Download or read book Mathematical Models of Cell Based Morphogenesis written by Hisao Honda and published by Springer Nature. This book was released on 2022-06-27 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the shape formation of living organisms using mathematical models. Genes are deeply related to the shape of living organisms, and elucidation of a pathway of shape formation from genes is one of the fundamental problems in biology. Mathematical cell models are indispensable tools to elucidate this problem. The book introduces two mathematical cell models, the cell center model and the vertex model, with their applications. The cell center model is applied to elucidate the formation of neat cell arrangements in epidermis, cell patterns consisting of heterogeneous-sized cells, capillary networks, and the branching patterns of blood vessels. The vertex model is applied to elucidate the wound healing mechanisms of the epithelium and ordered pattern formation involving apoptosis. Pattern formation with differential cell adhesion is also described. The vertex model is then extended from a two-dimensional (2D) to a three-dimensional (3D) model. A cell aggregate involving a large cavity is described to explain the development of the mammalian blastocyst or the formation of an epithelial vesicle. Epithelial tissues and the polarity formation process of the epithelium are also explained. The vertex model also recapitulates active remodeling of tissues and describes the twisting of tissue that contributes to understanding the cardiac loop formation of the embryonic tube. The book showcases that mathematical cell models are indispensable tools to understand the shape formation of living organisms. Successful contribution of the mathematical cell models means that the remodeling of collective cells is self-construction. Examining the successive iterations of self-constructions leads to understanding the remarkable and mysterious morphogenesis that occurs during the development of living organisms. The intended readers of this book are not only theoretical or mathematical biologists, but also experimental and general biologists, including undergraduate and postgraduate students who are interested in the relationship between genes and morphogenesis.

Download or read book Single Cell Based Models in Biology and Medicine written by Alexander Anderson and published by Springer Science & Business Media. This book was released on 2007-08-08 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at postgraduate students in a variety of biology-related disciplines, this volume presents a collection of mathematical and computational single-cell-based models and their application. The main sections cover four general model groupings: hybrid cellular automata, cellular potts, lattice-free cells, and viscoelastic cells. Each section is introduced by a discussion of the applicability of the particular modelling approach and its advantages and disadvantages, which will make the book suitable for students starting research in mathematical biology as well as scientists modelling multicellular processes.

Download or read book Mathematical Models for Biological Pattern Formation written by Philip K. Maini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 121st IMA volume, entitled MATHEMATICAL MODELS FOR BIOLOGICAL PATTERN FORMATION is the first of a new series called FRONTIERS IN APPLICATION OF MATHEMATICS. The FRONTIERS volumes are motivated by IMA pro grams and workshops, but are specially planned and written to provide an entree to and assessment of exciting new areas for the application of mathematical tools and analysis. The emphasis in FRONTIERS volumes is on surveys, exposition and outlook, to attract more mathematicians and other scientists to the study of these areas and to focus efforts on the most important issues, rather than papers on the most recent research results aimed at an audience of specialists. The present volume of peer-reviewed papers grew out of the 1998-99 IMA program on "Mathematics in Biology," in particular the Fall 1998 em phasis on "Theoretical Problems in Developmental Biology and Immunol ogy." During that period there were two workshops on Pattern Formation and Morphogenesis, organized by Professors Murray, Maini and Othmer. James Murray was one of the principal organizers for the entire year pro gram. I am very grateful to James Murray for providing an introduction, and to Philip Maini and Hans Othmer for their excellent work in planning and preparing this first FRONTIERS volume. I also take this opportunity to thank the National Science Foundation, whose financial support of the IMA made the Mathematics in Biology pro gram possible.

Download or read book Mathematical Models of Morphogenesis written by René Thom and published by . This book was released on 1983 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Pattern Formation in Morphogenesis written by Vincenzo Capasso and published by Springer Science & Business Media. This book was released on 2012-10-02 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Pattern Formation in Morphogenesis is a rich source of interesting and challenging mathematical problems. The volume aims at showing how a combination of new discoveries in developmental biology and associated modelling and computational techniques has stimulated or may stimulate relevant advances in the field. Finally it aims at facilitating the process of unfolding a mutual recognition between Biologists and Mathematicians of their complementary skills, to the point where the resulting synergy generates new and novel discoveries. It offers an interdisciplinary interaction space between biologists from embryology, genetics and molecular biology who present their own work in the perspective of the advancement of their specific fields, and mathematicians who propose solutions based on the knowledge grasped from biologists.

