Mathematical Models of Chemical Reactions
Author: Péter Érdi
Publisher: Manchester University Press
Published: 1989
Total Pages: 296
ISBN-13: 9780719022081
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Stochastic Chemical Kinetics
Author: Péter Érdi
Publisher: Springer
Published: 2014-05-06
Total Pages: 174
ISBN-13: 149390387X
DOWNLOAD EBOOKThis 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.
Deterministic Versus Stochastic Modelling in Biochemistry and Systems Biology
Author: Paola Lecca
Publisher: Elsevier
Published: 2013-04-09
Total Pages: 411
ISBN-13: 1908818212
DOWNLOAD EBOOKStochastic 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
Mathematical Modeling in Systems Biology
Author: Brian P. Ingalls
Publisher: MIT Press
Published: 2022-06-07
Total Pages: 423
ISBN-13: 0262545829
DOWNLOAD EBOOKAn introduction to the mathematical concepts and techniques needed for the construction and analysis of models in molecular systems biology. Systems techniques are integral to current research in molecular cell biology, and system-level investigations are often accompanied by mathematical models. These models serve as working hypotheses: they help us to understand and predict the behavior of complex systems. This book offers an introduction to mathematical concepts and techniques needed for the construction and interpretation of models in molecular systems biology. It is accessible to upper-level undergraduate or graduate students in life science or engineering who have some familiarity with calculus, and will be a useful reference for researchers at all levels. The first four chapters cover the basics of mathematical modeling in molecular systems biology. The last four chapters address specific biological domains, treating modeling of metabolic networks, of signal transduction pathways, of gene regulatory networks, and of electrophysiology and neuronal action potentials. Chapters 3–8 end with optional sections that address more specialized modeling topics. Exercises, solvable with pen-and-paper calculations, appear throughout the text to encourage interaction with the mathematical techniques. More involved end-of-chapter problem sets require computational software. Appendixes provide a review of basic concepts of molecular biology, additional mathematical background material, and tutorials for two computational software packages (XPPAUT and MATLAB) that can be used for model simulation and analysis.
Foundations of Chemical Reaction Network Theory
Author: Martin Feinberg
Publisher: Springer
Published: 2019-01-31
Total Pages: 475
ISBN-13: 3030038580
DOWNLOAD EBOOKThis book provides an authoritative introduction to the rapidly growing field of chemical reaction network theory. In particular, the book presents deep and surprising theorems that relate the graphical and algebraic structure of a reaction network to qualitative properties of the intricate system of nonlinear differential equations that the network induces. Over the course of three main parts, Feinberg provides a gradual transition from a tutorial on the basics of reaction network theory, to a survey of some of its principal theorems, and, finally, to a discussion of the theory’s more technical aspects. Written with great clarity, this book will be of value to mathematicians and to mathematically-inclined biologists, chemists, physicists, and engineers who want to contribute to chemical reaction network theory or make use of its powerful results.
Reaction Kinetics: Exercises, Programs and Theorems
Author: János Tóth
Publisher: Springer
Published: 2018-09-18
Total Pages: 476
ISBN-13: 1493986430
DOWNLOAD EBOOKFifty years ago, a new approach to reaction kinetics began to emerge: one based on mathematical models of reaction kinetics, or formal reaction kinetics. Since then, there has been a rapid and accelerated development in both deterministic and stochastic kinetics, primarily because mathematicians studying differential equations and algebraic geometry have taken an interest in the nonlinear differential equations of kinetics, which are relatively simple, yet capable of depicting complex behavior such as oscillation, chaos, and pattern formation. The development of stochastic models was triggered by the fact that novel methods made it possible to measure molecules individually. Now it is high time to make the results of the last half-century available to a larger audience: students of chemistry, chemical engineering and biochemistry, not to mention applied mathematics. Based on recent papers, this book presents the most important concepts and results, together with a wealth of solved exercises. The book is accompanied by the authors’ Mathematica package, ReactionKinetics, which helps both students and scholars in their everyday work, and which can be downloaded from http://extras.springer.com/ and also from the authors’ websites. Further, the large set of unsolved problems provided may serve as a springboard for individual research.
