Modeling Biological Systems

Principles and Applications

Author: James W. Haefner

Publisher: Springer Science & Business Media

ISBN: 1461541190

Category: Science

Page: 473

View: 5418

This book is intended as a text for a first course on creating and analyzing computer simulation models of biological systems. The expected audience for this book are students wishing to use dynamic models to interpret real data mueh as they would use standard statistical techniques. It is meant to provide both the essential principles as well as the details and equa tions applicable to a few particular systems and subdisciplines. Biological systems, however, encompass a vast, diverse array of topics and problems. This book discusses only a select number of these that I have found to be useful and interesting to biologists just beginning their appreciation of computer simulation. The examples chosen span classical mathematical models of well-studied systems to state-of-the-art topics such as cellular automata and artificial life. I have stressed the relationship between the models and the biology over mathematical analysis in order to give the reader a sense that mathematical models really are useful to biologists. In this light, I have sought examples that address fundamental and, I think, interesting biological questions. Almost all of the models are directly COIIl pared to quantitative data to provide at least a partial demonstration that some biological models can accurately predict.

Modeling Biological Systems:

Principles and Applications

Author: James W. Haefner

Publisher: Springer Science & Business Media

ISBN: 9780387250113

Category: Science

Page: 475

View: 4057

I Principles 1 1 Models of Systems 3 1. 1 Systems. Models. and Modeling . . . . . . . . . . . . . . . . . . . . 3 1. 2 Uses of Scientific Models . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 3 Example: Island Biogeography . . . . . . . . . . . . . . . . . . . . . 6 1. 4 Classifications of Models . . . . . . . . . . . . . . . . . . . . . . . . 10 1. 5 Constraints on Model Structure . . . . . . . . . . . . . . . . . . . . . 12 1. 6 Some Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1. 7 Misuses of Models: The Dark Side . . . . . . . . . . . . . . . . . . . 13 1. 8 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2 The Modeling Process 17 2. 1 Models Are Problems . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2. 2 Two Alternative Approaches . . . . . . . . . . . . . . . . . . . . . . 18 2. 3 An Example: Population Doubling Time . . . . . . . . . . . . . . . . 24 2. 4 Model Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2. 5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3 Qualitative Model Formulation 32 3. 1 How to Eat an Elephant . . . . . . . . . . . . . . . . . . . . . . . . . 32 3. 2 Forrester Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3. 3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 3. 4 Errors in Forrester Diagrams . . . . . . . . . . . . . . . . . . . . . . 44 3. 5 Advantages and Disadvantages of Forrester Diagrams . . . . . . . . . 44 3. 6 Principles of Qualitative Formulation . . . . . . . . . . . . . . . . . . 45 3. 7 Model Simplification . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3. 8 Other Modeling Problems . . . . . . . . . . . . . . . . . . . . . . . . 49 viii Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. 9 Exercises 53 4 Quantitative Model Formulation: I 4. 1 From Qualitative to Quantitative . . . . . . . . . . . . . . . . . Finite Difference Equations and Differential Equations 4. 2 . . . . . . . . . . . . . . . . 4. 3 Biological Feedback in Quantitative Models . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 4 Example Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4. 5 Exercises 5 Quantitative Model Formulation: I1 81 . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 1 Physical Processes 81 . . . . . . . . . . . . . . . 5. 2 Using the Toolbox of Biological Processes 89 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 3 Useful Functions 96 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 4 Examples 102 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5. 5 Exercises 104 6 Numerical Techniques 107 . . . . . . . . . . . . . . . . . . . . . . . 6. 1 Mistakes Computers Make 107 . . . . . . . . . . . . . . . . . . . . . . . . . . 6. 2 Numerical Integration 110 . . . . . . . . . . . . . . . . 6. 3 Numerical Instability and Stiff Equations 115 . . . . . . . . . . . . . .

Modeling Biological Systems

Principles and Applications

Author: James W. Haefner

Publisher: Springer Science & Business Media

ISBN: 9780412042010

Category: Science

Page: 473

View: 8066

This book is intended as a text for a first course on creating and analyzing computer simulation models of biological systems. The expected audience for this book are students wishing to use dynamic models to interpret real data mueh as they would use standard statistical techniques. It is meant to provide both the essential principles as well as the details and equa tions applicable to a few particular systems and subdisciplines. Biological systems, however, encompass a vast, diverse array of topics and problems. This book discusses only a select number of these that I have found to be useful and interesting to biologists just beginning their appreciation of computer simulation. The examples chosen span classical mathematical models of well-studied systems to state-of-the-art topics such as cellular automata and artificial life. I have stressed the relationship between the models and the biology over mathematical analysis in order to give the reader a sense that mathematical models really are useful to biologists. In this light, I have sought examples that address fundamental and, I think, interesting biological questions. Almost all of the models are directly COIIl pared to quantitative data to provide at least a partial demonstration that some biological models can accurately predict.

