New Algorithms for Macromolecular Simulation

363 Pages·2016·4.23 MB·English

by  Mark A., Leimkuhler B., Chipot Ch., Elber R., Laaksonen A., Schlick T., Schütte Ch., Skeel R. (Eds.)

Lecture Notes
in Computational Science
49
and Engineering
Editors
Timothy J. Barth
Michael Griebel
David E. Keyes
Risto M. Nieminen
Dirk Roose
Tamar Schlick
Benedict Leimkuhler Christophe Chipot Ron Elber
Aatto Laaksonen Alan Mark Tamar Schlick
Christophe Schütte Robert Skeel (Eds.)
New Algorithms
for Macromolecular
Simulation
With 90 Figures and 22 Tables
BA C
Editors
Benedict Leimkuhler Alan Mark
Department of Mathematics Laboratory of Biophysical Chemistry
University of Leicester University of Groningen
University Road Nijenborgh 4
Leicester LE1 7RH, U.K. 9747 AG, Groningen, The Netherlands
email:
Preface
This volume consists of a collection of papers given at the fourth edition of the Al-
gorithms for Macromolecular Modelling meeting held in Leicester, UK in August
2004. The purpose of the meeting series is to foster a high level discussion of math-
ematical formulation, algorithmic tools, and simulation methodology for improving
computational study of (primarily) biological molecules.
With the advent of supercomputers, workstation clusters, and parallel comput-
ing software, molecular modelling and simulation has become the essential coun-
terpart to experiment. Computer simulations are helping to link the static structural
information on proteins and nucleic acids obtained by X-ray crystallography and nu-
clear magnetic resonance with the dynamic behavior in the realistic environment of
the cell. Molecular dynamics (MD) and other modelling and simulation techniques
can offer an effective tool for refining experimental models and for probing sys-
tematically how molecules fold and reshape to perform the basic functions of life.
Some problems that are beyond experiment can also be tackled by modelling and
simulation. Indeed, experimentalists are becoming increasingly interested in mod-
elling to decipher detailed conformational and structural aspects of macromolecular
function. Yet many fundamental and practical limitations face biomolecular mod-
elers. They include the approximate nature of the governing force fields as well as
simulation protocols, the limited range of configurational sampling and relatively
short trajectory times, the neglect of quantum effects in classical molecular dynam-
ics, and the enormous computational requirements (needed to simulate a solvated
macro-molecular system with full details of the environment). New algorithmic ap-
proaches, hierarchical spatial representations, and improved computing platforms are
thus continuously in demand to enhance the reliability of macromolecular simula-
tions, enhance the scope of theoretical work, and address biological problems with
great specificity. In light of the the highly multidisciplinary nature of macromolecu-
lar modelling, educational efforts are also crucial for training the current generation
of young biomolecular modelers.
The purpose of this volume is to help shape a dialog between developers of
computational tools for biomolecular simulations and those biological and chemi-
cal scientists interested in modelling applications. In keeping with the spirit of the
VI Preface
3
AM meetings, the authorship is very broad, including chemists, physicists, biolo-
gists, mathematicians and computer scientists. The book is divided into to six parts
based on the content of submissions. The opening section considers novel modelling
paradigms for biomolecules, including articles on challenging applications such as
membrane proteins ( Bond et al), enzyme simulation (Ma et al), RNA modelling (
Laserson, Gan and Schlick), and sequence alignment (Joachims, Galor and Elber).
Part II presents the cornerstone of most molecular modelling: the classical picture
of the potential energy function and the minimization problem for molecular land-
scapes (Wales, Car and James), followed by an up to date overview of the protein
folding problem (Scheraga et al).
Computing trajectories on the classical energy landscape is the traditional goal of
molecular dynamics, although the ultimate purpose of these computations is usually
to construct an efficient sampling of the low energy basins and to determine the rel-
ative likelihood of transitions amongst them; mathematicians are paying increasing
attention to these issues. In Part III, we present a variety of perspectives on efficient
sampling based on dynamics and stochastic-dynamics, beginning with an overview
( Hampton et al) of biomolecular sampling methodology. Schemes for sampling
based on extended Hamiltonians are discussed in the article by Barth, Leimkuhler
and Sweet. Advances in hybrid Monte Carlo methods (Akhmatskaya and Reich)
and Langevin formulation (Akkermans) are then presented, followed by a study of
metastability (Huisinga and Schmidt) based on eigenstructure of the transfer opera-
tor.
