Schlick T. Molecular Modeling and Simulation: An Interdisciplinary Guide
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Interdisciplinary Applied Mathematics
Vo l u m e 2 1
Series Editors
S.S. Antman J.E. Marsden
L. Sirovich
Series Advisors
C.L. Bris L. Glass
P. S. Krishnaprasad R.V. Kohn
J.D. Murray S.S. Sastry
Geophysics and Planetary Sciences
Imaging, Vision, and Graphics
D. Geman
Mathematical Biology
L. Glass, J.D. Murray
Mechanics and Materials
R.V. Kohn
Systems and Control
S.S. Sastry, P.S. Krishnaprasad
Problems in engineering, computational science, and the physical and biological sciences
are using increasingly sophisticated mathematical techniques. Thus, the bridge between
the mathematical sciences and other disciplines is heavily traveled. The correspond-
ingly increased dialog between the disciplines has led to the establishment of the series:
Interdisciplinary Applied Mathematics.
The purpose of this series is to meet the current and future needs for the interaction
between various science and technology areas on the one hand and mathematics on the
other. This is done, firstly, by encouraging the ways that mathematics may be applied in
traditional areas, as well as point towards new and innovative areas of applications; and,
secondly, by encouraging other scientific disciplines to engage in a dialog with mathe-
maticians outlining their problems to both access new methods and suggest innovative
developments within mathematics itself.
The series will consist of monographs and high-level texts from researchers working
on the interplay between mathematics and other fields of science and technology.
For further volumes:
http://www.springer.com/series/1390
Reviews of First Edition (continued
from back cover)
“The interdisciplinary structural biology community has waited long for a book of this kind
which provides an excellent introduction to molecular modeling.” (Harold A. Scheraga, Cornell
University)
“A uniquely valuable introduction to the modeling of biomolecular structure and dynamics.
A rigorous and up-to-date treatment of the foundations, enlivened by engaging anecdotes and
historical notes.” (J. Andrew McCammon, Howard Hughes Medical Institute, University of
California at San Diego)
“The text is beautifully illustrated with many color illustrations. Even part of the text is type-
set in color. Not only the illustrations interrupt the very readable text, there are also many
box-insertions ...”(Adhemar Bultheel,Bulletinof the Belgian Mathematical Society, Vol. 11
(4), 2004)
“This textbook evolved from a graduate course in molecular modeling, and was expanded to
serve as an introduction to the field for scientists in other disciplines. ...The book is unique
in that it combines introductory molecular biology with advanced topics in modern simulation
algorithms .... the author provides 1000
+ references, and additionally includes reading lists
complementing the main text. This is an excellent introductory text that is a pleasure to read.”
(Henry van den Bedem, MathSciNet, September, 2004)
“This book provides an excellent introduction to the modeling of biomolecular structures and
dynamics. ...Thebook’s appendices complement the material in the main text through home-
work assignments, reading lists, and other information useful for teaching molecular modeling.
The book is intended for students of an interdisciplinary graduate course in molecular modeling
as well as for researchers (physicists, mathematicians and engineers) to get them started in com-
putational molecular biology.” (Ivan Krivy, University of Ostrava, Czech Republic, Zentralblatt
MATH, Issue 1011, 2003)
“The book ...isthe outcome of the author Tamar Schlick’s teaching experience at New York
University. It is a fantastic graduate textbook to get into structural biology. ...even the most
sophisticated problems are part of a gradual approach ....The book will obviously be of great
interest to students and teachers but it should also be very valuable for research scientists, espe-
ciallynewcomerstothefield...asareference book and a point of entry in the more specialised
literature.” (Benjamin Audit, Bioinformatics, January, 2003)
“The basic goal of this new text is to introduce students to molecular modelling and sim-
ulation and to the wide range of biomolecular problems being attacked by computational
techniques. . . . the text emphasises that the field is changing very rapidly and that it is full
of exciting discoveries. ...This book stimulates this excitement, while still providing students
manycomputationaldetails....Itcontainsdetailedillustrations throughout ... . It should appeal
to beginning graduate students ...in many scientific departments ... .” (Biotech International,
Vol. 15 (2), 2003)
