Table Of ContentMathematics and Biosciences in Interaction
Managing Editor
Wolfgang Alt
Division of Theoretical Biology
Botanical Institute
University of Bonn
Kirschallee 1
D-53115 Bonn
e-mail: wolf.alt@uni-bonn.de
Editorial Board
Fred Adler (Dept. Mathematics, Salt Lake City)
Mark Chaplain (Dept. Math. & Computer Sciences, Dundee)
Andreas Deutsch (Div. Theoretical Biology, Bonn)
Andreas Dress (Center for Interdisciplinary Research for Structure Formation (CIRSF), Bielefeld)
David Krakauer (Dept. of Zoology, Oxford)
Robert T. Tranquillo (Dept. Chem. Engineering, Minneapolis)
Mathematics and Biosciences in Interaction is devoted to the publication of advanced textbooks, mono
graphs, and multi-authored volumes on mathematical concepts in the biological sciences. It concentra
tes on truly interdisciplinary research presenting currently important biological fields and relevant
methods being developed and refined in close relation to problems and results relevant for experimental
bioscientists.
The series aims at publishing not only monographs by individual authors presenting their own results,
but welcomes, in particular, volumes arising from collaborations, joint research programs or works
hops. These can feature concepts and open problems as a result of such collaborative work, possibly
illustrated with computer software providing statistical analyses, simulations or visualizations.
The envisaged readership includes researchers and advanced students in applied mathematics -
numerical analysis as well as statistics, genetics, cell biology, neurobiology, bioinformatics, biophysics,
bio(medical) engineering, biotechnology, evolution and behavioral sciences, theoretical biology system
theory.
POLYME
and
CELLD YNAMICS
Multiscale Modeling and Numerical Simulations
Wolfgang Alt
Mark Chaplain
Michael Griebel
JCtrgen Lenz
Editors
Springer Basel AG
Editors:
Prof. Dr. Wolfgang Alt Prof. Dr. Michael Griebel
Abteilung Theoretische Biologie Institut für Angewandte Mathematik (IAM)
Botanisches Institut Abteilung Wissenschaftliches Rechnen und
Universität Bonn Numerische Simulation
Kirschallee 1 Universität Bonn
D-53115 Bonn Wegeier Str. 6
Germany D-53115 Bonn
Germany
Prof. Dr. Mark Chaplain Dr. Jürgen Lenz
Department of Mathematics Bioreact GmbH
University of Dundee Botanisches Institut
23 Perth Road Kirschallee 1
Dundee DDI 4HN 53115 Bonn
UK Germany
A CIP catalogue record for this book is available form the Library of Congress, Washington D.C., USA
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Die Deutsche Bibliothek verzeichnet diese Publikation in der Deutschen Nationalbiografie; detaillierte bibliografi
sche Daten sind im Internet über http://dnb.ddb.de abrufbar.
The use of registered names, trademarks etc. in this publication, even if not identified as such, does not imply
that they are exempt from the relevant protective laws and regulations or free for general use.
ISBN 978-3-0348-9417-3 ISBN 978-3-0348-8043-5 (eBook)
DOI 10.1007/978-3-0348-8043-5
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned,
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© 2003 Springer Basel AG
Originally published by Birkhäuser Verlag Basel, Switzerland in 2003
Softcover reprint of the hardcover 1st edition 2003
Member of the BertelsmannSpringer Publishing Group
Printed on acid-free paper produced from chlorine-free pulp. TFC «
Cover design: Armando Losa, graphic designer
Cover illustration: see p. 12, with the friendly permission of D.C. Rapaport
ISBN 978-3-0348-9417-3
987654321 www.birkhauser-science. com
Table of Contents
Preface ................................................................... vii
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i x . . . . . . . . . . . . . . . . . .
Part I: Molecular Dynamics and Protein Configuration
Introduction to Part I ....................................................... 3
Dennis C. Rapaport
Molecular Dynamics Studies of Micelle and Capsid Self-assembly 7
Daniel Hoffmann
A Functional Study on Saposin Band C Using Experimentally
Validated Models ..................................................... 19
Werner G. Krebs, Mark Gerstein
A Review of the Morph Server and the Macromolecular Motions Database:
A Standardized System for Analyzing and Visualizing
Macromolecular Motions in a Database Framework ...................... 29
Part II: Polymer Dynamics and Cell Motility
Introduction to Part II ...................................................... 45
Roland Rzehak, Andreas Arend, Diego Kienle, Walter Zimmennann
Brownian Dynamics of Flexible Polymers in Flow ....................... 49
uno Farkas, Imre Derenyi, Tamas Vicsek
A Microscopic Model for the Dynamics of Actin Filaments
in Motility Assays and Its Numerical Simulation . . . . . . . . . . . . . . . . . . . . .6 .9 . . .
