A Guide to Numerical Modelling in Systems Biology
A Guide to Numerical Modelling in Systems Biology

Author: Peter Deuflhard

Publisher: Springer

Published: 2015-07-06

Total Pages: 185

ISBN-13: 3319200593

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This book is intended for students of computational systems biology with only a limited background in mathematics. Typical books on systems biology merely mention algorithmic approaches, but without offering a deeper understanding. On the other hand, mathematical books are typically unreadable for computational biologists. The authors of the present book have worked hard to fill this gap. The result is not a book on systems biology, but on computational methods in systems biology. This book originated from courses taught by the authors at Freie Universität Berlin. The guiding idea of the courses was to convey those mathematical insights that are indispensable for systems biology, teaching the necessary mathematical prerequisites by means of many illustrative examples and without any theorems. The three chapters cover the mathematical modelling of biochemical and physiological processes, numerical simulation of the dynamics of biological networks and identification of model parameters by means of comparisons with real data. Throughout the text, the strengths and weaknesses of numerical algorithms with respect to various systems biological issues are discussed. Web addresses for downloading the corresponding software are also included.

Biological Modeling and Simulation
Biological Modeling and Simulation

Author: Russell Schwartz

Publisher: MIT Press

Published: 2008-07-25

Total Pages: 403

ISBN-13: 0262303396

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A practice-oriented survey of techniques for computational modeling and simulation suitable for a broad range of biological problems. 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.

Mathematical Modeling in Systems Biology
Mathematical Modeling in Systems Biology

Author: Brian P. Ingalls

Publisher: MIT Press

Published: 2022-06-07

Total Pages: 423

ISBN-13: 0262545829

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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.

A Biologist's Guide to Mathematical Modeling in Ecology and Evolution
A Biologist's Guide to Mathematical Modeling in Ecology and Evolution

Author: Sarah P. Otto

Publisher: Princeton University Press

Published: 2011-09-19

Total Pages: 745

ISBN-13: 1400840910

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Thirty years ago, biologists could get by with a rudimentary grasp of mathematics and modeling. Not so today. In seeking to answer fundamental questions about how biological systems function and change over time, the modern biologist is as likely to rely on sophisticated mathematical and computer-based models as traditional fieldwork. In this book, Sarah Otto and Troy Day provide biology students with the tools necessary to both interpret models and to build their own. The book starts at an elementary level of mathematical modeling, assuming that the reader has had high school mathematics and first-year calculus. Otto and Day then gradually build in depth and complexity, from classic models in ecology and evolution to more intricate class-structured and probabilistic models. The authors provide primers with instructive exercises to introduce readers to the more advanced subjects of linear algebra and probability theory. Through examples, they describe how models have been used to understand such topics as the spread of HIV, chaos, the age structure of a country, speciation, and extinction. Ecologists and evolutionary biologists today need enough mathematical training to be able to assess the power and limits of biological models and to develop theories and models themselves. This innovative book will be an indispensable guide to the world of mathematical models for the next generation of biologists. A how-to guide for developing new mathematical models in biology Provides step-by-step recipes for constructing and analyzing models Interesting biological applications Explores classical models in ecology and evolution Questions at the end of every chapter Primers cover important mathematical topics Exercises with answers Appendixes summarize useful rules Labs and advanced material available

Dynamical Modeling of Biological Systems
Dynamical Modeling of Biological Systems

Author: Stilianos Louca

Publisher: Stilianos Louca

Published: 2023-06-07

Total Pages: 545

ISBN-13:

