Elisa Franco

Timing molecular motion and production with a synthetic transcriptional clock

The realization of artificial biochemical reaction networks with unique functionality is one of the main challenges for the development of synthetic biology. Due to the reduced number of components, biochemical circuits constructed in vitro promise to be more amenable to systematic design and quantitative assessment than circuits embedded within living organisms. To make good on that promise, effective methods for composing subsystems into larger systems are needed. Here we used an artificial biochemical oscillator based on in vitro transcription and RNA degradation reactions to drive a variety of “load” processes such as the operation of a DNA-based nanomechanical device (“DNA tweezers”) or the production of a functional RNA molecule (an aptamer for malachite green). We implemented several mechanisms for coupling the load processes to the oscillator circuit and compared them based on how much the load affected the frequency and amplitude of the core oscillator, and how much of the load was effectively driven. Based on heuristic insights and computational modeling, an “insulator circuit” was developed, which strongly reduced the detrimental influence of the load on the oscillator circuit. Understanding how to design effective insulation between biochemical subsystems will be critical for the synthesis of larger and more complex systems.

Cooperative Constrained Control of Distributed Agents With Nonlinear Dynamics and Delayed Information Exchange: A Stabilizing Receding-Horizon Approach

This paper addresses the problem of cooperative control of a team of distributed agents with decoupled nonlinear discrete-time dynamics, which operate in a common environment and exchange-delayed information between them. Each agent is assumed to evolve in discrete-time, based on locally computed control laws, which are computed by exchanging delayed state information with a subset of neighboring agents. The cooperative control problem is formulated in a receding-horizon framework, where the control laws depend on the local state variables (feedback action) and on delayed information gathered from cooperating neighboring agents (feedforward action). A rigorous stability analysis exploiting the input-to-state stability properties of the receding-horizon local control laws is carried out. The stability of the team of agents is then proved by utilizing small-gain theorem results.

Distributed Fault Diagnosis using Sensor Networks and Consensus-based Filters

This paper considers the problem of designing distributed fault diagnosis algorithms for dynamic systems using sensor networks. A network of distributed estimation agents is designed where a bank of local Kalman filters is embedded into each sensor. The diagnosis decision is performed by a distributed hypothesis testing method that relies on a belief consensus algorithm. Under certain assumptions, both the distributed estimation and the diagnosis algorithms are derived from their centralized counterparts thanks to dynamic average-consensus techniques. Simulation results are provided to demonstrate the effectiveness of the proposed architecture and algorithm

Dynamically Reshaping Signaling Networks to Program Cell Fate via Genetic Controllers