Jurgen Lenz, Dieter Felix
Multiparticie Modeling of Actin-Myosin Networks:
From Molecular Interactions to Cell Motility. . . . . . . . . . . . . . . .. . .. .. .. .. . 7. 5
Angelique Stephanou, Xavier Ronot, Philippe Tracqui
Analysis of Cell Motility Combining Cytomechanical Model Simulations
and an Optical Flow Method . .. . . . . . . .. . .. .. . . . . . . . . . . . . . . . . . . . . 91. . . . . . .
Jeanie L. Drury, Micah Dembo
Micropipet Aspiration of the Human Neutrophil ......................... 113
Emmanuel Promayon, Jean-Louis Martiel, Philippe Tracqui
Physical-object-oriented 3D Simulations of Cell Deformations
and Migration ........................................................ 125
vi Table of Contents
Part III: Multicellular Dynamics
Introduction to Part III ..................................................... 141
Aaron Fogelson. Haoyu Yu. Andrew Kuharsky
Computational Modeling of Blood Clotting: Coagulation and
Three-dimensional Platelet Aggregation ................................ 145
Hans-Joachim Bungartz. Martin Kuhn. Miriam Mehl. Stefan Wurtz
Space-and Time-resolved Simulations of Processes in Biofilm Systems
on a Microscale ...................................................... 155
Dirk Drasdo
On Selected Individual-based Approaches to the Dynamics
in Multicellular Systems .............................................. 169
Andras Czir6k. Andreas Deutsch. Michael Wurzel
Individual-based Models of Cohort Migration in Cell Cultures ............ 205
Wolfgang Alt. Till Bretschneider. Ralf Muller
Interactive Movement, Aggregation, and Swarm Dynamics ............... 221
R. Brent Rice. Victor H. Barocas
A Discrete-cell Model of Tissue-equivalent Compaction .................. 243
Alexander R.A. Anderson
A Hybrid Discrete-continuum Technique for Individual-based
Migration Models ............................................ ........ 251
Alexander R.A. Anderson. Alan W Pitcairn
Application of the Hybrid Discrete-continuum Technique . . . . . . . . . . . . . 2.6 .1 . .
List of contributors and workshop participants ....... . . . . . . . . . . . . . . . . . .2 .8 .1 . . . . .
Index ...... ........ .................... ..................... .............. 285
Color Plates
Preface
It was at the inviting guest and seminar house 'Magdalena', run by the 'Franziskanerin
nen von Nonnenwerth' (Fransiscan nuns) in Bad Honnef near Bonn that in June 2000 the
International Workshop on Numerical Simulations of Polymer and Cell Dynamics took
place. In the peaceful but inspiring atmosphere of a monastery-like cloister, the workshop
collected ideas from more than 30 scientists from various fields and brought them into a
fruitful week of interdisciplinary exchange and collaboration. Coming from several Euro
pean countries, Israel, and the USA, the participants represented institutions or research
groups in applied and numerical mathematics, scientific computing, theoretical physics,
molecular biophysics, cell and molecular biology as well as chemical and biomedical
engineering.
The Workshop was financially supported by a DFG research program (SFB 256)
on 'Nonlinear Partial Differential Equations'. For the very effective local organization,
we express our thanks to all those who enabled the successful meeting, in particular to
our ever kind secretary Anke Thiedemann. At Bonn University, the two local organizing
groups in some sense span the wide spectrum of our common research interests, namely
the Division of Scientific Computing within the Institute of Applied Mathematics and the
Division of Theoretical Biology within the Botanical Institute. In the meantime, these
two groups are now even more focused on the central topic of this Workshop and of this
book, namely, Multiscale Modelling and Numerical Simulations with applications to the
physical chemistry of polymers and the biophysics of cells, and have implemented it into
the new DFG research program at our University (SFB 611) on 'Singular Phenomena and
Scaling in Mathematical Models' .
