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Interest in theoretical biology is rapidly growing and this 1981 book attempts to make the theory more accessible to experimentalists. Its primary purpose is to demonstrate to experimental molecular and cellular biologists the possible usefulness of mathematical models. Biologists with a basic command of calculus should be able to learn from the book what assumptions are implied by various types of equations, to understand in broad outline a number of major theoretical concepts, and to be aware of some of the difficulties connected with analytical and numerical solutions of mathematical problems. Thus they should be able to appreciate the significance of theoretical papers in their fields and to communicate usefully with theoreticians in the course of their work.

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Genre: Mathematics
Author: Segel
Publisher: CUP Archive
Release: 1980
File: 757 Pages
ISBN-13: 0521229251

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BOOK EXCERPT:

Interest in theoretical biology is rapidly growing and this 1981 book attempts to make the theory more accessible to experimentalists. Its primary purpose is to demonstrate to experimental molecular and cellular biologists the possible usefulness of mathematical models. Biologists with a basic command of calculus should be able to learn from the book what assumptions are implied by various types of equations, to understand in broad outline a number of major theoretical concepts, and to be aware of some of the difficulties connected with analytical and numerical solutions of mathematical problems. Thus they should be able to appreciate the significance of theoretical papers in their fields and to communicate usefully with theoreticians in the course of their work.

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Genre: Mathematics
Author: Lee A. Segel
Publisher: Cambridge University Press
Release: 1983-10-06
File: 768 Pages
ISBN-13: 0521270545

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An 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.

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Genre: Science
Author: Brian P. Ingalls
Publisher: MIT Press
Release: 2013-07-05
File: 408 Pages
ISBN-13: 9780262018883

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The dynamic development of various processes is a central problem of biology and indeed of all the sciences. The mathematics describing that development is, in general, complicated, because the models that are realistic are usually nonlinear. Consequently many biologists may not notice a possible application of theory. They may be unable to decide whether a particular model captures the essence of a system, or to appreciate that analysis of a model can reveal important aspects of biological problems and may even describe in detail how a system works. The aim of this textbook is to remedy the situation by adopting a general approach to model analysis and applying it several times to problems (drawn primarily from molecular and cellular biology) of gradually increasing biological and mathematical complexity. Although material of considerable sophistication is included, little mathematical background is required - only some exposure to elementary calculus; appendixes supply the necessary mathematics and the author concentrates on concepts rather than techniques. He also emphasizes the role of computers in giving a full picture of model behavior and complementing more qualitative analysis. Some problems suitable for computer analysis are also included. This is a class-tested textbook suitable for a one-semester course for advanced undergraduate and beginning graduate students in biology or applied mathematics. It can also be used as a source book for teachers and a reference for specialists.

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Genre: Mathematics
Author: Lee A. Segel
Publisher: Cambridge University Press
Release: 1984-03-30
File: 300 Pages
ISBN-13: 052127477X

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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.

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Genre: Mathematics
Author: Andreas Deutsch
Publisher: Springer Science & Business Media
Release: 2007-06-15
File: 382 Pages
ISBN-13: 9780817645588

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Mathematical Models in Biology is an introductory book for readers interested in biological applications of mathematics and modeling in biology. A favorite in the mathematical biology community, it shows how relatively simple mathematics can be applied to a variety of models to draw interesting conclusions. Connections are made between diverse biological examples linked by common mathematical themes. A variety of discrete and continuous ordinary and partial differential equation models are explored. Although great advances have taken place in many of the topics covered, the simple lessons contained in this book are still important and informative. Audience: the book does not assume too much background knowledge--essentially some calculus and high-school algebra. It was originally written with third- and fourth-year undergraduate mathematical-biology majors in mind; however, it was picked up by beginning graduate students as well as researchers in math (and some in biology) who wanted to learn about this field.

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Genre: Biology
Author: Leah Edelstein-Keshet
Publisher: SIAM
Release: 1988
File: 586 Pages
ISBN-13: 0898719143

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This textbook provides an introduction to dynamic modeling in molecular cell biology, taking a computational and intuitive approach. Detailed illustrations, examples, and exercises are included throughout the text. Appendices containing mathematical and computational techniques are provided as a reference tool.

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Genre: Science
Author: Christopher P. Fall
Publisher: Springer Science & Business Media
Release: 2007-06-04
File: 468 Pages
ISBN-13: 9780387224596

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This book demonstrates how an understanding of biological kinetics can lead to knowledge about the biological model being examined.

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Genre: Mathematics
Author: Lee A. Segel
Publisher: Cambridge University Press
Release: 1991
File: 220 Pages
ISBN-13: 0521391849

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Linear and non-linear models of populations, molecular evolution, phylogenetic tree construction, genetics, and infectious diseases are presented with minimal prerequisites.

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Genre: Mathematics
Author: Elizabeth S. Allman
Publisher: Cambridge University Press
Release: 2004
File: 370 Pages
ISBN-13: 0521525861

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Drawing on the latest research in the field, Systems Biology: Mathematical Modeling and Model Analysis presents many methods for modeling and analyzing biological systems, in particular cellular systems. It shows how to use predictive mathematical models to acquire and analyze knowledge about cellular systems. It also explores how the models are systematically applied in biotechnology. The first part of the book introduces biological basics, such as metabolism, signaling, gene expression, and control as well as mathematical modeling fundamentals, including deterministic models and thermodynamics. The text also discusses linear regression methods, explains the differences between linear and nonlinear regression, and illustrates how to determine input variables to improve estimation accuracy during experimental design. The second part covers intracellular processes, including enzymatic reactions, polymerization processes, and signal transduction. The author highlights the process–function–behavior sequence in cells and shows how modeling and analysis of signal transduction units play a mediating role between process and function. The third part presents theoretical methods that address the dynamics of subsystems and the behavior near a steady state. It covers techniques for determining different time scales, sensitivity analysis, structural kinetic modeling, and theoretical control engineering aspects, including a method for robust control. It also explores frequent patterns (motifs) in biochemical networks, such as the feed-forward loop in the transcriptional network of E. coli. Moving on to models that describe a large number of individual reactions, the last part looks at how these cellular models are used in biotechnology. The book also explains how graphs can illustrate the link between two components in large networks with several interactions.

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Genre: Mathematics
Author: Andreas Kremling
Publisher: CRC Press
Release: 2013-11-12
File: 379 Pages
ISBN-13: 9781466567894

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