Mathematical Modeling for Genes to Collective Cell Dynamics
Mathematical Modeling for Genes to Collective Cell Dynamics

Author: Tetsuji Tokihiro

Publisher: Springer Nature

Published: 2022-02-23

Total Pages: 179

ISBN-13: 981167132X

DOWNLOAD EBOOK

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.

Simple Mathematical Models of Gene Regulatory Dynamics
Simple Mathematical Models of Gene Regulatory Dynamics

Author: Michael C. Mackey

Publisher: Springer

Published: 2016-11-09

Total Pages: 128

ISBN-13: 3319453181

DOWNLOAD EBOOK

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.

A mathematical modeling framework to simulate and analyze cell type transitions
A mathematical modeling framework to simulate and analyze cell type transitions

Author: Daniella Schittler

Publisher: Logos Verlag Berlin GmbH

Published: 2015-03-20

Total Pages: 192

ISBN-13: 3832539352

DOWNLOAD EBOOK

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.

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

DOWNLOAD EBOOK

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.

Discrete and Topological Models in Molecular Biology
Discrete and Topological Models in Molecular Biology

Author: Nataša Jonoska

Publisher: Springer Science & Business Media

Published: 2013-12-23

Total Pages: 522

ISBN-13: 3642401937

DOWNLOAD EBOOK

Theoretical tools and insights from discrete mathematics, theoretical computer science, and topology now play essential roles in our understanding of vital biomolecular processes. The related methods are now employed in various fields of mathematical biology as instruments to "zoom in" on processes at a molecular level. This book contains expository chapters on how contemporary models from discrete mathematics – in domains such as algebra, combinatorics, and graph and knot theories – can provide perspective on biomolecular problems ranging from data analysis, molecular and gene arrangements and structures, and knotted DNA embeddings via spatial graph models to the dynamics and kinetics of molecular interactions. The contributing authors are among the leading scientists in this field and the book is a reference for researchers in mathematics and theoretical computer science who are engaged with modeling molecular and biological phenomena using discrete methods. It may also serve as a guide and supplement for graduate courses in mathematical biology or bioinformatics, introducing nontraditional aspects of mathematical biology.

Data-Driven Models for Dynamics of Gene Expression and Single Cells
Data-Driven Models for Dynamics of Gene Expression and Single Cells

Author: Tao Peng

Publisher:

Published: 2017

Total Pages: 146

ISBN-13: 9780355308167

DOWNLOAD EBOOK

This thesis uses mathematical models to study the dynamics of biological systems under the single cell level. In the first chapter we study a minimal gene regulatory network permissive of multi-lineage mesenchymal stem cell differentiation into four cell fates. We present a continuous model that is able to describe the cell fate transitions that occur during differentiation, and analyze its dynamics with tools from multistability, bifurcation, and cell fate landscape analysis, and via stochastic simulation. In the second chapter we adapt a classical self-organizing-map approach to single-cell gene expression data, such as those based on qPCR and RNA-seq. In this method, a cellular state map (CSM) is derived and employed to identify cellular states inherited in a population of measured single cells. Cells located in the same basin of the CSM are considered as in one cellular state while barriers between the basins provide information on transitions among the cellular states. Consequently, paths of cellular state transitions (e.g. differentiation) and a temporal ordering of the measured single cells are obtained. In the third chapter on the basis of the functional mapping assays of primary visual cortex, we conducted a quantitative assessment of both excitatory and inhibitory synaptic laminar connections to excitatory cells at single cell resolution, establishing precise layer-by-layer synaptic wiring diagrams of excitatory and inhibitory neurons in the visual cortex inferred by the mathematical model. In the fourth chapter we constructed a multi-scale mathematical model integrating the gene regulatory network and cell lineage to study the functions of key genes in controlling mouse embryonic epidermis development. In the fifth chapter we studied the selections of models when prior information is provided to infer the gene regulatory network combining the expression data and ChIP-seq data.

Computational Modeling Of Gene Regulatory Networks - A Primer
Computational Modeling Of Gene Regulatory Networks - A Primer

Author: Hamid Bolouri

Publisher: World Scientific Publishing Company

Published: 2008-08-13

Total Pages: 341

ISBN-13: 1848168187

DOWNLOAD EBOOK

This book serves as an introduction to the myriad computational approaches to gene regulatory modeling and analysis, and is written specifically with experimental biologists in mind. Mathematical jargon is avoided and explanations are given in intuitive terms. In cases where equations are unavoidable, they are derived from first principles or, at the very least, an intuitive description is provided. Extensive examples and a large number of model descriptions are provided for use in both classroom exercises as well as self-guided exploration and learning. As such, the book is ideal for self-learning and also as the basis of a semester-long course for undergraduate and graduate students in molecular biology, bioengineering, genome sciences, or systems biology./a

Network-based Mathematical Modeling in Cell and Developmental Biology
Network-based Mathematical Modeling in Cell and Developmental Biology

Author: Susan Mertins

Publisher: Frontiers Media SA

Published: 2024-08-22

Total Pages: 137

ISBN-13: 283255346X

DOWNLOAD EBOOK

The vast amount of knowledge in Cell Signaling gathered through reductionist efforts and omics technology is poised to approach a Systems Biology understanding of precise representations of cell structure and function and predictions at multi-scale levels despite the complexity. Super-resolution microscopy and single cell analysis are also providing opportunities to explore both spatial and temporal landscapes. Notably, many basic biological processes have been studied capturing mechanistic detail with the goal to understand cellular proliferation and differentiation, gene regulation, morphogenesis, metabolism, and cell-cell communication. Similarly, at the intracellular level, addressing functions such as self-assembly, phase separation, and transport is leading to insights not readily understood as linear pathways. Therefore, network-based mathematical modeling, delineating dynamic biochemical reactions through ordinary and partial differential equations, promises to discover emergent biological properties not heretofore expected.

Calculating the Secrets of Life
Calculating the Secrets of Life

Author: National Research Council

Publisher: National Academies Press

Published: 1995-04-06

Total Pages: 300

ISBN-13: 0309048869

DOWNLOAD EBOOK

As researchers have pursued biology's secrets to the molecular level, mathematical and computer sciences have played an increasingly important roleâ€"in genome mapping, population genetics, and even the controversial search for "Eve," hypothetical mother of the human race. In this first-ever survey of the partnership between the two fields, leading experts look at how mathematical research and methods have made possible important discoveries in biology. The volume explores how differential geometry, topology, and differential mechanics have allowed researchers to "wind" and "unwind" DNA's double helix to understand the phenomenon of supercoiling. It explains how mathematical tools are revealing the workings of enzymes and proteins. And it describes how mathematicians are detecting echoes from the origin of life by applying stochastic and statistical theory to the study of DNA sequences. This informative and motivational book will be of interest to researchers, research administrators, and educators and students in mathematics, computer sciences, and biology.

Models of Cellular Regulation
Models of Cellular Regulation

Author: Baltazar Aguda

Publisher: Oxford University Press

Published: 2008-07-31

Total Pages: 199

ISBN-13: 0198570910

DOWNLOAD EBOOK

This book illustrates the mechanisms and models linking the realms of molecular interactions and biological processes or functions. It addresses the need of mathematical modelers to learn how to formulate models of cellular processes and to understand how quantitative modeling can help sort through the complexities of molecular regulatory networks.