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This book introduces concepts and practical tools for dynamical mathematical modeling of biological systems. Dynamical models describe the behavior of a system over time as a result of internal feedback loops and external forcing, based on mathematically formulated dynamical laws, similarly to how Newton's laws describe the movement of celestial bodies. Dynamical models are increasingly popular in biology, as they tend to be more powerful than static regression models. This book is meant for undergraduate and graduate students in physics, applied mathematics and data science with an interest in biology, as well as students in biology with a strong interest in mathematical methods. The book covers deterministic models (for example differential equations), stochastic models (for example Markov chains and autoregressive models) and model-independent aspects of time series analysis. Plenty of examples and exercises are included, often taken or inspired from the scientific literature, and covering a broad range of topics such as neuroscience, cell biology, genetics, evolution, ecology, microbiology, physiology, epidemiology and conservation. The book delivers generic modeling techniques used across a wide range of situations in biology, and hence readers from other scientific disciplines will find that much of the material is also applicable in their own field. Proofs of most mathematical statements are included for the interested reader, but are not essential for a practical understanding of the material. The book introduces the popular scientific programming language MATLAB as a tool for simulating models, fitting models to data, and visualizing data and model predictions. The material taught is current as of MATLAB version 2022b. The material is taught in a sufficiently general way that also permits the use of alternative programming languages.

Multiscale Models in Mechano and Tumor Biology
Multiscale Models in Mechano and Tumor Biology

Author: Alf Gerisch

Publisher: Springer

Published: 2018-03-16

Total Pages: 205

ISBN-13: 3319733710

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This book presents and discusses the state of the art and future perspectives in mathematical modeling and homogenization techniques with the focus on addressing key physiological issues in the context of multiphase healthy and malignant biological materials. The highly interdisciplinary content brings together contributions from scientists with complementary areas of expertise, such as pure and applied mathematicians, engineers, and biophysicists. The book also features the lecture notes from a half-day introductory course on asymptotic homogenization. These notes are suitable for undergraduate mathematics or physics students, while the other chapters are aimed at graduate students and researchers.

Stochastic Dynamics in Computational Biology
Stochastic Dynamics in Computational Biology

Author: Stefanie Winkelmann

Publisher: Springer Nature

Published: 2021-01-04

Total Pages: 284

ISBN-13: 3030623874

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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.

Finite Difference Computing with Exponential Decay Models
Finite Difference Computing with Exponential Decay Models

Author: Hans Petter Langtangen

Publisher: Springer

Published: 2016-06-10

Total Pages: 210

ISBN-13: 3319294393

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This text provides a very simple, initial introduction to the complete scientific computing pipeline: models, discretization, algorithms, programming, verification, and visualization. The pedagogical strategy is to use one case study – an ordinary differential equation describing exponential decay processes – to illustrate fundamental concepts in mathematics and computer science. The book is easy to read and only requires a command of one-variable calculus and some very basic knowledge about computer programming. Contrary to similar texts on numerical methods and programming, this text has a much stronger focus on implementation and teaches testing and software engineering in particular.

Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models
Computing Characterizations of Drugs for Ion Channels and Receptors Using Markov Models

Author: Aslak Tveito

Publisher: Springer

Published: 2016-04-19

Total Pages: 279

ISBN-13: 331930030X

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Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various drugs. Examples in the text include stochastic calcium release from internal storage systems in cells, as well as stochastic models of the transmembrane potential. Well known Markov models are studied and a systematic approach to including the effect of mutations is presented. Lastly, the book shows how to derive the optimal properties of a theoretical model of a drug for a given mutation defined in terms of a Markov model.

Numerical Linear Algebra and Matrix Factorizations
Numerical Linear Algebra and Matrix Factorizations

Author: Tom Lyche

Publisher: Springer Nature

Published: 2020-03-02

Total Pages: 376

ISBN-13: 3030364682

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After reading this book, students should be able to analyze computational problems in linear algebra such as linear systems, least squares- and eigenvalue problems, and to develop their own algorithms for solving them. Since these problems can be large and difficult to handle, much can be gained by understanding and taking advantage of special structures. This in turn requires a good grasp of basic numerical linear algebra and matrix factorizations. Factoring a matrix into a product of simpler matrices is a crucial tool in numerical linear algebra, because it allows us to tackle complex problems by solving a sequence of easier ones. The main characteristics of this book are as follows: It is self-contained, only assuming that readers have completed first-year calculus and an introductory course on linear algebra, and that they have some experience with solving mathematical problems on a computer. The book provides detailed proofs of virtually all results. Further, its respective parts can be used independently, making it suitable for self-study. The book consists of 15 chapters, divided into five thematically oriented parts. The chapters are designed for a one-week-per-chapter, one-semester course. To facilitate self-study, an introductory chapter includes a brief review of linear algebra.