Mathematical Models for Cell Rearrangement PDF Download
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Author: George D. Mostow
Publisher:
ISBN: 9780300015980
Category : Biology
Languages : en
Pages : 271
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Book Description
Author: George D. Mostow
Publisher:
ISBN: 9780300015980
Category : Biology
Languages : en
Pages : 271
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Book Description
Author: Hisao Honda
Publisher: Springer Nature
ISBN: 9811929165
Category : Science
Languages : en
Pages : 195
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Book Description
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.
Author: Viktor V. Ivanov
Publisher: Elsevier
ISBN: 0080462723
Category : Computers
Languages : en
Pages : 355
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Book Description
This book gives the reader a survey of hundreds results in the field of the cell and cell associated objects modeling. Applications to modeling in the areas of AIDS, cancers and life longevity are investigated in this book. - Introduces and proves fundamental properties of evolutionary systems on optimal distribution of their various resources on their internal and external functions - Gives detailed analysis of applications to modeling 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 modeling of the cell and cell associated objects
Author: Lee A. Segel
Publisher: CUP Archive
ISBN: 9780521229258
Category : Mathematics
Languages : en
Pages : 776
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Book Description
Interest in theoretical biology is rapidly growing and this 1981 book attempts to make the theory more accessible to experimentalists. Its primary purpose is to demonstrate to experimental molecular and cellular biologists the possible usefulness of mathematical models. Biologists with a basic command of calculus should be able to learn from the book what assumptions are implied by various types of equations, to understand in broad outline a number of major theoretical concepts, and to be aware of some of the difficulties connected with analytical and numerical solutions of mathematical problems. Thus they should be able to appreciate the significance of theoretical papers in their fields and to communicate usefully with theoreticians in the course of their work.
Author: Khoren Ponsin
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
"Cell death by apoptosis plays a key role in several developmental processes such as tissue sculpting and homeostasis. During embryonic development of the urogenital system in mice, apoptosis plays a crucial role in removing a temporal structure called the Common Nephric Duct (CND), a necessary step to connect the ureter to the bladder epithelium. Evidence suggests that apoptotic cell removal generates pulling forces necessary for tissue rearrangement. Non-professional phagocytosis of apoptotic cells by neighbouring epithelial cells (referred to as non-professional efferocytosis) was observed during CND elimination. In this process, epithelial cells programmed to die are engulfed and subsequently phagocytosed by neighboring cells. This entire process involves five different stages of apoptosis, a cell drift and an apoptotic gradient along the CND. We develop a novel multiscale mathematical model that couples the different stages of efferocytosis and the cell types involved (e.g., apoptotic, phagocyte and engulfed) with the cellular drift equation system (advection) equation to provide spatiotemporal insights about this process.} We use the apoptotic gradient along the CND, the stationary distribution of cells in the different stages and the maintenance of a uniform diameter of the duct to parameterize the model. Using experimental data and boundary conditions, we adapt the model to different physiological conditions, including in vivo wild types, ex vivo non-treated embryos and ex vivo treated embryos. The mathematical model is then employed to perform tasks that are difficult or not possible to be conducted experimentally. With this approach, we quantify the dwell time at each stage of efferocytosis and dissect the relative contribution of efferocytosis, cell extrusion and proliferation individually and in combination to CND shortening/elongation continuously over time. We finally examine the effects of Blebbistatin treatment on CND dynamics and determine the role of actomyosin during CND elimination. Our results suggest that there is significant CND shortening forces in the absence of actomyosin activity, an interesting outcome of this modeling study in view of the generally recognized belief that morphogenetic forces are largely driven primarily by actomyosin activity. Indeed, this work provides an evidence that efferocytosis and actomyosin drive the CND elimination throughout time (i.e., not only at certain time points). It also provides a mathematical spatiotemporal framework for how cellular rearrangement could occur during embryonic development in the CND"--
Author: Daniella Schittler
Publisher: Logos Verlag Berlin GmbH
ISBN: 3832539352
Category : Mathematics
Languages : en
Pages : 192
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Book Description
The quantitative understanding of changes in cell types, referred to as cell type transitions, is fundamental to advance fields such as stem cell research, immunology, and cancer therapies. This thesis provides a mathematical modeling framework to simulate and analyze cell type transitions. The novel methodological approaches and models presented here address diverse levels which are essential in this context: Gene regulatory network models represent the cell type-determining gene expression dynamics. Here, a novel construction method for gene regulatory network models is introduced, which allows to transfer results from generic low-dimensional to realistic high-dimensional gene regulatory network models. For populations of cells, a generalized model class is proposed that accounts for multiple cell types, division numbers, and the full label distribution. Analysis and solution methods are presented for this new model class, which cover common cell population experiments and allow to exploit the full information from data. The modeling and analysis methods presented here connect formerly isolated approaches, and thereby contribute to a holistic framework for the quantitative understanding of cell type transitions.
