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This brief examines a deterministic, ODE-based model for gene regulatory networks (GRN) that incorporates nonlinearities and time-delayed feedback. An introductory chapter provides some insights into molecular biology and GRNs. The mathematical tools necessary for studying the GRN model are then reviewed, in particular Hill functions and Schwarzian derivatives. One chapter is devoted to the analysis of GRNs under negative feedback with time delays and a special case of a homogenous GRN is considered. Asymptotic stability analysis of GRNs under positive feedback is then considered in a separate chapter, in which conditions leading to bi-stability are derived. Graduate and advanced undergraduate students and researchers in control engineering, applied mathematics, systems biology and synthetic biology will find this brief to be a clear and concise introduction to the modeling and analysis of GRNs.

Mathematics. --- Systems Theory, Control. --- Mathematical and Computational Biology. --- Gene Expression. --- Control, Robotics, Mechatronics. --- Gene expression. --- Systems theory. --- Mathématiques --- Expression génique --- Gene regulatory networks -- Mathematical models. --- Gene regulatory networks. --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Operations Research --- Gene regulatory networks --- Mathematical models. --- System theory. --- Biomathematics. --- Control engineering. --- Robotics. --- Mechatronics. --- Circuits, Gene --- Gene circuits --- Gene modules --- Gene networks --- Genetic regulatory networks --- GRNs (Gene regulatory networks) --- Modules, Gene --- Networks, Gene regulatory --- Networks, Transcriptional --- Regulatory networks, Gene --- Transcriptional networks --- Genetic regulation --- Nucleotide sequence --- Genes --- Expression --- Mechanical engineering --- Microelectronics --- Microelectromechanical systems --- Automation --- Machine theory --- Control engineering --- Control equipment --- Control theory --- Engineering instruments --- Programmable controllers --- Biology --- Mathematics --- Systems, Theory of --- Systems science --- Science --- Philosophy

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The science of complex biological networks is transforming research in areas ranging from evolutionary biology to medicine. This is the first book on the subject, providing a comprehensive introduction to complex network science and its biological applications. With contributions from key leaders in both network theory and modern cell biology, this book discusses the network science that is increasingly foundational for systems biology and the quantitative understanding of living systems. It surveys studies in the quantitative structure and dynamics of genetic regulatory networks, molecular networks underlying cellular metabolism, and other fundamental biological processes. The book balances empirical studies and theory to give a unified overview of this interdisciplinary science. It is a key introductory text for graduate students and researchers in physics, biology and biochemistry, and presents ideas and techniques from fields outside the reader's own area of specialization.

Cellular control mechanisms. --- Biological systems. --- System analysis. --- Network analysis --- Network science --- Network theory --- Systems analysis --- System theory --- Mathematical optimization --- Biosystems --- Systems, Biological --- Biology --- Systems biology --- Cell regulation --- Biological control systems --- Cell metabolism --- Philosophy --- Gene regulatory networks. --- Circuits, Gene --- Gene circuits --- Gene modules --- Gene networks --- Genetic regulatory networks --- GRNs (Gene regulatory networks) --- Modules, Gene --- Networks, Gene regulatory --- Networks, Transcriptional --- Regulatory networks, Gene --- Transcriptional networks --- Genetic regulation --- Nucleotide sequence --- Régulation cellulaire --- Systèmes biologiques --- Systèmes, analyse de

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Genomic signal processing (GSP) can be defined as the analysis, processing, and use of genomic signals to gain biological knowledge, and the translation of that knowledge into systems-based applications that can be used to diagnose and treat genetic diseases. Situated at the crossroads of engineering, biology, mathematics, statistics, and computer science, GSP requires the development of both nonlinear dynamical models that adequately represent genomic regulation, and diagnostic and therapeutic tools based on these models. This book facilitates these developments by providing rigorous mathematical definitions and propositions for the main elements of GSP and by paying attention to the validity of models relative to the data. Ilya Shmulevich and Edward Dougherty cover real-world situations and explain their mathematical modeling in relation to systems biology and systems medicine. Genomic Signal Processing makes a major contribution to computational biology, systems biology, and translational genomics by providing a self-contained explanation of the fundamental mathematical issues facing researchers in four areas: classification, clustering, network modeling, and network intervention.

