UK Nonlinear News, August 1998

Dynamics of Cell and Tissue Motion

Edited by Wolfgang Alt, Andreas Deutsch and Graham Dunn

Mathematics and biosciences in interaction, Birkhäuser 1997

Reviewed by: Dr Steve Baigent.

In March 1995 some 45 biologists, physicists and mathematicians from Europe and North America assembled in Bonn-Roettgen for a workshop on cell and tissue motion. `Dynamics of Cell and Tissue Motion' is a wide-ranging selection of contributed articles which emerged from the workshop as the `hot topics' of cell locomotion. The resulting book is well-organised and contains a wealth of information for the cell motility specialist or someone interested in biomathematical modelling in the broader sense. For the dynamicist, the material covers a wide spectrum of dynamical systems, including moving boundary problems, integro-differential equations, stochastic differential equations, reaction-diffusion systems, cellular automata, and discrete-continuous hybrid models. The general emphasis, however, is on the model construction from the biology and experimental data, and the results of model simulations and their biological implications, rather than the mathematical details of the solution. In any case, most of the models are simply too complex for anything else but numerical study.

The book is arranged into four chapters, starting at the lowest level of organisation - motion of the single cell - and finishing with the highest level - tissue formation and morphogenesis. This reflects the favoured approach of identifying different organisational levels of multicellular systems, and then investigating the emergence from one level to the next. Each chapter consists of an introduction to the topic and the chapter layout, followed by the articles themselves, which deal with both experiment and theory, and concludes with a discussion and the identification of open problems.

Chapter I deals with motility of single cells, and in particular that of a cell crawling over a substratum by protrusion and retraction of filopodia and lamellipodia. The early articles cover experimental techniques for observing and quantifying cell movement, including new methods of image processing and statistical autocorrelation. Later articles in the chapter generally concern two-phase fluid continuum models for actomyosin dynamics within the cytoskeleton, as applied to cell division, protrusion-retraction dynamics and bacteria migration.

Chapter II deals with adhesion, traction and the regulation of these processes. The first few articles deal with experimental techniques for measuring adhesion and traction and how they relate to temporal and spatial patterns of cell motility. The later articles contrast receptor-mediated chemotaxis models with contact guidance models for cell migration, and discuss applications to wound healing. The last article compares wound healing and tumour growth, and raises the more general question of whether seemingly unrelated biological processes could be linked via universal mechanisms, and if mathematical modelling could unravel those links.

Chapter III takes a step up to the next organisational level and deals chiefly with self-organisation. In the first article, the authors describe a collection of models in which cells communicate by sensing their relative orientations. This contrasts the theme of the following articles which consider the cell aggregation through chemotaxis. The second article discusses a random-walk model, with its continuum limit, for myxobacteria migration and the rest of the chapter is devoted to a range of different models describing the well-known phenonema of streaming and aggregation for the slime mould dictyostelium discoideum. These last articles compare a variety of different discrete-continuous hybrid approaches to modelling dictyostelium pattern formation.

The fourth and final chapter looks at possible applications of classical continuum mechanics and statistical physics to modelling cell and tissue geometry and morphogenesis. The chapter opens with a discussion of how global mechanical stress fields can help direct cell movement during development, and how models incorporating stresses compare with models based on the positional information concept of Wolpert. Next follows a series of articles describing various models for pattern formation in plants, whose cell walls are rigid in comparison to those of animals. These include some interesting applications of plate bending and buckling theory to pattern formation. The final article in the chapter discusses an interesting application of the maximum entropy principle to determine the quasi-steady state growth of epithelial tissue.

Being of specialist material, and containing a good deal of biology, this book is heavy reading for a dynamicist without a reasonable knowledge of cell biology. Nevertheless, it is an excellent collection of experimentally-motivated and biologically realistic models for cell locomotion, and serves as a good example of biomathematics for biology's sake. 

Dr Stephen Baigent

Wellcome Trust Mathematical Biology Research Fellow
Centre for Nonlinear Dynamics and Its Applications
Department of Civil and Environmental Engineering
University College London
Gower Street
London WC1E 6BT

email: s.baigent@ucl.ac.uk



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