NMR structure calculation

1
NMR structure calculation
2
NMR??????
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? NOE?? ????
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3
Solving structures by NMR

• Structural restraints
• NOE, H-bonds
• J-couplings
• Residual dipolar couplings, T1/T2
• Chemical shifts

• Sample Preparation
• Cloning, expression, purification
• Isotope labelling
• 15N, 13C/15N, 2H/13C/15N

• Resonance Assignments
• Backbone
• Side chains

• Structure Calculation
• Distance geometry
• Restrained molecular dynamics
• Simulated annealing

Secondary Structure Chemical shift
Ensemble of 3D structures
4
Overview

• Structure representation
• Types of NMR data conversion into restraints
• Structure calculation methods
• Structure validation

5
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Structure calculation
Conformation
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  Simulation)
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10
NMR experimental observables providing structural
information

• Backbone conformation from chemical shifts
  (Chemical Shift Index - CSI) ?, ?
• Distance restraints from NOEs
• Hydrogen bond restraints
• Backbone and side chain dihedral angle restraints
  from scalar couplings
• Orientation restraints from residual dipolar
  couplings

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• CSI??????????????????
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12
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• 1H-1H NOE
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• NOE
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• Unique??????
• Ambiguous?????
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NMR data 1 NOE

• For short mixing times NOE cross peak intensity
  is proportional to 1/r6 of two protons.
• NOE 1/r6 f(tc)
• For well structured areas of a macromolecule
  f(tc) can be considered to be constant. (in
  practice this is assumed to be true for all parts
  of the molecule)
• Calibration of cross peaks by using a proton pair
  of known local geometry (distance)
• Because of multiple simplifying assumptions of
  the relationship between NOE and distance it is
  usually used only qualitatively (class NOEs in
  three bins strong, medium and weak)

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Approaches to identifying NOEs

• 15N- or 13C-dispersed 1H-1H NOESY

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Special NOESY experiments

• Filtered, edited NOE based on selection of NOEs
  from two molecules with unique labeling patterns.

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1H-1H distances from NOEs
Long-range (tertiary structure)
Sequential
Intra-residue
Medium-range (helices)
Challenge is to assign all peaks in NOESY spectra
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NMR data 1 NOE

• Conversion of NOE into distances
• Strong 1.8 - 2.7 Å
• Medium 1.8 - 3.3 Å
• Weak 1.8 - 5 Å
• Lower bound because of vdw radii of atoms

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NOE pseudo-energy potential

• Generate fake energy potentials representing
  the cost of violating the distance or angle
  restraints. Heres an example of a distance
  restraint potential

KNOE(rij-riju)2 if rijgtriju
0 if rijlltrij lt riju
VNOE
KNOE(rij-rij1)2 if rijltrijl
where rijl and riju are the lower and upper
bounds of our distance restraint, and KNOE is
some chosen force constant, typically 250 kcal
mol-1 nm-2 So its somewhat permissible to
violate restraints but it raises V
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NOE pseudo-energy potential
VNOE
Potential rises steeply with degree of violation
0
rijl riju
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Number of NOEs are more important than accuracy
of individual NOEs
Structure calculation of protein G (56 aa) with
increasing numbers of NOES
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Restraints and uncertainty

• Large of restraints low values of RMSD
• Large of restraints for key hydrophobic side
  chains

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Dealing with ambiguous restraints

• often not possible to tell which atoms are
  involved in a NOESY crosspeak, either because of
  a lack of stereospecific assignments or because
  multiple protons have the same chemical shift.
• sometimes an ambiguous restraint is included but
  is expressed ambiguously in the restraint file,
  e.g. 3 HA --gt 6 HB, where the wildcard
  indicates that the beta protons of residue 6 are
  not stereospecifically assigned. This is quite
  commonly done for stereochemical ambiguities.
• it is also possible to leave ambiguous restraints
  out and then try to resolve them iteratively
  using multiple cycles of calculation. This is
  often done for restraints that involve more
  complicated ambiguities, e.g. 3 HA--gt10 HN, 43
  HN, or 57 HN, where three amides all have the
  same shift.
• can also make stereospecific assignments
  iteratively using what are called floating
  chirality methods.

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Example of resolving an ambiguityduring
structure calculation
A
9-11 Å
9.52 ppm
B
4.34 ppm
range of inter-atomic distances observed in trial
ensemble
3-4 Å
C
4.34 ppm
Due to resonance overlap between atoms B and C,
an NOE crosspeak between 9.52 ppm and 4.34 ppm
could be A to C or A to B - this restraint is
ambiguous.
But if an ensemble generated with this ambiguous
restraint shows that A is never close to B, then
the restraint must be A to C.
25
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• CANDID/CYANA
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• ????NOE??
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• ??????????????????????????? (??gt90)
• SANE
• ?????????NOE??