Moreover, during the (longer than anticipated) period between collecting the first
contributions to this Volume and its final publication within the Birkhauser book series
'Mathematics and Biosciences in Interaction " collaborations between workshop partici
pants increased. Thus, the articles in the three parts of this book reflect the scientific dis
course during the workshop and afterwards. The topics are of ongoing importance, since
they address a series of principle problems in mathematical modeling and adequate meth
ods for numerical simulation. All contributions have been carefully reviewed by expert
referees in the field and by the editors.
Besides 16 color plates and a subject index at the end of the book, there is an updated
address list not only of all corresponding authors but also of all workshop participants.
The editors hope that their study of the presented scientific concepts and methods will
stimulate the reader's own research ideas or activities.
Bonn, Wolfgang Alt, Mark Chaplain,
September 2002 Michael Griebel, Jiirgen Lenz
Introduction
The theme of these workshop proceedings, namely, modeling and simulation of poly
mer and cell dynamics, is, on the one hand, 'classical', as it concerns the description,
explanation, and reproduction of the basic mechanisms of the application of force and
the resulting motion. Hence, it essentially requires adequate methods from physical and
mathematical theories on spatial and temporal scaling levels that are beyond quantum
mechanics but are below systems theory of whole-body organisms and their evolution
(see table on page xi).
On the other hand, the theme is quite 'modem', as it asks for quantitative solutions
to basic questions in Molecular and Cell Biology, now the central field of life sciences,
including relevant applications in biotechnology and medicine. In addition, the topics and
concepts presented here are part of an ever-continuing attempt to understand the border
lines between the more 'passive' dynamics of pure matter, as molecules or polymers, and
the more 'active' processes of structuring, organization, and regulation within living units,
such as biological cells, tissues, or organs.
Therefore, the scientific contributions collected in this book, dealing with typical
case studies of polymer and cell dynamics, are ordered into three parts of increasing 'bi
ological complexity'. Part I on Molecular Dynamics and Protein Configuration shows
how to represent the assembly and formation of elementary lipid or protein aggregates and
how to study and classify geometric configuration changes in functional domains of en
zymes or 'motor' proteins. Applications range from biomedical engineering to molecular
pharmaceutics to a potential treatment of specific diseases.
Moving to the more complex realm of polymer organization, Part II on Polymer
Dynamics and Cell Motility first deals with typical deformations of polymer chains, fil
aments, or networks and their interaction with surrounding media, ligands, cross-linkers,
or molecular motors. These models of polymer dynamics, at least potentially, serve as
ingredients for modeling and simulation on the next higher organizational level: shape
changes and motility of single cells such as leukocytes, fibroblasts, or tumor cells. The
aim of such theoretical analyses is not only to explain possible mechanisms of cell dy
namics but also to offer quantitative tools for the characterization and classification of
different cell types with potential applications to immunology and cancer research.
Finally, Part III on Multicellular Systems translates some of these concepts and
methods, developed for multiparticle systems, to the level of cell-cell and cell-medium
interactions and adds the necessary modeling elements for cell growth kinetics, cell ad
hesion, or cell-cell communication by chemical signalling and control loops or by me
chanical force transduction via extracellular matrices. In particular, it presents simulation
models and corresponding applications for the investigation of blood clotting, biofilm
x Introduction
formation, which occurs, for example, in waste-water technology, and tissue formation
and regeneration, relevant in wound healing, tumor invasion, or angiogenesis. Again, the
quantitative analyses offered can help to improve data evaluation of 2D and 3D assays for
cell and tissue behavior in vitro and in situ.
It is obvious that in order to explore the modeling of such phenomena in this wide
range of biochemical, biotechnical, and biomedical applications - from molecular dynam
ics to tissue formation - very differing scales have to be considered: spatial scales reaching
from nanometers to centimeters, temporal scales from microseconds to hours. Although
in various recent biological research programs such tasks as 'exploring the whole genome
and proteome of an organism' or 'remodeling and simulation of the whole ceIl' have been
announced by referring to the increased computational power of new computer gener
ations, it seems to be unrealizable to include the very microscale models directly into
simulation models on very macroscale levels (both spatially and temporally). Rather, the
modeling experience so far shows that it is already challenging enough to consider pairs or
triples of particular submodels on certain selected micro-, meso-and macro-scale levels,
relative to one another.