Modeling Biological Systems

Principles and Applications

Author: James W. Haefner

Publisher: Springer Science & Business Media

ISBN: 1461541190

Category: Science

Page: 473

View: 5890

This book is intended as a text for a first course on creating and analyzing computer simulation models of biological systems. The expected audience for this book are students wishing to use dynamic models to interpret real data mueh as they would use standard statistical techniques. It is meant to provide both the essential principles as well as the details and equa tions applicable to a few particular systems and subdisciplines. Biological systems, however, encompass a vast, diverse array of topics and problems. This book discusses only a select number of these that I have found to be useful and interesting to biologists just beginning their appreciation of computer simulation. The examples chosen span classical mathematical models of well-studied systems to state-of-the-art topics such as cellular automata and artificial life. I have stressed the relationship between the models and the biology over mathematical analysis in order to give the reader a sense that mathematical models really are useful to biologists. In this light, I have sought examples that address fundamental and, I think, interesting biological questions. Almost all of the models are directly COIIl pared to quantitative data to provide at least a partial demonstration that some biological models can accurately predict.

Biological Modeling and Simulation

A Survey of Practical Models, Algorithms, and Numerical Methods

Author: Russell Schwartz

Publisher: MIT Press

ISBN: 0262303396

Category: Science

Page: 408

View: 2957

There are many excellent computational biology resources now available for learning about methods that have been developed to address specific biological systems, but comparatively little attention has been paid to training aspiring computational biologists to handle new and unanticipated problems. This text is intended to fill that gap by teaching students how to reason about developing formal mathematical models of biological systems that are amenable to computational analysis. It collects in one place a selection of broadly useful models, algorithms, and theoretical analysis tools normally found scattered among many other disciplines. It thereby gives the aspiring student a bag of tricks that will serve him or her well in modeling problems drawn from numerous subfields of biology. These techniques are taught from the perspective of what the practitioner needs to know to use them effectively, supplemented with references for further reading on more advanced use of each method covered. The text, which grew out of a class taught at Carnegie Mellon University, covers models for optimization, simulation and sampling, and parameter tuning. These topics provide a general framework for learning how to formulate mathematical models of biological systems, what techniques are available to work with these models, and how to fit the models to particular systems. Their application is illustrated by many examples drawn from a variety of biological disciplines and several extended case studies that show how the methods described have been applied to real problems in biology.

Principles and Models of Biological Transport

Author: Morton H. Friedman

Publisher: Springer Science & Business Media

ISBN: 9780387792408

Category: Technology & Engineering

Page: 510

View: 2872

Focus, Organization, and Content This book, like the first edition, deals with the mass transport processes that take place in living systems, with a focus on the normal behavior of eukaryotic cells and the - ganisms they constitute, in their normal physiological environment. As a consequence of this focus, the structure and content of the book differ from those of traditional transport texts. We do not start with the engineering principles of mass transport (which are well presented elsewhere) and then seek biological applications of these principles; rather, we begin with the biological processes themselves, and then - velop the models and analytical tools that are needed to describe them. This approach has several consequences. First of all, it drives the content of the text in a direction distinctively different from conventional transport texts. This is - cause the tools and models needed to describe complex biological processes are often different from those employed to describe more well-characterized inanimate systems. Many biological processes must still be described phenomenologically, using me- odologies like nonequilibrium thermodynamics. Simple electrical analogs employing a paucity of parameters can be more useful for characterization and prediction than complex theories based on the behavior of more well-defined systems on a laboratory bench. By allowing the biology to drive the choice of analysis tools and models, the latter are consistently presented in the context of real biological systems, and analysis and biology are interwoven throughout.

Mathematical Modeling in Systems Biology

An Introduction

Author: Brian P. Ingalls

Publisher: MIT Press

ISBN: 0262315645

Category: Science

Page: 424

View: 3049

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.

