Download or read book Waves in Mathematical Models of Intracellular Calcium and Other Excitable Systems written by Wenjun Zhang and published by . This book was released on 2011 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: Oscillations in cytoplasmic calcium concentration are a crucial control mechanism in almost every cell type. Two important classes of oscillation are of particular interest: solitary and periodic waves. Both types of waves are commonly observed in physical experiments and found in mathematical models of calcium dynamics and other excitable systems. In this thesis, we try to understand these two classes of wave solutions. We first investigate wave solutions of the canonical excitable model, the FitzHugh-Nagumo (FHN) equations. We analyze the FHN equations using geometric singular perturbation theory and numerical integration, and find some new codimension-two organizing centres of the overall dynamics. Many analytical results about the FHN model in its classical form have already been established. We devise a transformation to change the form of the FHN equations we study into the classical form to make use of the results. This enables us to show how basic features of the bifurcation structure of the FHN equations arise from the singular limit. We then study waves of a representative calcium model. We analyze the dynamics of the calcium model in the singular limit, and show how homoclinic and Hopf bifurcations of the full system arise as perturbations of singular homoclinic and Hopf bifurcations. We compare the wave solutions in the FHN model and the calcium model, and show that the dynamics of the two models differ in some respects (most importantly, in the way in which diffusion enters the equations). We conclude that the FHN model should not uniformly be used as a prototypical model for calcium dynamics. Motivated by phenomena seen in the FHN and calcium models, we then investigate reduction techniques for excitable systems, including the quasi-steady state approximation and geometric singular perturbation theory, and show that criticality of Hopf bifurcations may be changed when applying these reduction methods to slow-fast biophysical systems. This suggests that great care should be taken when using reduction techniques such as these, to ensure that spurious conclusions about the dynamics of a model are not drawn from the dynamics of a reduced version of the model. Finally, we describe the class of numerical algorithms used to compute features of the detailed bifurcation sets for the FHN and calcium models, and show how these were used to locate a non-structurally stable heteroclinic connection between periodic orbits in a calcium model; this is the first time such a global bifurcation has been computed.
Download or read book Mathematical Modeling and Analysis of Intracellular Calcium Dynamics written by Alireza Atri and published by . This book was released on 1996 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Models of Calcium Signalling written by Geneviève Dupont and published by Springer. This book was released on 2016-06-07 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the ways in which mathematical, computational, and modelling methods can be used to help understand the dynamics of intracellular calcium. The concentration of free intracellular calcium is vital for controlling a wide range of cellular processes, and is thus of great physiological importance. However, because of the complex ways in which the calcium concentration varies, it is also of great mathematical interest.This book presents the general modelling theory as well as a large number of specific case examples, to show how mathematical modelling can interact with experimental approaches, in an interdisciplinary and multifaceted approach to the study of an important physiological control mechanism. Geneviève Dupont is FNRS Research Director at the Unit of Theoretical Chronobiology of the Université Libre de Bruxelles; Martin Falcke is head of the Mathematical Cell Physiology group at the Max Delbrück Center for Molecular Medicine, Berlin; Vivien Kirk is an Associate Professor in the Department of Mathematics at the University of Auckland, New Zealand; James Sneyd is a Professor in the Department of Mathematics at The University of Auckland, New Zealand.
Download or read book Some Mathematical Questions in Biology written by Hans G. Othmer and published by American Mathematical Soc.. This book was released on 1989-12-31 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the 22nd annual Symposium on Some Mathematical Questions in Biology, held in May, 1988 in Las Vegas. The diversity of current research in the dynamics of excitable media is reflected in the six papers in this volume. The topics covered include a mathematical treatment of phase-locking, numerical results for models of synchronization in the mammalian sinoatrial node, simulations of a model of the hippocampus, and wave propagation in excitable media. Both experimental and theoretical aspects are treated. Aimed at mathematicians, physiologists, and cardiologists, the book requires only background in differential equations. Readers will gain a broad perspective on current research activity in the modeling, analysis, and simulation of systems with excitable media.
Download or read book Mathematical Physiology written by James Keener and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: Divided into two parts, the book begins with a pedagogical presentation of some of the basic theory, with chapters on biochemical reactions, diffusion, excitability, wave propagation and cellular homeostasis. The second, more extensive part discusses particular physiological systems, with chapters on calcium dynamics, bursting oscillations and secretion, cardiac cells, muscles, intercellular communication, the circulatory system, the immune system, wound healing, the respiratory system, the visual system, hormone physiology, renal physiology, digestion, the visual system and hearing.
