Residual Dipolar Couplings in
Structure Determination of
Biomolecules
J. H. Prestegard, C. M. Bougault and A. I. Kishore
Chem. Rev. 2004, 104, 3519-3540
Presented
By
Mumdooh A. Mohammed
Outline
• Introduction to Residual Dipolar Coupling
(RDC).
• Complementary NMR observables.
• Alignment of Samples.
• RDC Data Acquisition.
• Structure Interpretation of RDC.
• Limitations opposing RDC.
1
Theory of Residual Dipolar Coupling
Any isolated spin is considered as a very small magnet that
produce magnetic field around it. The surrounding spins fell the
field of that spin, and vise is versa.
This give rise to a mutual interaction between the two spins that is
called Dipole-Dipole interaction.
D jk = b jk (3 (Iˆ j ⋅ e jk )(Iˆk ⋅ e jk ) − Iˆ j ⋅ Iˆk )
Where bjk is a constant called the
dipole-dipole coupling constant.
b jk
ejk
j
k
µ γ γ h
= − 0 j 3k
4 π r jk
If the two interacting spins have
a spin quantum number of ½,
then the above expression for
the dipole-dipole interaction is
reduced to.
B
ejk
j
θ
k
D jk = b jk (3(Iˆ j ⋅ e jk )(Iˆk ⋅ e jk ) − Iˆ j ⋅ Iˆk )
1
1⎞
⎛ 1
= b jk ⎜ 3⎛⎜ cosθ ⎞⎟⎛⎜ cosθ ⎞⎟ − ⎟
⎠⎝ 2
⎠ 4⎠
⎝ ⎝2
b jk ⎛ 3 cos 2 θ − 1 ⎞
=
⎜
⎟
2 ⎝
2
⎠
2
Dipole-Dipole interaction is dependent of the spin separation and
the orientation of the molecule that contain the two interacting
spins. For a rigid molecule the dipolar coupling is:
D jk = −
µ 0γ j γ k h ⎡ 3 cos 2 θ − 1⎤
⎥
2
(2πr )3 ⎣⎢
⎦
If the molecule performs tumbling motion
this average out to:
D jk = −
µ0γ j γ k h 3 cos 2 θ − 1
2
(2πr )3
Where the average is carried out over
the molecule motion.
RDC will add to the
Hamiltonian of the system
and then give rise to the
splitting that is already exist
due to scalar coupling, since
they commute with each
other as indicated in the
opposite graph.
From Ref 3
JHNN+DHNN
3
Complementary NMR observables
There are other anisotropies that arise due to partial alignment
and give rise to constraints that can be used in addition to the
RDC in structure calculations. Those are:
• Chemical shift anisotropy (CSA).
• Pseudocontact shifts in paramagnetic
Systems.
• Cross-Correlated relaxation.
Chemical shift anisotropy
CSA is dependent on the shielding of
the electronic clouds, which contain
anisotropic components in addition to
the isotropic ones. I n case of liquids
the CSA is averaged out to zero due
to random tumbling of the molecules.
But in case of partial aligned
molecules the CSA is not averaged
out to zero and it give rise to shifts of
resonances given by an expression
similar to that of the RDC due to its
dependence on the orientation of the
molecules.
From:
http://www.shef.ac.uk/che
mistry/orbitron/AOs/2p/ind
ex.html
4
Pseudocontact shifts in paramagnetic
Systems
If there is an anisotropic paramagnetic centre in the
molecule, this will give rise to nuclear momentparamagnetic moment coupling, which introduces a set of
shifts that is dependent of the paramagnetic centre,
properties only.
Cross-Correlated relaxation
The correlation relaxation due to the dipole-dipole
interaction arises from two ways:
1- the electronic and nuclear dipoles.
2- the nuclear-nuclear relaxation.
Interference between these two mechanisms provide
similar angular information about the system under
consideration.
5
Sample Alignment
There are a lot of methods used for alignment of samples for RDC
studies among those:
1- Inherent anisotropy of the magnetic susceptibility of the
molecule under interest.
2- Bicelles and other media based on it.
3- Bacteriophage.
4- Polyacrylamide Gels.
Anisotropy of the magnetic
susceptibility of the molecule
The inherent anisotropy of the susceptibility of some
paramagnetic centers offers the simplest way of sample
alignment. These paramagnetic centers may be naturally
occurring or intentionally introduced to the biomolecule for order
purposes.
Another naturally occurring way
for alignment is the diamagnetic
anisotropy, which may be
sufficient for order alignment in
case of anisotropic entities such
as aromatic rings.
B0
Myoglobin
6
Bicelles
From Ref 1
From Ref 6
Alignment of Bicelles
From Ref 1
7
From Ref 3
Bacteriophage
The filamentous phages are used in alignment of nucleic acid
systems as well as protein systems.
They are filaments of length in the order of about 100 nm and
diameter 10 nm. They are covered by a protein coat and highly
negatively charged.
The sample can be recovered by high speed centrifugation.
8
Polyacrylamide Gels
In this case, proteins are diffused into gels and then gels are
stretched or squeezed to control the alignment tensor.
From Ref 4
Practical and theoretical
Considerations of alignment media
• Critical choice of medium.
• Considerations about alignment factors
such as concentration, charge,
hydrophobicity, etc.
• The importance of availability of more than
one suitable medium.
9
RDC Data Acquisition
Information about the Dipolar coupling constant can be inferred by
two ways:
1- Frequency resolved method.
