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

Siegal-Gaskins, Dan and Franco, Elisa and Zhou, Tiffany and Murray, Richard M. (2015) An analytical approach to bistable biological circuit discrimination using real algebraic geometry. Journal of the Royal Society Interface, 12 (108). Art. No. 20150288. ISSN 1742-5689.

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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 geometry—to 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.

Item Type:Article
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URLURL TypeDescription Paper
Murray, Richard M.0000-0002-5785-7481
Additional Information:© 2015 The Author(s) Published by the Royal Society. Received March 31, 2015. Accepted June 1, 2015. Authors' contributions: The project was conceived by D.S.-G., E.F. and R.M.M. D.S.-G. and E.F. performed the mathematical analyses, with computational support provided by T.Z. The paper was written by D.S.-G. and E.F. and edited by all of the coauthors. Competing interests. We declare we have no competing interests. Funding: This research is funded in part by the National Science Foundation through grant CMMI 1266402, and the Gordon and Betty Moore Foundation through grant no. GBMF2809 to the Caltech Programmable Molecular Technology Initiative. Acknowledgements: A large number of people contributed to this work with insights and comments. The authors particularly thank Andras Gyorgy, Yutaka Hori, Scott C. Livingston, Anne Shiu, Eduardo Sontag, Elisenda Feliu, Zvi H. Rosen, Jaap Top and Brian Ingalls.
Funding AgencyGrant Number
NSFCMMI 1266402
Gordon and Betty Moore FoundationGBMF2809
Record Number:CaltechAUTHORS:20150903-084342383
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Official Citation:Siegal-Gaskins D, Franco E, Zhou T, Murray RM. 2015 An analytical approach to bistable biological circuit discrimination using real algebraic geometry. J. R. Soc. Interface 12: 20150288.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:60043
Deposited By: Tony Diaz
Deposited On:08 Sep 2015 03:23
Last Modified:08 Sep 2015 03:23

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