Download or read book A Bifurcation Analysis of a Mathematical Model of Intracellular Calcium Waves written by David Simpson (MSc.) and published by . This book was released on 2003 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Physiology written by James Keener and published by Springer Science & Business Media. This book was released on 2010-06-04 with total page 1067 pages. Available in PDF, EPUB and Kindle. Book excerpt: Divided into two volumes, the book begins with a pedagogical presentation of some of the basic theory, with chapters on biochemical reactions, diffusion, excitability, wave propagation and cellular homeostasis. The second, more extensive part discusses particular physiological systems, with chapters on calcium dynamics, bursting oscillations and secretion, cardiac cells, muscles, intercellular communication, the circulatory system, the immune system, wound healing, the respiratory system, the visual system, hormone physiology, renal physiology, digestion, the visual system and hearing. New chapters on Calcium Dynamics, Neuroendocrine Cells and Regulation of Cell Function have been included. Reviews from first edition: Keener and Sneyd's Mathematical Physiology is the first comprehensive text of its kind that deals exclusively with the interplay between mathematics and physiology. Writing a book like this is an audacious act! -Society of Mathematical Biology Keener and Sneyd's is unique in that it attempts to present one of the most important subfields of biology and medicine, physiology, in terms of mathematical "language", rather than organizing materials around mathematical methodology. -SIAM review
Download or read book Mathematical Modelling and Analysis of Calcium Oscillations in Excitable and Non excitable Cell Lines written by Bharati Krishna Hegde and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Information is transmitted from the cell surface to various specific targets in the cell via several cellular signaling pathways. Cytosolic free calcium (Ca2+)is one of the most versatile and ubiquitous intracellular messengers since it is able to regulate diverse number of functions such as proliferation, secretion, fertilization, metabolism, learning and memory. In the last couple of years, evidence has been accumulating that Ca2+ ion is able to integrate information from multiple signaling pathways and convert this information into a code which regulates events ranging from contraction to modification of gene expression (Berridge et al. 1998). It was shown that Ca2+ concentration displays oscillatory behavior in response to agonist stimulation in avariety of cells (Goldbeter 1996) and the frequency of these oscillations increases with the concentration of agonist, a behavior called frequency encoding which has led to the concept that many Ca2+-regulated processes are controlled by these codes (Berridge 1998). Although the presence of Ca2+ oscillations and the sources of Ca2+ pools involved is known in many cell types, it is yet not known how the various frequencies of Ca2+ oscillations are converted into codes that regulate the numerous cellular events. Recently a number of cellular targets that decode Ca2+ signals and are tuned to the frequency of Ca2+ oscillations have been identified. Prominent among them arecalcium-calmodulin kinase II (CAM II) and protein kinase C (PKC). The objective of this work is to study and mathematically model the oxytocinand vasopressin-induced Ca2+ oscillations in cells of normal rat liver (Clone 9) and cells of pregnant human myometrium. The proposed model accounts for the receptor-controlled Ca2+ oscillations involving positive feedback leading to activation of phospholipaseC (PLC) and negative feedback from PKC onto G-proteins which simulates many of the features of observed intracellular Ca2+. The model also incorporates the concept that coordinated Ca2+ signals in a group of hepatocytes require bothe(r)ective gap junctions and the presence of agonist at each cell surface. Another objective of this research is to understand the relevance of frequency-encoded signals by performing an analysis of frequencies of Ca2+ oscillations using the Fast Fourier Transform and the Wavelet Transform. The validity of the model was confirmed by using statistical tests to check if the frequencies and amplitudes of the experimental Ca2+ oscillations match with those of the modelled oscillations.
Download or read book Neuro informatics and Neural Modelling written by F. Moss and published by Gulf Professional Publishing. This book was released on 2001-06-26 with total page 1081 pages. Available in PDF, EPUB and Kindle. Book excerpt: How do sensory neurons transmit information about environmental stimuli to the central nervous system? How do networks of neurons in the CNS decode that information, thus leading to perception and consciousness? These questions are among the oldest in neuroscience. Quite recently, new approaches to exploration of these questions have arisen, often from interdisciplinary approaches combining traditional computational neuroscience with dynamical systems theory, including nonlinear dynamics and stochastic processes. In this volume in two sections a selection of contributions about these topics from a collection of well-known authors is presented. One section focuses on computational aspects from single neurons to networks with a major emphasis on the latter. The second section highlights some insights that have recently developed out of the nonlinear systems approach.
Download or read book Mathematical Modeling of Biological Systems Volume II written by Andreas Deutsch and published by Springer Science & Business Media. This book was released on 2007-10-12 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume II of this two-volume, interdisciplinary work is a unified presentation of a broad range of state-of-the-art topics in the rapidly growing field of mathematical modeling in the biological sciences. Highlighted throughout are mathematical and computational apporaches to examine central problems in the life sciences, ranging from the organization principles of individual cells to the dynamics of large populations. The chapters are thematically organized into the following main areas: epidemiology, evolution and ecology, immunology, neural systems and the brain, and innovative mathematical methods and education. The work will be an excellent reference text for a broad audience of researchers, practitioners, and advanced students in this rapidly growing field at the intersection of applied mathematics, experimental biology and medicine, computational biology, biochemistry, computer science, and physics.
