The main goal of synthetic biology is to harness the power of biological genetic expression in order to perform various tasks, which could often have an impact on many aspects of our lives ranging from healthcare, pharmaceutical, to renewable energy and environments. These tasks are often carried out through synthetic genetic circuits composed of genetic parts like promoters, RBS, terminators, and inducible gene regulators. Numerous studies have expanded the toolbox for synthetic circuitry and established the guideline of circuitry assembly in the past decade. As the field advances, regulatory sRNA is emerging as a powerful tool in synthetic biology. These regulatory sRNAs are versatile and designable, more importantly, they offer a fast dynamic in genetic circuitry due to the fast production rates and degradation rates of RNA molecules. However, little work has been done to create a theoretical foundation for RNA circuit design. With the ultimate goal of gaining full control of RNA circuitry dynamics, this work focuses on building the theoretical foundation to understand and guide the design of RNA synthetic circuitry. A prerequisite to building such a foundation is to create a modeling framework that accurately describes the dynamics of RNA circuits. In the first part of this work, we build an effective model composed of ordinary differential equations to describe transcriptional RNA genetic circuitry and validate the model using a three-level cascade as a test case. We develop a sensitivity analysis based parameterization procedure that requires only a handful of simple experiments that can be performed in parallel using rapid cell-free transcription-translation (TX-TL) reactions. This part of the work establishes a fundamental method to predict circuit dynamics, which allow us to build more complex systems. Next, we expand the repertoire of synthetic gene networks built from these regulators by constructing a transcriptional negative autoregulation (NAR) network out of small RNAs (sRNAs). Using parameter sensitivity analysis, we design a simple set of experiments that allow us to accurately predict the NAR circuit dynamic in TX-TL. We also transfer the successful network design into Escherichia coli and show that our sRNA transcriptional network is functional in vivo. In the third part of this work, we investigate into an interesting observation where the transfer functions of inducible systems are altered by small transcriptional activating RNAs (STARs). We combine theory, computational model and experimental results to uncover the underlying causes of this phenomenon. Based on which, we establish the design principle of transfer function manipulation and dynamic range amplification induced by STARs. Together the work presented here establishes a theoretical foundation of RNA circuitry design. We anticipate that this foundation would support the development of new mathematical and computational models that provide insights and guidance for RNA circuitry design -which ultimately contributes to the advancement of synthetic circuitry engineering.

A step-by-step guide to using computational tools to solve problems in cell biology Combining expert discussion with examples that can be reproduced by the reader, A Cell Biologist's Guide to Modeling and Bioinformatics introduces an array of informatics tools that are available for analyzing biological data and modeling cellular processes. You learn to fully leverage public databases and create your own computational models. All that you need is a working knowledge of algebra and cellular biology; the author provides all the other tools you need to understand the necessary statistical and mathematical methods. Coverage is divided into two main categories: Molecular sequence database chapters are dedicated to gaining an understanding of tools and strategies—including queries, alignment methods, and statistical significance measures—needed to improve searches for sequence similarity, protein families, and putative functional domains. Discussions of sequence alignments and biological database searching focus on publicly available resources used for background research and the characterization of novel gene products. Modeling chapters take you through all the steps involved in creating a computational model for such basic research areas as cell cycle, calcium dynamics, and glycolysis. Each chapter introduces a new simulation tooland is based on published research. The combination creates a rich context for ongoing skill and knowledge development in modeling biological research systems. Students and professional cell biologists can develop the basic skills needed to learn computational cell biology. This unique text, with its step-by-step instruction, enables you to test and develop your new bioinformatics and modeling skills. References are provided to help you take advantage of more advanced techniques, technologies, and training.

The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory

An introduction to the mathematical concepts and techniques needed for the construction and analysis of models in molecular systems biology. Systems techniques are integral to current research in molecular cell biology, and system-level investigations are often accompanied by mathematical models. These models serve as working hypotheses: they help us to understand and predict the behavior of complex systems. This book offers an introduction to mathematical concepts and techniques needed for the construction and interpretation of models in molecular systems biology. It is accessible to upper-level undergraduate or graduate students in life science or engineering who have some familiarity with calculus, and will be a useful reference for researchers at all levels. The first four chapters cover the basics of mathematical modeling in molecular systems biology. The last four chapters address specific biological domains, treating modeling of metabolic networks, of signal transduction pathways, of gene regulatory networks, and of electrophysiology and neuronal action potentials. Chapters 3–8 end with optional sections that address more specialized modeling topics. Exercises, solvable with pen-and-paper calculations, appear throughout the text to encourage interaction with the mathematical techniques. More involved end-of-chapter problem sets require computational software. Appendixes provide a review of basic concepts of molecular biology, additional mathematical background material, and tutorials for two computational software packages (XPPAUT and MATLAB) that can be used for model simulation and analysis.

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