For example, the molecular dynamics approach used in Part I is based on 'meso
scopic' approximations of field potentials gained from more 'microscopic' quantum dy
namics and finally leads to relatively 'macroscopic' geometric and dynamic descriptions
of whole proteins or even of protein assemblies (such as micelles or capsoids).
Based on such 'molecular' submodels, the multiparticle models for polymer dy
namics in Part II use lumped groups of protein-monomers and their approximate ('elas
tic') interaction properties as 'mesocopic' ingredients to simulate the more 'macroscopic'
motion of single polymer chains. Furthermore, Part II presents a modeling approach for
polymer network dynamics, where again lumped groups, now of polymer-filaments, are
analogously used as units of a multiparticle model for simulating the spontaneous cluster
ing and bundeling of an actin-myosin cortex near the model plasma membrane.
Finally, in Part III this whole story of multi scale modeling is repeated on the level of
multicellular systems, namely, by developing individual-based multiparticle models using
'mesoscopic' interaction potentials or fields derived from more 'microscopic' submodels
for chemical or mechanical cell-cell interactions, in order to simulate aggregation and
tissue-formation dynamics.
On these different modeling levels, one common scaling problem appears: should a
sub model be explicitly used, e.g., by complete calculation on the relatively 'microscopic'
scale, or only in a 'coarse-grained' version, e.g., by implementing a rescaled and more
easily computable approximation of it? Typical examples occur when polymers (Part II)
or celIs (Part III) are embedded in a viscous fluid or gel and thereby 'influence' each other
indirectly by global flow or tension. Then high-power simulations can solve the full hy
drodynamic or viscoelastic evolution equations (or realize the corresponding stochastic
multiparticle process), and, alternatively, 'cheaper' simulations can use analytical or nu
merical approximations of pseudo-steady-state solutions (or of continuum versions of the
discrete model) to compute the required expressions for flow or tension only at discrete
positions of polymers or cells. The decision whether to choose the microscopic or the
meso scopic scaling variant usually depends on the desired or required output of the actual
Introduction xi
Scaling of Simulation Models for Polymer and Cell Dynamics
Particles Space Time Interactions Models & methods
scale scale forces & motions
Atoms ~A ~ j1sec Gravity, electromagnetic, SchrOdinger & Hartree-Fock
weak forces, (quasi-)periodic equations, MOLECULAR
or chaotic, dynamic states DYNAMICS, interaction
potentials
Molecules ~nm ~ msec Covalent binding, weak (Stochastic) multi-particle
bonds, hydration, stochastic systems, orientation & hinge
rotation, diffusion dynamics, protonation
dynamics, Poisson equation
Polymers 50nm sec Drag & elasticity, (Semi-)flexible string model,
~
~ j1m conformational changes, Stokeslet approximations,
flickering, diffusion THERMODYNAMICS,
binding & rupture dynamics
Polymer 10 min Steric restriction, (Stochastic) multi-particle
systems ~ lOOj1m cross-linking, shear forces, models, cross-linking &
mixture & segregation, contraction, two-phase flow
deformation, flow equations, (an-)isotropic
(non-)Newtonian fluids
Cells 50j1m mm Receptor kinetics, cell 'Tensegrity' model, adhesion
~ mm ~h adhesion, tension & pressure, kinetics & dynamics, free
cytoplasm flow, deformation, boundary problems, surface
translocation tension & viscosity
Cell lOmm h Exterior fluid, matrix, cell Immersed particle model,
collections ~ cm ~ days contact, stress & shear forces, two-phase gel dynamics,
individual motion, multi-particle and lattice
deformation, pushing & models, diffusion equations
tugging & hybrid models
macroscopic model, i.e., which averaged quantities or indices are going to be presented
as simulation results.
Thus, on any level of dynamic phenomena in biophysics or biology, namely, for
proteins, polymers, cells, tissues, organisms, populations, and ecosystems, mathemati
cal modeling and numerical simulation have to find and use the appropriate strata of
spatial and corresponding temporal scales. One of the most important future tasks will
be to study more completely the relationship between submodels on the corresponding
scaling levels.
This requires analytical and numerical work, i.e., formal derivations and proven
approximation theorems as well as appropriate, compatible, and effective numerical al
gorithms. The algorithms appearing in these proceedings, either those used explicitly or
merely mentioned, are mainly standard methods that have been developed for dynamic