Increasingly, molecular simulation is used to evaluate free energies or potentials
of mean force, for example to the determine protein-ligand binding affinities, an es-
sential challenge in de novo drug design. This topic is discussed in Part IV. In the
articles of Chipot and Darve, free energy calculation methods based on evolving a
system from one state to another are presented and compared. An alternative ap-
proach, based on replica-exchange methods, is considered in the article of Woods,
King and Essex.
The final two parts of the volume focus on modification of the foundations of
molecular simulation. In Part V, articles by Baker, Bashford and Case and Sagui,
Roland , Pedersen and Darden consider alternative models of solvation, in the one
case using a simplified implicit solvent model to increase efficiency and facilitate
treatment of more complex macromolecules, in the other case focussing on more
accurate electrostatic models based on higher order multipoles than are tradition-
ally used. The last section, including articles by Tu and Laaksonen, and Lee, Sagui
and Roland focusses on incorporation of even more accurate treatment of molecular
interactions by use of quantum-mechanical calculations.
Authors have been asked to explain terminology and notation carefully and to
provide complete bibliographies, enhancing the usefulness of the book as an ad-
vanced textbook for graduate study and multidisciplinary research preparation.
3
During the AM meeting, an panel discussion was held at which certain questions
regarding the direction of the field were put to a small group of leading practitioners
drawn from the various fields covered by the conference. A summary of this dis-
cussion is included at the end of the book. Their candid responses, along with some
Preface VII
additional comments and questions raised by the assembled audience, are meant to
be taken in the spirit of friendly and open exchange.
3
In 2004, the AM meeting was funded by grants from the Engineering and Phys-
ical Sciences Research Council (UK), the National Science Foundation (US), the
National Institutes of Health (US), the Burroughs Wellcome Foundation (US). It was
an official cooperative activity of the Society for Industrial and Applied Mathemat-
ics. A website for the meeting series is maintained at www.am-3.org.
Leicester, UK Benedict Leimkuhler
Nancy, France Christophe Chipot
Ithaca, New York Ron Elber
Stockholm, Sweden Aatto Laaksonen
Groningen, The Netherlands Alan Mark
New York, New York Tamar Schlick
Berlin, Germany Christof Schütte
West Lafayette, Indiana Robert Skeel
August 2005
Contents
Part I Macromolecular Models: From Theories
to Effective Algorithms
Membrane Protein Simulations: Modelling a Complex Environment
P.J. Bond, J. Cuthbertson, S.S. Deol, L.R. Forrest, J. Johnston, G. Patargias,
M.S.P. Sansom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1 Introduction – Membrane Proteins and Their Importance . . . . . . . . . . . . . . . 3
2 Membrane Protein Environments in Vivo and in Vitro . . . . . . . . . . . . . . . . . . 5
3 Simulation Methods for Membranes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4 Using Simulations to Explore Membrane Protein Systems . . . . . . . . . . . . . . 6
5 Complex Solvents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
6 Detergent Micelles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
7 Lipid Bilayers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
8 Self-Assembly and Complex Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Modeling and Simulation Based Approaches
for Investigating Allosteric Regulation in Enzymes
M.Q. Ma, K. Sugino, Y. Wang, N. Gehani, A.V. Beuve . . . . . . . . . . . . . . . . . . . . . 21
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2 Modeling and Simulation of sGC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Exploring the Connection Between Synthetic and Natural RNAs
in Genomes via a Novel Computational Approach
U. Laserson, H.H. Gan, T. Schlick . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
1 Introduction: Importance of RNA Structure and Function . . . . . . . . . . . . . . 35
2 Exploring the Connection between Synthetic
and Natural RNAs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
X Contents
4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
5 Conclusions and Future Directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Learning to Align Sequences:
A Maximum-Margin Approach
T. Joachims, T. Galor, R. Elber . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2 Sequence Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3 Inverse Sequence Alignment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4 A Maximum-Margin Approach to Learning
the Cost Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5 Training Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
7 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Part II Minimization of Complex Molecular Landscapes
Overcoming Energetic and Time Scale Barriers Using
the Potential Energy Surface
D.J. Wales, J.M. Carr, T. James . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2 Discrete Path Sampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3 Basin-Hopping Global Optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
The Protein Folding Problem
H.A. Scheraga, A. Liwo, S. Oldziej, C. Czaplewski, J. Pillardy, J. Lee, D.R.