Tamar Schlick
Molecular Modeling
and Simulation
An Interdisciplinary Guide
2nd edition
123
Prof. Tamar Schlick
New York University
Courant Institute of Mathematical Sciences
and Department of Chemistry
251 Mercer Street
New York, NY 10012
USA
schlick@nyu.edu
Editors
S.S. Antman
Department of Mathematics
and
Institute for Physical Science
and Technology
University of Maryland
College Park, MD 20742, USA
ssa@math.umd.edu
J.E. Marsden
Control and Dynamical Systems
Mail Code 107-81
California Institute of Technology
Pasadena, CA 91125, USA
marsden@cds.caltech.edu
L. Sirovich
Department of Biomathematics
Laboratory of Applied Mathematics
Mt. Sinai School of Medicine
Box 1012
New York, NY 10029
USA
Lawrence.Sirovich@mssm.edu
ISSN 0939-6047
ISBN 978-1-4419-6350-5 e-ISBN 978-1-4419-6351-2
DOI 10.1007/978-1-4419-6351-2
Springer New York Dordrecht Heidelberg London
Library of Congress Control Number: 2010929799
Mathematics Subject Classification (2010): MSC 2010: 62P10, 65C05, 65C10, 65C20, 68U20, 92B05,
92C05, 92C40, 92E10, 97M60
c
Springer Science+Business Media, LLC 2010
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Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
About the Cover
Molecular modelers are artists in some respects. Their subjects are complex,
irregular, multiscaled, highly dynamic, and sometimes multifarious, with diverse
states and functions. To study these complex phenomena, modelers must apply
computer programs based on precise algorithms that stem from solid laws and
theories from mathematics, physics, and chemistry. Like innovative chefs, they
also borrow their inspiration from other fields and blend the ingredients and ideas
to create appealing inventive dishes.
The West-Coast-inspired landscape paintings of artist Wayne Thiebaud, whose
work Reservoir Study decorated the cover of the first edition of this book, em-
bodied that productive blend of nonuniformity with orderliness as well as the
multiplicity in perspectives and interpretations central to molecular modeling.
For this edition, the collage on the back cover (created with Shereef Elmetwaly)
reflects such an amalgam of foundations, techniques, and applications. The com-
puter salad image on the front cover (created with Namhee Kim and James Van
Arsdale) further reflects a vision for the near future when modeling and simulation
techniques will be reliable so as to compute folded structures and other desired as-
pects of biomolecular structure, motion, and function. I hope such creative blends
will trigger readers’ appetite for more creations to come.
vi About the Cover
To the memory of my beloved aunt Cecilia, who filled my life with
love, joy, beauty, and courage which I will forever carry with me.
Book URLs
For Text:
www.biomath.nyu.edu/index/book.html
For Course:
www.biomath.nyu.edu/index/course/IndexMM.html
Preface
As I update parts of this textbook seven years after the original edition, I find
the progress in the field to be overwhelming, almost unfitting to justify maintain-
ing the same book. In fact, the sports analogy “Bigger, faster, stronger” seems
most appropriate to the field of biomolecular modeling. Indeed, as modeling and
simulation are used to probe more biological and chemical processes — with
improved force fields and algorithms and faster computational platforms — new
discoveries are being made that help interpret as well as extend experimental data.
To experimentalists and theoreticians alike, modeling remains a valuable, albeit
challenging, tool for probing numerous conformational, dynamic, and thermo-
dynamic questions. We can certainly anticipate more exciting developments in
biomolecular modeling as the first decade of this new century has ended and an-
other began. At the same time, we should be reminded by the wisdom of the great
French mathematician and scientist Pierre Simon de Laplace, who I quote more
than once in this text, who also said: “Ce que nous connaissons est peu de chose;
ce que nous ignorons est immense”. (What we know is little; what we do not know
is immense).
Besides small additions and revisions made throughout the text and displayed
materials to reflect the latest literature and field developments, some chapters
have undergone more extensive revisions for this second edition. These include
Chapters 1 and 2 that provide a historical perspective and an overview of current
applications to biomolecular systems; Chapter 4, which reflects modified protein
classification with new protein examples and sequence statistics; the chapter Top-
ics in Nucleic Acids (now expanded into two chapters, 6 and 7), which includes
recent developments in RNA structure and function; the force field chapters 8–10,
which contain new sections on enhanced sampling methods; Chapter 15,which