Systems Biology

Principles, Methods, and Concepts

Author: A.K. Konopka

Publisher: CRC Press

ISBN: 1420015125

Category: Science

Page: 256

View: 9798

With extraordinary clarity,the Systems Biology: Principles, Methods, and Concepts focuses on the technical practical aspects of modeling complex or organic general systems. It also provides in-depth coverage of modeling biochemical, thermodynamic, engineering, and ecological systems. Among other methods and concepts based in logic, computer science, and dynamical systems, it explores pragmatic techniques of General Systems Theory. This text presents biology as an autonomous science from the perspective of fundamental modeling techniques. A complete resource for anyone interested in biology as an exact science, it includes a comprehensive survey, review, and critique of concepts and methods in Systems Biology.

Dynamic Models in Biology

Author: Stephen P. Ellner,John Guckenheimer

Publisher: Princeton University Press

ISBN: 1400840961

Category: Science

Page: 352

View: 2137

From controlling disease outbreaks to predicting heart attacks, dynamic models are increasingly crucial for understanding biological processes. Many universities are starting undergraduate programs in computational biology to introduce students to this rapidly growing field. In Dynamic Models in Biology, the first text on dynamic models specifically written for undergraduate students in the biological sciences, ecologist Stephen Ellner and mathematician John Guckenheimer teach students how to understand, build, and use dynamic models in biology. Developed from a course taught by Ellner and Guckenheimer at Cornell University, the book is organized around biological applications, with mathematics and computing developed through case studies at the molecular, cellular, and population levels. The authors cover both simple analytic models--the sort usually found in mathematical biology texts--and the complex computational models now used by both biologists and mathematicians. Linked to a Web site with computer-lab materials and exercises, Dynamic Models in Biology is a major new introduction to dynamic models for students in the biological sciences, mathematics, and engineering.

An Introduction to Systems Biology

Design Principles of Biological Circuits

Author: Uri Alon

Publisher: CRC Press

ISBN: 1584886420

Category: Mathematics

Page: 320

View: 5284

Thorough and accessible, this book presents the design principles of biological systems, and highlights the recurring circuit elements that make up biological networks. It provides a simple mathematical framework which can be used to understand and even design biological circuits. The textavoids specialist terms, focusing instead on several well-studied biological systems that concisely demonstrate key principles. An Introduction to Systems Biology: Design Principles of Biological Circuits builds a solid foundation for the intuitive understanding of general principles. It encourages the reader to ask why a system is designed in a particular way and then proceeds to answer with simplified models.

Mathematical Models for Society and Biology

Author: Edward Beltrami

Publisher: Academic Press

ISBN: 0124046932

Category: Social Science

Page: 288

View: 8777

Mathematical Models for Society and Biology, 2e, is a useful resource for researchers, graduate students, and post-docs in the applied mathematics and life science fields. Mathematical modeling is one of the major subfields of mathematical biology. A mathematical model may be used to help explain a system, to study the effects of different components, and to make predictions about behavior. Mathematical Models for Society and Biology, 2e, draws on current issues to engagingly relate how to use mathematics to gain insight into problems in biology and contemporary society. For this new edition, author Edward Beltrami uses mathematical models that are simple, transparent, and verifiable. Also new to this edition is an introduction to mathematical notions that every quantitative scientist in the biological and social sciences should know. Additionally, each chapter now includes a detailed discussion on how to formulate a reasonable model to gain insight into the specific question that has been introduced. Offers 40% more content – 5 new chapters in addition to revisions to existing chapters Accessible for quick self study as well as a resource for courses in molecular biology, biochemistry, embryology and cell biology, medicine, ecology and evolution, bio-mathematics, and applied math in general Features expanded appendices with an extensive list of references, solutions to selected exercises in the book, and further discussion of various mathematical methods introduced in the book

Modeling Crop Production Systems

Principles and Application

Author: P Singh

Publisher: CRC Press

ISBN: N.A

Category: Technology & Engineering

Page: 510

View: 4866

The use of simulation models is a necessity and also an aid in the decision-making process in sustainable agricultural systems. Organizing the experimental knowledge of crop production systems without the book keeping and deductive methods of mathematics is very difficult. This book aims to guide readers in the process by which the properties of the systems can be grasped in the framework of mathematical structure with minimal mathematical prerequisites. The objective of this book is to help the undergraduate, graduate and post-graduate students in the disciplines of agronomy, plant breeding, agricultural meteorology, crop physiology, agricultural economics, entomology, plant pathology, soil science and ecology (environmental science). This book may also be useful for administrators in various agricultural universities in order to direct research, extension and teaching activities. Planners at national and state levels may also benefit from this book.

