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NMR: prediction of molecular alignment from
structure using the PALES software
Markus Zweckstetter
Department for NMR-Based Structural Biology, Max Planck Institute for Biophysical Chemistry, Am Fassberg 11, 37077 Goettingen, Germany. Correspondence should be
addressed to M.Z. ([email protected]).
© 2008 Nature Publishing Group http://www.nature.com/natureprotocols
Published online 27 March 2008; doi:10.1038/nprot.2008.36
Orientational restraints such as residual dipolar couplings promise to overcome many of the problems that traditionally limited
liquid-state nuclear magnetic resonance spectroscopy. Recently, we developed methods to predict a molecular alignment tensor and
thus residual dipolar couplings for a given molecular structure. This provides many new opportunities for the study of the structure
and dynamics of proteins, nucleic acids, oligosaccharides and small molecules. This protocol details the use of the software PALES
(Prediction of AlignmEnt from Structure) for prediction of an alignment tensor from a known three-dimensional (3D) coordinate file
of a solute. The method is applicable to alignment of molecules in many neutral and charged orienting media and takes into account
the molecular shape and 3D charge distribution of the molecule.
INTRODUCTION
Structural studies of proteins and nucleic acids are critical for
understanding biological processes at the molecular level. With the
ability to determine atomic resolution structure, dynamics and
folding of biological macromolecules in semiphysiological conditions, nuclear magnetic resonance (NMR) has become an eminent
tool in structural biology1. Traditionally, structure determination
by NMR has relied on the measurement of a large number of
semiquantitative local restraints. The most important of these is the
1H–1H nuclear overhauser effect (NOE), which provides distance
information for pairs of protons separated by less than B5 Å. The
accuracy of the NOE-derived distance usually decreases with the
actual value of the distance because the precision of the measured
intensity decreases with longer distance. Due to the strictly local
nature of the NOE, several questions become difficult to answer
with NMR.
Residual dipolar couplings (RDCs) can be observed in solution
when a molecule is aligned with the magnetic field: either as a result
of its own magnetic susceptibility anisotropy, caused by an anisotropic environment such as an oriented liquid crystalline phase or
an anisotropically compressed gel. When alignment can be kept
sufficiently weak, the NMR spectra retain the simplicity normally
observed in regular isotropic solution, while allowing quantitative
measurement of a wide variety of RDCs, even in macromolecules2,3. Several dilute liquid crystalline media are now available
and RDC measurements are highly efficient, making RDCs a
generally applicable tool for NMR structure determination4,5.
RDCs describe the orientation of internuclear vectors with respect
to the external magnetic field6,7. Thus, they contain long-range
orientational information that can overcome many of the limitations of the traditional NMR structure determination process. For
example, RDCs can be used to refine structures determined by
conventional methods8, solve structures directly9, validate structures10, analyze relative orientations of molecular fragments or
domains11, study dynamic effects12 or characterize intrinsically
disordered proteins13,14.
Weak alignment of biological macromolecules in dilute liquid
crystalline phases or anisotropically compressed gels can result
from steric or electrostatic interactions with the alignment med-
ium. We demonstrated that both magnitude and orientation of
the steric component of the molecular alignment tensor can be
accurately predicted from the molecule’s three-dimensional (3D)
shape15. The approach is called Prediction of ALignmEnt from
Structure (PALES). Further on, we and others demonstrated that
the approach is not restricted to nearly neutral alignment media.
RDCs observed for proteins and nucleic acids dissolved in dilute
suspensions of the highly negatively charged filamentous phage can
be predicted from the 3D structure of a biomolecule16,17. A highly
oversimplified model, one which approximated the electrostatic
interaction between a solute and an ordered phage particle (as that
between the solute charge topography and the electric field of the
phage), predicted the solute’s alignment tensor with reasonable
accuracy17. Recently, we showed that the simple electrostatic model
is also applicable to partial alignment at low pH and in surfactant
liquid crystalline systems18. In the case of uniformly charged
systems, as nucleic acids aligned in negatively charged bacteriophage, the rhombicity and orientation of the alignment tensor can
also be predicted using only a steric interaction model17,19. The
steric interaction model might be further simplified such that the
molecule is not represented in atomic detail, but rather by its
hydrodynamic shape20, gyration tensor19, moment of inertia21 or
the problem is solved analytically22. Fast and simple analytical
solutions allow incorporation of alignment prediction into molecular dynamics simulations. However, these predictions are less
accurate than those obtained by the PALES simulation method.
The ability to predict a molecular alignment tensor and thus
RDCs for a given molecular structure opens the door to many new
opportunities: for example, it can be used to differentiate between
monomeric and homodimeric states15; validate 3D structures of
protein complexes23; determine the relative orientation of protein
domains24; classify protein-fold families on the basis of unassigned
NMR data25; refine nucleic acid structures26; determine the global
structure of branched nucleic acids27; characterize the conformation of intrinsically disordered proteins28–30; and analyze dynamic
systems such as multidomain proteins, nucleic acids and oligosaccharides31,32. The electrostatic alignment model offers additional
unique opportunities, such as distinction between parallel and
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© 2008 Nature Publishing Group http://www.nature.com/natureprotocols
antiparallel arrangements of homodimeric systems33, the identification of domain swaps in oligomeric proteins (S. Rumpel and
M.Z., personal communication) or the analysis of nonspecific
protein–DNA interactions34.
Here, I present a detailed protocol for prediction of an alignment
tensor for a given 3D molecular structure using PALES.
The PALES software
Prediction of molecular alignment is at the heart of the PALES
program. In addition, many other functions for analysis of RDCs
are available in PALES. This includes the estimation of axial and
rhombic components of molecular alignment tensors in the
absence of structural information35,36, back-calculation of alignment tensors from RDCs using well-defined molecular fragments37, analysis of uncertainty in back-calculated tensors38, as
well as efficient handling of dipolar couplings, alignment tensors
and corresponding ProteinDataBank (PDB) files. The PALES software is fully applicable to proteins15, nucleic acids17 and oligosaccharides. All tasks can be performed on the command line and
more complex projects can be set up as scripts. Use of default
parameters allows concise argument lists. For example, ‘pales -pdb
ref.pdb’ performs a PALES shape-prediction for the molecular
structure recorded in ‘ref.pdb’, using an infinite wall model with a
sample volume fraction of 5% and a diameter of the liquid crystal
particle of 40 Å (see below for further details). Alternatively, a
graphical user interface is available that integrates the various RDC
analysis tools with the text editor Vi, the 2D plotting program
Grace, and the molecular graphics program Rasmol.