Ripoll, J.A. Vila, R. Kazmierkiewicz, J.A. Saunders, Y.A. Arnautova, K.D.
Gibson, A. Jagielska, M. Khalili, M. Chinchio, M. Nanias, Y.K. Kang, H.
Schafroth, A. Ghosh, R. Elber, M. Makowski . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
2 Early Approaches to Structure Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3 Global Optimization of Crystal Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
4 All-atom Treatment of Protein A and the Villin Headpiece . . . . . . . . . . . . . 91
5 Hierarchical Approach to Predict Structures
of Large Protein Molecules . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
6 Performance in CASP Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
7 Computation of Folding Pathways . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
8 Molecular Dynamics with the UNRES Model . . . . . . . . . . . . . . . . . . . . . . . . 95
9 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Contents XI
Part III Dynamical and Stochastic-Dynamical Foundations
for Macromolecular Modelling
Biomolecular Sampling: Algorithms,
Test Molecules, and Metrics
S.S. Hampton, P. Brenner, A. Wenger, S. Chatterjee, J.A. Izaguirre . . . . . . . . . . . 103
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
2 Sampling Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
3 Test Systems, Methods, and Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Approach to Thermal Equilibrium
in Biomolecular Simulation
E. Barth, B. Leimkuhler, C. Sweet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
2 Molecular Dynamics Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
3 Thermostatting using Nosé-Hoover Chains, Nosé-Poincaré
and RMT Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130
4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
The Targeted Shadowing Hybrid Monte Carlo (TSHMC) Method
E. Akhmatskaya, S. Reich . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
2 Description of the Basic HMC Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
3 Störmer-Verlet Time-Stepping Method
and Modified Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
4 Targeted Shadowing HMC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144
5 Computer Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
The Langevin Equation for Generalized Coordinates
R.L.C. Akkermans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
2 Generalized Coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
3 Generalized Langevin Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158
4 Point Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
XII Contents
Metastability and Dominant Eigenvalues of Transfer Operators
W. Huisinga, B. Schmidt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
2 Markovian Molecular Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169
3 Markov Chains, Transfer Operators,
and Metastability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
4 Upper and Lower Bounds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
5 Illustrative Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
6 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
Part IV Computation of the Free Energy
Free Energy Calculations in Biological Systems. How Useful Are They
in Practice?
C. Chipot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
2 Methodological Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
3 Free Energy Calculations and Drug Design . . . . . . . . . . . . . . . . . . . . . . . . . . 194
4 Free Energy Calculations and Signal Transduction . . . . . . . . . . . . . . . . . . . . 199
5 Free Energy Calculations and Peptide Folding . . . . . . . . . . . . . . . . . . . . . . . . 201
6 Free Energy Calculations and Membrane Protein Association . . . . . . . . . . . 204
7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Numerical Methods for Calculating the Potential of Mean Force
E. Darve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
2 Generalized Coordinates and Lagrangian Formulation . . . . . . . . . . . . . . . . . 218
3 Derivative of the Free Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
4 Potential of Mean Constraint Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
5 Adaptive Biasing Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
Replica-Exchange-Based Free-Energy Methods
C.J. Woods, M.A. King, J.W. Essex . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
2 Free Energy Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
3 Hydration of Water and Methane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
4 Halide Binding to a Calix[4]Pyrrole Derivative . . . . . . . . . . . . . . . . . . . . . . . 255
5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257