Mathematical Modelling
Author: Simon Serovajsky
Publisher: CRC Press
Published: 2021-11-24
Total Pages: 589
ISBN-13: 1000503984
DOWNLOAD EBOOKMathematical Modelling sets out the general principles of mathematical modelling as a means comprehending the world. Within the book, the problems of physics, engineering, chemistry, biology, medicine, economics, ecology, sociology, psychology, political science, etc. are all considered through this uniform lens. The author describes different classes of models, including lumped and distributed parameter systems, deterministic and stochastic models, continuous and discrete models, static and dynamical systems, and more. From a mathematical point of view, the considered models can be understood as equations and systems of equations of different nature and variational principles. In addition to this, mathematical features of mathematical models, applied control and optimization problems based on mathematical models, and identification of mathematical models are also presented. Features Each chapter includes four levels: a lecture (main chapter material), an appendix (additional information), notes (explanations, technical calculations, literature review) and tasks for independent work; this is suitable for undergraduates and graduate students and does not require the reader to take any prerequisite course, but may be useful for researchers as well Described mathematical models are grouped both by areas of application and by the types of obtained mathematical problems, which contributes to both the breadth of coverage of the material and the depth of its understanding Can be used as the main textbook on a mathematical modelling course, and is also recommended for special courses on mathematical models for physics, chemistry, biology, economics, etc.
Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology
Author: David Holcman
Publisher: Springer
Published: 2017-10-04
Total Pages: 377
ISBN-13: 3319626272
DOWNLOAD EBOOKThis book focuses on the modeling and mathematical analysis of stochastic dynamical systems along with their simulations. The collected chapters will review fundamental and current topics and approaches to dynamical systems in cellular biology. This text aims to develop improved mathematical and computational methods with which to study biological processes. At the scale of a single cell, stochasticity becomes important due to low copy numbers of biological molecules, such as mRNA and proteins that take part in biochemical reactions driving cellular processes. When trying to describe such biological processes, the traditional deterministic models are often inadequate, precisely because of these low copy numbers. This book presents stochastic models, which are necessary to account for small particle numbers and extrinsic noise sources. The complexity of these models depend upon whether the biochemical reactions are diffusion-limited or reaction-limited. In the former case, one needs to adopt the framework of stochastic reaction-diffusion models, while in the latter, one can describe the processes by adopting the framework of Markov jump processes and stochastic differential equations. Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology will appeal to graduate students and researchers in the fields of applied mathematics, biophysics, and cellular biology.
Chemistry: The Key to our Sustainable Future
Author: Minu Gupta Bhowon
Publisher: Springer Science & Business Media
Published: 2013-11-08
Total Pages: 356
ISBN-13: 9400773897
DOWNLOAD EBOOKChemistry: The Key to our Sustainable Future is a collection of selected contributed papers by participants of the International Conference on Pure and Applied Chemistry (ICPAC 2012) on the theme of “Chemistry: The Key for our Future” held in Mauritius in July 2012. In light of the significant contribution of chemistry to benefit of mankind, this book is a collection of recent results generated from research in chemistry and interdisciplinary areas. It covers topics ranging from nanotechnology, natural product chemistry to analytical and environmental chemistry. Chemistry: The Key to our Sustainable Future is written for graduates, postgraduates, researchers in industry and academia who have an interest in the fields ranging from fundamental to applied chemistry.
Coping with Complexity: Model Reduction and Data Analysis
Author: Alexander N. Gorban
Publisher: Springer Science & Business Media
Published: 2010-10-21
Total Pages: 356
ISBN-13: 3642149413
DOWNLOAD EBOOKThis volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 – September 4, 2009. The book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.