Molecular alignment
The average orientation of a weakly aligned macromolecule with
respect to the magnetic field is described by a second-rank tensor S,
with a maximum of five independent elements7. The elements of
this traceless tensor are
Sij ¼1=2o3 cos yi cos yj dij 4
6 jÞ
ði; j ¼ x; y; z; dij ¼ 1 for i ¼ j; dij ¼ 0 for i ¼
ð1Þ
where yi is the angle between the molecular axis i and the
magnetic field, and the brackets o4 denote time or ensemble
averaging. The eigenvectors and eigenvalues of this real and
symmetric matrix S correspond to the axes, the magnitude and
the rhombicity of the molecular alignment tensor. This tensor can
be related to the coordinate system of the molecule by a 3D Euler
rotation that accomplishes the diagonalization of the ordering
matrix.
For a pair of spin-1/2 nuclei P and Q, separated by a distance rPQ,
the dPQ dipolar coupling is related to the average orientation of the
whole molecule by
3
dPQ ¼ SLS m0 gP gQ h=ð8p3 orPQ
4Þ
cos fPQ
Si;j Sij cos fPQ
i
j
ð2Þ
SLS is the Lipari–Szabo generalized order parameter, which scales
dPQ for the effect of fast librations of the internuclear vector39. gP
and gQ are the gyromagnetic ratios, h is Planck’s constant, m0 is the
magnetic permeability of vacuum, rPQ is the internuclear distance
and fiPQ is the angle between the P–Q internuclear vector and the
680 | VOL.3 NO.4 | 2008 | NATURE PROTOCOLS
ith molecular axis. In the principal axis frame (superscript d),
equation (2) can be rewritten as
2
dPQ ¼ ðyPQ ; fPQ Þ ¼ 1=2 DPQ
max ½Aa ð3 cos yPQ 1Þ
+ 3=2 Ar sin2 yPQ cosð2fPQ Þ
ð3Þ
Aa ¼ Szzd is the axial component of the alignment tensor and
Ar ¼ 2/3 (Sxxd Syyd) is its rhombic component with |Szzd| 4 |Syyd|
Z|Sxxd|, yPQ and fPQ being cylinder coordinates defining the
vector orientation relative to this tensor; DPQmax ¼ SLS m0gPgQh/
(8p3hrPQ3i) is the dipolar interaction value for the P–Q internuclear
vector.
Back-calculation of the alignment tensor
If well-defined structures of complete macromolecules, their domains
or smaller fragments thereof are available, an alignment tensor S can be
calculated from the observed dipolar couplings (‘-bestFit’ module in
PALES). All five independent elements of the alignment matrix can be
determined, provided a minimum of five experimental RDCs are
available. More couplings may be required if any pair of internuclear
vectors are nearly parallel to each other, or if more than three vectors are
located in a single plane. Two approaches for best-fitting an alignment
tensor to experimental RDCs are in common use: iterative least-squares
minimization and singular value decomposition (SVD). SVD obtains a
solution for the linear equation system formed by equation (3) by
calculating the Moore–Penrose inverse of the directional cosine
matrix37. The transformation returns an alignment tensor for which
calculated RDCs have the least-squares deviation from the observed
ones. It is more stable than iterative least-squares minimization and
requires only a minimum of five RDCs. Therefore, SVD is particularly
useful when only a limited set of dipolar couplings are available.
If previous knowledge of any of the alignment tensor parameters
is available, an iterative least-squares procedure (Levenberg–
Marquardt in the RDC software PALES) that minimizes the
differences between experimentally observed diPQ(exp) values and
those back-calculated from equation (3) becomes the method of
choice40. In this method, any of the five independent alignment
parameters may be held fixed. Under these conditions, if threefold
or higher symmetry exists, the rhombic component is known to be
zero and the dimensionality of the search can be reduced to four.
Evaluation of alignment tensor accuracy
To estimate the uncertainty in alignment tensor values obtained by
best-fitting experimental RDCs to a given structure, the backcalculation may be repeated many times (B1,000 times), but
each time with different Gaussian noise added to the experimental
RDCs. In this so-called Monte-Carlo approach, only those solutions are accepted for which all back-calculated RDCs are within a
given margin of the original experimental dipolar couplings. This
procedure works quite well when the error in the data is dominated
by the random measurement error in the dipolar coupling. To
indirectly account for uncertainties in the structure, it was suggested to set the amplitude of the added noise to 2–3 times higher
than the measurement uncertainty37. In the program PALES, this
approach is optimized by iteratively adjusting the amplitude of the
noise added to the dipolar couplings such that an adjustable
fraction of the solutions are accepted when using an acceptance
margin that is twofold larger than the r.m.s. amplitude of the
added noise.
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When structural noise dominates the error in the SVD fit, the
noise is effectively distributed very differently for different data
points. Therefore, a second method for evaluating the uncertainty
in the alignment tensor, the so-called ‘structural noise Monte-Carlo
method’, was implemented38. In the ‘structural noise Monte-Carlo
method’, noise is added to the original structure with an amplitude
to match the root mean square deviation (RMSD) between the
experimental and back-calculated RDCs. The noise is introduced
into the structure by slightly reorienting the selected vector orientations in a random manner such that the deviations between the
original and final vectors are described by a Gaussian cone-shaped
distribution, with a standard deviation scone and a relative probability of sin(b) exp(b2/scone2) for an angle b between the original
and modified orientation. The spread in the alignment parameters
obtained for these noise-corrupted structures, when using the
coupling constants calculated for the original structure (i.e., yielding a perfect fit if no structural noise were added), then provides
another unbiased measure for the spread in the alignment parameters. On average, the Losonczi Monte-Carlo method, when
implemented in the way described above (‘-mcDc’ module in
PALES), and the structural noise Monte-Carlo method (‘-mcStruc’
module in PALES) yield uncertainties that are quite similar to one
another. However, some differences can occur when considering
small fragments and the ‘structural noise Monte-Carlo method’ is
recommended, in general.
Prediction of molecular alignment from the 3D shape of a
molecule
When the interaction between the macromolecular solute and the
nematogenic particles is predominantly steric in nature, the alignment tensor can be accurately predicted from the solute’s 3D shape
(‘-stPales’ module in PALES)15. This is quite different from the
procedures described above where the alignment tensor is derived
from a fit of experimental RDCs to a known structure. Although
the steric prediction approach by definition can never exceed the
goodness of fit obtained by the SVD method, it offers different
attractive features, as it predicts molecular ordering and RDCs from
a simple steric obstruction model.
