Table Of ContentD. M. Soumpasis T. M. Jovin (Eds.)
Computation
of Biomolecular Structures
Achievements, Problems
and Perspectives
With 66 Figures
Springer-Verlag
Berlin Heidelberg New York London Paris
Tokyo Hong Kong Barcelona Budapest
Dr. Dikeos Mario Soumpasis
Max-Planck-Institut fur
Biophysikalische Chemie
Abt. Molekulare Biologie
W-3400 Gottingen, FRG
Dr. Thomas M. Jovin
Max-Planck-Institut fUr
Biophysikalische Chemie
Abt. Molekulare Biologie
W-3400 Gottingen, FRG
ISBN-13: 978-3-642-77800-1 e-ISBN-13: 978-3-642-77798-1
DO I: 10.1007/978-3-642-77798-1
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Preface
Computational techniques have become an indispensable part of Molecular Biology,
Biochemistry, and Molecular Design. In conjunction with refined experimental methods
and powerful hardware, they enable us to analyze and visualize biomolecular structures,
simulate their motions and to a variable degree understand their physicochemical properties
and function. In addition, they provide essentially the only way to analyze and correlate the
astronomical amounts of experimental sequence and structural data accumulating in
international databases.
We have good reasons to believe that further advances in this area will eventually
enable us to predict with sufficient accuracy many structural and functional properties of
fairly large biomolecules, given their sequence and specified environmental conditions.
However, it is also important to realize that in achieving this goal, we encounter several
serious problems of conceptual and methodological nature, the solution of which requires
new approaches and algorithms. For example, we need better force fields, more efficient
optimization routines, an adequate description of electrostatics and hydration, reliable
methods to compute free energies, and ways to extent the length of molecular dynamics
simulations by several orders of magnitude.
In March 1990 we organized a workshop at Schloss Ringberg, near Tegernsee,
FRG, with the goal to overview some recent representative applications, discuss the
existing problems, and identify promising new approaches. The volume at hand contains
16 contributions that originated with the lectures given at Schloss Ringberg. They
deliberately cover a wide rage of topics constituting the intersection between Molecular
Biology, Biochemistry, Physical Chemistry, Statistical Physics, Applied Mathematics, and
Computer Science. Many subjects are covered in this volume for the first time. We hope
that the interested reader will be informed of current activities and future perspectives in this
exciting area of research. The extensive bibliographies provided in the articles are a
valuable source of information and stimulus for further studies.
We wish to thank the Max-Planck-Gesellschaft, the Bundesministerium fUr
Forschung und Technologie, and the Dr. Rudolf Schloessmann Stiftung for funding the
Schloss Ringberg Workshop, and the Springer Verlag for its cooperation.
Special thanks are due to Mrs. Renate Jenssen for her great help with the
organization, to Reinhard Klement and Jackie Reiners for editorial assistance, and to all
contributors of this volume.
Gottingen, July 1992
D.M. Soumpasis and T.M. Jovin
Contents
Structure Analysis and Prediction
Structure Detennination from NMR - Application to Cram bin
J.Anton C. Rullmann, Alexandre M.J.J. Bonvin, Rolf Boelens,
and Robert Kaptein
From Sequence Similarity to Structural Homology of Proteins 15
Christian Sander and Reinhard Schneider
Equilibrium Distribution of Secondary Structures for Large RNA 29
John S. MCCaskill
Doing sequence analysis by inspecting the order in which neural networks learn 43
S0ren Brunak
Computational Approaches to Nucleic Acid Structure 55
Wilma K. Olson
A New Program for the Analysis of Nucleic Acid Structure: Implications for
Nucleic Acid Structure Interpretation 65
Marla S. Babcock and Wilma K. Olson
Modeling DNA Backbone Structures 87
Chang-Shung Tung
Specific Systems
Serine and Cysteine Proteases and their Natural Inhibitors: Structures and
Implications for Function and Drug Design 99
Robert Huber
Principles of Protein - Protein Recognition in Protease-Inhibitor and Antigen-
Antibody Complexes 103
Joel Janin, Jacqueline Cherfils and Stephane Duquerroy
Subtleties in Designing DNA Sequence Specific Ligands 115
Mamizo Randrianarivelo and Krystyna Zakrzewska
The Structure of DNA Four-Way Junctions 137
Eberhard von Kitzing, David M.J. Lilley and Stephan Diekmann
Physical Chemistry and Dynamics
Rapid Confonnational Investigations of Organic Molecules 157
Rodney M.J. Cotterill, Eric Platt and Barry Robson