Download or read book An Introduction to Mathematical Modeling in Physiology Cell Biology and Immunology written by James Sneyd and published by American Mathematical Soc.. This book was released on 2002 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: In many respects, biology is the new frontier for applied mathematicians. This book demonstrates the important role mathematics plays in the study of some biological problems. It introduces mathematicians to the biological sciences and provides enough mathematics for bioscientists to appreciate the utility of the modelling approach. The book presents a number of diverse topics, such as neurophysiology, cell biology, immunology, and human genetics. It examines how research is done, what mathematics is used, what the outstanding questions are, and how to enter the field. Also given is a brief historical survey of each topic, putting current research into perspective. The book is suitable for mathematicians and biologists interested in mathematical methods in biology.
Download or read book Tutorials in Mathematical Biosciences II written by James Sneyd and published by Springer Science & Business Media. This book was released on 2005-06-22 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a series of models in the general area of cell physiology and signal transduction, with particular attention being paid to intracellular calcium dynamics, and the role played by calcium in a variety of cell types. Calcium plays a crucial role in cell physiology, and the study of its dynamics lends insight into many different cellular processes. In particular, calcium plays a central role in muscular contraction, olfactory transduction and synaptic communication, three of the topics to be addressed in detail in this book. In addition to the models, much of the underlying physiology is presented, so that readers may learn both the mathematics and the physiology, and see how the models are applied to specific biological questions. It is intended primarily as a graduate text or a research reference. It will serve as a concise and up-to-date introduction to all those who wish to learn about the state of calcium dynamics modeling, and how such models are applied to physiological questions.
Download or read book Waves in Neural Media written by Paul C. Bressloff and published by Springer Science & Business Media. This book was released on 2013-10-17 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: Waves in Neural Media: From Single Neurons to Neural Fields surveys mathematical models of traveling waves in the brain, ranging from intracellular waves in single neurons to waves of activity in large-scale brain networks. The work provides a pedagogical account of analytical methods for finding traveling wave solutions of the variety of nonlinear differential equations that arise in such models. These include regular and singular perturbation methods, weakly nonlinear analysis, Evans functions and wave stability, homogenization theory and averaging, and stochastic processes. Also covered in the text are exact methods of solution where applicable. Historically speaking, the propagation of action potentials has inspired new mathematics, particularly with regard to the PDE theory of waves in excitable media. More recently, continuum neural field models of large-scale brain networks have generated a new set of interesting mathematical questions with regard to the solution of nonlocal integro-differential equations. Advanced graduates, postdoctoral researchers and faculty working in mathematical biology, theoretical neuroscience, or applied nonlinear dynamics will find this book to be a valuable resource. The main prerequisites are an introductory graduate course on ordinary differential equations or partial differential equations, making this an accessible and unique contribution to the field of mathematical biology.
Download or read book Understanding Calcium Dynamics written by Martin Falcke and published by Springer Science & Business Media. This book was released on 2003-09-11 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written as a set of tutorial reviews on both experimental facts and theoretical modelling, this volume is intended as an introduction and modern reference in the field for graduate students and researchers in biophysics, biochemistry and applied mathematics.
Download or read book The Endocrinology of Parturition written by Roger Smith (Prof.) and published by Karger Medical and Scientific Publishers. This book was released on 2001-01-01 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Understanding the processes by which we ourselves are born is arguably one of the greatest current challenges in clinical medicine. The prevention of preterm delivery, the cause of 70-80% of neonatal morbidity, has become a key area of research. 'The Endocrinology of Parturition' provides an encyclopedia of human parturition which charts the progress of this goal. ̈ In nineteen chapters of authoritative writing this volume covers a wide range of topics from the comparative endocrinology of mammalian parturition and the socio-economic impact of preterm delivery to the relative merits of current tocolytics. Hormonal actions involved in the process of parturition and the role of different hormones are discussed in detail. Several new approaches like the concept of parturition as a variant of inflammatory response or the role of the wide spectrum of known cytokines are introduced. This timely book in a highly dynamic research area is of special interest to birth-clinical obstetricians, endocrinologists and reproductive biologists as well as general practitioners involved in obstetrics.
Download or read book Journal of the National Cancer Institute written by and published by . This book was released on 1993 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cellular Oscillatory Mechanisms written by Miguel Maroto and published by Springer Science & Business Media. This book was released on 2008-12-19 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Oscillatory dynamics are a central feature of a wide range of biological processes. This text fully explores cellular oscillations, focusing particularly on elucidating the basic mechanisms that underlie these oscillations.
