Ania-Ariadna Baetica

Natural biological systems use feedback regulation to effectively respond and adapt to their changing environment. Even though in engineered systems we understand how accurate feedback can be depending on the electronic or mechanical parts that it is implemented with, we largely lack a similar theoretical framework to study feedback regulation in biological systems. Specifically, it is not fully understood or quantified how accurate or robust the implementation of biological feedback actually is. In this paper, we study the sensitivity of biological feedback to variations in biochemical parameters using five example circuits: positive autoregulation, negative autoregulation, double-positive feedback, positive-negative feedback, and double-negative feedback (the toggle switch). We find that some of these examples of biological feedback are subjected to fundamental performance trade-offs, and we propose multi-objective optimization as a framework to study their properties. The impact of this work is to improve robust circuit design for synthetic biology and to improve our understanding of feedback for systems biology.

Natural biological systems use a complex network of feedback regulation to effectively respond to their changing environment. Even though in engineered systems we understand how accurate feedback can be depending on the electronic or mechanical parts that it is implemented with, we largely lack a similar theoretical framework to study biological feedback. Specifically, it is not fully understood or quantified how accurate or robust the implementation of biological feedback actually is. In this paper, we study the sensitivity of biological feedback to variations in biochemical parameters using five example circuits: positive autoregulation, negative autoregulation, double-positive feedback, positive-negative feedback and double-negative feedback (the toggle switch). We find that of these examples of biological feedback are subjected to fundamental trade-offs, and we propose multi-objective optimisation as a framework to study them. The impact of this work is to improve robust circuit design for synthetic biology and to improve our understanding of systems biology.

Integral feedback control is commonly used in mechanical and electrical systems to achieve zero steady-state error following an external disturbance. Equivalently, in biological systems, a property known as robust perfect adaptation guarantees robustness to environmental perturbations and return to the pre-disturbance state. Previously, Briat et al proposed a biomolecular design for integral feedback control (robust perfect adaptation) called the antithetic feedback motif. The antithetic feedback controller uses the sequestration binding reaction of two biochemical species to record the integral of the error between the current and the desired output of the network it controls. The antithetic feedback motif has been successfully built using synthetic components in vivo in Escherichia coli and Saccharomyces cerevisiae cells. However, these previous synthetic implementations of antithetic feedback have not produced perfect integral feedback control due to the degradation and dilution of the two controller species. Furthermore, previous theoretical results have cautioned that integral control can only be achieved under stability conditions that not all antithetic feedback motifs necessarily fulfill. In this paper, we study how to design antithetic feedback motifs that simultaneously achieve good stability and small steady-state error properties, even as the controller species are degraded and diluted. We provide simple tuning guidelines to achieve flexible and practical synthetic biological implementations of antithetic feedback control. We use several tools and metrics from control theory to design antithetic feedback networks, paving the path for the systematic design of synthetic biological controllers.

The finite state projection (FSP) approach to solving the chemical master equation has enabled successful inference of discrete stochastic models to predict single-cell gene regulation dynamics. Unfortunately, the FSP approach is highly computationally intensive for all but the simplest models, an issue that is highly problematic when parameter inference and uncertainty quantification takes enormous numbers of parameter evaluations. To address this issue, we propose two new computational methods for the Bayesian inference of stochastic gene expression parameters given single-cell experiments. We formulate and verify an Adaptive Delayed Acceptance Metropolis-Hastings (ADAMH) algorithm to utilize with reduced Krylov-basis projections of the FSP. We then introduce an extension of the ADAMH into a Hybrid scheme that consists of an initial phase to construct a reduced model and a faster second phase to sample from the approximate posterior distribution determined by the constructed model. We test and compare both algorithms to an adaptive Metropolis algorithm with full FSP-based likelihood evaluations on three example models and simulated data to show that the new ADAMH variants achieve substantial speedup in comparison to the full FSP approach. By reducing the computational costs of parameter estimation, we expect the ADAMH approach to enable efficient data-driven estimation for more complex gene regulation models.

