Table Of ContentLecture Notes
in Computational Science 4
and Engineering
Editors
M.Griebel,Bonn
D.E.Keyes,Norfolk
R.M.Nieminen,Espoo
D.Roose,Leuven
T.Schlick,NewYork
Texts and Monographs in Physics
Series Editors: R. Balian W. Beiglbock H. Grosse E. H. Lieb
N. Reshetikhin H. Spohn W Thirring
Springer-Verlag Berlin Heidelberg GmbH
Peter Deuflhard Ja n Hermans
Benedict Leimkuhler Alan E. Mark
Sebastian Reich Robert D. Skeel (Eds.)
Computational
Molecular Dynamics:
Challenges,
Methods, Ideas
Proceedings of the
2nd International Symposium on Algorithms
for Macromolecular Modelling,
Berlin, May 21-24, 1997
With 117 Figures and 22 Tables
Springer
Editors
Peter Deuflhard AlanE.Mark
Konrad-Zuse-Zentrum Berlin (ZIB) Laboratorium fiir Physikalische Chemie
Takustrasse 7 ETHZentrum
D-14195 Berlin-Dahlem, Germany CH-8092 Ziirich, Switzerland
[email protected] [email protected]
JanHermans Sebastian Reich
Department of Biochemistry Department of Mathematics
and Biophysics and Statistics
University of North Carolina University of Surrey
Chapel Hill, NC 27599-7260, USA Guildford, Surrey GU2 5XH,
[email protected] United Kingdom
[email protected]
Benedict Leimkuhler
Department of Mathematics Robert D. Skeel
University of Kansas Department of Computer Science
405 Snow HalI University of Illinois
Lawrence, KS 66045, USA 1304 West Springfield Avenue
[email protected] Urbana, IL 61801-6631, USA
[email protected]
Front cover figure created by Thomas Steinke and Olaf Paetsch,
Konrad-Zuse-Zentrum (ZIB), Berlin-Dahlem, Germany
Mathematics Subject Classification (1991): 34C35, 65-06, 68-06, 70-06, 81-06, 82-06, 92-06
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Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Computational molecular dynamics: challenges, methods, ideas; proceedings of the 2nd International Symposium
on Algorithms for Macromolecular Modelling, Berlin,May 21-24, 1997; with 22 tables I Peter Deuflhard ..• (ed.).
Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Singapore; Tokyo: Springer, 1999
(Lecture notes in computational science and engineering; 4)
ISBN 978-3-540-63242-9 ISBN 978-3-642-58360-5 (eBook)
DOI 10.1007/978-3-642-58360-5
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Preface
In May 21 - 24, 1997the Second International Symposiumon Algorithms for
Macromolecular Modelling was held in the new building ofthe Konrad Zuse
Zentrum on the attractive Science Campus ofthe Free University of Berlin.
Organizersofthesymposiumweretheeditorsofthis book, plusBernieBrooks
and Wilfred van Gunsteren. The event brought together computational sci
entists infields like biochemistry, biophysics, physicalchemistry, orstatistical
physics and numerical analysts as well as computer scientists working on the
advancement ofalgorithms, for a totalofover 120 participants from 19coun
tries. In the course ofthe symposium, it was agreed not to write traditional
proceedings, but rather to produce a representative volume that combines
survey articles and original papers (all refereed) that would give an account
ofthe current state ofthe art ofMolecular Dynamics (MD).
At present, the main challenge of computational molecular dynamics
stems from the huge discrepancy oftimescales: phenomena of interest, such
as proteinfolding oractivesitedocking, occurona micro-ormillisecondtime
scale while we are routinely able to do computations on a scale ofonly oneor
a few nanoseconds. Inorderto bridge this gap, a drasticspeedup ofour algo
rithmsandsoftwareappearsnecessary- besidesanyspeeduporiginatingfrom
advancesincomputertechnology. However, this will not beenoughto achieve
our goal. In addition, there is the need to explore further the potential for
improved physical modelling and to develop both new theoretical concepts
and new algorithmic ideas. That is why this volume deliberately allocates
considerable space to new concepts and ideas from physics and mathematics.
Withthe mainchallengeand the generalintentionsoftheeditorsin mind,
the volume begins with an Introductory Survey by a longtime leader in the
field, HERMAN BERENDSEN, drawingon his longexperience and deep insight
into the current status of molecular simulations and their future as an in
creasingly important method in structural biology and chemistry. With his
unique personalinsight, this articlewill bethe beginningofmanydiscussions
as the book as a whole will serve as a forum for alternative views and further
perspectives.
The remaining 28 articles have been grouped in five chapters that reflect
the main topics of the Berlin meeting. As in any interdisciplinary volume,
there is a degree ofarbitrariness in the allocation ofsome ofthe articles.
