PID and state feedback controllers using DNA strand displacement reactions

Nucleic acid-based chemistry is a strong candidate framework for the construction of future synthetic biomolecular control circuits. Previous work has demonstrated the capacity of circuits based on DNA strand displacement (DSD) reactions to implement digital and analogue signal processing in vivo , including in mammalian cells. To date, however, feedback control system designs attempted within this framework have been restricted to extremely simple proportional or proportional-integral controller architectures. In this letter, we significantly extend the potential complexity of such controllers by showing how time-delays, numerical differentiation (to allow PID control), and state feedback may be implemented via chemical reaction network-based designs. Our controllers are implemented and tested using VisualDSD, a rapid-prototyping tool that allows precise analysis of computational devices implemented using nucleic acids, via both deterministic and stochastic simulations of the DSD reactions.11Nscopu

Implementing nonlinear feedback controllers using DNA strand displacement reactions

We show how an important class of nonlinear feedback controllers can be designed using idealized abstract chemical reactions and implemented via DNA strand displacement (DSD) reactions. Exploiting chemical reaction networks (CRNs) as a programming language for the design of complex circuits and networks, we show how a set of unimolecular and bimolecular reactions can be used to realize input-output dynamics that produce a nonlinear quasi sliding mode (QSM) feedback controller. The kinetics of the required chemical reactions can then be implemented as enzyme-free, enthalpy/entropy driven DNA reactions using a toehold mediated strand displacement mechanism via Watson-Crick base pairing and branch migration. We demonstrate that the closed loop response of the nonlinear QSM controller outperforms a traditional linear controller by facilitating much faster tracking response dynamics without introducing overshoots in the transient response. The resulting controller is highly modular and is less affected by retroactivity effects than standard linear designs

PID control of biochemical reaction networks

Principles of feedback control have been shown to naturally arise in biological systems and have been applied with success to build synthetic circuits. Here, we present an implementation of a proportional–integral–derivative (PID) controller as a chemical reaction network with mass-action kinetics. This makes the controller synthesizable in vitro using DNA strand displacement technology, owing to its demonstrated capability of realizing arbitrary reaction-network designs as interacting DNA molecules. Previous related work has studied biological PID architectures using linearizations of nonlinear dynamics arising in both the controller components and in the plant. In this article, we present a proof of correctness of our nonlinear design in closed loop using arguments from singular perturbation theory. As an application to show the effectiveness of our controller, we provide numerical simulations on a genetic model to perform PID feedback control of protein expression

Computational Design of Nucleic Acid Feedback Control Circuits

The design of synthetic circuits for controlling molecular-scale processes is an important goal of synthetic biology, with potential applications in future in vitro and in vivo biotechnology. In this paper, we present a computational approach for designing feedback control circuits constructed from nucleic acids. Our approach relies on an existing methodology for expressing signal processing and control circuits as biomolecular reactions. We first extend the methodology so that circuits can be expressed using just two classes of reactions: catalysis and annihilation. We then propose implementations of these reactions in three distinct classes of nucleic acid circuits, which rely on DNA strand displacement, DNA enzyme and RNA enzyme mechanisms, respectively. We use these implementations to design a Proportional Integral controller, capable of regulating the output of a system according to a given reference signal, and discuss the trade-offs between the different approaches. As a proof of principle, we implement our methodology as an extension to a DNA strand displacement software tool, thus allowing a broad range of nucleic acid circuits to be designed and analyzed within a common modeling framework

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

On the stability of nucleic acid feedback control systems

Recent work has shown how chemical reaction network theory may be used to design dynamical systems that can be implemented biologically in nucleic acid-based chemistry. While this has allowed the construction of advanced open-loop circuitry based on cascaded DNA strand displacement (DSD) reactions, little progress has so far been made in developing the requisite theoretical machinery to inform the systematic design of feedback controllers in this context. Here, we develop a number of foundational theoretical results on the equilibria, stability, and dynamics of nucleic acid controllers. In particular, we show that the implementation of feedback controllers using DSD reactions introduces additional nonlinear dynamics, even in the case of purely linear designs, e.g. PI controllers. By decomposing the effects of these non-observable nonlinear dynamics, we show that, in general, the stability of the linear system design does not necessarily imply the stability of the underlying chemical reaction network, which can be lost under experimental variability when feedback interconnections are introduced. We provide an in-depth theoretical analysis, and present an example to illustrate when the linear design does not capture the instability of the full nonlinear system implemented as a DSD reaction network, and we further confirm these results using Visual DSD, a bespoke software tool for simulating nucleic acid-based circuits. Our analysis highlights the many interesting and unique characteristics of this important new class of feedback control systems. (C) 2020 Elsevier Ltd. All rights reserved.11Nsciescopu

Design and analysis of DNA controllers

Reliable biochemical implementations of linear controllers can provide a large set of tools for the design and analysis of control in Synthetic Biology. Theoretical frameworks are now available to represent feedback control systems as chemical reaction networks which can be readily translated into equivalent nucleic acid-based chemistry. However, the development of tools for constructing and analysing such controllers is still in its infancy. Nucleic acid-based chemistry is a strong candidate framework for the construction of future synthetic biomolecular control circuits. The capacity of strand displacement reactions with Deoxyribonucleic Acid (DNA) to implement analogue signal processing in vitro and in vivo makes them a promising candidate to embed synthetic feedback control circuitry in biomolecular environments. However, little progress has so far been made in developing the requisite theoretical machinery to inform the systematic design of feedback controllers in this context. Here, the potential complexity of such controllers is extended significantly by showing how time-delays, numerical differentiation (to allow proportional-integral-derivative control), and state feedback may be implemented via chemical reaction network-based designs. This work also provides a number of foundational theoretical results on the equilibria, stability, and dynamics of nucleic acid controllers, and the analysis highlights the many interesting and unique characteristics of this important new class of feedback control systems. In particular, that the implementation of feedback controllers using DNA strand displacement reactions introduces additional nonlinear dynamics, even in the case of purely linear control designs, and a robust design of the linear system does not imply the robustness of its chemical implementation. The robustness of the controllers to experimental uncertainty is analysed with the structured singular value (µ) analysis tool, which is extended with a model of how parametric uncertainty in the system affects the location of its equilibrium. This framework provides more reliable results than sampled based statistical methods, where analysis via Monte Carlo simulation fails to uncover the worst-case uncertainty combination found by µ-analysis. The implementations of the examples and controllers in nucleic acid-based chemistry are simulated and checked using the Visual DSD simulation package, a bespoke software tool for simulating nucleic acid-based circuits

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

Analysis of finite-time regulation property of biomolecular PI controller

In practical applications of dynamic DNA nanotechnology, a biomolecular controller is required for maintaining the operation of the molecular actuator at a desired condition based on the information from molecular sensors. By making use of the DNA strand displacement mechanism as a “programming language” in the controller design, a biomolecular PI controller has been proposed. However, this PI control system has been verified only at the simulation level, and a theoretical regulation analysis is still required. Accordingly, in this study, we perform a rigorous regulation analysis of the biomolecular PI control system. Specifically, we theoretically prove that the output signal approaches the target level at a quasi-steady state. To this end, we apply the concept of finite-time regulation property to the biomolecular PI control system