Cellular signal transduction. --- Genetic regulation. --- Genomics --- Signal Transduction --- Gene Expression. --- Gene Regulatory Networks. --- Models, Genetic. --- Models, Statistical. --- Mathematical models. --- genetics. --- Gene regulatory networks. --- Circuits, Gene --- Gene circuits --- Gene modules --- Gene networks --- Genetic regulatory networks --- GRNs (Gene regulatory networks) --- Modules, Gene --- Networks, Gene regulatory --- Networks, Transcriptional --- Regulatory networks, Gene --- Transcriptional networks --- Gene expression --- Gene expression regulation --- Gene regulation --- Biosynthesis --- Cellular control mechanisms --- Molecular genetics --- Cellular information transduction --- Information transduction, Cellular --- Signal transduction, Cellular --- Bioenergetics --- Information theory in biology --- Genetic regulation --- Nucleotide sequence --- Genome research --- Genomes --- Regulation --- Research --- Gene Expression --- Models, Genetic --- Models, Statistical

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The complexity of living organisms surpasses our unaided habilities of analysis. Hence, computational and mathematical methods are necessary for increasing our understanding of biological systems. At the same time, there has been a phenomenal recent progress allowing the application of novel formal methods to new domains. This progress has spurred a conspicuous optimism in computational biology. This optimism, in turn, has promoted a rapid increase in collaboration between specialists of biology with specialists of computer science. Through sheer complexity, however, many important biological problems are at present intractable, and it is not clear whether we will ever be able to solve such problems. We are in the process of learning what kind of model and what kind of analysis and synthesis techniques to use for a particular problem. Some existing formalisms have been readily used in biological problems, others have been adapted to biological needs, and still others have been especially developed for biological systems. This Research Topic has examples of cases (1) employing existing methods, (2) adapting methods to biology, and (3) developing new methods. We can also see discrete and Boolean models, and the use of both simulators and model checkers. Synthesis is exemplified by manual and by machine-learning methods. We hope that the articles collected in this Research Topic will stimulate new research.

model checking --- Logic programing --- Answer set programing --- attractors of Boolean networks --- synthesis of biochemical models --- Gene Regulatory Networks --- Boolean networks --- biochemical networks

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Genetic Regulatory Networks (GRNs) in biological organisms are primary engines for cells to enact their engagements with environments, via incessant, continually active coupling. In differentiated multicellular organisms, tremendous complexity has arisen in the course of evolution of life on earth. Engineering and science have so far achieved no working system that can compare with this complexity, depth and scope of organization. Abstracting the dynamics of genetic regulatory control to a computational framework in which artificial GRNs in artificial simulated cells differentiate while connected in a changing topology, it is possible to apply Darwinian evolution in silico to study the capacity of such developmental/differentiated GRNs to evolve. In this volume an evolutionary GRN paradigm is investigated for its evolvability and robustness in models of biological clocks, in simple differentiated multicellularity, and in evolving artificial developing 'organisms' which grow and express an ontogeny starting from a single cell interacting with its environment, eventually including a changing local neighbourhood of other cells. These methods may help us understand the genesis, organization, adaptive plasticity, and evolvability of differentiated biological systems, and may also provide a paradigm for transferring these principles of biology's success to computational and engineering challenges at a scale not previously conceivable.

Gene regulatory networks --- Self-organizing systems --- Engineering & Applied Sciences --- Biology --- Health & Biological Sciences --- Genetics --- Computer Science --- Mathematical models --- Self-organizing systems. --- Mathematical models. --- Learning systems (Automatic control) --- Self-optimizing systems --- Circuits, Gene --- Gene circuits --- Gene modules --- Gene networks --- Genetic regulatory networks --- GRNs (Gene regulatory networks) --- Modules, Gene --- Networks, Gene regulatory --- Networks, Transcriptional --- Regulatory networks, Gene --- Transcriptional networks --- Engineering. --- Artificial intelligence. --- Computational intelligence. --- Computational Intelligence. --- Artificial Intelligence (incl. Robotics). --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Simulation methods --- Fifth generation computers --- Neural computers --- Construction --- Industrial arts --- Technology --- Cybernetics --- Intellect --- Learning ability --- Synergetics --- Genetic regulation --- Nucleotide sequence --- Artificial Intelligence.