Stochastic Chemical Reaction Systems In Biology

Author : Hong Qian,Hao Ge
Publisher : Springer Nature
Page : 364 pages
File Size : 49,9 Mb
Release : 2021-10-18
Category : Mathematics
ISBN : 9783030862527

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Stochastic Chemical Reaction Systems in Biology by Hong Qian,Hao Ge Pdf

This book provides an introduction to the analysis of stochastic dynamic models in biology and medicine. The main aim is to offer a coherent set of probabilistic techniques and mathematical tools which can be used for the simulation and analysis of various biological phenomena. These tools are illustrated on a number of examples. For each example, the biological background is described, and mathematical models are developed following a unified set of principles. These models are then analyzed and, finally, the biological implications of the mathematical results are interpreted. The biological topics covered include gene expression, biochemistry, cellular regulation, and cancer biology. The book will be accessible to graduate students who have a strong background in differential equations, the theory of nonlinear dynamical systems, Markovian stochastic processes, and both discrete and continuous state spaces, and who are familiar with the basic concepts of probability theory.

Author : Péter Érdi,Gábor Lente
Publisher : Springer
Page : 174 pages
File Size : 47,5 Mb
Release : 2014-05-06
Category : Science
ISBN : 9781493903870

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Stochastic Chemical Kinetics by Péter Érdi,Gábor Lente Pdf

This volume reviews the theory and simulation methods of stochastic kinetics by integrating historical and recent perspectives, presents applications, mostly in the context of systems biology and also in combustion theory. In recent years, due to the development in experimental techniques, such as optical imaging, single cell analysis, and fluorescence spectroscopy, biochemical kinetic data inside single living cells have increasingly been available. The emergence of systems biology brought renaissance in the application of stochastic kinetic methods.

Author : Mukhtar Ullah,Olaf Wolkenhauer
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 55,6 Mb
Release : 2011-07-12
Category : Mathematics
ISBN : 9781461404781

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Stochastic Approaches for Systems Biology by Mukhtar Ullah,Olaf Wolkenhauer Pdf

This textbook focuses on stochastic analysis in systems biology containing both the theory and application. While the authors provide a review of probability and random variables, subsequent notions of biochemical reaction systems and the relevant concepts of probability theory are introduced side by side. This leads to an intuitive and easy-to-follow presentation of stochastic framework for modeling subcellular biochemical systems. In particular, the authors make an effort to show how the notion of propensity, the chemical master equation and the stochastic simulation algorithm arise as consequences of the Markov property. The text contains many illustrations, examples and exercises to illustrate the ideas and methods that are introduced. Matlab code is also provided where appropriate. Additionally, the cell cycle is introduced as a more complex case study. Senior undergraduate and graduate students in mathematics and physics as well as researchers working in the area of systems biology, bioinformatics and related areas will find this text useful.

Author : Luca Marchetti,Corrado Priami,Vo Hong Thanh
Publisher : Springer
Page : 238 pages
File Size : 55,5 Mb
Release : 2017-09-27
Category : Computers
ISBN : 9783319631134

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Simulation Algorithms for Computational Systems Biology by Luca Marchetti,Corrado Priami,Vo Hong Thanh Pdf

This book explains the state-of-the-art algorithms used to simulate biological dynamics. Each technique is theoretically introduced and applied to a set of modeling cases. Starting from basic simulation algorithms, the book also introduces more advanced techniques that support delays, diffusion in space, or that are based on hybrid simulation strategies. This is a valuable self-contained resource for graduate students and practitioners in computer science, biology and bioinformatics. An appendix covers the mathematical background, and the authors include further reading sections in each chapter.

Author : David F. Anderson,Thomas G. Kurtz
Publisher : Springer
Page : 84 pages
File Size : 45,9 Mb
Release : 2015-04-23
Category : Mathematics
ISBN : 9783319168951

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Stochastic Analysis of Biochemical Systems by David F. Anderson,Thomas G. Kurtz Pdf

This book focuses on counting processes and continuous-time Markov chains motivated by examples and applications drawn from chemical networks in systems biology. The book should serve well as a supplement for courses in probability and stochastic processes. While the material is presented in a manner most suitable for students who have studied stochastic processes up to and including martingales in continuous time, much of the necessary background material is summarized in the Appendix. Students and Researchers with a solid understanding of calculus, differential equations and elementary probability and who are well-motivated by the applications will find this book of interest. David F. Anderson is Associate Professor in the Department of Mathematics at the University of Wisconsin and Thomas G. Kurtz is Emeritus Professor in the Departments of Mathematics and Statistics at that university. Their research is focused on probability and stochastic processes with applications in biology and other areas of science and technology. These notes are based in part on lectures given by Professor Anderson at the University of Wisconsin – Madison and by Professor Kurtz at Goethe University Frankfurt.

