Aug 30, 2014

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

BioRxiv : the Preprint Server for Biology
Dan Siegal-GaskinsRichard M Murray

Abstract

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 19th-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, param...Continue Reading

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Mentioned in this Paper

Size
Transcription Repressor/Corepressor
Nuclear Magnetic Resonance, Biomolecular
Anatomical Space Structure
Simulation
Gene Circuits
Monomer

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