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 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 Cellular Biophysics and Modeling written by Greg Conradi Smith and published by Cambridge University Press. This book was released on 2019-03-14 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: What every neuroscientist should know about the mathematical modeling of excitable cells, presented at an introductory level.
Download or read book Mathematical Analysis of Complex Cellular Activity written by Richard Bertram and published by Springer. This book was released on 2015-10-09 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains two review articles on mathematical physiology that deal with closely related topics but were written and can be read independently. The first article reviews the basic theory of calcium oscillations (common to almost all cell types), including spatio-temporal behaviors such as waves. The second article uses, and expands on, much of this basic theory to show how the interaction of cytosolic calcium oscillators with membrane ion channels can result in highly complex patterns of electrical spiking. Through these examples one can see clearly how multiple oscillatory processes interact within a cell, and how mathematical methods can be used to understand such interactions better. The two reviews provide excellent examples of how mathematics and physiology can learn from each other, and work jointly towards a better understanding of complex cellular processes. Review 1: Richard Bertram, Joel Tabak, Wondimu Teka, Theodore Vo, Martin Wechselberger: Geometric Singular Perturbation Analysis of Bursting Oscillations in Pituitary Cells Review 2: Vivien Kirk, James Sneyd: Nonlinear Dynamics of Calcium
Download or read book Master s Theses Directories written by and published by . This book was released on 2003 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Education, arts and social sciences, natural and technical sciences in the United States and Canada".
Download or read book Truth Revealed written by United States. Congress. House. Committee on Government Reform. Subcommittee on Human Rights and Wellness and published by . This book was released on 2004 with total page 338 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 Cumulated Index Medicus written by and published by . This book was released on 1971 with total page 1164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 with total page 196 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 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 Differential Equations Models in Biology Epidemiology and Ecology written by Stavros Busenberg and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past forty years have been the stage for the maturation of mathematical biolo~ as a scientific field. The foundations laid by the pioneers of the field during the first half of this century have been combined with advances in ap plied mathematics and the computational sciences to create a vibrant area of scientific research with established research journals, professional societies, deep subspecialty areas, and graduate education programs. Mathematical biology is by its very nature cross-disciplinary, and research papers appear in mathemat ics, biology and other scientific journals, as well as in the specialty journals devoted to mathematical and theoretical biology. Multiple author papers are common, and so are collaborations between individuals who have academic bases in different traditional departments. Those who seek to keep abreast of current trends and problems need to interact with research workers from a much broader spectrum of fields than is common in the traditional mono-culture disciplines. Consequently, it is beneficial to have occasions which bring together significant numbers of workers in this field in a forum that encourages the exchange of ideas and which leads to a timely publication of the work that is presented. Such an occasion occurred during January 13 to 16, 1990 when almost two hun dred research workers participated in an international conference on Differential Equations and Applications to Biology and Population Dynamics which was held in Claremont.
Download or read book Simulating Analyzing and Animating Dynamical Systems written by Bard Ermentrout and published by SIAM. This book was released on 2002-01-01 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students provides sophisticated numerical methods for the fast and accurate solution of a variety of equations, including ordinary differential equations, delay equations, integral equations, functional equations, and some partial differential equations, as well as boundary value problems. It introduces many modeling techniques and methods for analyzing the resulting equations. Instructors, students, and researchers will all benefit from this book, which demonstrates how to use software tools to simulate and study sets of equations that arise in a variety of applications. Instructors will learn how to use computer software in their differential equations and modeling classes, while students will learn how to create animations of their equations that can be displayed on the World Wide Web. Researchers will be introduced to useful tricks that will allow them to take full advantage of XPPAUT's capabilities.
Download or read book Mathematical Foundations of Neuroscience written by G. Bard Ermentrout and published by Springer Science & Business Media. This book was released on 2010-07-01 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book applies methods from nonlinear dynamics to problems in neuroscience. It uses modern mathematical approaches to understand patterns of neuronal activity seen in experiments and models of neuronal behavior. The intended audience is researchers interested in applying mathematics to important problems in neuroscience, and neuroscientists who would like to understand how to create models, as well as the mathematical and computational methods for analyzing them. The authors take a very broad approach and use many different methods to solve and understand complex models of neurons and circuits. They explain and combine numerical, analytical, dynamical systems and perturbation methods to produce a modern approach to the types of model equations that arise in neuroscience. There are extensive chapters on the role of noise, multiple time scales and spatial interactions in generating complex activity patterns found in experiments. The early chapters require little more than basic calculus and some elementary differential equations and can form the core of a computational neuroscience course. Later chapters can be used as a basis for a graduate class and as a source for current research in mathematical neuroscience. The book contains a large number of illustrations, chapter summaries and hundreds of exercises which are motivated by issues that arise in biology, and involve both computation and analysis. Bard Ermentrout is Professor of Computational Biology and Professor of Mathematics at the University of Pittsburgh. David Terman is Professor of Mathematics at the Ohio State University.
Download or read book Multiple Time Scales written by Jeremiah U. Brackbill and published by Academic Press. This book was released on 2014-05-10 with total page 457 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiple Time Scales presents various numerical methods for solving multiple-time-scale problems. The selection first elaborates on considerations on solving problems with multiple scales; problems with different time scales; and nonlinear normal-mode initialization of numerical weather prediction models. Discussions focus on analysis of observations, nonlinear analysis, systems of ordinary differential equations, and numerical methods for problems with multiple scales. The text then examines the diffusion-synthetic acceleration of transport iterations, with application to a radiation hydrodynamics problem and implicit methods in combustion and chemical kinetics modeling. The publication ponders on molecular dynamics and Monte Carlo simulations of rare events; direct implicit plasma simulation; orbit averaging and subcycling in particle simulation of plasmas; and hybrid and collisional implicit plasma simulation models. Topics include basic moment method, electron subcycling, gyroaveraged particle simulation, and the electromagnetic direct implicit method. The selection is a valuable reference for researchers interested in pursuing further research on the use of numerical methods in solving multiple-time-scale problems.
Download or read book Mathematical Modeling in Systems Biology written by Brian P. Ingalls and published by MIT Press. This book was released on 2022-06-07 with total page 423 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Invertebrate Nervous Systems Their Significance for Mammalian Neurophysiology written by Cornelis Adrianus Gerrit Wiersma and published by . This book was released on 1967 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: A biography of the Austrian scientist whose discoveries in nuclear physics played a major part in developing atomic energy.
Download or read book Neuronal Dynamics written by Wulfram Gerstner and published by Cambridge University Press. This book was released on 2014-07-24 with total page 591 pages. Available in PDF, EPUB and Kindle. Book excerpt: This solid introduction uses the principles of physics and the tools of mathematics to approach fundamental questions of neuroscience.