The finite state projection (FSP) approach to solving the chemical master equation has enabled successful inference of discrete stochastic models to predict single-cell gene regulation dynamics. Unfortunately, the FSP approach is highly computationally intensive for all but the simplest models, an issue that is highly problematic when parameter inference and uncertainty quantification takes enormous numbers of parameter evaluations. To address this issue, we propose two new computational methods for the Bayesian inference of stochastic gene expression parameters given single-cell experiments. We formulate and verify an Adaptive Delayed Acceptance Metropolis-Hastings (ADAMH) algorithm to utilize with reduced Krylov-basis projections of the FSP. We then introduce an extension of the ADAMH into a Hybrid scheme that consists of an initial phase to construct a reduced model and a faster second phase to sample from the approximate posterior distribution determined by the constructed model. We test and compare both algorithms to an adaptive Metropolis algorithm with full FSP-based likelihood evaluations on three example models and simulated data to show that the new ADAMH variants achieve substantial speedup in comparison to the full FSP approach. By reducing the computational costs of parameter estimation, we expect the ADAMH approach to enable efficient data-driven estimation for more complex gene regulation models.

Summary: Integral control is commonly used in mechanical and electrical systems to ensure perfect adaptation. A proposed design of integral control for synthetic biological systems employs the sequestration of two biochemical controller species. The unbound amount of controller species captures the integral of the error between the current and the desired state of the system. However, implementing integral control inside bacterial cells using sequestration feedback has been challenging due to the controller molecules being degraded and diluted. Furthermore, integral control can only be achieved under stability conditions that not all sequestration feedback networks fulfill. In this work, we give guidelines for ensuring stability and good performance (small steady-state error) in sequestration feedback networks. Our guidelines provide simple tuning options to obtain a flexible and practical biological implementation of sequestration feedback control. Using tools and metrics from control theory, we pave the path for the systematic design of synthetic biological circuits.

It has been an ongoing scientific debate whether biological parameters are conserved across experimental setups with different media, pH values, and other experimental conditions. Our work explores this question using Bayesian probability as a rigorous framework to assess the biological context of parameters in a model of the cell growth controller in You et al . When this growth controller is uninduced, the E. coli cell population grows to carrying capacity; however, when the circuit is induced, the cell population growth is regulated to remain well below carrying capacity. This growth control controller regulates the E. coli cell population by cell–cell communication using the signaling molecule AHL and by cell death using the bacterial toxin CcdB. To evaluate the context dependence of parameters such as the cell growth rate, the carrying capacity, the AHL degradation rate, the leakiness of AHL, the leakiness of toxin CcdB, and the IPTG induction factor, we collect experimental data from the growth control circuit in two different media, at two different pH values, and with several induction levels. We define a set of possible context-dependencies that describe how these parameters may differ with the experimental conditions and we develop mathematical models of the growth controller across the different experimental contexts. We then determine whether these parameters are shared across experimental contexts or whether they are context-dependent. For each of these possible context-dependencies, we use Bayesian inference to assess its plausibility and to estimate the growth controller’s parameters assuming this context-dependency. Ultimately, we find that there is significant experimental context-dependence in this circuit. Moreover, we also find that the estimated parameter values are sensitive to our assumption of a context relationship.

An ongoing area of study in synthetic biology has been the design and construction of synthetic circuits that maintain homeostasis at the population level. Here, we are interested in designing a synthetic control circuit that regulates the total cell population and the relative ratio between cell strains in a culture that contains two different cell strains. We have developed a dual feedback control strategy that uses two separate control loops to achieve the two control objectives respectively. We have implemented the strategy in a population regulation circuit where both the total population size and relative cell strain ratio can be set by reference signals. The circuit shows robustness and adaptation to perturbations in cell growth rate and changes in cell numbers. The control architecture is general and could apply to any organism for which synthetic biology tools for quorum sensing, comparison between outputs, and growth control are available.