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Practical improvements instructure calculation

• Conventional approach relies on interactive
  assignment of NOEs very laborious
• ARIA ambiguous restraints
• use all NOEs in a spectrum even when unassigned
  and allow automatic assignment during successive
  structure calculation rounds
• i.e. discarding NOEs that are inconsistent with
  emerging structure
• Combine with fully automated assignment
  procedures to arrive at fully automated structure
  calculation

27
Iterative structure calculation with assignment
of ambiguous restraints
start with some set of unambiguous NOEs and
calculate an ensemble
there are programs such as ARIA, with automatic
routines for iterative assignment of ambiguous
restraints. The key to success is to make
absolutely sure the restraints you start with are
right!
source http//www.pasteur.fr/recherche/unites/Bin
fs/aria/
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How many restraints to get a high-resolution NMR
structure?

• usually 15-20 NOE distance restraints per
  residue, but the total is not as important as
  how many long-range restraints you have, meaning
  long-range in the sequence i-jgt 5, where i and
  j are the two residues involved
• good NMR structures usually have 3.5
  long-range distance restraints per residue in the
  structured regions
• to get a very good quality structure, it is
  usually also necessary to have some
  stereospecific assignments.

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NMR data 2 H-bonds

• Usually inferred from H2O/D2O exchange
  protection Hence a priory not known which groups
  form the H-bond. Hence only used during structure
  refinement to improve convergence, and precision
  of the family of structure.
• significant impact on structure quality measures

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Backbone Hydrogen Bonds

• NH chemical shift at low field (high ppm)
• Slow rate of NH exchange with solvent
• Characteristic pattern of NOEs
• (Scalar couplings across the H-bond)
• When H-bonding atoms are known ? can impose a
  series of distance/angle constraints to enforce
  standard H-bond geometries

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NMR data 3 J couplings
3J(HN,Ha)
b
HN
q f-60º
a,310
Ha
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Dihedral angles from scalar couplings

• Must accommodate multiple solutions? multiple J
  values
• But database shows few occupy higher energy
  conformations

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Dihedral angle potential

• Convert J data into allowed dihedral angles and
  introduce a restraining potential to maintain the
  allowed angles
• Directly restrain against J-couplings
• Vkj (Jobs-Jcalc)2

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Orientational constraints from residual dipolar
couplings (RDC)
Ho
1H
1H
13C
Reports angle of inter-nuclear vector relative to
magnetic field Ho
15N
1H
1H
15N
1H

• Requires medium to partially align molecules
• Must accommodate multiple solutions? multiple
  orientations

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Alignment tensor and RDC DAB
DAB(q,f) DaAB (3cos2q-1) R(sin2qcos2f)3/2
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15N-1H dipolar couplings
A
5 (w/v) DTDPCDHPC (31)
neutral
(a) 3 CTAB
positive
residue
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Structure refinement
with NOEs
NOEs RDC (A) (B)
NOEs RDC (A)
7.3 3.1Å
4.5 2.1Å
3.4 1.5Å
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Methods for structure calculation

• distance geometry (DG)
• restrained molecular dynamics (rMD)
• simulated annealing (SA)
• hybrid methods

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Starting points for calculations

• to get the most unbiased, representative
  ensemble, it is wise to start the calculations
  from a set of randomly generated starting
  structures.
• Alternatively, in some methods the same initial
  structure is used for each trial structure
  calculation, but the calculation trajectory is
  pushed in a different initial direction each time
  using a random-number generator.

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DG--Distance geometry

• In distance geometry, one uses the NOE-derived
  distance restraints to generate a distance
  matrix, which one then uses as a guide in
  calculating a structure
• Structures calculated from distance geometry will
  produce the correct overall fold but usually have
  poor local geometry (e.g. improper bond angles,
  distances)
• Hence distance geometry must be combined with
  some extensive energy minimization method to
  generate physically reasonable structures

42
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• Vtotal Vbond Vangle Vdihedr Vvdw Vcoulomb
  VNMR
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43
Restrained molecular dynamics

• Molecular dynamics involves computing the
  potential energy V with respect to the atomic
  coordinates. Usually this is defined as the sum
  of a number of terms
• Vtotal Vbond Vangle Vdihedr VvdW Vcoulomb
  VNMR
• the first five terms here are real energy terms
  corresponding to such forces as van der Waals and
  electrostatic repulsions and attractions, cost of
  deforming bond lengths and angles...these come
  from some standard molecular force field like
  CHARMM or AMBER
• the NMR restraints are incorporated into the VNMR
  term, which is a pseudoenergy or
  pseudopotential term included to represent the
  cost of violating the restraints