The first chapter, on Conformational Dynamics, includes discussion ·of
several rather recent computational approaches to treat the dominant slow
modes of molecular dynamical systems. In the first paper, SCHULTEN and
his group review the new field of "steered molecular dynamics" (SMD), in
which "large" external forces are applied in order to be able to study un
bindingofligands and conformationchanges ontime scales accessible to MD
VI Preface
simulations. The second paper, byHELMS & MCCAMMON, surveys a wide
range ofdifferent computational techniques for the exploration ofconforma
tional transitions of proteins, including the use ofstochastic dynamics with
the Poisson-Boltzmann approximation as a simple solvent model. The ar
ticle by EICHINGER ET AL. combines several speedup techniques: multiple
time stepping algorithms adapted to fit fast multipole methods (see also the
last chapter of this book), the previously mentioned SMD technique, and
GRUBMULLER'S method of "computational flooding", which uses local po
tential modifications in order to successively drive the system to different
low-energy basins. The novel approach taken by DEUFLHARD ET AL. em
ploys ideas from the mathematics ofdynamical systems to construct certain
almost invariant sets in phase space, which can be interpreted as chemical
conformations; their algorithm also supplies patterns and rates ofconforma
tional changes. In the last paper ofthis chapter, TOLSTUROKOV & VIRNIK
describe another use ofdynamical systems tools and propose a simplified set
ofdifferentialequationsfor the descriptionofan observedhysteresis behavior
in water adsorption-desorption of nucleic acids.
The second chapter, on Thermodynamic Modelling, is devoted largely to
methods for computing free energies and potentials ofmean force. The paper
by HERMANS ET AL. reviews experimental and theoretical techniques for
studying the stability of protein-ligand complexes, including a new method
for computing absolute free energies of binding with MD simulations, and
summarizesrecent applications from their laboratory. MARK ET AL. describe
a new method to estimate relative binding free energies ofa series ofrelated
ligands on the basis of a single simulated trajectory of a reference state in
which a specially constructed, artificial ligand is modelled with a special
"soft" potential function. KUCZERA describes a multiple-dimension approach
bywhich conformation space is explored, while the potential ofmean force is
simultaneouslycomputed. Thejointpaper from the groupsofLESYNG and of
MCCAMMON reviews an algorithm for the prediction ofionization constants
in proteins; calculations of the relevant protein-solvent system are based on
thealreadymentionedPoisson-Boltzmannequation. ThepaperbySTRAUB &
ANDRICIOAEIemploysthe Tsallisstatisticstospeedupphasespacesampling.
In the final article of this chapter, NEUMAIER ET AL. construct empirical
potentials for possible use in off-lattice protein studies.
The third chapter, on Enhanced Time-Stepping Algorithms, opens with a
personalaccount onlong-timestep integrationby SCHLICK. She assesses both
the successes and the limitations ofvarious algorithmic approaches including
implicit discretization, harmonic/anharmonicseparation ofmodes, and force
splitting techniques combined with Langevin dynamics. The second paper,
by ELBER ET AL., describes a large step-size approximation of stochastic
path integrals arising from Langevin dynamics - requiring, however, knowl
edge about both initial and final states. Onthe basis ofa detailed case study
ASCHER & REICH argue that implicit discretizations should not be used
with timesteps significantly larger than typical periods of the fast oscilla-
Preface VII
tions. In the paper by BERNE, the r-RESPA multiple timestepping (MTS)
method is described and applied in the context ofHybrid Monte Carlometh
ods for sampling techniques such as J-Walking and S-Walking with the aim
of a more rapid exploration of rugged energy landscapes. In the next pa
per, SKEEL & IZAGUIRRE advocate the use of MTS in a mollified impulse
method to overcome resonance instabilities that are inherent in the standard
impulsemethod. YetanotherMTS-likeapproachcanbefound inthepaperby
JANEZIC & MERZEL, who suggest to split offa harmonic high frequency part
ofthe motion and integrate that analytically. Finally, LEIMKUHLER demon
strates the stability of the recently proposed explicit symplectic integrators
(with fixed timestep) in the numerical integration ofrigid body motion over
long time spans.
The fourth chapter, on Quantum-Classical Simulations, deals with the
integration of molecular systems, parts of which are modelled in terms of
quantum mechanics, where a full quantum mechanical treatment would be
impossible. In the first paper, JUNGWIRTH & GERBER treat clusters ofinert
gases by calculating effective single-mode potentials from classical molecular
dynamics which are then used in quantum calculations. An extension be
yond the separability approximation is also suggested. The quality of the
quantum-classical molecular dynamics (QCMD) model compared with full
quantum mechanics (QM) and the Born-Oppenheimer approximation (BO)
isconsideredby SCHUTTE & BORNEMANN in termsofapproximationtheory.
TheyalsosuggestanextendedQCMD modelthat mayopennewperspectives
in the case ofenergy level crossings, where BO is known to break down. Re
cently developed structure-preserving numerical integrators for this QCMD
modelare given by NETTESHEIM & SCHUTTE. Symplecticmultiple timestep
pingvariantsofthese integrators arederived in the paper by NETTESHEIM &
REICH. An alternative scheme is presented by HOCHBRUCK & LUBICH, who
suggest that a type of mollified exponential integrators are especially well
suited for highly oscillatory systems such as QCMD and the Car-Parrinello
approximation. The latter approximationis also used in the paper by MEIER
ET AL. on ab-initio MD simulations ofcatalysis in a polymerization process.
