Mathematical Modeling in Systems Biology: An Introduction

by Brian P. Ingalls

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 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.

Genres: Science

408 pages, Hardcover

First published July 5, 2013

Reviews

[John · Rating 4 out of 5]

"Mathematical Modeling in Systems Biology" is written to be read as a math book, where you stop and do the exercises. I'm pleased to report that it is still informative for those who want a faster reading, but you will feel like you are missing out due to the amount of content you end up skipping over. Even the quicker-paced reader will come to understand an interesting variety of simple ("just complex enough to do something different than the previous models") biological system models across a range of biological settings. These settings include metabolism, gene regulation, signal transduction, and electrophysiology, starting from the more fundamental biochemical kinetics.

You'll find this book most rewarding if you already have an understanding of system dynamics more generally: negative feedback, positive feedback, filter-like behaviors, logic-gate like behaviors, etc. The level of the mathematics is perfect for somebody like me, who took calculus and differential equations, and while not having an occasion to use them very often, still has an appreciation for these dynamics.

At all times, this book is exceptionally clear and direct. This book might feel a bit undermotivated or undercontextualized at times, which is made up for by the sharp pace allowed by the beautiful spareness of mathematical presentation, which means you will be past the quite rare uninteresting bit before you know it.

It's good to know this book is still on my shelf, available should I choose to go back and do the exercises, or freshen myself up on some particular dynamics.

[Tessa · Rating 4 out of 5]

Very clear language and a nice introductory treatment of differential models in cell biology (e.g. enzyme kinetics, gene regulatory networks, action potentials). I finally understood some model analysis methods (bifurcation diagrams, sensitivity analysis, etc.) that I'd previously seen because they were presented here with such engaging context. Only issue I see is a lack of worked examples within the text body, but the solutions to all the exercises are available on the author's website and most of the models are computational.

[Philip · Rating 5 out of 5]

I have read a lot of books on this subject, and this is the one I'd most recommend. I know no other book with such a wealth of important applications, so clearly and elegantly explained. This book brings the reader right up to the level of current research and shows, explicitly, how the calculations are actually done.

[Dominik · Rating 4 out of 5]

Nice introduction, I missed chapter summaries and a glossary