Dynamics of DNA Oligomers: Harmonic and Anharmonic Motions 165
Angel E. Garcia
Surface Boundary Conditions: A Simulation Model for Macromolecules 201
Andre H. Juffer and Herman J.C. Berendsen
VIII
Computation oflonic Distributions around Charged Biomolecular Structures
using the PMF Approach 207
Reinhard Klement
Formal Aspects of the Potential of Mean Force Approach 223
Dikeos M. Soumpasis
List of Contributors 241
Subject Index 243
Structure Determination from NMR - Application to Crambin
J.A.C. Rullmann *, A.M.J.J. Bonvin, R. Boelens and R. Kaptein
Department of NMR Spectroscopy
University of Utrecht
Padualaan 8
3584 CH Utrecht
the Netherlands
INTRODUCTION :j:
In the last decade NMR spectroscopy has proven to be an invaluable tool for
determining solution structures of medium sized macromolecules. Advances in
magnet technology and electronic data processing led to the development of two-
dimensional NMR methods, in which all signals are characterized by two reso-
nance frequencies rather than one (Ernst et al., 1987). This made it possible to
solve the resonance assignment problem (Wuthrich, 1986). Finally, calculational
procedures were developed, or rather adapted, to generate molecular structures
that are in agreement with the data derived from the NMR experiment. In our work
we mostly use Distance Geometry (Havel et al., 1983; Havel and Wuthrich, 1984,
1985; Braun and Go, 1985), Distance bounds Driven Dynamics (Kaptein et al.,
1988; Scheek et al., 1989) and restrained Molecular Dynamics (van Gunsteren e t
al., 1983; Clore et al., 1985; Kaptein et al., 1985, 1988; Scheek et al., 1989). Other
methods, such as the Ellipsoid Algorithm (Billeter et al., 1987) and Simulated
Annealing (Nilges et al., 1988), which is similar to DDD, may be useful as well.
The primary source of information is the nuclear Overhauser effect (NOE), which
is magnetization transfer between protons caused by dipolar cross-relaxation (Neu-
haus and Williamson, 1989). It gives rise to cross peaks in the 2D-NOE spectrum
between those protons that are close enough in space for the effect to be operative.
The NOE strength is directly related to the interproton distance, and can be cali-
brated against the NOE observed for two protons at a known, fixed distance. Often
NOEs have been classified as weak, medium or strong, and translated into distance
upper bounds of e.g. 4,3 and 2.5 A (Wuthrich, 1986). Depending on the experiment
and the type of contact a more conservative estimate may be appropriate. This
* E-mail
2
qualitative interpretation often suffices to obtain well defined structures: generally a
whole network of interconnecting NOEs can be observed and assigned, which
together with packing considerations determine the structure quite well, at least for
globular proteins. Increasingly, however, the attention shifts toward a quantitative
modelling of the NOE data, from which more precise structural information can be
obtained. In the following we give a brief description of the methods that have been
developed in our group, and discuss their application to determine the solution
structure of crambin.
THEORY
The normalized intensities in a 20-NOE spectrum recorded with mixing time t m,
are given by the matrix equation (Macura and Ernst, 1980)
(1 )
Matrix R represents the external and cross relaxation contributions. Since the
dipolar interaction is a function of time, the relaxation rates are intimately connected
with the molecular motion. The elements of R can be expressed as (Neuhaus and
Williamson, 1989; Tropp, 1980)
~ ( (0) (1) (2) J
Rjj = K £..i Jij (0) + 3Jij (co) + 6Jij (2co) + Rleak
r~i
(2)
(0) (2) J
Rij = K ( - Jij (0) + 6Jij (2co)
with K = (21t/5) y4112 (liol41t) 2. The spectral densities J are cosine Fourier transforms
(m) foo (m)
J.. (co) = C.. (t) cos(cot) dt (3)
lj IJ
o
where the C(t) are correlation functions describing the time evolution of the inter-
proton vectors; they are defined as
(m) Y2m (cI>lija (bt)) Y2*m ( cI>liaj b (0) ))
\ (4)
Cij (t) = r~(O) r~(t)
lj IJ
3
Here the angular brackets indicate an ensemble average; rand Wlab denote the
length and polar angles of the interproton vector in the laboratory frame of coordi-
nates. Ideally the correlation functions may be computed from a very long MD tra-
jectory. With present day computational facilities C(t) can only be computed with
sufficient statistical accuracy for t-values of the order of 10 ps. Fortunately, for many
interproton vectors C(t) is observed to reach a plateau value after a few ps, indi-
cating that fast picosecond motions are well separated from slower processes
(Olejniczak et al., 1984; Koning, 1990).
