Mathematical Model for Studying Combined Effect of Individual Cell Behavior on Developing Tissue Shape in Plants

Mathematical Model for Studying Combined Effect of Individual Cell Behavior on Developing Tissue Shape in Plants

Author: Mikahl Banwarth-Kuhn

Publisher:

Published: 2019

Total Pages: 97

ISBN-13: 9781392170335

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The development of an organ or organism is a complex process that includes many interacting components. Scientific inquiries in developmental biology have motivated the creation of novel mathematical tools to better understand how distributions of cellular identities and phenotypes are attained through spatiotemporal regulation of cell behaviors and gene regulation. One of the central problems in animal and plant developmental biology is deciphering how chemical and mechanical signals interact within a tissue to produce organs of defined size, shape, and function. Plant development is much different from animals since the majority of organs are continually produced throughout the life of the plant and the presence of the cell wall imposes a unique constraint on cell behaviors. How exactly cell wall mechanical properties influence cell behaviors that lead to stem cell maintenance and correct organ formation is still largely unknown. To address this problem, a novel, subcellular element computational model of growth of stem cells within the multilayered shoot apical meristem (SAM) of Arabidopsis thaliana is developed and calibrated using experimental data. Novel features of the model include separate, detailed descriptions of cell wall extensibility and mechanical stiffness, deformation of the middle lamella, and increase in cytoplasmic pressure generating internal turgor pressure. The model is used to test novel hypothesized mechanisms of formation of the shape and structure of the growing, multilayered SAM based on WUS concentration of individual cells controlling cell growth rates and layer-dependent anisotropic mechanical properties of subcellular components of individual cells determining anisotropic cell expansion directions. Model simulations also provide a detailed prediction of distribution of stresses in the growing tissue which can be tested in future experiments.


Mathematical Models of Cell-Based Morphogenesis

Mathematical Models of Cell-Based Morphogenesis

Author: Hisao Honda

Publisher: Springer Nature

Published: 2022-06-27

Total Pages: 195

ISBN-13: 9811929165

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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.


Dynamics of Cell and Tissue Motion

Dynamics of Cell and Tissue Motion

Author: Wolfgang Alt

Publisher: Springer Science & Business Media

Published: 1997

Total Pages: 364

ISBN-13: 9783764357818

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Understanding the dynamics of cell and tissue motion forms an essential step in understanding the dynamics of life and biological self-organization. Biological motion is one of the most obvious expressions of self-organization, as it requires autonomous creation and regulated action of forces leading to shape formation and translocation of cells and tissues. The topics of the book include intracellular motility and cytoplasma dynamics (e.g. cell division), single cell movement in varying extracellular media (e.g. chemotaxis or contact guidance), cell aggregation and cooperative motion (e.g. cellular swarms or slugs) and, finally, cell-cell interactions in developing tissues (e.g. embryogenesis or plant movement). The dynamics underlying biological motion are explained, on the one hand, by various methods of image processing and correlation analysis, and on the other hand by using physico-chemical theories, developing corresponding mathematical models and performing continuum field or stochastic simulations. Thus, the study is of an interdisciplinary character typically found in theoretical and mathematical biology. Its presentation is intended to reach a broad audience – from theoretically interested bioscientists, physicians and biophysicists to applied mathematicians interested in the application of nonlinear dynamical systems and simulation algorithms. The most important feature of the book is that it considers possible synergetic mechanisms of interaction and cooperation on different microscopic levels: on the molecular level of cytoskeletal polymers, membrane proteins and extracellular matrix filaments, as well as on the level of cells and cellular tissues. New results concern the aspects of filament or cell alignment, various modes of force transduction and the formation of global stress fields. The latter aspect of mechanical cell-cell communication is emphasized in order to complement the much more well-studied phenomena of chemical, genetical or electrophysical communication.


Mathematical Modelling in Plant Biology

Mathematical Modelling in Plant Biology

Author: Richard J. Morris

Publisher: Springer

Published: 2018-11-05

Total Pages: 230

ISBN-13: 3319990705

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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.


Mathematical Modeling of Biological Systems, Volume I

Mathematical Modeling of Biological Systems, Volume I

Author: Andreas Deutsch

Publisher: Springer Science & Business Media

Published: 2007-06-15

Total Pages: 378

ISBN-13: 0817645586

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Volume I 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. The chapters are thematically organized into the following main areas: cellular biophysics, regulatory networks, developmental biology, biomedical applications, data analysis and model validation. 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.


Mathematical Models and Methods for Living Systems

Mathematical Models and Methods for Living Systems

Author: Luigi Preziosi

Publisher: Springer

Published: 2016-11-09

Total Pages: 332

ISBN-13: 3319426796

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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.


Single-Cell-Based Models in Biology and Medicine

Single-Cell-Based Models in Biology and Medicine

Author: Alexander Anderson

Publisher: Springer Science & Business Media

Published: 2007-08-08

Total Pages: 346

ISBN-13: 376438123X

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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.


Mathematical Models of the Cell and Cell Associated Objects

Mathematical Models of the Cell and Cell Associated Objects

Author: Viktor V. Ivanov

Publisher: Elsevier

Published: 2006-05-10

Total Pages: 355

ISBN-13: 0080462723

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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


Multi-Scale Modeling for Morphogenesis of Healthy and Diseased Tissue

Multi-Scale Modeling for Morphogenesis of Healthy and Diseased Tissue

Author: Seth Amin Figueroa

Publisher:

Published: 2017

Total Pages: 163

ISBN-13: 9780355307382

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In organisms, tissue development and maintenance must be precisely timed and spatially coordinated to ensure proper form and function. This can be difficult both to develop and to maintain in the complex environments present in organisms, and thus a mechanism that can be finely tuned and regulated must be present. Therefore, when studying the underlying principles of morphogenesis, it is important to consider the crucial biochemical, cellular, and tissue scales simultaneously. This creates a need for a mathematical and computational approach to understanding the complex biology of development. One way of achieving a high level of precision of control is through stem cell lineages. These lineages employ the use of stem cells and their progeny to maintain certain properties necessary for proper tissue function. One such system is found in the stratified inter-follicular epidermis. Here, we develop and use a two dimensional, multi-scale, cell lineage model to explore the molecular, cellular, and physical properties of healthy and diseased epidermis. The model recapitulates a variety of healthy epithelial tissue shapes, including the formation and maintenance of undulating structures, known as rete-ridges. We find that the dermis compliance and the cell-cell adhesion at the dermis-epidermis junction, in conjunction with internal physical pressures due to cell lineage dynamics, play an important role in the tissue morphology. We explore these dynamics to get a better understanding of morphological changes found in diseased skin, including thickening of the tissue and deformation of rete-ridges. Another system in which the molecular mechanisms and cell dynamics driving morphogenesis remains unclear is in diversification of feather vane shapes. Here, we integrate a two dimensional, multi modular mathematical model with transcriptome profiling to elucidate the anisotropic signaling modules which break symmetry, alter cell shape, and generate diverse feather shapes. Overall, this work provides multi-dimensional frameworks to study development and applies them to various biological tissues to better understand their underlying processes.