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Systems and Control Theoretic Approaches to Engineer Robust Systems and Control Theoretic Approaches to Engineer Robust Biological Systems by Yili Qian Submitted to the Department of Mechanical Engineering in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2020 ○c Massachusetts Institute of Technology 2020. All rights reserved. Author................................................................ Department of Mechanical Engineering August 7, 2020 Certified by. Domitilla Del Vecchio Professor of Mechanical Engineering Thesis Supervisor Accepted by . Nicolas G. Hadjiconstantinou Chairman, Department Committee on Graduate Theses 2 Systems and Control Theoretic Approaches to Engineer Robust Biological Systems by Yili Qian Submitted to the Department of Mechanical Engineering on August 7, 2020, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract Synthetic biology is an emerging field of research aimed to engineer biological systems by inserting programmed DNA molecules into living cells. These DNAs encode the production and subsequent interactions of biomolecules that allow the cells to have novel sensing, computing, and actuation capabilities. However, most success stories to date rely heavily on trial and error. This is mainly because genetic systems are context-dependent: the expression level of a synthetic gene often depends not only on its own regulatory inputs, but also on the expression of other supposedly unconnected genes. This lack of modularity leads to unexpected behaviors when multiple genetic subsystems are composed together, making it difficult to engineer complex systems that function predictably and robustly in practice. This thesis characterizes resource competition as a form of context dependence, and presents control theoretic approaches to engineer robust, context-independent gene networks. We first present a systems framework to model resource competition, which results in a hidden layer of unintended interactions among genetic subsystems. These unintended interactions lead to failure of the composed network in experi- ment. We then introduce a set of biomolecular controllers - designed to solve an output regulation problem in vivo - that can decouple a genetic subsystem’s output from its context. We describe challenges applying classical control theory to engineer such controllers due to the physical constraints in living cells, and then present novel theory-guided engineering solutions. Finally, we point to additional design consid- erations when regulating multiple subsystems using multiple controllers in a single cell. These works have the potential to enhance the robustness of future synthetic biological systems and to fully unleash their power to address pressing societal needs in environment, energy, and health. Thesis Supervisor: Domitilla Del Vecchio Title: Professor of Mechanical Engineering 3 4 Acknowledgments First and foremost, I am extremely grateful to my advisor, Prof. Domitilla Del Vecchio, for her relentless support over the past seven years. Her commitment to and enthusiasm for research is second to none. She is such a role model. I’d like to thank my thesis committee members, Profs. Harry Asada, Richard Braatz, and Eduardo Sontag for their feedback on my work. I enjoy working with Prof. Ron Weiss on a number of projects and I want to thank him for his guidance. My deep appreciation goes to my friends and colleagues in the Del Vecchio lab. Many breakthroughs in my research were inspired by conversations with you. I espe- cially want to thank Hsin-Ho and Ross for their patience in teaching me cell culture and cloning, and answering my naïve biology questions. I cannot imagine finishing this thesis without you. I am deeply indebted to Ted, for all the theoretical inspi- rations I gained through our discussions. I want to thank José and Abdullah for bringing my attention to the difficult research questions that lingered in mymind for the last seven years. Andras, Cameron, Carlos, Fiona, Francesca, Heejin, M.Ali., Max, M.N., Narmada, Nithin, Penny, Rushina, Shaoshuai, Simone, and Ukjin, it is my great fortune to be a colleague with you and thank you for all the support, fun, and intellectual stimulations. My undergraduate mentees Hussein and Anh have pro- vided me many inspirations, and I enjoy working with them. I want to thank Joe for providing all the administrative supports behind the curtain. I am thankful for my friends at MIT and in the greater Boston area, especially my long-time roommates Rujian, Fangchang, and Qingkai, for all the joyful and unforgettable moments. I am heartfully indebted to my dear parents, Wei Qian and Lei Zhou. They have provided me endless support and encouragement over the years, and made many sacrifices for me to finish this thesis. I love you and I missyou. The work reported in this thesis was supported in part by AFOSR grant FA9550- 14-1-0060 and FA9550-12-1-0129, ONR award N000141310074, NSF-CMMI award 1727189, and NIH NIGMS grant P50 GMO98792. 5 6 Contents 1 Introduction 25 1.1 Overview of synthetic biology . 