PT  - JOURNAL ARTICLE
AU  - Dan Siegal-Gaskins
AU  - Elisa Franco
AU  - Tiffany Zhou
AU  - Richard M. Murray
TI  - An analytical approach to bistable biological circuit discrimination using real algebraic geometry
AID  - 10.1101/008581
DP  - 2014 Jan 01
TA  - bioRxiv
PG  - 008581
4099  - http://biorxiv.org/content/early/2014/09/04/008581.short
4100  - http://biorxiv.org/content/early/2014/09/04/008581.full
AB  - Summary Small 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 the challenge of 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 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 their operational range. The demonstrated predictive power and ease of use of Sturm’s theorem suggests that algebraic geometric techniques may be underutilized in biomolecular circuit analysis.