This introduction to the crustacean stomatogastric nervous system (STNS) describes some of the best-understood neural networks in the animal kingdom at cellular, network, behavioural, comparative and evolutionary levels of analysis.
The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Séminaire de Mathématiques Supérieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine. The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight - discuss innovative methods for the analysis of biological processes, - contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.
Networked systems are all around us. The accumulated evidence of systems as complex as a cell cannot be fully understood by studying only their isolated constituents, giving rise to a new area of interest in research ? the study of complex networks. In a broad sense, biological networks have been one of the most studied networks, and the field has benefited from many important contributions. By understanding and modeling the structure of a biological network, a better perception of its dynamical and functional behavior is to be expected. This unique book compiles the most relevant results and novel insights provided by network theory in the biological sciences, ranging from the structure and dynamics of the brain to cellular and protein networks and to population-level biology.
Biophysical models have been used in biology for decades, but they have been limited in scope and size. In this book, Bernhard Ø. Palsson shows how network reconstructions that are based on genomic and bibliomic data, and take the form of established stoichiometric matrices, can be converted into dynamic models using metabolomic and fluxomic data. The Mass Action Stoichiometric Simulation (MASS) procedure can be used for any cellular process for which data is available and allows a scalable step-by-step approach to the practical construction of network models. Specifically, it can treat integrated processes that need explicit accounting of small molecules and protein, which allows simulation at the molecular level. The material has been class-tested by the author at both the undergraduate and graduate level. All computations in the text are available online in MATLAB® and Mathematica® workbooks, allowing hands-on practice with the material.
This volume presents a timely and comprehensive overview of biological networks at all organization levels in the spirit of the complex system approach. It discusses the transversal issues and fundamental principles as well as the overall structure, dynamics, and modeling of a wide array of biological networks at the molecular, cellular, and population levels. Anchored in both empirical data and a strong theoretical background, the book therefore lends valuable credence to the complex systems approach.
Models help us understand the dynamics of real-world processes by using the computer to mimic the actual forces that are known or assumed to result in a system's behavior. This book does not require a substantial background in mathematics or computer science.
From the spontaneous rapid firing of cortical neurons to the spatial diffusion of disease epidemics, biological systems exhibit rich dynamic behaviour over a vast range of time and space scales. Unifying many of these diverse phenomena, Dynamics of Biological Systems provides the computational and mathematical platform from which to understand the underlying processes of the phenomena. Through an extensive tour of various biological systems, the text introduces computational methods for simulating spatial diffusion processes in excitable media, such as the human heart, as well as mathematical tools for dealing with systems of nonlinear ordinary and partial differential equations, such as neuronal activation and disease diffusion. The mathematical models and computer simulations offer insight into the dynamics of temporal and spatial biological systems, including cardiac pacemakers, artificial electrical defibrillation, pandemics, pattern formation, flocking behaviour, the interaction of autonomous agents, and hierarchical and structured network topologies. Tools from complex systems and complex networks are also presented for dealing with real phenomenological systems. With exercises and projects in each chapter, this classroom-tested text shows students how to apply a variety of mathematical and computational techniques to model and analyze the temporal and spatial phenomena of biological systems. MATLAB® implementations of algorithms and case studies are available on the author’s website.
This volume is a tutorial for the study of dynamical systems on networks. It discusses both methodology and models, including spreading models for social and biological contagions. The authors focus especially on “simple” situations that are analytically tractable, because they are insightful and provide useful springboards for the study of more complicated scenarios. This tutorial, which also includes key pointers to the literature, should be helpful for junior and senior undergraduate students, graduate students, and researchers from mathematics, physics, and engineering who seek to study dynamical systems on networks but who may not have prior experience with graph theory or networks. Mason A. Porter is Professor of Nonlinear and Complex Systems at the Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, UK. He is also a member of the CABDyN Complexity Centre and a Tutorial Fellow of Somerville College. James P. Gleeson is Professor of Industrial and Applied Mathematics, and co-Director of MACSI, at the University of Limerick, Ireland.
Biological Network Analysis: Trends, Approaches, Graph Theory, and Algorithms considers three major biological networks, including Gene Regulatory Networks (GRN), Protein-Protein Interaction Networks (PPIN), and Human Brain Connectomes. The book's authors discuss various graph theoretic and data analytics approaches used to analyze these networks with respect to available tools, technologies, standards, algorithms and databases for generating, representing and analyzing graphical data. As a wide variety of algorithms have been developed to analyze and compare networks, this book is a timely resource. - Presents recent advances in biological network analysis, combining Graph Theory, Graph Analysis, and various network models - Discusses three major biological networks, including Gene Regulatory Networks (GRN), Protein-Protein Interaction Networks (PPIN) and Human Brain Connectomes - Includes a discussion of various graph theoretic and data analytics approaches