Robustness analysis of a nucleic acid controller for a dynamic biomolecular process using the structured singular value

In the field of synthetic biology, theoretical frameworks and software tools are now available that allow control systems represented as chemical reaction networks to be translated directly into nucleic acid-based chemistry, and hence implement embedded control circuitry for biomolecular processes. However, the development of tools for analysing the robustness of such controllers is still in its infancy. An interesting feature of such control circuits is that, although the transfer function of a linear system can be easily implemented via a chemical network of catalysis, degradation and annihilation reactions, this introduces additional nonlinear dynamics, due to the annihilation kinetics. We exemplify this problem for a dynamical biomolecular feedback system, and demonstrate how the structured singular value (μ) analysis framework can be extended to rigorously analyse the robustness of this class of system. We show that parametric uncertainty in the system affects the location of its equilibrium, and that this must be taken into account in the analysis. We also show that the parameterisation of the system can be scaled for experimental feasibility without affecting its robustness properties, and that a statistical analysis via Monte Carlo simulation fails to uncover the worst-case uncertainty combination found by μ-analysis.</p

Design of an embedded inverse-feedforward biomolecular trackingcontroller for enzymatic reaction processes

Feedback control is widely used in chemical engineering to improve the performance and robustness of chemical processes. Feedback controllers require a ‘subtractor’ that is able to compute the error between the process output and the reference signal. In the case of embedded biomolecular control circuits, subtractors designed using standard chemical reaction network theory can only realise one-sided subtraction, rendering standard controller design approaches inadequate. Here, we show how a biomolecular controller that allows tracking of required changes in the outputs of enzymatic reaction processes can be designed and implemented within the framework of chemical reaction network theory. The controller architecture employs an inversion-based feedforward controller that compensates for the limitations of the one-sided subtractor that generates the error signals for a feedback controller. The proposed approach requires significantly fewer chemical reactions to implement than alternative designs, and should have wide applicability throughout the fields of synthetic biology and biological engineering

Design and analysis of genetic feedback architectures for synthetic biology

Synthetic Biology seeks to design and assemble novel biological systems with favourable properties. It allows us to comprehend and modify the fundamental mechanisms of life and holds significant promise in revolutionizing current technologies ranging from medicine and biomanufacturing to energy and environmental protection. Biological processes constitute remarkably complex dynamical systems operating impeccably well in messy and constantly changing environments. Their ability to do so is rooted in sophisticated molecular control architectures crafted by natural evolutionary innovation over billions of years. Such control architectures, often blended with human-engineering approaches, are the key to realizing efficient and reliable synthetic biological systems. Aiming to accelerate the development of the latter, the present thesis addresses some fundamental challenges in biomolecular systems and control design. We begin by elucidating biological mechanisms of temporal gradient computation, enabling cells to adjust their behaviour in response to anticipated environmental changes. Specifically, we introduce biomolecular motifs capable of functioning as highly tunable and accurate signal differentiators to input molecular signals around their nominal operation. We investigate strategies to deal with high-frequency input signal components which can be detrimental to the performance of most differentiators. We ascertain the occurrence of such motifs in natural regulatory networks and demonstrate the potential of synthetic experimental realizations. Our motifs can serve as reliable speed biosensors and can form the basis for derivative feedback control. Motivated by the pervasiveness of Proportional-Integral-Derivative (PID) controllers in modern technological applications, we present the realization of a PID controller via biomolecular reactions employing, among others, our differentiator motifs. This biomolecular architecture represents a PID control law with set point weighting and filtered derivative action, offering robust regulation of a single-output biological process with enhanced dynamic performance and low levels of stochastic noise. It is characterized by significant ease of tuning and can be of particular experimental interest in molecular programming applications. Finally, we investigate efficient regulation strategies for multi-output biological processes with internal coupling interactions, expanding previously established single-output control approaches. More specifically, we propose control schemes allowing for robust manipulation of the outputs in various ways, namely manipulation of their product/ratio, linear combinations of them as well as manipulation of each of the outputs independently. Our analysis is centered around two-output biological processes, yet the scalability of the proposed regulation strategies to processes with a higher number of outputs is highlighted. In parallel, their experimental implementability is explored in both in vivo and in vitro settings