Introduction Engineering of cell fate through synthetic gene circuits requires methods to precisely implement control around native decision-making pathways and offers the potential to direct developmental programs and redirect aberrantly activated cell processes. We set out to develop molecular network diverters, a class of genetic control systems, to activate or attenuate signaling through a mitogen-activated protein kinase (MAPK) pathway, the yeast mating pathway, to conditionally route cells to one of three distinct fates. The molecular network diverter (controller) interfaces with a native signaling pathway to conditionally route cells to one of three fates in response to distinct environmental signals. Signal A (left) and signal B (right) trigger the positive and negative elements of the diverter via their cognate switches to activate or inhibit, respectively, signaling through the yeast mating pathway. Methods We used a combination of genetic elements—including pathway regulators, RNA-based transducers, and constitutive and pathway-responsive promoters—to build modular network diverters. We measured the impact of these genetic control systems on pathway activity by monitoring fluorescence from a transcriptional pathway reporter. Cell fate determination was measured through halo assays, in which mating-associated cell cycle arrest above a certain concentration of pheromone from wild-type cells results in a “halo” or cleared region around a disk saturated in pheromone. A phenomenological model of our system was built to elucidate design principles for dual diverters that integrate opposing functions while supporting independent routing to alternative fates. Results We identified titratable positive (Ste4) and negative (Msg5) regulators of pathway activity that result in divergent cell fate decisions when controlled from network diverters. A positive diverter, controlling Ste4 through a feedback architecture, routed cells to the mating fate, characterized by pathway activation in the absence of pheromone. A negative diverter, controlling Msg5 through a nonfeedback architecture, routed cells to the nonmating fate, characterized by pathway inhibition in the presence of pheromone. When integrated into a dual-diverter architecture, the opposing functions of these positive and negative diverters resulted in antagonism, which prevented independent routing to the alternative fates. However, a modified architecture that incorporated both constitutive and feedback regulation over the pathway regulators enabled conditional routing of cells to one of three fates (wild type, mating, or nonmating) in response to specified environmental signals. Discussion Our work identified design principles for networks that induce differentiation of cells in response to environmental signals and that enhance the robust performance of integrated mutually antagonistic genetic programs. For example, integrated negative regulators can buffer a system against noise amplification mediated through positive-feedback loops by providing a resistance to amplification. Negative feedback can play an important role by reducing population heterogeneity and mediating robust, long-term cell fate decisions. The dual-diverter configuration enables routing to alternative fates and minimizes impact on the opposing diverter by integrating differential regulatory strategies on functionally redundant genes. Molecular network diverters provide a foundation for robustly programming spatial and temporal control over cell fate. Toward Synthetic Biology The detection of an appropriate point to intervene in a cellular pathway and minimize off-target effects on other cellular processes present problems for the design of circuits that control cellular signaling pathways and thus direct cell function. Galloway et al. (p. 1358, published online 15 August; see the Perspective by Sarkar) report progress on these challenges in the yeast Saccharomyces cerevisiae. A molecular control system was developed to direct the yeast cells to one of three cell fates. To avoid disruption of other cellular controls, exogenous ribozyme-based controllers that interfaced with the endogenous control circuits were used, which avoided genetic alteration to the cells. After enhancing the control circuits with feedback loops to make their behavior more reliable, the circuits were used to modulate the abundance of particular components that acted as critical regulators of yeast cell-fate decisions. This allowed direction of cell fate in response to a chosen chemical stimulus. These strategies may be adaptable to allow similar direction of the physiological state of mammalian cells, for example, to allow therapeutic applications of synthetic biology. A synthetic control module inserted into yeast cells allows control of cell fate in response to an environmental signal. [Also see Perspective by Sarkar] Engineering of cell fate through synthetic gene circuits requires methods to precisely implement control around native decision-making pathways and offers the potential to direct cell processes. We demonstrate a class of genetic control systems, molecular network diverters, that interface with a native signaling pathway to route cells to divergent fates in response to environmental signals without modification of native genetic material. A method for identifying control points within natural networks is described that enables the construction of synthetic control systems that activate or attenuate native pathways to direct cell fate. We integrate opposing genetic programs by developing network architectures for reduced antagonism and demonstrate rational tuning of performance. Extension of these control strategies to mammalian systems should facilitate the engineering of complex cellular signaling systems.

Structurally robust biological networks

BackgroundThe molecular circuitry of living organisms performs remarkably robust regulatory tasks, despite the often intrinsic variability of its components. A large body of research has in fact highlighted that robustness is often a structural property of biological systems. However, there are few systematic methods to mathematically model and describe structural robustness. With a few exceptions, numerical studies are often the preferred approach to this type of investigation.ResultsIn this paper, we propose a framework to analyze robust stability of equilibria in biological networks. We employ Lyapunov and invariant sets theory, focusing on the structure of ordinary differential equation models. Without resorting to extensive numerical simulations, often necessary to explore the behavior of a model in its parameter space, we provide rigorous proofs of robust stability of known bio-molecular networks. Our results are in line with existing literature.ConclusionsThe impact of our results is twofold: on the one hand, we highlight that classical and simple control theory methods are extremely useful to characterize the behavior of biological networks analytically. On the other hand, we are able to demonstrate that some biological networks are robust thanks to their structure and some qualitative properties of the interactions, regardless of the specific values of their parameters.

