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Simple Mathematical Models of Gene Regulatory Dynamics

2016-11-09 Medical
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Release : 2016-11-09
Genre : Medical
Kind : eBook
Book Rating : 181/5 ( reviews)

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Book Synopsis Simple Mathematical Models of Gene Regulatory Dynamics by : Michael C. Mackey

Download or read book Simple Mathematical Models of Gene Regulatory Dynamics written by Michael C. Mackey. This book was released on 2016-11-09. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Approximation of Gene Expression Patterns by Linear and Quadratic Regulatory Relations and Analysis of Gene Networks

2004
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Release : 2004
Genre :
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Book Rating : /5 ( reviews)

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Book Synopsis A Mathematical Modeling and Approximation of Gene Expression Patterns by Linear and Quadratic Regulatory Relations and Analysis of Gene Networks by :

Download or read book A Mathematical Modeling and Approximation of Gene Expression Patterns by Linear and Quadratic Regulatory Relations and Analysis of Gene Networks written by . This book was released on 2004. Available in PDF, EPUB and Kindle. Book excerpt: This thesis mainly concerns modeling, approximation and inference of gene regulatory dynamics on the basis of gene expression patterns. The dynamical behavior of gene expressions is represented by a system of ordinary di erential equations. We introduce a gene-interaction matrix with some nonlinear entries, in particular, quadratic polynomials of the expression levels to keep the system solvable. The model parameters are determined by using optimization. Then, we provide the time-discrete approximation of our time-continuous model. We analyze the approximating model under the aspect of stability. Finally, from the considered models we derive gene regulatory networks, discuss their qualitative features of the networks and provide a basis for analyzing networks with nonlinear connections.

Modeling with Nonsmooth Dynamics

2020-02-22 Mathematics
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Release : 2020-02-22
Genre : Mathematics
Kind : eBook
Book Rating : 875/5 ( reviews)

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Book Synopsis Modeling with Nonsmooth Dynamics by : Mike R. Jeffrey

Download or read book Modeling with Nonsmooth Dynamics written by Mike R. Jeffrey. This book was released on 2020-02-22. Available in PDF, EPUB and Kindle. Book excerpt: This volume looks at the study of dynamical systems with discontinuities. Discontinuities arise when systems are subject to switches, decisions, or other abrupt changes in their underlying properties that require a ‘non-smooth’ definition. A review of current ideas and introduction to key methods is given, with a view to opening discussion of a major open problem in our fundamental understanding of what nonsmooth models are. What does a nonsmooth model represent: an approximation, a toy model, a sophisticated qualitative capturing of empirical law, or a mere abstraction? Tackling this question means confronting rarely discussed indeterminacies and ambiguities in how we define, simulate, and solve nonsmooth models. The author illustrates these with simple examples based on genetic regulation and investment games, and proposes precise mathematical tools to tackle them. The volume is aimed at students and researchers who have some experience of dynamical systems, whether as a modelling tool or studying theoretically. Pointing to a range of theoretical and applied literature, the author introduces the key ideas needed to tackle nonsmooth models, but also shows the gaps in understanding that all researchers should be bearing in mind. Mike Jeffrey is a researcher and lecturer at the University of Bristol with a background in mathematical physics, specializing in dynamics, singularities, and asymptotics.

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

2017
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Release : 2017
Genre :
Kind : eBook
Book Rating : 167/5 ( reviews)

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Book Synopsis Data-Driven Models for Dynamics of Gene Expression and Single Cells by : Tao Peng

Download or read book Data-Driven Models for Dynamics of Gene Expression and Single Cells written by Tao Peng. This book was released on 2017. Available in PDF, EPUB and Kindle. Book excerpt: 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

2008-08-13 Science
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Release : 2008-08-13
Genre : Science
Kind : eBook
Book Rating : 187/5 ( reviews)

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Book Synopsis Computational Modeling Of Gene Regulatory Networks - A Primer by : Hamid Bolouri

Download or read book Computational Modeling Of Gene Regulatory Networks - A Primer written by Hamid Bolouri. This book was released on 2008-08-13. Available in PDF, EPUB and Kindle. Book excerpt: 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

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