The steric obstruction algorithm consists of a one-dimensional
translational grid search combined with uniform sampling of
molecular orientations (Fig. 1a): the nematogen is approximated
by an infinite wall (bicelles; ‘-bic’ parameter in PALES) or infinite
cylinder (Pf1 bacteriophage; ‘-pf1’ parameter in PALES), oriented
parallel to the magnetic field (z axis). The center of gravity of the
solute is moved on a one-dimensional grid, with a spacing between
grid points of 0.2 Å, away from the surface of the liquid crystal
model (‘-dGrid’ parameter in PALES). At each step, a set of 2,196
different molecular orientations is sampled. These 2,196 orientaFigure 1 | Schematic outline of the PALES algorithm for the prediction of
molecular alignment in the case of steric obstruction. (a) One-dimensional
translational grid (black diamonds) in front of an infinite wall or cylinder
(blue rectangle) on which the molecule is moved during the simulation. At
each position, different orientations of the molecule are uniformly sampled
(right panel). (b) When the molecule is close to the surface of a liquid crystal
particle (blue rectangle), it clashes in certain orientations (shown in red),
whereas other orientations are sterically allowed (shown in green). When the
molecule is far away from the liquid crystal particle, all orientations are
equally probable. For details, see the section ‘Prediction of molecular
alignment from the 3D shape of a molecule’.
tions are obtained in a two-step procedure. First, the z axis of the
molecule samples 122 points (minimum number of points) on a
unit sphere that were determined by a double cubic lattice method
(‘-dot’ parameter in PALES)41. This provides a highly uniform
sampling of the sphere. In a second step, the molecule is rotated
around the z axis in steps of 201 (‘-digPsi’ parameter in PALES).
For each orientation, the program evaluates whether the solute
sterically clashes with the nematogen, that is, if any of the solute atoms
has a coordinate within the wall or cylinder model. For example, for a
disk-shaped nematogen and a rod-shaped solute molecule, a larger
fraction of molecules oriented orthogonal to the disks will be
obstructed than those molecules parallel to the disk surface, resulting
in net ordering of the remaining nonobstructed molecules (Fig. 1b).
For these nonobstructed orientations/positions, an alignment matrix
S is calculated according to equation (1). The overall molecular
alignment tensor Smol is simply the linear average over all nonexcluded S matrices. Using periodic boundary conditions, sampling is
restricted to distances r between the solute center of gravity and the
center of the bilayer or cylinder for which r o d/(2Vf ) (wall model),
or r o d/(4Vf )1/2 (cylinder), where d (two times the ‘-rM’ parameter
in PALES) is either the wall thickness (40 Å for bicelles) or the
cylinder diameter (67 Å for Pf1) and Vf is the nematogen volume
fraction. The imperfect alignment of liquid crystals is taken into
account by multiplication of Smol with the order parameter of the
liquid crystal (‘-lcS’ parameter in PALES). Note that the biomolecule
is represented in atomic detail in PALES simulations.
Prediction of molecular alignment from the 3D charge
distribution and shape of a molecule
The obstruction model only includes a steric term, and orientations
of all nonobstructed orientations and positions of the protein
are weighted equally. In the case of a charged liquid crystal as
bacteriophage Pf1 (ref. 42), this simple model fails. Considering
that bacteriophage is highly negatively charged (–0.47 e nm2
average surface charge density), it becomes clear that electrostatic
interactions between protein molecules and liquid crystal particles
cause the probabilities of sterically allowed solute orientations to
depend strongly on this orientation and the distance from the
liquid crystal particle (Fig. 2).
a
b
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To take into account electrostatic effects, each nonexcluded
S matrix is weighted according to its Boltzmann probability, PB,
after calculating the corresponding electrostatic potential of the
solute (‘-elPales’ module in PALES). Continuum electrostatic
theory43 is used for calculating the electrostatic interaction energy:
the solute is embedded in a dielectric medium containing
excess ions in addition to the counter ions neutralizing the solute
and nematogen. The nonlinear Poisson–Boltzmann (PB) equation
is used to derive the electrostatic potential44,45. Even within
the simplifications of a continuum description, calculations of
the electrostatic potentials would require solving a full 3D electrostatics problem for each distance and orientation of the solute with
respect to the surface of the charged liquid crystal particle. Instead,
we further simplify the problem by treating the solute as a particle
in the external field of the liquid crystal. Moreover, we assume
that the nematogen carries a uniform charge density (‘-chSurf’
parameter in PALES) instead of discrete surface charges.
The nonlinear 3D PB equation is then solved only once, in the
absence of the solute, yielding an electrostatic potential j(r). The
distance- and orientation-dependent electrostatic free energy of
the protein comprising partial charges qi at positions ri are then
approximated by
DGel ðr; OÞ ¼ Si qi f½ri ðr; OÞ:
The Boltzmann factor PB ¼ exp[DGel(r,O)/kBT] provides relative
electrostatic weights when averaging the individual alignment
tensors, derived for each orientation and distance, to yield an
overall solute alignment tensor:
Z
Z
¼
A
P
ðr;
OÞ
dr
dO=
PB ðr; OÞ dr dO:
ð5Þ
Amol
ij
B
ij
MATERIALS
EQUIPMENT
. Hardware: Computer running Unix, Linux, Mac OS X or Windows
operating system
. Software: PALES is available to academic users for free download from
http://www.mpibpc.mpg.de/groups/griesinger/zweckstetter/_links/
software_pales.htm
. Input files (see also Supplementary Data):
. 3D coordinate file; most standard PDB files are recognized, including
multiple chain and segment molecules
PB = exp[–∆Ge1(r,Ω)/kB T ]
Figure 2 | Schematic outline of the PALES algorithm simulating weak ordering
of molecules in charged alignment media. A protein is embedded in the
external electrostatic field of the liquid crystal. Electrostatic interactions
between the protein molecule and a liquid crystal particle cause the
probabilities of sterically allowed solute orientations to depend strongly on
this orientation and the distance from the liquid crystal particle. For details,
see the section ‘Prediction of molecular alignment from the 3D charge
distribution and shape of a molecule’.
For a flat surface (‘-bic’ parameter in PALES), an analytical solution
of the nonlinear PB equation exists44,45. For uniformly charged
cylinders such as bacteriophage (‘-pf1’ parameter in PALES), the
method of Stigter46 is used assuming symmetric monovalent ions
and vanishing potential at infinity.
Input and output files used in the protocol can be found in the
Supplementary Data online. In addition, a shell script is provided
for running the PALES tasks outlined in the protocol.
. RDC
table (Table 1); required for best-fitting RDCs to a molecular
structure (‘-bestFit’ module of PALES), but not essential for prediction
of molecular alignment (‘-stPales’ and ‘-elPales’ modules of PALES)
. For prediction of molecular alignment induced by uniformly charged
cylinders (‘-elPales -pf1’):
. File containing the charges of the molecule (Table 2; see also Step 14).
