Design, Analysis, And Computational Methods For Engineering Synthetic Biological Networks

This thesis advances our understanding of three important aspects of biological systems engineering: analysis, design, and computational methods. First, biological circuit design is necessary to engineer biological systems that behave consistently and follow our design specifications. We contribute by formulating and solving novel problems in stochastic biological circuit design. Second, computational methods for solving biological systems are often limited by the nonlinearity and high dimensionality of the system’s dynamics. This problem is particularly extreme for the parameter identification of stochastic, nonlinear systems. Thus, we develop a method for parameter identification that relies on data-driven stochastic model reduction. Finally, biological system analysis encompasses understanding the stability, performance, and robustness of these systems, which is critical for their implementation. We analyze a sequestration feedback motif for implementing biological control. First, we discuss biological circuit design for the stationary and the transient distributional responses of stochastic biochemical systems. Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture their dynamics. The chemical master equation is a commonly used stochastic model that describes how the probability distribution of a chemically reacting system varies with time. Here we design the distributional response of these stochastic models by formulating and solving it as a constrained optimization problem. Second, we analyze the stability and the performance of a biological controller implemented by a sequestration feedback network motif. Sequestration feedback networks have been implemented in synthetic biology using an array of biological parts. However, their properties of stability and performance are poorly understood. We provide insight into the stability and performance of sequestration feedback networks. Additionally, we provide guidelines for the implementation of sequestration feedback networks. Third, we develop computational methods for the parameter identification of stochastic models of biochemical reaction networks. It is often not possible to find analytic solutions to problems where the dynamics of the underlying biological circuit are stochastic, nonlinear or both. Stochastic models are often challenging due to their high dimensionality and their nonlinearity, which further limits the availability of analytical tools. To address these challenges, we develop a computational method for data-driven stochastic model reduction and we use it to perform parameter identification. Last, we provide concluding remarks and future research directions.</p

Population regulation in microbial consortia using dual feedback control

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 containing two different cell strains. We have developed a dual feedback control strategy that uses two separate control loops to achieve the two functions respectively. By combining both of these control loops, we have created a population regulation circuit where both the total population size and relative cell type ratio can be set by reference signals. The dynamics of the regulation circuit show 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

Design Guidelines For Sequestration Feedback Networks

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 systems

Recursively constructing analytic expressions for equilibrium distributions of stochastic biochemical reaction networks

Noise is often indispensable to key cellular activities, such as gene expression, necessitating the use of stochastic models to capture its dynamics. The chemical master equation (CME) is a commonly used stochastic model of Kolmogorov forward equations that describe how the probability distribution of a chemically reacting system varies with time. Finding analytic solutions to the CME can have benefits, such as expediting simulations of multiscale biochemical reaction networks and aiding the design of distributional responses. However, analytic solutions are rarely known. A recent method of computing analytic stationary solutions relies on gluing simple state spaces together recursively at one or two states. We explore the capabilities of this method and introduce algorithms to derive analytic stationary solutions to the CME. We first formally characterize state spaces that can be constructed by performing single-state gluing of paths, cycles or both sequentially. We then study stochastic biochemical reaction networks that consist of reversible, elementary reactions with two-dimensional state spaces. We also discuss extending the method to infinite state spaces and designing the stationary behaviour of stochastic biochemical reaction networks. Finally, we illustrate the aforementioned ideas using examples that include two interconnected transcriptional components and biochemical reactions with two-dimensional state spaces

Hard Limits And Performance Tradeoffs In A Class Of Sequestration Feedback Systems

Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism implemented using the sequestration binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of sequestration feedback and contribute to a more general theory of biological control systems

Population regulation in microbial consortia using dual feedback control

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 containing two different cell strains. We have developed a dual feedback control strategy that uses two separate control loops to achieve the two functions respectively. By combining both of these control loops, we have created a population regulation circuit where both the total population size and relative cell type ratio can be set by reference signals. The dynamics of the regulation circuit show 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

Design Guidelines For Sequestration Feedback Networks

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 systems

Hard Limits And Performance Tradeoffs In A Class Of Sequestration Feedback Systems

Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism implemented using the sequestration binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of sequestration feedback and contribute to a more general theory of biological control systems

Hard Limits and Performance Tradeoffs in a Class of Antithetic Integral Feedback Networks

Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism called antithetic integral feedback, which can be implemented using the binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of antithetic integral feedback and contribute to a more general theory of biological control systems