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

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 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.

SUBMITTER: Siegal-Gaskins D

PROVIDER: S-EPMC4528596 | biostudies-literature | 2015 Jul

REPOSITORIES: biostudies-literature

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

Siegal-Gaskins Dan D Franco Elisa E Zhou Tiffany T Murray Richard M RM

Journal of the Royal Society, Interface 20150701 108

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 explor ...[more]

PMID: 26109633

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Project description:BACKGROUND: In the continuum between a stroke and a circle including all possible ellipses, some eccentricities seem more "biologically preferred" than others by the motor system, probably because they imply less demanding coordination patterns. Based on the idea that biological motion perception relies on knowledge of the laws that govern the motor system, we investigated whether motorically preferential and non-preferential eccentricities are visually discriminated differently. In contrast with previous studies that were interested in the effect of kinematic/time features of movements on their visual perception, we focused on geometric/spatial features, and therefore used a static visual display. METHODOLOGY/PRINCIPAL FINDINGS: In a dual-task paradigm, participants visually discriminated 13 static ellipses of various eccentricities while performing a finger-thumb opposition sequence with either the dominant or the non-dominant hand. Our assumption was that because the movements used to trace ellipses are strongly lateralized, a motor task performed with the dominant hand should affect the simultaneous visual discrimination more strongly. We found that visual discrimination was not affected when the motor task was performed by the non-dominant hand. Conversely, it was impaired when the motor task was performed with the dominant hand, but only for the ellipses that we defined as preferred by the motor system, based on an assessment of individual preferences during an independent graphomotor task. CONCLUSIONS/SIGNIFICANCE: Visual discrimination of ellipses depends on the state of the motor neural networks controlling the dominant hand, but only when their eccentricity is "biologically preferred". Importantly, this effect emerges on the basis of a static display, suggesting that what we call "biological geometry", i.e., geometric features resulting from preferential movements is relevant information for the visual processing of bidimensional shapes.

Dataset Information

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

Publications

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

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