. File containing the electrostatic potential (Table 3).
PROCEDURE
Preparation of input
1| Prepare the coordinate file or download a 3D structure from the PDB (http://www.rcsb.org/pdb) (e.g., ‘pdb1ubq.ent’). When
multiple models are present in the coordinate file, select one and remove the others by using your preferred editor. Remove
unwanted parts of the structure (or use PALES selection flags (see Step 3)). If the PDB file does not contain protons, add
protons to the structure using, for example, the program Reduce (http://kinemage.biochem.duke.edu/software/reduce.php)
(e.g., ‘pdb1ubqH.ent’; see Supplementary Data to know how to add protons to a crystal structure using the program Reduce).
If you are only interested in prediction of the molecular alignment tensor (and not RDCs), go to Step 9.
m CRITICAL STEP For alignment prediction, all atoms in the PDB file will be used (including pseudo atoms such as ‘ANI’),
when no appropriate selection command line arguments are specified.
2| Prepare the RDC input table (e.g., ‘dObs.tab’; Supplementary Data). The table must include a ‘VARS’ line and a
‘FORMAT’ line that label the corresponding columns of the table and define its data type, respectively (Table 1). Lines with a
‘#’ sign as first character as well as empty lines are ignored. The table must include columns for residue ID, three-character
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© 2008 Nature Publishing Group http://www.nature.com/natureprotocols
TABLE 1 | Example of a PALES RDC input table (selection of 1H-15N RDCs observed in the 76-residue protein ubiquitin weakly aligned in bicelles)2.
VARS RESID_I
FORMAT %5d
3
4
5
6
7
13
14
15
16
17
18
20
21
23
25
26
RESNAME_I
%6s
ILE
PHE
VAL
LYS
THR
ILE
THR
LEU
GLU
VAL
GLU
SER
ASP
ILE
ASN
VAL
ATOMNAME_I
%6s
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
N
RESID_J
%5d
3
4
5
6
7
13
14
15
16
17
18
20
21
23
25
26
RESNAME_J
%6s
ILE
PHE
VAL
LYS
THR
ILE
THR
LEU
GLU
VAL
GLU
SER
ASP
ILE
ASN
VAL
ATOMNAME_J
%6s
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
H
D
%9.3f
8.271
10.489
9.871
9.152
3.700
6.947
9.713
9.851
1.909
0.041
10.513
4.071
2.119
9.098
2.948
8.892
DD
%9.3f
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
1.000
W
%.2f
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
1.00
residue name and the atom name for both atoms that are involved in the dipolar coupling. Segment ID and Chain ID are
optional. The ‘D’ column gives the RDC value in Hz. Hetero- and homonuclear RDCs involving C, N, H, P and F atoms can be used
simultaneously. When no experimental RDCs are available, any nonzero dummy values can be entered (in this case, go directly
to Step 9). The ‘DD’ column gives an indication of the experimental RDC error (relative to 1DNH). The weight column ‘W’ is used
for comparison of input and calculated RDCs (e.g., for calculation of root-mean-square deviations between input and calculated
RDCs) and should be normalized to 1DNH according to the gyromagnetic ratios of the involved nuclei and the internuclear
distance, that is, W(1DNH) ¼ 1.000, W(1DCC) B 5.05, W(1DNC) B 8.33, W(1DCH) B 0.48, W(2DHnC) B 3.33. Note that values
in column ‘W’ do not influence best-fitting or prediction of
molecular alignment tensors and therefore also not RDCs
TABLE 2 | Example of a PALES charge file for the 76-residue
back-calculated from calculated/predicted alignment tensors.
protein ubiquitin.
For best-fitting or prediction of molecular alignment, input
1
Terminus
Charge
0.711
6
Default
Charge
0.989 and calculated RDCs are scaled automatically by the dipolar
11
Default
Charge
0.989 interaction value for a specific internuclear vector. For
16
Default
Charge
0.924 one-bond backbone RDCs, optimized values of the internuclear
18
Default
Charge
0.924 distance are used for calculation of the dipolar interaction
21
Default
Charge
0.924 value. For all other RDCs, internuclear distances are taken from
24
Default
Charge
0.924 the 3D coordinate file.
27
Default
Charge
0.989 m CRITICAL STEP The atom notation in the RDC table must
29
Default
Charge
0.989 match that of the PDB file. Check, in particular, the notation
32
Default
Charge
0.924 of amide protons (i.e., ‘H’ or ‘HN’).
33
34
39
42
48
51
52
54
58
59
63
64
68
72
74
76
76
Default
Default
Default
Default
Default
Default
Default
Default
Default
Default
Default
Default
Default
Default
Default
O
OXT
Charge
Charge
Charge
Charge
Charge
Charge
Charge
Charge
Charge
Charge
Charge
Charge
Charge
Charge
Charge
Charge
Charge
0.989
0.924
0.924
0.993
0.989
0.924
0.924
0.993
0.924
0.039
0.989
0.924
0.231
0.993
0.993
0.491
0.491
TABLE 3 | Part of a PALES input file that contains the values for the
electrostatic potential.
0.00
1.00E + 03
2.00E + 03
3.00E + 03
4.00E + 03
5.00E + 03
6.00E + 03
7.00E + 03
8.00E + 03
2.22 105
2.18 105
2.14 105
2.10 105
2.06 105
2.02 105
1.98 105
1.95 105
1.91 105
The first column specifies the distance from the surface of the alignment medium (in nm); the second
column specifies the value of the electrostatic potential (in e kBT1). Files containing the electrostatic
potential of Pf1 phage at different salt concentrations can be downloaded from http://www.mpibpc.
mpg.de/groups/griesinger/zweckstetter/_links/software_pales.htm.
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TABLE 4 | Parameters reported by PALES in RDC output files (see Supplementary Data).
Parameter
DATA SAUPE
Definition
Five independent values (S(zz), S(xx-yy), S(xy), S(xz), S(yz)) of the alignment tensor7
DATA IRREDUCIBLE
Irreducible representation of the alignment tensor47
DATA IRREDUCIBLE
GENERAL_MAGNITUDE
General magnitude of the alignment tensor4,47
DATA MAPPING
Sauson–Flamsteed coordinates (i.e., x and y coordinates for the x, y and z axis of the alignment tensor)
DATA MAPPING INV
Sauson–Flamsteed coordinates of the inverted axes of the alignment tensor (relative to DATA MAPPING)
DATA EIGENVALUES
Eigenvalues (Sxx_d,Syy_d,Szz_d) of the alignment tensor (i.e., the values of the alignment tensor in the principal
axis frame)
DATA EIGENVECTORS
Eigenvectors for diagonalization of the alignment tensor
DATA Q_EULER_ANGLES
Euler angles for rotation of the alignment tensor into the principal axis frame, that is, for diagonalization of the
alignment tensor. Values are specified according to the definition used in quantum mechanics, that is, for clockwise
rotation about the three independent axes z (angle ALPHA), y ¢ (angle BETA) and z 00 (angle GAMMA). Four different
Euler angles are reported due to the fourfold degeneracy of alignment tensors
DATA EULER_ANGLES
Euler angles for rotation into the principal axis frame using a rotation about three dependent axes x (angle psi),
y (angle theta) and z (angle phi). Two solutions are provided
DATA Da
Da ¼ 1/2 Szzd
DATA Dr
Dr ¼ 1/3 (Sxxd Syyd)
DATA Aa
Axial component of the alignment tensor Aa ¼ Szzd.