The splitting of lines is related to the
dipolar coupling constant
2- Intensity based Methods.
The occurrence of intensity reduction
of lines is identified as coupling
Between two nuclei.
RDC Data Acquisition
There are more one possible method to measure RDC. Those are
dependent on the type of Nuclei and the number of bonds between
them. Structure information will differ according to the type of
experiment done.
• One-Bond HN-N and C-H RDCs.
• Other protein backbone RDCs.
• One-Bond C-C and C-H RDCs in side
chains.
• H-H RCDs.
10
One-Bond HN-N and C-H RDCs
There are some limitations to the
measurement of RDC, that arise from:
1-Unresolved proton peaks specially in case
of protonated samples.
2-Distortion of line shapes and reduction of
line intensity due to long range 1H-15N or 1H13C couplings.
These limitations can be resolved by the
application of various pulse sequences. The
choice of specific pulse sequence depends
on: Field Intensity, Degree of Alignment,
Labeling level and the size of the system
under consideration.
Examples of sequences used for detecting
RDC are: IPAP (A) or DIPSAP (B).
Other more advanced sequences can
also be used for increasing accuracy
of RDC.
Shown are examples of spin-state
selection elements:
(C) S3E
(D) S3CT
(E) α/β
11
More advanced types
of experiments apply
the HSQC/TROSY or
CT- HSQC/TROSY
sequences For much
more precise RDC
measurements.
Shown is example of
CT- HSQC/TROSY
sequence in addition
to part of the obtained
spectrum
Other protein backbone RDCs
In order to completely define
the order parameters, five
independent parameters, a
set of five independent
measurements of RDCs
should be carried out.
Amongst those RDCs are:
1D
N-C’
1D
1
1
N-Cα DCα-C’ DCα-Cβ
2
2
3
2D
N-Cα DHN-C’ DHN-Cα DHN-Cα
12
One-Bond C-C and C-H RDCs in side
chains
The above measurements are crucial for study of backbone fold
and characterization of pair interactions. But the study of side
chains is also important for structure refinement.
The RDCs used in this case are:
1D
2
1
H-C DH-H DC-C
The measurements of these RDCs are facilitated using J-modCT-HSQC, IPAP-CT-HSQC or 3D CB-(CA)CONH.
The measured couplings should be interpreted carefully due to
possible second order effects.
H-H RCDs
The RDCs for the case of pair of protons provide an extra
constraint that give more advantages for RDC due to:
1- It is long ranged.
2- Provide both angular and distance constraints.
3- It does not need labeled samples, but on the other hand it
is hard to be measured.
Possible sequences for measuring Long range DH-H are:
ACME and CT-COSY.
13
Isotropic
Isotropic
Aligned
Aligned
CT-COSY of Trimannoside in
Bicelle media.
Plots of intensity ratio used to
extract RDC
Structure Interpretation of RDC
The information obtained from RDC is both orientational and
distance restraints, that can be used in a variety of applications to
biological macromolecules, such as:
• Additional constraints in structure determination and
refinement.
• Direct structure determination.
• A tool for structure validation or homology searches.
• Orientational relationships between components.
14
Additional constraints in structure
determination and refinement
The orientation constraint contained in RDC is used in
structure determination with other structure constraints
such as NOEs, CSA offsets and PC shifts.
In this case a number of programs are used in structure
determination by simulated Annealing.
Examples of these programs are:
XPLOR/CNS
DYANA
AMBER
Structure of galactin-3 in absence and presence of ligand.
15
Direct structure determination
RDC may also be used in
direct structure calculation via
the so called protein fragment
assembly strategy. Among
programs that use this method
are:
CASP
ROSETTA
Orientational relationships between
components
RDC can be used, via the
application of protein
fragment assembly strategy,
in the study of orientational
relationships between
components of interacting
Biomolecules (protein pairs,
protein-nucleotide
complexes or protein-ligand
complexes).
16
A tool for structure validation or
homology searches
RDC can be used in
complementary way to the
above strategies, in which the
distribution of RDCs of two
proteins may be compared
and give important information
about homology.
An example of program that is
used in such case is
PALES
Limitations opposing RDC
Despite of the powerful information available from RDC, it has
some limitations:
1- The major limitation is the absence of translational
constraints.
2- Another limitation is the error due to internal motion of
molecule. But this can be used in studying of motion in
complement with the spin relaxation studies.
17
Summary
RDC is a powerful tool that can be used
alone or with other NMR constraints in
a wide range of applications using a
huge variety of software for automatic
calculations.
References
1. Jennifer A. Whiles, Raymond Deems, Regitze R. Vold, and Edward
A. Dennis, Bioorganic Chemistry 30 (2002) 431–442.
2. Rebecca S. Lipsitz andNico Tjandra, Annu. Rev. Biophys. Biomol.
Struct. 2004. 33:387–413.
3. J.H. Prestegard, nature structural biology • NMR supplement • july
1998, 517-522.
4. C. Andrew Fowler, Fang Tian, Hashim M. Al-Hashimi,and James H.
Prestegard, J. Mol. Biol. (2000) 304, 447-460.
5. Elizabeth C. Pollock, Solution NMR studies of RNA: A Dissertation
Presented to the Faculty of the Graduate School of Yale University,
2004.
6. Lorens van Dam, Göran Karlsson, Katarina Edwards, Biochimica et
Biophysica Acta 1664 (2004) 241– 256.
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