Download or read book Mathematical Models and Methods for Living Systems written by Luigi Preziosi and published by Springer. This book was released on 2016-11-09 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of these lecture notes is to give an introduction to several mathematical models and methods that can be used to describe the behaviour of living systems. This emerging field of application intrinsically requires the handling of phenomena occurring at different spatial scales and hence the use of multiscale methods.Modelling and simulating the mechanisms that cells use to move, self-organise and develop in tissues is not only fundamental to an understanding of embryonic development, but is also relevant in tissue engineering and in other environmental and industrial processes involving the growth and homeostasis of biological systems. Growth and organization processes are also important in many tissue degeneration and regeneration processes, such as tumour growth, tissue vascularization, heart and muscle functionality, and cardio-vascular diseases.

Download or read book Mathematical Modelling in Plant Biology written by Richard J. Morris and published by Springer. This book was released on 2018-11-05 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Progress in plant biology relies on the quantification, analysis and mathematical modeling of data over different time and length scales. This book describes common mathematical and computational approaches as well as some carefully chosen case studies that demonstrate the use of these techniques to solve problems at the forefront of plant biology. Each chapter is written by an expert in field with the goal of conveying concepts whilst at the same time providing sufficient background and links to available software for readers to rapidly build their own models and run their own simulations. This book is aimed at postgraduate students and researchers working the field of plant systems biology and synthetic biology, but will also be a useful reference for anyone wanting to get into quantitative plant biology.

Download or read book Mathematical Models for Cell Rearrangement written by George D. Mostow and published by . This book was released on 1975-01-01 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Models of the Cell and Cell Associated Objects written by Viktor Vladimirovich Ivanov and published by Elsevier Science Limited. This book was released on 2006 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book contains five main parts: Introduction: Evolutionary System and Development Modelling; Part I: A Survey of MM of CAO (cell associated objects); Part II: MM (mathematical models) of Development; Part III: Introduction to Applications; Appendix: Mathematics of Development. The part I gives the reader a survey of hundreds results in the field of the cell and cell associated objects modelling, which are not easy accessible. The original four parts of the book have no analogy in the literature, except the previous book of the first author 'Model Development and Optimization', KAP, 1999, and the book 'Mathematical Modeling in Economics, Ecology and the Environment', KAP, 1999, by N. Hritonenko, Yu. Yatsenko (Yu. Yatsenko is a pupil of the first author of the cell book). The present book is different from the previous mainly by much more profound investigation of such a complicated object as the cell and by much more detailed description of applications to modelling AIDS, cancers, and life longevity. Key features: - Inlet novel class of non-linear mathematical models based on the general theory of evolutionary systems and their development . - Introducing and proving fundamental properties of evolutionary systems on optimal distribution of their various resources on their internal and external functions. - Proof of effective applicability of that class of models to complicated objects such as the cell and the immune network . - Detailed modelling complicated processes such as the cell cycle, protein folding, immune network response, etc. - Detailed analysis of applications to modelling AIDS, cancers, and life longevity. - Introducing and grounding the respective numerical algorithms and software. - Detailed analysis of hundreds of scientific works in the field of mathematical modelling of the cell and cell associated objects. Key features: - Inlet novel class of non-linear mathematical models based on the general theory of evolutionary systems and their development . - Introducing and proving fundamental properties of evolutionary systems on optimal distribution of their various resources on their internal and external functions. - Proof of effective applicability of that class of models to complicated objects such as the cell and the immune network . - Detailed modelling complicated processes such as the cell cycle, protein folding, immune network response, etc. - Detailed analysis of applications to modelling AIDS, cancers, and life longevity. - Introducing and grounding the respective numerical algorithms and software. - Detailed analysis of hundreds of scientific works in the field of mathematical modelling of the cell and cell associated objects.