DATA Ar
Rhombic component of the tensor Ar ¼ 2/3 (Sxxd Syyd)
DATA Da_HN
Axial component (in Hz) of the alignment tensor normalized to the dipolar interaction constant of the one-bond NH
internuclear vector (Da_HN ¼ 1/2 DNHmax Aa ¼ 1/2 21585.19 Aa)
DATA rhombicity
Rhombicity R ¼ Ar/Aa of the alignment tensor (range: [0, 2/3])
DATA N
Number of RDCs used in the calculation
DATA RMS
Root-mean-square deviation between input and calculated RDCs
DATA Chi2
w2 value between input and calculated RDCs
DATA CORR R
Pearson’s linear correlation coefficient between input and calculated RDCs (range: [1, 1])
DATA Q SAUPE
RDC Q-factor calculated according to Q ¼ {Si¼1,..,N [dinorm(exp) dinorm(calc)]2/ N}1/2/Dr.m.s. , with N being the
number of measured and normalized couplings, dinorm(exp). Dr.m.s. refers to the root-mean-square value of RDCs for
randomly distributed internuclear vectors. It can be calculated directly from experimental dipolar couplings
Dr.m.s. ¼ [Si¼1,..,N (dinorm)2]1/2 (‘-qRms’ flag) or from the axial and rhombic component of the alignment tensor
Dr.m.s. ¼ [2 (Danorm)2 (4 + 3R2)/5]1/2, with Danorm being the normalized axial component (‘-qDa’ flag; this is the default
selection)
DATA REGRESSION OFFSET
Vertical offset of straight line fit to a comparison of input and calculated RDCs
DATA REGRESSION SLOPE
Slope of straight line fit to a comparison of input and calculated RDCs
DATA REGRESSION BAX
SLOPE
Average of slope obtained from straight line fits of y ¼ ax + b and x ¼ cy + d, that is, BAX SLOPE ¼ 0.5 (a + 1/c)
Best-fitting experimental RDCs to 3D structure
3| Run PALES to best-fit experimental RDCs to the 3D structure by executing the following command on the command line:
PALES -bestFit -pdb pdb1ubqH.ent -inD dObs.tab -outD dCalc.Svd.tab
m CRITICAL STEP Include the ‘-bestFit’ flag.
? TROUBLESHOOTING
4| Check if the RDC table and PDB file were properly read in by PALES. PALES reports some information (including errors and
warnings on the command line as stderr). The first two lines indicate which PDB file and RDC table were provided as input, how
many residues and atoms were recognized in the PDB file and how many residues and couplings were there in the RDC table. The
first line starting with ‘REMARK’ reports how many atom pairs (RDCs) in the input table could be matched to internuclear vectors
in the PDB file (i.e., how many RDCs will be used for best-fitting). The second ‘REMARK’ line reports the selection criteria applied
to the PDB file.
? TROUBLESHOOTING
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5| Inspect the output file (e.g., ‘dCalc.Svd.tab’). Determine the degree of alignment from the norm of the irreducible
representation of the alignment tensor (‘DATA IRREDUCIBLE GENERAL_MAGNITUDE’) or the magnitude of its largest eigenvalue
(‘Szz_d’). ‘Szz_d’ normalized to 1DNH can be found in the ‘DATA Da_HN’ parameter. ‘DATA Da_HN’ is generally in the range
B5–20 Hz. Using ‘DATA Da_HN’ or ‘Szz_d’ can be misleading in the case of high rhombicity. Evaluate the orientation of the
alignment tensor that is described by three Euler angles ‘ALPHA’ (clockwise rotation around z, leading to new system x¢,y¢,z¢), ‘BETA’
(clockwise rotation around y’, leading to new system x00 ,y00,z00 ) and ‘GAMMA’ (clockwise rotation around z00 ). Four equivalent Euler
orientations are reported due to the sign ambiguity of the eigenvectors. Check the RDC statistics, that is, did PALES use the number
of RDCs you supplied (parameter ‘DATA N’), what is Pearson’s correlation coefficient between experimental and back-calculated
RDCs (‘DATA CORR R’), is the dipolar coupling Q value sufficiently low (‘DATA Q SAUPE’; Q values for high-resolution structures range
from 17% when comparing experimental ubiquitin dipolar couplings with its 1.8-Å X-ray structure to 11% when comparing dipolar
couplings for the third IgG-binding domain of streptococcal protein G with its 1.1-Å X-ray structure), are there systematic errors
in the experimental RDCs that cause an offset (‘DATA REGRESSION OFFSET’) between experimental and back-calculated RDCs or a
slope (‘DATA REGRESSION SLOPE’) deviating from one (further details can be found in Table 4).
m CRITICAL STEP For high-resolution X-ray structures (solved at a resolution of 2.5 Å or better), Pearson’s correlation coefficient
between experimental and calculated couplings (‘DATA CORR R’) is expected to be above 0.9.
? TROUBLESHOOTING
6| Refine the RDC input table. Search the column ‘D_DIFF’, which lists the difference between experimental and calculated RDCs, for
values that significantly exceed the values obtained for most of the other residues. Check the NMR spectra and determine, if signal
overlap or low signal-to-noise ratio is responsible for the large deviations. Under these circumstances, remove the corresponding RDC
values from the input table (e.g., by marking them out with a ‘#’ sign in the beginning of the line) and repeat Steps 3–6.
7| Visualize the orientation of the alignment tensor (optional). Rerun PALES by including the ‘-pdbRot’ flag, that is, ‘PALES
-bestFit -pdb pdb1ubqH.ent -inD dObs.tab -outD dCalc.Svd.tab -pdbRot rot.pdb -nosurf –H’.
In the PDB output file (e.g., ‘rot.pdb’), the molecule will be rotated such that the alignment tensor is parallel to the laboratory
frame. Load the PDB output file into any molecular visualization program and activate the axes of the laboratory frame.