Author : Christian Mazza,Michel Benaim
Publisher : CRC Press
Page : 274 pages
File Size : 42,6 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 9781466514942

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Stochastic Dynamics for Systems Biology by Christian Mazza,Michel Benaim Pdf

Stochastic Dynamics for Systems Biology is one of the first books to provide a systematic study of the many stochastic models used in systems biology. The book shows how the mathematical models are used as technical tools for simulating biological processes and how the models lead to conceptual insights on the functioning of the cellular processing

Author : Paola Lecca,Ian Laurenzi,Ferenc Jordan
Publisher : Elsevier
Page : 411 pages
File Size : 53,8 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9781908818218

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Deterministic Versus Stochastic Modelling in Biochemistry and Systems Biology by Paola Lecca,Ian Laurenzi,Ferenc Jordan Pdf

Stochastic kinetic methods are currently considered to be the most realistic and elegant means of representing and simulating the dynamics of biochemical and biological networks. Deterministic versus stochastic modelling in biochemistry and systems biology introduces and critically reviews the deterministic and stochastic foundations of biochemical kinetics, covering applied stochastic process theory for application in the field of modelling and simulation of biological processes at the molecular scale. Following an overview of deterministic chemical kinetics and the stochastic approach to biochemical kinetics, the book goes onto discuss the specifics of stochastic simulation algorithms, modelling in systems biology and the structure of biochemical models. Later chapters cover reaction-diffusion systems, and provide an analysis of the Kinfer and BlenX software systems. The final chapter looks at simulation of ecodynamics and food web dynamics. Introduces mathematical concepts and formalisms of deterministic and stochastic modelling through clear and simple examples Presents recently developed discrete stochastic formalisms for modelling biological systems and processes Describes and applies stochastic simulation algorithms to implement a stochastic formulation of biochemical and biological kinetics

Author : Gábor Lente
Publisher : Springer
Page : 135 pages
File Size : 43,5 Mb
Release : 2015-03-09
Category : Science
ISBN : 9783319154824

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Deterministic Kinetics in Chemistry and Systems Biology by Gábor Lente Pdf

This book gives a concise overview of the mathematical foundations of kinetics used in chemistry and systems biology. The analytical and numerical methods used to solve complex rate equations with the widely used deterministic approach will be described, with primary focus on practical aspects important in designing experimental studies and the evaluation of data. The introduction of personal computers transformed scientific attitudes in the last two decades considerably as computational power ceased to be a limiting factor. Despite this improvement, certain time-honored approximations in solving rate equations such as the pre-equilibrium or the steady-state approach are still valid and necessary as they concern the information content of measured kinetic traces. The book shows the role of these approximations in modern kinetics and will also describe some common misconceptions in this field.

Author : Stefanie Winkelmann,Christof Schütte
Publisher : Springer Nature
Page : 284 pages
File Size : 46,6 Mb
Release : 2021-01-04
Category : Mathematics
ISBN : 9783030623876

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Stochastic Dynamics in Computational Biology by Stefanie Winkelmann,Christof Schütte Pdf

The aim of this book is to provide a well-structured and coherent overview of existing mathematical modeling approaches for biochemical reaction systems, investigating relations between both the conventional models and several types of deterministic-stochastic hybrid model recombinations. Another main objective is to illustrate and compare diverse numerical simulation schemes and their computational effort. Unlike related works, this book presents a broad scope in its applications, from offering a detailed introduction to hybrid approaches for the case of multiple population scales to discussing the setting of time-scale separation resulting from widely varying firing rates of reaction channels. Additionally, it also addresses modeling approaches for non well-mixed reaction-diffusion dynamics, including deterministic and stochastic PDEs and spatiotemporal master equations. Finally, by translating and incorporating complex theory to a level accessible to non-mathematicians, this book effectively bridges the gap between mathematical research in computational biology and its practical use in biological, biochemical, and biomedical systems.

Author : Darren J. Wilkinson
Publisher : CRC Press
Page : 296 pages
File Size : 41,7 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 1584885408

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Stochastic Modelling for Systems Biology by Darren J. Wilkinson Pdf

Although stochastic kinetic models are increasingly accepted as the best way to represent and simulate genetic and biochemical networks, most researchers in the field have limited knowledge of stochastic process theory. The stochastic processes formalism provides a beautiful, elegant, and coherent foundation for chemical kinetics and there is a wealth of associated theory every bit as powerful and elegant as that for conventional continuous deterministic models. The time is right for an introductory text written from this perspective. Stochastic Modelling for Systems Biology presents an accessible introduction to stochastic modelling using examples that are familiar to systems biology researchers. Focusing on computer simulation, the author examines the use of stochastic processes for modelling biological systems. He provides a comprehensive understanding of stochastic kinetic modelling of biological networks in the systems biology context. The text covers the latest simulation techniques and research material, such as parameter inference, and includes many examples and figures as well as software code in R for various applications. While emphasizing the necessary probabilistic and stochastic methods, the author takes a practical approach, rooting his theoretical development in discussions of the intended application. Written with self-study in mind, the book includes technical chapters that deal with the difficult problems of inference for stochastic kinetic models from experimental data. Providing enough background information to make the subject accessible to the non-specialist, the book integrates a fairly diverse literature into a single convenient and notationally consistent source.