Author: Michael C. Mackey
Publisher: Springer
ISBN: 3319453181
Category : Medical
Languages : en
Pages : 128
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Book Description
This is a short and self-contained introduction to the field of mathematical modeling of gene-networks in bacteria. As an entry point to the field, we focus on the analysis of simple gene-network dynamics. The notes commence with an introduction to the deterministic modeling of gene-networks, with extensive reference to applicable results coming from dynamical systems theory. The second part of the notes treats extensively several approaches to the study of gene-network dynamics in the presence of noise—either arising from low numbers of molecules involved, or due to noise external to the regulatory process. The third and final part of the notes gives a detailed treatment of three well studied and concrete examples of gene-network dynamics by considering the lactose operon, the tryptophan operon, and the lysis-lysogeny switch. The notes contain an index for easy location of particular topics as well as an extensive bibliography of the current literature. The target audience of these notes are mainly graduates students and young researchers with a solid mathematical background (calculus, ordinary differential equations, and probability theory at a minimum), as well as with basic notions of biochemistry, cell biology, and molecular biology. They are meant to serve as a readable and brief entry point into a field that is currently highly active, and will allow the reader to grasp the current state of research and so prepare them for defining and tackling new research problems.
Author: Frederik Graw
Publisher: Springer
ISBN: 3319458337
Category : Technology & Engineering
Languages : en
Pages : 167
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Book Description
This contributed volume comprises research articles and reviews on topics connected to the mathematical modeling of cellular systems. These contributions cover signaling pathways, stochastic effects, cell motility and mechanics, pattern formation processes, as well as multi-scale approaches. All authors attended the workshop on "Modeling Cellular Systems" which took place in Heidelberg in October 2014. The target audience primarily comprises researchers and experts in the field, but the book may also be beneficial for graduate students.
Author: Philip K. Maini
Publisher: Springer Science & Business Media
ISBN: 1461301335
Category : Mathematics
Languages : en
Pages : 327
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Book Description
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.
Author: Tetsuji Tokihiro
Publisher: Springer Nature
ISBN: 981167132X
Category : Science
Languages : en
Pages : 179
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Book Description
This book describes the dynamics of biological cells and their mathematical modeling. The topics cover the dynamics of RNA polymerases in transcription, construction of vascular networks in angiogenesis, and synchronization of cardiomyocytes. Statistical analysis of single cell dynamics and classification of proteins by mathematical modeling are also presented. The book provides the most up-to-date information on both experimental results and mathematical models that can be used to analyze cellular dynamics. Novel experimental results and approaches to understand them will be appealing to the readers. Each chapter contains 1) an introductory description of the phenomenon, 2) explanations about the mathematical technique to analyze it, 3) new experimental results, 4) mathematical modeling and its application to the phenomenon. Elementary introductions for the biological phenomenon and mathematical approach to them are especially useful for beginners. The importance of collaboration between mathematics and biological sciences has been increasing and providing new outcomes. This book gives good examples of the fruitful collaboration between mathematics and biological sciences.
