The capacity for multistability in small gene regulatory networks

Siegal-Gaskins, Dan; Grotewold, Erich; Smith, Gregory D.

doi:10.1186/1752-0509-3-96

Cited by 36 publications

(38 citation statements)

References 61 publications

(66 reference statements)

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“…Although relatively little known within the biological sciences, Sturm's theorem has found applicability in a number of other areas where polynomials play an important role, including computational mathematics [25], dynamical systems [26,27], robotics [28] and finance [29]. Additional biological applications are possible, for example, as a tool to predict a large number of new bistable topologies or rule out those that do not have the capacity for bistability (such as chemical reaction network theory, previously [13,24]). …”

Section: Discussionmentioning

confidence: 99%

“…The bistable regions (in a -g space) for these single gene circuits are shown in figure 2a. (The one-dimensional regions of bistability shown in bifurcation diagrams in [23,24] are plotted for comparison.) It can be seen that the l repressor circuit is bistable over a larger range and with lower values of the degradation rate constant.…”

Section: Bistable Single-gene Circuitsmentioning

confidence: 99%

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An analytical approach to bistable biological circuit discrimination using real algebraic geometry

Siegal-Gaskins

Franco

Zhou

et al. 2015

J. R. Soc. Interface.

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Biomolecular circuits with two distinct and stable steady states have been identified as essential components in a wide range of biological networks, with a variety of mechanisms and topologies giving rise to their important bistable property. Understanding the differences between circuit implementations is an important question, particularly for the synthetic biologist faced with determining which bistable circuit design out of many is best for their specific application. In this work we explore the applicability of Sturm's theorem-a tool from nineteenth-century real algebraic geometryto comparing 'functionally equivalent' bistable circuits without the need for numerical simulation. We first consider two genetic toggle variants and two different positive feedback circuits, and show how specific topological properties present in each type of circuit can serve to increase the size of the regions of parameter space in which they function as switches. We then demonstrate that a single competitive monomeric activator added to a purely monomeric (and otherwise monostable) mutual repressor circuit is sufficient for bistability. Finally, we compare our approach with the Routh-Hurwitz method and derive consistent, yet more powerful, parametric conditions. The predictive power and ease of use of Sturm's theorem demonstrated in this work suggest that algebraic geometric techniques may be underused in biomolecular circuit analysis.

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Section: Discussionmentioning

confidence: 99%

Section: Bistable Single-gene Circuitsmentioning

confidence: 99%

An analytical approach to bistable biological circuit discrimination using real algebraic geometry

Siegal-Gaskins

Franco

Zhou

et al. 2015

J. R. Soc. Interface.

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“…We also derive sufficient conditions on the constant term of the characteristic polynomial to destabilize the equilibria. Our results are relevant because networks using exclusively monomeric repressors do not generally yield bistable behaviors [15], [16]. We conclude with numerical simulations which identify the region in parameter space where the system is bistable.…”

Section: Introductionmentioning

confidence: 73%

A bistable biomolecular network based on monomeric inhibition reactions

Mardanlou

Samaniego

Franco

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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We model an experimentally plausible implementation of a synthetic RNA-based biochemical toggle switch proposed in previous work by the authors. We show that the system structure is suited to exhibit multistationarity for arbitrary choice of the parameters. The network is based on in vitro transcription and nucleic acid strand displacement reactions. It is composed of two distinct RNA polymerases producing mutually inhibiting RNA aptamers. The aptamer inhibitors create an overall positive loop, where regulation is achieved by modulating the activity of the polymerases rather than the promoter activity. Inhibition occurs via stoichiometric binding of RNA monomers to enzymes and is not a cooperative phenomenon; the only nonlinearities in the differential equations are given by second order reaction rates. Enzyme activity is recovered in the presence of DNA strands that displace the aptamers from their target, and mediate their degradation; recovery is also a bimolecular binding process. Numerical analysis shows that the system admits bistability in a wide range of parameters.

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“…In these studies, it is found that a switch between the two stable states can be achieved by building a layer DNFL model or a cascade DNFL model [16][17][18][19][20][21][22] or by applying stimulation to the DNFL [23][24][25][26]8,27]. In some cases, an unresponsive switch could be necessary, and an unusually sensitive method could also be necessary to describe the ultrasensitization of the cellular signaling in other cases.…”

Section: Introductionmentioning

confidence: 99%