Author : Peter Schuster
Publisher : Springer
Page : 728 pages
File Size : 50,5 Mb
Release : 2016-10-14
Category : Science
ISBN : 9783319395029

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Stochasticity in Processes by Peter Schuster Pdf

This book has developed over the past fifteen years from a modern course on stochastic chemical kinetics for graduate students in physics, chemistry and biology. The first part presents a systematic collection of the mathematical background material needed to understand probability, statistics, and stochastic processes as a prerequisite for the increasingly challenging practical applications in chemistry and the life sciences examined in the second part. Recent advances in the development of new techniques and in the resolution of conventional experiments at nano-scales have been tremendous: today molecular spectroscopy can provide insights into processes down to scales at which current theories at the interface of physics, chemistry and the life sciences cannot be successful without a firm grasp of randomness and its sources. Routinely measured data is now sufficiently accurate to allow the direct recording of fluctuations. As a result, the sampling of data and the modeling of relevant processes are doomed to produce artifacts in interpretation unless the observer has a solid background in the mathematics of limited reproducibility. The material covered is presented in a modular approach, allowing more advanced sections to be skipped if the reader is primarily interested in applications. At the same time, most derivations of analytical solutions for the selected examples are provided in full length to guide more advanced readers in their attempts to derive solutions on their own. The book employs uniform notation throughout, and a glossary has been added to define the most important notions discussed.

Author : Péter Érdi,János Tóth
Publisher : Manchester University Press
Page : 296 pages
File Size : 42,9 Mb
Release : 1989
Category : Chemical reactions
ISBN : 0719022088

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Mathematical Models of Chemical Reactions by Péter Érdi,János Tóth Pdf

Author : Jan A. Freund,Thorsten Pöschel
Publisher : Springer
Page : 512 pages
File Size : 54,7 Mb
Release : 2008-01-11
Category : Science
ISBN : 9783540453963

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Stochastic Processes in Physics, Chemistry, and Biology by Jan A. Freund,Thorsten Pöschel Pdf

The theory of stochastic processes originally grew out of efforts to describe Brownian motion quantitatively. Today it provides a huge arsenal of methods suitable for analyzing the influence of noise on a wide range of systems. The credit for acquiring all the deep insights and powerful methods is due ma- ly to a handful of physicists and mathematicians: Einstein, Smoluchowski, Langevin, Wiener, Stratonovich, etc. Hence it is no surprise that until - cently the bulk of basic and applied stochastic research was devoted to purely mathematical and physical questions. However, in the last decade we have witnessed an enormous growth of results achieved in other sciences - especially chemistry and biology - based on applying methods of stochastic processes. One reason for this stochastics boom may be that the realization that noise plays a constructive rather than the expected deteriorating role has spread to communities beyond physics. Besides their aesthetic appeal these noise-induced, noise-supported or noise-enhanced effects sometimes offer an explanation for so far open pr- lems (information transmission in the nervous system and information p- cessing in the brain, processes at the cell level, enzymatic reactions, etc.). They may also pave the way to novel technological applications (noise-- hanced reaction rates, noise-induced transport and separation on the na- scale, etc.). Key words to be mentioned in this context are stochastic r- onance, Brownian motors or ratchets, and noise-supported phenomena in excitable systems.

Author : Edda Klipp,Wolfram Liebermeister,Christoph Wierling,Axel Kowald,Hans Lehrach,Ralf Herwig
Publisher : John Wiley & Sons
Page : 593 pages
File Size : 54,8 Mb
Release : 2013-06-20
Category : Medical
ISBN : 9783527644995

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Systems Biology by Edda Klipp,Wolfram Liebermeister,Christoph Wierling,Axel Kowald,Hans Lehrach,Ralf Herwig Pdf

This advanced textbook is tailored to the needs of introductory course in Systems Biology. It has a compagnion website (www.wiley-vch.de/home/systemsbiology)with solutions to questions in the book and several additional extensive working models. The book is related to the very successful previous title 'Systems Biology in Practice' and has incorporated the feedback and suggestions from many lecturers worldwide. The book addresses biologists as well as engineers and computer scientists. The interdisciplinary team of acclaimed authors worked closely together to ensure a comprehensive coverage with no overlaps in a homogenous and compelling style.

Author : Arianna Bianchi,Thomas Hillen,Mark A. Lewis,Yingfei Yi
Publisher : Springer Nature
Page : 267 pages
File Size : 53,6 Mb
Release : 2019-10-02
Category : Mathematics
ISBN : 9783030225834

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The Dynamics of Biological Systems by Arianna Bianchi,Thomas Hillen,Mark A. Lewis,Yingfei Yi Pdf

The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Séminaire de Mathématiques Supérieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine. The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight - discuss innovative methods for the analysis of biological processes, - contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.