? TROUBLESHOOTING
8| Determine the uncertainty in the alignment tensor parameters. Execute PALES with the command line flag ‘-mcStruc’ and
set the number of Monte Carlo steps to B1,000 (‘-map 1000’):
PALES -bestFit -pdb pdb1ubqH.ent -inD dObs.tab -outD dCalc.McStruc.tab -mcStruc -map
1000 -outDa tMag.tab -outMap tCoor.tab -outAng tAng.tab -outA tSaupe.tab
Alignment tensor parameters for each Monte Carlo step are written to files by specifying the ‘-outDa’, ‘-outMap’,
‘-outAng’ and ‘-outA’ flags. Extract the uncertainty in the alignment tensor parameters from the ‘DATA STATISTICS
MAPPING’ fields in the output file (e.g., ‘dCalc.McStruc.tab’).
m CRITICAL STEP The RDC weight factors (in the column ‘W’ of the RDC input table) must have the correct values (see Step 2).
Prediction of molecular alignment from the 3D shape of a biomolecule
9| Perform the alignment prediction using the steric interaction model. When no RDCs are available (either experimental RDCs
or dummy values), execute one of the following commands on the command line.
PALES -pdb pdb1ubqH.ent -H
If you have prepared an RDC input table (e.g., ‘dObs.tab’), execute
PALES -pdb pdb1ubqH.ent -H -inD dObs.tab
If you want to store the output into a file (e.g., ‘dCalc.Steric.tab’), execute
PALES -pdb pdb1ubqH.ent -H -inD dObs.tab –outD dCalc.Steric.tab
This is identical to executing
PALES -stPales -bic -wv 0.05 -pdb pdb1ubqH.ent -inD dObs.tab -outD dCalc.Steric.tab -H
The ‘-bic’ flag selects the infinite wall model (e.g., when using bicelles). For the infinite cylinder model, ‘-bic’ should
be replaced by ‘-pf1’. The orientation of the bilayer/cylinder relative to the magnetic field cannot be changed. Specify the
concentration of the liquid crystalline phase (‘-wv 0.05’ in g ml1).
m CRITICAL STEP Inclusion of protons (‘-H’ flag) can significantly influence the predicted alignment tensor.
? TROUBLESHOOTING
10| Evaluate the results of alignment prediction in the output file (e.g., ‘dCalc.Steric.tab’). Control the simulation parameters
(lines starting with ‘DATA PALES’). The default value of the order parameter of the liquid crystal is 0.8 (‘DATA PALES LC_ORDER’).
The magnitude of alignment (‘DATA Da_HN’) scales linearly with the concentration of the dilute liquid crystalline medium.
Inspect the various quality measures of calculated RDCs such as root-mean-square deviation (‘DATA RMS’), Pearson’s linear
correlation coefficient (‘DATA CORR R’) and RDC quality factor (‘DATA Q SAUPE’).
? TROUBLESHOOTING
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11| Test the influence of variations in the 3D structure. Discard flexible parts of the structure (in this case residues 73–76) by
manually editing the PDB file or by using PALES PDB selection flags, for example,
PALES -stPales -bic -wv 0.05 -pdb pdb1ubqH.ent -inD dObs.tab -outD dCalc.Steric.tab -H -r1
1 -rN 72
Repeat the procedure with differing selections (e.g., ‘-r1 2 -rN 72’ or ‘-r1 1 -rN 74’) and evaluate the influence on
alignment prediction.
m CRITICAL STEP Especially with nearly spherical and small proteins, ill-defined/flexible termini can strongly influence the simulation.
? TROUBLESHOOTING
12| Test the convergence of the alignment prediction. For most molecules, default simulation parameters give reasonable
results. Rerun PALES with increased resolution of the orientational (‘-digPsi’ and ‘-dot’) and translational grid
‘-dGrid’ (in Å) and a modified value for the uniform atom radius ‘-rA’ (in Å) (see this section). Additionally, the selection
of surface accessible atoms can be suppressed by the inclusion of the ‘-nosurf ’ flag (i.e., all atoms are taken into account).
PALES -stPales -bic -wv 0.05 -pdb pdb1ubqH.ent -inD dObs.tab -outD dCalc.StericHR.tab -H
-dGrid 0.1 -dot 133 -digPsi 36 -rA 1.9 -nosurf
Compare the correlation between experimental and predicted couplings obtained for different simulation parameters
(e.g., ‘DATA CORR R’ values in ‘dCalc.Steric.tab’ and ‘dCalc.StericHR.tab’).
m CRITICAL STEP The molecular alignment prediction can never exceed the goodness of fit obtained by the SVD method.
13| Compare the predicted orientation of alignment with that obtained from best-fitting RDCs. Extract the alignment tensor
values (‘DATA SAUPE’) from the output file obtained by SVD (e.g., ‘dCalc.McStruc.tab’ in Step 8) and from the output file obtained
by alignment prediction (e.g., ‘dCalc.Steric.tab’ in Step 11). Run PALES with the following flags
PALES -anA -inS1 -4.3110e-04 1.5328e-04 -2.0599e-04 -4.8808e-04 -3.9182e-04 -inS2
-3.9955e-04 -6.7056e-05 -3.1392e-04 -7.6731e-04 -4.0968e-04 -outA dCp.Saupe.tab
In the output file (e.g., ‘dCp.Saupe.tab’), seek out the following parameters that describe the angles between the axes of the
two tensors in three and five dimensions, as well as their collinearity, respectively: ‘DATA ANGLE_3D_AXES (X/Y/Z)’, ‘DATA
ANGLE_5D_SPACE’ and ‘DATA COLL_5D’. Further details regarding these parameters can be found in ref. 47.
m CRITICAL STEP Saupe values have to be given in the order S(zz), S(xx-yy), S(xy), S(xz) and S(yz).
Prediction of molecular alignment from the surface charge distribution and molecular shape
14| Set up the file listing the charges of the molecule (Table 2). Generate an initial version of this file (e.g., ‘charge.tab’) by
running PALES:
PALES -anPdb -pdb pdb1ubqH.ent -outPka charge.tab -el -outP out.PdbSim.tab -pkaDef -pH 7.0
Display the charge file (e.g., ‘charge.tab’) using your preferred editor. The file contains four columns. Columns 1–4 specify the
residue number, the name of the atom where the charge is located, the type of information provided (i.e., the charge value or
the pKa) and the charge or pKa value, respectively. When ‘default’ is specified in column 2, PALES distributes the total charge of
a titratable group evenly over the heavy atoms involved (e.g., both NZ atoms for Arg, but only Nz for Lys). For column 3, the
two options are ‘charge’ and ‘pKa’.