Geometry of unsteady fluid transport during fluid–structure interactions

We describe the application of tools from dynamical systems to define and quantify the unsteady fluid transport that occurs during fluid–structure interactions and in unsteady recirculating flows. The properties of Lagrangian coherent structures (LCS) are used to enable analysis of flows with arbitrary time-dependence, thereby extending previous analytical results for steady and time-periodic flows. The LCS kinematics are used to formulate a unique, physically motivated definition for fluid exchange surfaces and transport lobes in the flow. The methods are applied to numerical simulations of two-dimensional flow past a circular cylinder at a Reynolds number of 200; and to measurements of a freely swimming organism, the Aurelia aurita jellyfish. The former flow provides a canonical system in which to compare the present geometrical analysis with classical, Eulerian (e.g. vortex shedding) perspectives of fluid–structure interactions. The latter flow is used to deduce the physical coupling that exists between mass and momentum transport during self-propulsion. In both cases, the present methods reveal a well-defined, unsteady recirculation zone that is not apparent in the corresponding velocity or vorticity fields. Transport rates between the ambient flow and the recirculation zone are computed for both flows. Comparison of fluid transport geometry for the cylinder crossflow and the self-propelled swimmer within the context of existing theory for two-dimensional lobe dynamics enables qualitative localization of flow three-dimensionality based on the planar measurements. Benefits and limitations of the implemented methods are discussed, and some potential applications for flow control, unsteady propulsion, and biological fluid dynamics are proposed.

Cooperative Control of Distributed Agents with Nonlinear Dynamics and Delayed Information Exchange: a Stabilizing Receding-Horizon Approach

This paper addresses the problem of cooperative control of a team of distributed agents with nonlinear discrete-time dynamics. Each agent is assumed to evolve in discrete-time based on locally computed control laws and by exchanging delayed state information with a subset of neighboring cooperating agents. The cooperative control problem is formulated in a receding-horizon (RH) framework, where the control laws depend on the local state variables (feedback action) and on delayed information gathered from cooperating neighboring agents (feedforward action). A rigorous stability analysis is carried out exploiting the stabilizing properties of the RH local control laws on one hand and input-to-state stability (ISS) arguments on the other hand. In particular, it is shown that, under suitable assumptions, each controlled agent is ISS under the action of the local control law. The stability of the team of agents is then proved by utilizing small-gain theorem results.

Cooperative control of discrete-time agents with delayed information exchange: A receding-horizon approach

Cooperative control by a team of distributed agents is considered in this paper. Each agent is assumed to evolve in discrete-time and exchange delayed state information with a subset of neighboring or cooperating agents. The control design formulation is based on the definition of a finite-horizon cost function that includes both the regulation and cooperation objectives. The cooperative control problem is formulated in a receding-horizon framework, where the control law can be explicitly broken up in two components: one due to feedback from the local state variables and the other based on delayed information gathered from cooperating neighboring agents. The global stability and performance analysis of the overall system is shown and simulation results are used to illustrate the effectiveness of the proposed control scheme.

A Structural Classification of Candidate Oscillatory and Multistationary Biochemical 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 systems with a sign-definite Jacobian, for instance, cycle-based criteria related to the famous Thomas’ conjectures have been largely used to characterize oscillatory and multistationary dynamic outcomes. We build on the rich literature focused on the identification of potential oscillatory and multistationary behaviors using parameter-free criteria. We propose a classification for sign-definite non-autocatalytic biochemical networks, which summarizes several existing results in the literature. We call weak (strong) candidate oscillators systems which can possibly (exclusively) transition to instability due to the presence of a complex pair of eigenvalues, while we call weak (strong) candidate multistationary systems those which can possibly (exclusively) transition to instability due to the presence of a real eigenvalue. For each category, we provide a characterization based on the exclusive or simultaneous presence of positive and negative cycles in the associated sign graph. Most realistic examples of biochemical networks fall in the gray area of systems in which both positive and negative cycles are present: Therefore, both oscillatory and bistable behaviors are in principle possible. However, many canonical example circuits exhibiting oscillations or bistability fall in the categories of strong candidate oscillators/multistationary systems, in agreement with our results.

pH-controlled assembly of DNA tiles

We demonstrate a strategy to trigger and finely control the assembly of supramolecular DNA nanostructures with pH. Control is achieved via a rationally designed strand displacement circuit that responds to pH and activates a downstream DNA tile self-assembly process. We observe that the DNA structures form under neutral/basic conditions, while the self-assembly process is suppressed under acidic conditions. The strategy presented here demonstrates a modular approach toward building systems capable of processing biochemical inputs and finely controlling the assembly of DNA-based nanostructures under isothermal conditions. In particular, the presented architecture is relevant for the development of complex DNA devices able to sense and respond to molecular markers associated with abnormal metabolism.