Robust H∞ feedback control for uncertain stochastic delayed genetic regulatory networks with additive and multiplicative noise

The official published version can found at the link below.Noises are ubiquitous in genetic regulatory networks (GRNs). Gene regulation is inherently a stochastic process because of intrinsic and extrinsic noises that cause kinetic parameter variations and basal rate disturbance. Time delays are usually inevitable due to different biochemical reactions in such GRNs. In this paper, a delayed stochastic model with additive and multiplicative noises is utilized to describe stochastic GRNs. A feedback gene controller design scheme is proposed to guarantee that the GRN is mean-square asymptotically stable with noise attenuation, where the structure of the controllers can be specified according to engineering requirements. By applying control theory and mathematical tools, the analytical solution to the control design problem is given, which helps to provide some insight into synthetic biology and systems biology. The control scheme is employed in a three-gene network to illustrate the applicability and usefulness of the design.This work was funded by Royal Society of the U.K.; Foundation for the Author of National Excellent Doctoral Dissertation of China. Grant Number: 2007E4; Heilongjiang Outstanding Youth Science Fund of China. Grant Number: JC200809; Fok Ying Tung Education Foundation. Grant Number: 111064; International Science and Technology Cooperation Project of China. Grant Number: 2009DFA32050; University of Science and Technology of China Graduate Innovative Foundation

Proportional-Integral Degradation (PI-Deg) control allows accurate tracking of biomolecular concentrations with fewer chemical reactions

We consider the design of synthetic embedded feedback circuits that can implement desired changes in the concentration of the output of a biomolecular process (reference tracking in control terminology). Such systems require the use of a "subtractor", to generate an error signal that captures the difference between the current and desired value of the process output. Unfortunately, standard implementations of the subtraction operator using chemical reaction networks are one-sided, i.e. they cannot produce negative error signals. Previous attempts to deal with this problem by representing signals as the difference in concentrations of two different biomolecular species lead to a doubling of the number of chemical reactions required to generate the circuit, hence sharply increasing the difficulty of experimental implementations and limiting the complexity of potential designs. Here we propose an alternative approach that introduces a degradation term into the classical proportion-integral control scheme. The extra tuning flexibility of the resulting PI-Deg controller compensates for the limitations of the one-sided subtraction operator, providing robust high-performance tracking of concentration changes with a minimal number of chemical reactions

Synthetic in vitro transcriptional oscillators

The construction of synthetic biochemical circuits from simple components illuminates how complex behaviors can arise in chemistry and builds a foundation for future biological technologies. A simplified analog of genetic regulatory networks, in vitro transcriptional circuits, provides a modular platform for the systematic construction of arbitrary circuits and requires only two essential enzymes, bacteriophage T7 RNA polymerase and Escherichia coli ribonuclease H, to produce and degrade RNA signals. In this study, we design and experimentally demonstrate three transcriptional oscillators in vitro. First, a negative feedback oscillator comprising two switches, regulated by excitatory and inhibitory RNA signals, showed up to five complete cycles. To demonstrate modularity and to explore the design space further, a positive-feedback loop was added that modulates and extends the oscillatory regime. Finally, a three-switch ring oscillator was constructed and analyzed. Mathematical modeling guided the design process, identified experimental conditions likely to yield oscillations, and explained the system's robust response to interference by short degradation products. Synthetic transcriptional oscillators could prove valuable for systematic exploration of biochemical circuit design principles and for controlling nanoscale devices and orchestrating processes within artificial cells

Enzyme-Free Nucleic Acid Dynamical Systems

An important goal of synthetic biology is to create biochemical control systems with the desired characteristics from scratch. Srinivas et al. describe the creation of a biochemical oscillator that requires no enzymes or evolved components, but rather is implemented through DNA molecules designed to function in strand displacement cascades. Furthermore, they created a compiler that could translate a formal chemical reaction network into the necessary DNA sequences that could function together to provide a specified dynamic behavior