25 1.2 Robustness problems in synthetic biology . 29 1.3 Statement of contributions . 30 1.4 Thesis organization . 32 2 Characterization of unintended interactions in genetic circuits 35 2.1 Introduction . 35 2.2 General modeling framework . 37 2.3 Effective interaction graphs . 41 2.4 Experiment: activation cascade . 48 2.4.1 Genetic circuit . 48 2.4.2 Model guided design to mitigate unintended interactions . 50 2.5 Summary . 52 3 Robustness of genetic subsystems to disturbances 53 3.1 Introduction . 53 3.2 Robustness to constant disturbances . 55 3.2.1 Physical constraints arising from cell growth . 56 3.2.2 Quasi-integral control (QIC) for set-point regulation . 58 3.2.3 Type I and II QICs to regulate genetic subsystems . 63 3.2.4 Type I QIC realization: phosphorylation cycle . 69 3.2.5 Type II QIC realization: small RNA (sRNA) interference . 72 7 3.3 Robust tracking performance . 74 3.3.1 A singular singular perturbation (SSP) problem . 75 3.3.2 Model reduction of SSP systems . 77 3.3.3 QIC tracking performance . 88 3.4 Experiment: sRNA-mediated QIC . 90 3.4.1 Genetic circuit . 92 3.4.2 Model guided controller tuning for set-point regulation . 95 3.5 Summary . 101 4 Robustness of networked systems to unintended interactions 103 4.1 Introduction . 103 4.2 Motivating example . 106 4.3 Problem formulation . 110 4.4 Technical background: monotone systems . 112 4.5 Network disturbance decoupling with monotone subsystems . 115 4.6 Network disturbance decoupling with near-monotone subsystems . 122 4.7 Application to decentralized QIC-regulated genetic circuits . 128 4.8 Summary . 136 5 Conclusions and future work 139 5.1 Conclusions . 139 5.2 Extensions and future directions . 141 A Appendix for Chapter 2 145 A.1 Derivation of graphical rules . 145 B Appendix for Chapter 3 149 B.1 Modeling dilution in mass action kinetics . 149 B.2 Proof of Theorem 3.1 . 151 B.3 Counterexample: increasing only part of the controller reaction rates 154 B.4 Proof of Lemma 3.4 . 156 B.5 Analysis of phosphorylation-mediated type I QIC . 158 8 B.6 Analysis of sRNA-mediated type II QIC . 165 B.7 Additional simulations . 170 B.8 Simulation parameters . 172 B.9 Experimental methods . 173 C Appendix for Chapter 4 175 C.1 Proof of Lemma 4.3 . 175 C.2 Proof of Lemma 4.4 . 179 C.3 Proof of Lemma 4.5 . 180 C.4 Small-gain theorem for convergent-input-convergent-output system . 182 C.5 Disturbance attenuation of feedback-regulated subsystems . 184 C.6 Lipschitz properties of subsystem characteristics . 186 9 10 List of Figures 1-1 Architecture of synthetic biology systems. Genetic parts (a) can be assembled to create genetic subsystems (b) that have inputs and outputs. Interconnection of genetic subsystems creates intracellular systems (e.g., ge- netic circuits) that has sensing, computing, and actuation capabilities. Mul- tiple populations of cells with different encoded programs can create complex synthetic ecology. The focus of this thesis is to provide systems and control theoretic underpinnings to design robust intracellular system from genetic subsystems. ................................ 26 11 1-2 Applications of synthetic biology. (a) A cell type classifier circuit used for cancer diagnostic ex vivo [172]. A reference profile of miRNAs that are expressed in cancer cells is used to construct a genetic logic circuit realized through RNA interactions. When transfected into a cancer cell, the output of the logic circuit triggers expression of a fluorescence protein. (b) Bacteria can be engineered to be smart drug delivery vehicles [44]. A consortium of engineered bacteria is delivered to the target tumor site. Each cell contains a genetic clock, a cell lysis gene, a therapeutic protein production gene and a cell-cell communication module. The synchronized clocks control cell lysis to release the therapeutic proteins periodically. (c) Synthetic genetic circuits increase the specificity and safety of cancer immunotherapy [30]. Receptors can be engineered to trigger T cell activity when cancer cells are detected. Feedback loops can be used to regulate T cell activity to avoid side effects. (d) A synthetic lineage control circuit. By regulating the expression of three transcription factors according to a temporal pattern, hIPSCs can be repro- grammed into insulin-secreting beta-like cell for treating diabetes [136]. 27 1-3 Thesis organization. ........................... 33 2-1 Setup of a genetic circuit with limited resources. (a) Schematic of gene expression process in a subsystem i. (b) In a genetic circuit, all sub- systems are connected through prescribed interactions (i.e., transcriptional regulation) and are competing for a conserved amount of resources in the host cell. .................................. 38 2-2 Rules to draw effective interactions in any genetic circuit with resource limitation. Black solid edges represent prescribed regulatory interactions, red dashed edges represent unintended interactions due to re- source limitation. If a black and a red edge have the same head and tail, we indicate their combined effects with a gray edge.
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