Check if all titratable groups (for proteins: aspartates, glutamates, arginines, lysines and histidines) are present in the charge
file. Check, in particular, the ionizable residues in flexible loops/termini that are often missing in X-ray structures. Also confirm
that PALES assigned charges to the N- and C-terminus. At pH 7, the N- and C-terminus should have a charge of 0.711 and
0.982. Add any missing charges to the charge file. For missing/incomplete side-chain coordinates, specify ‘CB’ as charge
location. Rerun PALES supplying the refined charge file:
PALES -anPdb -pdb pdb1ubqH.ent -pka charge.tab -el -elInfo -outP out.PdbSim.tab -nopkaDef
When executing this command, the serial number (from the PDB file) and the coordinates of the atoms at which the charges
were placed are reported on the command line. Look at the information about the monopole and dipole moment of the charge
distribution provided on the command line.
m CRITICAL STEP The file containing the charges needs to be checked carefully.
m CRITICAL STEP A PDB file with full protonation is required to correctly generate the charge.tab file.
? TROUBLESHOOTING
15| Perform alignment prediction using the electrostatic interaction model for an infinite cylinder:
PALES -elPales -pf1 -wv 0.01 -H -nacl 0.2 -pot pot.M¼0.20_T¼25.tab -pdb pdb1ubqH.ent
-pka charge.tab -inD dObs.tab -outD dCalc.Electrostatic.tab
The ‘-pf1’ flag selects the infinite cylinder model (e.g., when using bacteriophage). Specify the concentration of the liquid
crystalline phase (‘-wv 0.01’ in g ml1). The file containing the electrostatic potential can be downloaded from http://
www.mpibpc.mpg.de/groups/griesinger/zweckstetter/_links/software_pales.htm (see also Table 3).
m CRITICAL STEP Use the ‘-elPales’ flag to select the electrostatic prediction algorithm.
686 | VOL.3 NO.4 | 2008 | NATURE PROTOCOLS
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m CRITICAL STEP Include the ‘-nacl’ command line argument specifying the salt concentration (in M; in the above example,
0.2 M) at which the one-dimensional potential of the uniformly charged cylinder (e.g., ‘pot.M¼0.20_T¼25.tab’) was calculated.
? TROUBLESHOOTING
© 2008 Nature Publishing Group http://www.nature.com/natureprotocols
16| Look at the information reported on the command line. Check if any error messages (lines starting with ‘ERROR’) or
warnings (lines starting with ‘WARNING’) were reported. Determine whether all files were properly read by PALES.
m CRITICAL STEP The PDB file and all charges must have been read into PALES.
? TROUBLESHOOTING
17| Display the output file (e.g., ‘dCalc.Electrostatic.tab’). Control the simulation parameters (lines starting with ‘DATA PALES’).
The default value of the order parameter of the liquid crystal in case of an infinite cylinder (i.e., bacteriophage) is set to 0.9
(‘DATA PALES LC_ORDER’). Prediction of the magnitude of alignment (‘DATA IRREDUCIBLE GENERAL_MAGNITUDE’ or ‘DATA
Da_HN’) is less accurate and generally provides only approximate values at intermediate salt concentrations (B0.1–0.2 M).
Also check Pearson’s linear correlation coefficient (‘DATA CORR R’) between experimental and predicted RDCs.
? TROUBLESHOOTING
18| Test the convergence of the alignment prediction. For most molecules, default simulation parameters give reasonable
results. Check this by running PALES according to the following (see also Step 12):
PALES -elPales -pf1 -wv 0.01 -H -nacl 0.2 -pot pot.M¼0.20_T¼25.tab -pdb pdb1ubqH.ent -pka
charge.tab -inD dObs.tab -outD dCalc.Electrostatic.tab -dot 133 -digPsi 36 -rA 1.9 -nosurf
19| Test the influence of the used charge distribution. Copy the charge file (e.g., ‘charge.tab’) and rename it
(e.g., ‘charge_Full.tab’). Replace all partial charges except for histidines by full charges (i.e., +1 or –1 in column 4 of
‘charge_Full.tab’). Rerun the alignment prediction using the modified charge file:
PALES -elPales -pf1 -wv 0.01 -H -nacl 0.2 -pot pot.M¼0.20_T¼25.tab -pdb pdb1ubqH.ent
-pka charge_Full.tab -inD dObs.tab -outD dCalc.Electrostatic_Full.tab
Compare the result of the prediction with that obtained in Step 15 (i.e., is the correlation between experimental and predicted
RDCs improved). Change the charge assigned to histidines and repeat Steps 15–19.
m CRITICAL STEP The degree of charge assigned to histidines can significantly influence the alignment prediction.
20| Test the influence of variations in the 3D structure. Prediction of molecular alignment from the surface charge distribution
and shape of a molecule is highly sensitive to the positions of the charges. This should be tested by using other models of an
NMR ensemble or by using a different crystal structure and repeating Steps 15–19.
m CRITICAL STEP Flexible termini containing ionizable residues can significantly influence the prediction.
? TROUBLESHOOTING
21| Compare the predicted orientation of the alignment with that obtained from the best-fitting of RDCs according to Step 13.
TIMING
Prediction of molecular alignment using the steric interaction model is straightforward. Download a coordinate file from the
ProteinDataBank (Step 1) and perform an alignment prediction (Step 9). PALES runs take generally less than a second. The
time-consuming steps are the setup of the RDC input table and, in the case of an electrostatic alignment prediction,
the setup of the file containing the charges of the molecule. Once this has been performed, several PALES jobs can be
executed simultaneously by using simple scripts.
? TROUBLESHOOTING
Troubleshooting advice can be found in Table 5.
TABLE 5 | Troubleshooting table.
Step
3
Problem
PALES cannot be executed
Possible reason
Wrong binary file of PALES
Solution
Download PALES compiled on the correct
operating system. Note: There is a
specific binary for MAC PowerPCs
4, 9, 16
PALES reports ‘PDB Error opening PDB file
pdb1ubqH.ent ’
Wrong PDB file name or directory
location
Correct name of file or specify correct
directory
PALES reports ‘RdTable File open error: dObs.
tab ’ and ‘Error reading DC input dObs.tab ’
RDC input table missing
Correct name of file or specify correct
directory
NATURE PROTOCOLS | VOL.3 NO.4 | 2008 | 687
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TABLE 5 | Troubleshooting table (continued).