Handbook of Systems Biology

Concepts and Insights

Author: Marian Walhout,Marc Vidal,Job Dekker

Publisher: Academic Press

ISBN: 012385945X

Category: Science

Page: 552

View: 385

This book provides an entry point into Systems Biology for researchers in genetics, molecular biology, cell biology, microbiology and biomedical science to understand the key concepts to expanding their work. Chapters organized around broader themes of Organelles and Organisms, Systems Properties of Biological Processes, Cellular Networks, and Systems Biology and Disease discuss the development of concepts, the current applications, and the future prospects. Emphasis is placed on concepts and insights into the multi-disciplinary nature of the field as well as the importance of systems biology in human biological research. Technology, being an extremely important aspect of scientific progress overall, and in the creation of new fields in particular, is discussed in 'boxes' within each chapter to relate to appropriate topics. 2013 Honorable Mention for Single Volume Reference in Science from the Association of American Publishers' PROSE Awards Emphasizes the interdisciplinary nature of systems biology with contributions from leaders in a variety of disciplines Includes the latest research developments in human and animal models to assist with translational research Presents biological and computational aspects of the science side-by-side to facilitate collaboration between computational and biological researchers

Epigenetics and Systems Biology

Author: Leonie Ringrose

Publisher: Academic Press

ISBN: 0128030763

Category: Medical

Page: 286

View: 1118

Epigenetics and Systems Biology highlights the need for collaboration between experiments and theoretical modeling that is required for successful application of systems biology in epigenetics studies. This book breaks down the obstacles which exist between systems biology and epigenetics researchers due to information barriers and segmented research, giving real-life examples of successful combinations of systems biology and epigenetics experiments. Each section covers one type of modeling and one set of epigenetic questions on which said models have been successfully applied. In addition, the book highlights how modeling and systems biology relate to studies of RNA, DNA, and genome instability, mechanisms of DNA damage signaling and repair, and the effect of the environment on genome stability. Presents original research in a wider perspective to reveal potential for synergies between the two fields of study Provides the latest experiments in primary literature for the modeling audience Includes chapters written by experts in systems biology and epigenetics who have vast experience studying clinical applications

Theoretical Ecology

Principles and Applications

Author: Robert May

Publisher: Oxford University Press on Demand

ISBN: 0199209995

Category: Computers

Page: 257

View: 6078

Robert May's seminal book has played a central role in the development of ecological science. Originally published in 1976, this influential text has overseen the transition of ecology from an observational and descriptive subject to one with a solid conceptual core. Indeed, it is a testament to its influence that a great deal of the novel material presented in the earlier editions has now been incorporated into standard undergraduate textbooks. It is now a quarter of a century since the publication of the second edition, and a thorough revision is timely. Theoretical Ecology provides a succinct, up-to-date overview of the field set in the context of applications, thereby bridging the traditional division of theory and practice. It describes the recent advances in our understanding of how interacting populations of plants and animals change over time and space, in response to natural or human-created disturbance. In an integrated way, initial chapters give an account of the basic principles governing the structure, function, and temporal and spatial dynamics of populations and communities of plants and animals. Later chapters outline applications of these ideas to practical issues including fisheries, infectious diseases, tomorrow's food supplies, climate change, and conservation biology. Throughout the book, emphasis is placed on questions which as yet remain unanswered. The editors have invited the top scientists in the field to collaborate with the next generation of theoretical ecologists. The result is an accessible, advanced textbook suitable for senior undergraduate and graduate level students as well as researchers in the fields of ecology, mathematical biology, environment and resources management. It will also be of interest to the general reader seeking a better understanding of a range of global environmental problems.

Bayesian Networks in R

with Applications in Systems Biology

Author: Radhakrishnan Nagarajan,Marco Scutari,Sophie Lèbre

Publisher: Springer Science & Business Media

ISBN: 1461464463

Category: Computers

Page: 157

View: 5328

Bayesian Networks in R with Applications in Systems Biology is unique as it introduces the reader to the essential concepts in Bayesian network modeling and inference in conjunction with examples in the open-source statistical environment R. The level of sophistication is also gradually increased across the chapters with exercises and solutions for enhanced understanding for hands-on experimentation of the theory and concepts. The application focuses on systems biology with emphasis on modeling pathways and signaling mechanisms from high-throughput molecular data. Bayesian networks have proven to be especially useful abstractions in this regard. Their usefulness is especially exemplified by their ability to discover new associations in addition to validating known ones across the molecules of interest. It is also expected that the prevalence of publicly available high-throughput biological data sets may encourage the audience to explore investigating novel paradigms using the approaches presented in the book.