In the last paper of this chapter, IZVEKOV describes an algorithm for the
calculation ofabsorption spectra based on exciton-phonon interactions.
The fifth and final chapter, on Parallel Force Field Evaluation, takes
account of the fact that the bulk of CPU time spent in MD simulations
is required for evaluation of the force field. In the first paper, BOARD
and his coworkers present a comparison of the performance of various
parallel implementations of Ewald and multipole summations together with
recommendations for their application. The second paper, by PHILLIPS ET
AL., addresses the special problems associated with the design of parallel
MD programs. Conflicting issues that shape the design of such codes are
identified and the use offeatures suchas multiple threadsand message-driven
execution is described. The final paper, by OKUNBOR & MURTY, compares
three force decomposition techniques (the checkerboardpartitioningmethod,
VIII Preface
the force-row interleaving method, and the force-stripped row method) in
the context ofa benchmark test problem.
August 31, 1998
Peter Deufihard
Jan Hermans
Benedict Leimkuhler
Alan E. Mark
Sebastian Reich
Robert D. Skeel
Table of Contents
Introductory Survey
Molecular Dynamics Simulations: The Limits and Beyond. ........... 3
Herman J.C. Berendsen
I Conformational Dynamics
Steered Molecular Dynamics. 39
0 0 0 0 •• 0 0 •• 0 0 •• 0 • 0 0 0 • 0 •• 0 0 •• 0 0 •• 0 0 0 0 0 0
Sergei Izrailev, Sergey Stepaniants, Barry Isralewitz, Dorina
Kosztin, Hui Lu, Ferenc Molnar, Willy Wriggers, Klaus Schulten
Conformational Transitions ofProteins from Atomistic Simulations o. 66
0 •
Volkhard Helms, Jo Andrew McCammon
Conformational Dynamics Simulations ofProteins 78
0 0 0 •• 0 0 •• 0 0 •• 0 0 0 0 0 0
Markus Eichinger, Berthold Heymann, Helmut Heller, Helmut
Grubmuller, Paul Tavan
ComputationofEssentialMolecularDynamicsbySubdivisionTechniques 98
Peter Deuflhard, Michael Dellnitz, Oliver Junge, ChristofSchutte
Mathematical Model ofthe Nucleic Acids Conformational Transitions
with Hysteresis over Hydration-Dehydration Cycle. 116
00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Michael Yeo Tolstorukov, Konstantin Mo Virnik
II Thermodynamic Modelling
Simulation Studies ofProtein-Ligand Interactions ... 129
0 0 0 • 0 0 0 0 • 0 ••• 0 ••
Jan Hermans, Geoffrey Mann, Lu Wang, Li Zhang
Estimating Relative Free Energies from a Single Simulation ofthe Ini-
tial State o. 149
0 0 ••• 0 ••• 0 •••• 0 0 0 •••• 0 0 0 0 0 ••• 0 0 0 0 0 0 0 0 • 0 0 0 0 0 • 0 0 0 0 • 0 ••
Alan E. Mark, Heiko Schiifer, Haiyan Liu, Wilfred van Gunsteren
Exploration ofPeptide Free Energy Surfaces 163
0 •• 0 •• 0 ••••••••••••••• 0 •
KrzysztofKuczera
Prediction of pKas ofTitratable Residues in Proteins Using a Poisson
Boltzmann Model ofthe Solute-Solvent System 176
0 0 0 ••••••••••• 0 0 0 ••••
X Table ofContents
Jan Antosiewicz, Elibieta Blachut-Okrasinska, Tomasz Grycuk,
James M. Briggs, Stanislaw T. Wlodek, Bogdan Lesyng, 1. Andrew
McCammon
Exploiting Tsallis Statistics 197
John E. Straub, loan Andricioaei
New Techniques for the Construction ofResidue Potentials for Protein
Folding 212
Arnold Neumaier, Stefan Dallwig, Waltraud Huyer, Hermann
Schichl
III Enhanced Time-Stepping Algorithms
Some Failures and Successes of Long-Timestep Approaches to
Biomolecular Simulations .. ...................................... 227
Tamar Schlick
Application of a Stochastic Path Integral Approach to the Computa-
tions ofan Optimal Path and Ensembles ofTrajectories 263
Ron Elber, Benoit Roux, Roberto Olender
OnSomeDifficultiesinIntegratingHighlyOscillatoryHamiltonianSys-
terns 281
Uri M. Ascher, Sebastian Reich
Molecular Dynamics in Systems with Multiple Time Scales: Reference
System Propagator Algorithms 297
Bruce J. Berne
The Five Femtosecond Time Step Barrier 318
Robert D. Skeel, Jesus A. Izaguirre
Long Time Step MD Simulations Using Split Integration Symplectic
Method 332
Dusanka Janeiic, Franci Merzel
Comparison ofGeometric Integrators for Rigid Body Simulation 349
Benedict J. Leimkuhler
IV Quantum-Classical Simulations
New Methods in Quantum Molecular Dynamics of Large Polyatomic
Systems 365
Pavel Jungwirth, R. Benny Gerber