© 2008 Nature Publishing Group http://www.nature.com/natureprotocols
Step
Problem
Possible reason
Solution
Number of RDCs in RDC input table does not
match number of RDCs selected by PALES
Atom names in RDC input file are
not identical to those in the PDB
file (e.g., amide protons are
named ‘H’ and not ‘HN’)
Adjust atom names and residue numbers
in RDC input table
PALES reports ‘REMARK 0 couplings selected
(inclusive max)’ on the command line
Atom names or residue numbers in
RDC input file are not identical to
those in the PDB file
Adjust atom names in RDC input table
The correlation between experimental and
back-calculated RDCs is unexpectedly low
Wrong structure selected.
Alternatively, residue numbering
in RDC input table differs
from that in PDB file
Select correct structure. Correct for
offset in residue numbering using the
‘-s1’ and ‘-a1’ PALES flags
The RDC quality factor reported by PALES
differs from that calculated by other programs
Different definitions of the RDC
quality factor
Try out two other methods for calculation
of the RDC quality factor by specifying
the ‘-qRms’ or the ‘-qStd’ flag when
running PALES
‘PALES –pdb pdb1ubqH.ent –inD
dObs.tab’ is executed, but PALES appears to
perform alignment prediction instead of
best-fitting RDCs
The ‘-bestFit’ flag was not included
Include the ‘-bestFit’ flag when running
PALES
The output file (e.g., ‘dCalc.Svd.tab’) is empty
except for a few remark lines
PALES selected zero RDCs from the
input table
Adjust atom names in RDC input table
The dipolar interaction values (column ‘DD’
in output file) all have the same value, although
the internuclear distances in the PDB file are
different
PALES automatically adjusted the
distances between backbone
heavy atoms and their hydrogen
atoms
Include the ‘-nofixedDI’ flag when
running PALES
7
In ‘rot.pdb’, only one molecule is present,
although the output file (e.g., ‘dCalc.Svd.tab’)
contains four sets of Euler angles
PALES randomly selects one of the
four possible orientations
Include the ‘-rotID’ flag and specify the
rotation number (from 0 to 3) you would
like to select (e.g., ‘-rotID 2’)
10, 17
No RDCs but the alignment tensor
parameters are reported in the output file
(e.g., ‘dCalc.Steric.tab’)
No RDC input table was specified
Supply an RDC input table (Step 2).
This is not used for the simulation itself,
but tells PALES which RDCs you are
interested in
11, 20
The number of atoms selected by PALES (e.g.,
‘REMARK 113 atoms selected for simulation’) is
almost invariant to the removal of certain parts
of the molecule
PALES selected only surface
accessible atoms for the simulation
Tell PALES to use all atoms by including
the ‘-nosurf’ flag
14
There is no charge assigned to the N-terminal
amino group of the protein in the charge
file
Residue numbers in the PDB file do
not start with 1
Manually assign a positive charge to the
nitrogen atom of the first residue
14, 15
PALES reports ‘WARNING: There is no residue 45
or the proper atom in the given PDB file!’.
A residue number or atom name has
been specified in the charge file
that is not present in the PDB file
Modify charge file or PDB file
16
PALES reports ‘Warning: Potentials between
neighboring cells overlapping, cutoff 6.000000e06! - - -4 Magnitude of alignment tensor wrong!’
Concentration of alignment medium (specified by the ‘-wv’ flag)
is too high for the used ionic
strength
Reduce the concentration of the
alignment medium or the ionic strength
at which the simulation is performed
5
5, 10, 17
688 | VOL.3 NO.4 | 2008 | NATURE PROTOCOLS
© 2008 Nature Publishing Group http://www.nature.com/natureprotocols
PROTOCOL
Note: Supplementary information is available via the HTML version of this article.
ACKNOWLEDGMENTS I am grateful to Ad Bax for his guidance during my
postdoctoral stay in his lab and his continuous support to develop PALES. Many
thanks also to Frank Delaglio for useful discussions and access to source code
handling input/output of dipolar couplings and PDB files, as well as best-fit of
dipolar couplings to PDB files. This work was supported by the Max Planck Society
and the DFG through grants ZW71/1-1 to 3-1.
Published online at http://www.natureprotocols.com
Reprints and permissions information is available online at http://npg.nature.com/
reprintsandpermissions
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12. Meiler, J., Prompers, J.J., Peti, W., Griesinger, C. & Bruschweiler, R. Model-free
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60
40
RDC predicted [Hz]
ANTICIPATED RESULTS
An order matrix describes the preferred orientation of
molecules (proteins, nucleic acids, oligosaccharides, small
molecules) that have been dissolved in media (dilute liquid
crystalline phases, anisotropic gels) that preferentially interact
with the solute through steric and electrostatic interactions.
When the user defines which internuclear vectors he or she is
interested in (by supplying an RDC input table), PALES also
calculates RDCs from the predicted alignment matrices.
Additional information about a predicted alignment tensor and
RDCs can be found in the output files (Table 4 and
Supplementary Data). This includes the PALES simulation
parameters, the irreducible representation of the order matrix,
Sauson–Flamsteed coordinates to visualize tensor orientations,
the tensor eigensystem and its corresponding Euler angles,
and various quantities for quality assessment of calculated
RDCs: root-mean-square deviation, Pearson’s linear correlation
coefficient and RDC quality factor (Fig. 3).
20
0
–20
–40
–20
0
20
RDC experimental [Hz]
Figure 3 | Comparison between experimental one-bond 1H-15N RDCs and
values predicted from the 3D charge distribution and shape of the 76-residue
protein ubiquitin (PDB code: 1D3Z; mean structure). Experimental values were
measured in 5 mg ml1 Pf1 bacteriophage, 50 mM NaCl, 10 mM NaH2PO4/
Na2HPO4, pH 6.5.
13. Mohana-Borges, R., Goto, N.K., Kroon, G.J.A., Dyson, H.J. & Wright, P.E.
Structural characterization of unfolded states of apomyoglobin using residual
dipolar couplings. J. Mol. Biol. 340, 1131–1142 (2004).
14. Bertoncini, C.W. et al. Release of long-range tertiary interactions potentiates
aggregation of natively unstructured alpha-synuclein. Proc. Natl. Acad. Sci. USA
102, 1430–1435 (2005).
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liquid crystalline phase: aid to protein structure determination by NMR. J. Am.
Chem. Soc. 122, 3791–3792 (2000).
16. Ferrarini, A. Modeling of macromolecular alignment in nematic virus suspensions.
Application to the prediction of NMR residual dipolar couplings. J. Phys. Chem. B
107, 7923–7931 (2003).
17. Zweckstetter, M., Hummer, G. & Bax, A. Prediction of charge-induced molecular
alignment of biomolecules dissolved in dilute liquid crystalline phases. Biophys. J.
86, 3444–3460 (2004).
18. Zweckstetter, M. Prediction of charge-induced molecular alignment: residual
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