Mathematical Concepts and Methods in Modern Biology

Using Modern Discrete Models

Author: Raina Robeva,Terrell Hodge

Publisher: Academic Press

ISBN: 0124157939

Category: Mathematics

Page: 372

View: 3692

Mathematical Concepts and Methods in Modern Biology offers a quantitative framework for analyzing, predicting, and modulating the behavior of complex biological systems. The book presents important mathematical concepts, methods and tools in the context of essential questions raised in modern biology. Designed around the principles of project-based learning and problem-solving, the book considers biological topics such as neuronal networks, plant population growth, metabolic pathways, and phylogenetic tree reconstruction. The mathematical modeling tools brought to bear on these topics include Boolean and ordinary differential equations, projection matrices, agent-based modeling and several algebraic approaches. Heavy computation in some of the examples is eased by the use of freely available open-source software. Features self-contained chapters with real biological research examples using freely available computational tools Spans several mathematical techniques at basic to advanced levels Offers broad perspective on the uses of algebraic geometry/polynomial algebra in molecular systems biology

Dielectric Relaxation in Biological Systems

Physical Principles, Methods, and Applications

Author: Valerica Raicu,Yuri Feldman

Publisher: OUP Oxford

ISBN: 0191510041

Category: Science

Page: 432

View: 9091

The study of dielectric properties of biological systems and their components is important not only for fundamental scientific knowledge but also for its applications in medicine, biology, and biotechnology. The associated technique - known as dielectric spectroscopy - has enabled researchers to quickly and accurately acquire time- or frequency-spectra of permittivity and conductivity and permitted the derivation and testing of realistic electrical models for cells and organelles. This text covers the theoretical basis and practical aspects of the study of dielectric properties of biological systems, such as water, electrolyte and polyelectrolytes, solutions of biological macromolecules, cells suspensions and cellular systems. The authors' combined efforts provide a comprehensive and cohesive book that takes advantage of the expertise of multiple scientists involved in cutting-edge research in the specific sub-fields of bio-dielectric spectroscopy while maintaining its self-consistency through numerous discussions. The first six chapters cover theoretical, methodological and experimental aspects of relaxation and dispersion in biological dielectrics at molecular, cellular and cellular aggregate level. Applications are presented in the following chapters which are organized in the order of increased complexity, beginning with pure water, amino acids and proteins, continuing with vesicles and simple cells such as erythrocytes, and then with more complex, organelle-containing cells and cellular aggregates. Due to its broad coverage, the text could be used as a reference book by researchers, and as a textbook for upper-level undergraduate classes and graduate classes in (bio) physics, medical physics, quantitative biology, and engineering.

The Nature of Mathematical Modeling

Author: Neil A. Gershenfeld

Publisher: Cambridge University Press

ISBN: 9780521570954

Category: Mathematics

Page: 344

View: 3043

This book first covers exact and approximate analytical techniques (ordinary differential and difference equations, partial differential equations, variational principles, stochastic processes); numerical methods (finite differences for ODE's and PDE's, finite elements, cellular automata); model inference based on observations (function fitting, data transforms, network architectures, search techniques, density estimation); as well as the special role of time in modeling (filtering and state estimation, hidden Markov processes, linear and nonlinear time series). Each of the topics in the book would be the worthy subject of a dedicated text, but only by presenting the material in this way is it possible to make so much material accessible to so many people. Each chapter presents a concise summary of the core results in an area, providing an orientation to what they can (and cannot) do, enough background to use them to solve typical problems, and pointers to access the literature for particular applications.

Principles of Mathematical Modeling

Author: Clive L. Dym

Publisher: Academic Press

ISBN: 9780122265518

Category: Mathematics

Page: 303

View: 6817

This book provides a readable and informative introduction to the development and application of mathematical models in science and engineering. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools (dimensional analysis, scaling techniques, and approximation and validation techniques). The second half then applies these foundational tools to a broad variety of subjects, including exponenttial growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, and social decision making. An extensive collection of more than 360 problems offer ample opportunity in both a formal course and for the individual reader. (Midwest).