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A guide to numerical modelling in systems biology
Deuflhard P., Röblitz S., Springer Publishing Company, Incorporated, New York, NY, 2015. 168 pp. Type: Book (978-3-319200-58-3)
Date Reviewed: Nov 24 2015

I had hoped to acquire further notions in systems biology, a new interdisciplinary area aimed at modeling and identifying the parameters of biochemical, physiological, molecular, and genetic processes, while also finding tools to build such models. This is in line with the authors’ statement in the preface that this is “not a book on systems biology but on computational methods in systems biology.” Unfortunately, after having read the whole volume twice, the actual scope does not include the range of computational techniques found in systems biology literature or research papers. Instead, it focuses almost solely on the mundane mathematical topic of ordinary differential equations (ODEs) and their parameter estimation, with a few examples: population dynamics, multiple dose administration of drugs, biomolecular reactions, enzyme kinetics, the predator/prey game, and the menstrual cycle. These examples taken together do not represent the diversity and range of systems biology, especially at the level of molecular, genetic, ribonucleic acid (RNA), anti-body, and so on [1].

Chapter 1 introduces the basic properties of ODEs (classes, uniqueness, sensitivity, stability, singularity) or initial value problems, and relates them to some of the small examples listed above. Chapter 2 studies ODEs from the point of view of numerical techniques for simulation: discretization errors, accuracy, stability, Runge-Kutta integration, extrapolation, collocation methods, and more. Chapter 3 deals with parameter identification in ODEs, from least squares techniques to generalized matrix inverses and nonlinear gradient methods, with some numerical illustrations. The appendix contains five specific algorithms. An additional appendix lists some numerical analysis software packages. There is also a set of references and a good index.

Reflecting back on the preface, one may not be convinced that this volume will make the mathematics presented more understandable than many of the more pedagogical books in mathematics (for example, even an old reference like Varaiya’s [2]) that have excelled in illustrating the key notions, through geometrical figures or time dependent evolutions, in the same amount of pages (or less), a wider diversity of techniques, and several biological problems. In this volume, however, chapters 2 and 3 provide an in-depth look at many of the simulation or identification validation techniques that are required if uncertainty is high and/or samples are few. In this way, it extends the raw output from the listed software packages, but does not explain well how they operate. It should therefore be compared more with other work in automatic control and the identification of biological systems (such as the International Federation of Automatic Control (IFAC) Symposiums on Biological and Medical Systems (BMS)).

Thus, the prime readership for this volume is to be found more amongst advanced researchers in systems biology trying to find reasons for unstable results of some ODE simulation or identification packages.

Reviewer:  Prof. L.-F. Pau, CBS Review #: CR143971 (1602-0106)
1) Crampin, E. J. System identification challenges from systems biology. In Proc. of the 14th IFAC Symposium on System Identification. International Federation of Automatic Control, 2006, 81–93.
2) Varaiya, P. P. Notes on optimization. Van Nostrand Reinhold Co., New York, NY, 1972.
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