Biology subjects

Elisa Franco

Publications and source records attributed to Elisa Franco.

4 recordsLinked to original sources

bioRxiv2016

An algebraic approach to parameter optimization in bimolecular bistable systems

In a synthetic biological network it may often be desirable to maximize or minimize parameters such as reaction rates, fluxes and total concentrations of reagents, while preserving a given dynamic behavior. We consider the problem of parameter optimization in biomolecular bistable circuits. We show that, under some assumptions often satisfied by bistable biological networks, it is possible to derive algebraic conditions on the parameters that determine when bistability occurs. These (global) algebraic conditions can be included as nonlinear constraints in a parameter optimization problem. We derive bistability conditions using Sturm's theorem for Gardner and Collins toggle switch. Then we optimize its nominal parameters to improve switching speed and robustness to a subset of uncertain parameters.

Systems Biology↗

bioRxiv2014

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

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 Sturms 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 Sturms theorem demonstrated in this work suggests that algebraic geometric techniques may be underutilized in biomolecular circuit analysis.

Systems Biology↗

bioRxiv2013

A structural classification of candidate oscillators and multistationary systems

Molecular systems are uncertain: the variability of reaction parameters and the presence of unknown interactions can weaken the predictive capacity of solid mathematical models. However, strong conclusions on the admissible dynamic behaviors of a model can often be achieved without detailed knowledge of its specific parameters. In particular, starting with Thomas' conjectures, loop-based criteria have been largely used to characterize oscillatory and multistationary dynamic outcomes in systems with a sign definite Jacobian.\n\nWe build on the rich literature focused on the identification of potential oscillatory and multistationary behaviors based on parameter-free criteria. We propose a classification for sign-definite non autocatalytic biological networks which summarize several existing results in the literature, adding new results when necessary. We define candidate oscillators and multistationary systems based on their admissible transitions to instability. We introduce four categories: strong/weak candidate oscillatory/multistationary systems, which correspond to networks in which all/some of the existing feedback loops are negative/positive. We provide necessary and sufficient conditions characterizing strong and weak candidate oscillators and multistationary systems based on the exclusive or simultaneous presence of positive and negative loops in their linearized dynamics. We also consider the case in which the overall system is the connection of several stable aggregate monotone components, providing conditions in terms of positive/negative loops in a suitable network with aggregate monotone systems as nodes.\n\nMost realistic examples of biological networks fall in the gray area of systems in which both positive and negative cycles are present: therefore, both oscillatory and bistable behavior are in principle possible. Native systems with a large number of components are often interconnections of monotone modules, where negative/positive loops among modules characterize oscillatory and bistable behaviors, in agreement with our results. Finally, we note that many canonical example circuits exhibiting oscillations or bistability fall in the categories of strong candidate oscillators/multistationary systems.

Systems Biology↗

bioRxiv2013

Negative autoregulation matches production and demand in synthetic transcriptional networks

We propose a negative feedback architecture that regulates activity of artificial genes, or \"genelets\", to meet their output downstream demand, achieving robustness with respect to uncertain open-loop output production rates. In particular, we consider the case where the outputs of two genelets interact to form a single assembled product. We show with analysis and experiments that negative autoregulation matches the production and demand of the outputs: the magnitude of the regulatory signal is proportional to the \"error\" between the circuit output concentration and its actual demand. This two-device system is experimentally implemented using in vitro transcriptional networks, where reactions are systematically designed by optimizing nucleic acid sequences with publicly available software packages. We build a predictive ordinary differential equation (ODE) model that captures the dynamics of the system, and can be used to numerically assess the scalability of this architecture to larger sets of interconnected genes. Finally, with numerical simulations we contrast our negative autoregulation scheme with a cross-activation architecture, which is less scalable and results in slower response times.

Synthetic Biology↗