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.

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, parametric conditions. The predictive power and ease of use of Sturm's theorem demonstrated in this work suggests that algebraic geometric techniques may be underutilized in biomolecular circuit analysis.

Many natural metabolites have antibacterial, antiviral, or anticancer effects and can be developed into new drugs. However, working with the microorganisms that produce these products can be challenging since they are not as well characterized as a model organism like Escherichia coli. In this paper, we investigate the potential for a cell-free transcription-translation (TX-TL) system to provide a rapid prototyping platform for characterizing new genetic pathways. We use the valinomycin biosynthesis pathway as a test case, and we show successful heterologous expression of the heterodimeric valinomycin synthetase (VlmSyn, Vlm1: 374 kDa and Vlm2: 284 kDa) from Streptomyces tsusimaensis within the TX-TL system. Using LC-MS analysis, we find that valinomycin is produced at low but detectable levels, even when only one out of the three basic precursors is fed into the system. Our work represents another step towards applying cell-free biosynthesis to the discovery and characterization of new natural products. IntroductionNatural products have been a key source for new drugs, including antibacterial, antiviral, and anticancer compounds, for over 30 years [1]. Recent developments in large-scale genetics and metabolomics have revealed that the chemical space of secondary metabolites still remains largely unexplored [2]. However, the characterization of new biosynthetic pathways and the small molecules they produce has been difficult, partly due to the challenges of working with the natural product producing organisms in the laboratory. Synthetic biology can solve this problem through robust heterologous expression of the biosynthetic pathways within more well-understood host organisms, such as Escherichia coli or Saccharomyces cerevisiae.Cell-free protein expression systems are quickly emerging as a useful tool for synthetic biology research. They take advantage of native transcription-translation machinery and allow for the simultaneous in vitro expression of multiple genes in the form of either plasmid or linear DNA [3,4]. Cell-free systems offer many benefits over cell-based expression, including the elimination of the need for an appropriate host strain, the ability to easily control specific reaction conditions, the absence of cell processes that could extraneously influence the behavior of the targeted gene network, and a greater tolerance for proteins and metabolites toxic to living cells [3]. Reactions in cell-free systems can be performed in a day, as opposed to one week with in vivo methods, allowing for more rapid design-build-test cycles [5]. Researchers have recently shown cell-free systems to have potential in the areas of rapid pathway prototyping [3][4][5], genetic network design [3,6], and high-yield protein production [7].