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Mathematical Modeling of Biological Systems, Volume I: Celular Biophysics, Regulatory Networks, Development, Biomedicine, and Data Analysis

A. Deutsch, L. Brusch, H. Byrne, G. de Vries, and H. Herzel, editors
Publication Date: 
Number of Pages: 
Modeling and Simulation in Science, Engineering and Technology
[Reviewed by
William J. Satzer
, on

Biology has no equivalent of Newton’s laws or Maxwell’s equations and almost certainly never will. If one accepts that, then doing mathematical biology is going to be considerably different than doing mathematical physics. Where and how can mathematicians profitably engage with biologists? Judging from this volume, the interaction works best where biologists work with mathematicians to identify the central problems in the life sciences and collaborate to develop effective mathematical and computational approaches. Those central problems span the gamut from the organization of individual cells to the dynamics of populations, and many of them are discussed in this book.

Mathematical Modeling of Biological Systems derives from the 2005 Conference on Mathematical and Theoretical Biology. Volume 1 has thirty-two papers that address topics in five broad areas: cellular biophysics, regulatory networks, development, biomedical applications and data analysis. The papers are highly specialized and there are no expository introductions. A general theme is the progression in each application area from experimental research to mathematical modeling, from there to construction of a more abstract mathematical framework and thence to new biological hypotheses. Desirable tools are efficient algorithms for complex computations and visualization, especially in the areas of molecular biology and genetics.

Here’s a sampling of the papers in this volume:

  • a clever application of queuing theory to a biocatalytic system wherein the authors use the concept of “mass service” to replace the usual mass action principle;
  • use of transition networks (from graph theory via computer science) to model transitions between stable states in simulations of molecular dynamics;
  • mathematical modeling and computational analysis of pigmentation pattern formation in butterfly wings;
  • analysis of the early stages of atherosclerosis based on arterial geometry (especially vessel curvature) and wall shear stress; and
  • evaluation of gene expression using singular value decomposition of DNA microarray data.

This is a volume directed at specialists, but it is possible to find one’s way to interesting results without too much specialized knowledge. The range of applications is enormous, and this is just Volume 1. Topics addressed in Volume 2 include epidemiology, immunology, evolution and ecology.

Bill Satzer ( is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.


Part I. Cellular Biophysics

Multiparticle Direct Simulation of Photosynthetic Electron Transport Processes / Ilya B. Kovalenko, Galina Yu. Riznichenko

Selective Regulation of Protein Activity by Complex Ca2+ Oscillations: A Theoretical Study / Beate Knoke, Marko Marhl, Stefan Schuster

Phase Separation in Eukaryotic Directional Sensing / Andrea Gamba, Antonio de Candia, Stefano Di Talia, Antonio Coniglio, Federico Bussolino, Guido Serini

Protein Domains of GTPases on Membranes: Do They Rely on Turing's Mechanism? / Lutz Brusch, Perla Del Conte-Zerial, Yannis Kalaidzidis, Jochen Rink, Bianca Habermann, Marino Zerial, Andreas Deutsch

In Vitro Tubulogenesis of Endothelial Cells: Analysis of a Bifurcation Process Controlled by a Mechanical Switch / Philippe Tracqui, Patrick Namy, Jacques Ohayon

Nonexponential Time Distributions in Biocatalytic Systems: Mass Service Replacing Mass Action / Peter W. Kühl, Manfred Jobmann