Neglecting the latter a model description of C(t) can be set up in terms of two
characteristic times, 'tp' the time in which C(t) decays to the initial plateau value,
and 'tc ' the correlation time for the overall rotation of the molecule. Assuming iso-
tropic tumbling, and transforming to molecule fixed coordinates wmol one has
(Olejniczak et al., 1984)
C.(.m ) (t) = -e-x-p:-(4-t- f-t=c)- C.i.nt(t) (5)
lj n lj
where the internal motion correlation functions Cint(t) are defined as
I. nt 4n L2 Y2 n (WmI. ). ol (t) ) Y2*n ( Wml. j. ol (0) ))
C t =- \ (6)
ij ( ) 5 r~(O) r~(t)
n=-2 lj I)
According to the addition theorem Cijint(O) = (rij-6). Following the approach deve-
loped by Lipari and Szabo (1982) for 13C relaxation, the plateau value of the cor-
relation function, Cijint('tp), can thus be defined quite generally as Sij2(rij-6), where
Sij2 is a generalized order parameter. It has a value between 0 and 1, and can be
calculated from an MD trajectory by using Eq. 6 and estimating the plateau value for
each interproton vector. Within this simplified model the functions C int(t) can be
written as
(7)
where the initial decay has been written as an exponential. Combining Eqs. 3-5
and 7, and assuming that 'tp « 'tc ' which means that the (1-S2) term related to the
initial decay vanishes, one arrives at (Olejniczak et al., 1984; Koning, 1990)
4
(8)
Neglecting all internal motion Eq. 8 may be further simplified by setting Sij2 = 1 for
all proton pairs, and taking distances rijfrom a single model structure.
Eq. 1 is the basis for simulations of NOE spectra, taking direct and indirect
relaxation pathways into account. When a model for the structure and dynamics of
the molecule is available, the NOEs can be calculated from the spectral densities
and Eq. 1 by standard matrix techniques. The opposite route from experimental
NOEs to relaxation parameters is not possible directly, since the experimental NOE
matrix is incomplete. We have shown, however, that the experimental data may be
supplemented by NOEs calculated from a model (Boelens et al., 1988, 1989). The
combined NOE matrix is transformed back to a corrected relaxation matrix, from
which new distances are calculated using Eqs. 2 and 8. Upper and lower bound
margins are related to the precision with which relaxation matrix elements can be
calculated, i.e. their variation with 'tm. Structure calculations are then performed
using the new distance restraints, which now reflect the effects from direct and
indirect magnetization transfer. The whole process is repeated until convergence is
obtained. A complete description of this Iterative Relaxation Matrix Approach (IRMA)
can be found elsewhere (Boelens et al., 1988, 1989; Koning, 1990). Similar proce-
dures have now been implemented by other groups as well (Borgias et al., 1990).
The calculation of internal mobility corrections from MD has been implemented
and tested on DNA fragments recently (Koning, 1990). Different types of interproton
vectors were shown to have different mobilities. The structures clearly improved
upon introduction of Sl values into the spectral densities.
The quality of an NMR structure has often been expressed in terms of the
residual restraint energy or sum of violations. A more direct comparison between
experimental data and model structure is possible in terms of the agreement
between measured and calculated NOE intensities. This can be expressed as an
NMR R-factor, analogous to what is done in X-ray structure refinement (Rullmann
et al., 1990; Borgias et al., 1990). A simple, but effective definition is
L L wij('tm) IA;xP('tm)-A;alc('tm)1
i,j 'tm
R= ~--~-----------e~x~p------- (9)
L L wij ('tm) Aij ('tm)
i,i 'tm
