonlinear and continuous nature of analog circuits yields an intricate functional landscape, which makes their design counter-intuitive, their characterization laborious and their analysis delicate. Here, using droplet-based microfluidics, we map with high resolution and dimensionality the bifurcation diagrams of two synthetic, out-of-equilibrium and nonlinear programs: a bistable DNA switch and a predator-prey DNA oscillator. The diagrams delineate where function is optimal, dynamics bifurcates and models fail. Inverse problem solving on these large-scale data sets indicates interference from enzymatic coupling. Additionally, data mining exposes the presence of rare, stochastically bursting oscillators near deterministic bifurcations.

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“…However, Lipshtat et al found that stochastic effects can give rise to bistability even without cooperativity [32]. In another study, Ma et al found that stochastic fluctuations can stabilize the unstable steady state in the deterministic system, giving rise to tristability [33]. In addition, Biancalani et al identified multiplicative noise as the source of bistability in the stochastic case [34].…”

Section: Introductionmentioning

confidence: 99%

A computational method for the investigation of multistable systems and its application to genetic switches

et al. 2016

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BackgroundGenetic switches exhibit multistability, form the basis of epigenetic memory, and are found in natural decision making systems, such as cell fate determination in developmental pathways. Synthetic genetic switches can be used for recording the presence of different environmental signals, for changing phenotype using synthetic inputs and as building blocks for higher-level sequential logic circuits. Understanding how multistable switches can be constructed and how they function within larger biological systems is therefore key to synthetic biology.ResultsHere we present a new computational tool, called StabilityFinder, that takes advantage of sequential Monte Carlo methods to identify regions of parameter space capable of producing multistable behaviour, while handling uncertainty in biochemical rate constants and initial conditions. The algorithm works by clustering trajectories in phase space, and iteratively minimizing a distance metric. Here we examine a collection of models of genetic switches, ranging from the deterministic Gardner toggle switch to stochastic models containing different positive feedback connections. We uncover the design principles behind making bistable, tristable and quadristable switches, and find that rate of gene expression is a key parameter. We demonstrate the ability of the framework to examine more complex systems and examine the design principles of a three gene switch. Our framework allows us to relax the assumptions that are often used in genetic switch models and we show that more complex abstractions are still capable of multistable behaviour.ConclusionsOur results suggest many ways in which genetic switches can be enhanced and offer designs for the construction of novel switches. Our analysis also highlights subtle changes in correlation of experimentally tunable parameters that can lead to bifurcations in deterministic and stochastic systems. Overall we demonstrate that StabilityFinder will be a valuable tool in the future design and construction of novel gene networks.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-016-0375-z) contains supplementary material, which is available to authorized users.

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Small-Number Effects: A Third Stable State in a Genetic Bistable Toggle Switch

Cited by 31 publications

References 23 publications

Motif analysis for small-number effects in chemical reaction dynamics

Motif analysis for small-number effects in chemical reaction dynamics

High-resolution mapping of bifurcations in nonlinear biochemical circuits

A computational method for the investigation of multistable systems and its application to genetic switches

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