Download or read book Cellular Automaton Modeling of Biological Pattern Formation written by Andreas Deutsch and published by Springer Science & Business Media. This book was released on 2007-12-26 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a challenging application field of cellular automata: pattern formation in biological systems, such as the growth of microorganisms, dynamics of cellular tissue and tumors, and formation of pigment cell patterns. These phenomena, resulting from complex cellular interactions, cannot be deduced solely from experimental analysis, but can be more easily examined using mathematical models, in particular, cellular automaton models. While there are various books treating cellular automaton modeling, this interdisciplinary work is the first one covering biological applications. The book is aimed at researchers, practitioners, and students in applied mathematics, mathematical biology, computational physics, bioengineering, and computer science interested in a cellular automaton approach to biological modeling.

Download or read book Allgemeine Entwickelungsgeschichte Der Organismen written by Ernst Haeckel von and published by . This book was released on 1866 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Models in Biology written by Leah Edelstein-Keshet and published by SIAM. This book was released on 1988-01-01 with total page 629 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.

Download or read book Mathematical Models in Developmental Biology written by Stephen Childress and published by . This book was released on 1978 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Multiscale Modeling of Developmental Systems written by and published by Academic Press. This book was released on 2007-12-18 with total page 605 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical and computational biology is playing an increasingly important role in the biological sciences. This science brings forward unique challenges, many of which are, at the moment, beyond the theoretical techniques available. Developmental biology, due to its complexity, has lagged somewhat behind its sister disciplines (such as molecular biology and population biology) in making use of quantitative modeling to further biological understanding. This volume comprises work that is among the best developmental modeling available and we feel it will do much to remedy this situation. This book is aimed at all those with an interest in the interdisciplinary field of computer and mathematical modeling of multi-cellular and developmental systems. It is also a goal of the Editors to attract more developmental biologists to consider integrating modeling components into their research. Most importantly, this book is intended to serve as a portal into this research area for younger scientists – especially graduate students and post-docs, from both biological and quantitative backgrounds. * Articles written by leading exponents in the field * Provides techniques to address multiscale modeling * Coverage includes a wide spectrum of modeling approaches * Includes descriptions of the most recent advances in the field

Download or read book Mathematical Models in Biological Discovery written by D.L. Solomon and published by Springer Science & Business Media. This book was released on 2013-03-13 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: When I was asked to help organize an American Association for the Advancement of Science symposium about how mathematical models have con tributed to biology, I agreed immediately. The subject is of immense importance and wide-spread interest. However, too often it is discussed in biologically sterile environments by "mutual admiration society" groups of "theoreticians", many of whom have never seen, and most of whom have never done, an original scientific experiment with the biolog ical materials they attempt to describe in abstract (and often prejudiced) terms. The opportunity to address the topic during an annual meeting of the AAAS was irresistable. In order to try to maintain the integrity ;,f the original intent of the symposium, it was entitled, "Contributions of Mathematical Models to Biological Discovery". This symposium was organized by Daniel Solomon and myself, held during the 141st annual meeting of the AAAS in New York during January, 1975, sponsored by sections G and N (Biological and Medical Sciences) of the AAAS and the North American Regions of the Biometric Society, and supported by grant BMS 75-0280) from the National Science Foundation. What follows in this volume are papers by nine of the participants who not only felt that they had something to say in a symposium entitled, "Contributions of Mathematical Models to Biological Discovery", but who falso were willing to record their ideas in more detail here.

Download or read book Foundations of Mathematical Biology written by Robert J. Rosen and published by Elsevier. This book was released on 2013-10-02 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Foundations of Mathematical Biology, Volume II: Cellular Systems describes the properties of cellular systems and their relationship to the development of multicellular organisms. This volume is composed of five chapters that present the mathematical tools applied in evaluating these systems. Chapters 1 illustrates the use of continuous time systems to examine the relationship between the properties of individual cells and the general problems of morphogenesis in developing systems, specifically how these properties could manifest themselves in morphological terms. Chapter 2 demonstrates the systems of rate equations or first-order differential equations to deal with the regulation of individual chemical processes and sequences of such processes, at both the genetic and metabolic levels. Chapter 3 discusses the application of the theory of automata to the evaluation of the concept and principles of embryology, while Chapter 4 presents some relational cell models to study the metabolism-repair cellular systems. Chapter 5 looks into the concept and systems of a compartment. This book will prove useful to mathematical and cell biologists and researchers.

Download or read book A Primer in Mathematical Models in Biology written by Lee A. Segel and published by SIAM. This book was released on 2013-05-09 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook on mathematical modelling techniques with powerful applications to biology, combining theoretical exposition with exercises and examples.