44
SA-Simulated annealing

• SA is essentially a special implementation of rMD
  and uses similar potentials but employs raising
  the temperature of the system and then slow
  cooling in order not to get trapped in local
  energy minima
• SA is very efficient at locating the global
  minimum of the target function

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Further refinements

• Refinement of structure including full force
  field and e.g. explicit water molecules
• May improve structural quality but may also
  increase experimental violations

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NMR structure calculations

• Objective is to determine all conformations
  consistent with the experimental data
• Programs that only do conformational search lead
  to bad chemistry ? use molecular force fields
  improve molecular properties
• Some programs try to do both at once
• Need a reasonable starting structure
• NMR data is not perfect noise, incomplete data ?
  multiple solutions (conformational ensemble)

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NMR ensemble

• NMR methods do not calculate a single structure,
  but rather repeat structure calculations many
  times to generate an ensemble of structures
• Structure calculations are designed to thoroughly
  explore all regions of conformational space that
  satisfy the experimentally derived restraints
• At the same time, they often impose some physical
  reasonableness on the system, such as bond
  angles, distances and proper stereochemistry.
• The ideal result is an ensemble which
• A. satisfies all the experimental restraints
  (minimizes violations)
• B. at the same time accurately represents the
  full permissible conformational space under the
  restraints
• C. looks like a real protein

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NMR ensemble
The fact that NMR structures are reported as
ensembles gives them a fuzzy appearance which
is both informative and sometimes annoying

• Secondary structures well defined, loops
  variable
• Interiors well defined, surfaces more variable
• Trends the same for backbone and side chains
• More dynamics at loops/surface
• Constraints in all directions in the interior

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Minimized average structure

• a minimized average is just that a mean
  structure is calculated from the ensemble and
  then subjected to energy minimization to restore
  reasonable geometry, which is often lost in the
  calculation of a mean
• this is NMRs way of generating a single
  representative structure from the data. It is
  much easier to visualize structural features from
  a minimized average than from the ensemble
• for highly disordered regions a minimized average
  will not be informative and may even be
  misleading--such regions are sometimes left out
  of the minimized average
• sometimes when an NMR structure is deposited in
  the PDB, there will be separate entries for both
  the ensemble and the minimized average. It is
  nice when people do this. Alternatively, a member
  of the ensemble may be identified which is
  considered the most representative (often the one
  closest to the mean)

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NMR structures include hydrogen coordinates

• X-ray structures do not generally include
  hydrogen atoms in atomic coordinate files,
  because the heavy atoms dominate the diffraction
  pattern and the hydrogen atoms are not explicitly
  seen.
• By contrast, NMR restraints such as NOE distance
  restraints and hydrogen bond restraints often
  explicitly include the positions of hydrogen
  atoms. Therefore, these positions are reported in
  the PDB coordinate files.

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Assessing the quality of NMR structures

• Number of experimental constraints
• RMSD of structural ensemble (subjective!)
• Violation of constraints- number, magnitude
• Molecular energies
• Comparison to known structures PROCHECK
• Back-calculation of experimental parameters

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Acceptance criteria choosing structures for an
ensemble

• typical to generate 50 or more trial structures,
  but not all will converge to a final structure
  that is physically reasonable or consistent with
  the experimentally derived NMR restraints. We
  want to throw such structures away rather than
  include them in our reported ensemble.
• these are typical acceptance criteria for
  including calculated structures in the ensemble
• no more than 1 NOE distance restraint violation
  greater than 0.4 Å
• no dihedral angle restraint violations greater
  than 5
• no gross violations of reasonable molecular
  geometry
• sometimes structures are rejected on other
  grounds as well
• too many residues with backbone angles in
  disfavored regions of Ramachandran space
• too high a final potential energy in the rMD
  calculation

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Precision of NMR Structures (Resolution)

• judged by RMSD of superimposed ensemble of
  accepted structures
• RMSDs for both backbone (Ca, N, CCO) and all
  heavy atoms (i.e. everything except hydrogen) are
  typically reported, e.g.
• bb 0.6 Å
• heavy 1.4 Å
• sometimes only the more ordered regions are
  included in the reported RMSD, e.g. for a 58
  residue protein you will see RMSD (residues 5-58)
  if residues 1-4 are completely disordered.

54
Reporting ensemble RMSD

• Two major ways of calculating RMSD of the
  ensemble
• pairwise compute RMSDs for all possible pairs of
  structures in the ensemble, and calculate the
  mean of these RMSDs
• from mean calculate a mean structure from the
  ensemble and measure RMSD of each ensemble
  structure from it, then calculate the mean of
  these RMSDs
• pairwise will generally give a slightly higher
  number, so be aware that these two ways of
  reporting RMSD are not completely equal. Usually
  the Materials and Methods, or a footnote
  somewhere in the paper, will indicate which is
  being used.

55
Assessing structure quality

• run the ensemble through the program PROCHECK-NMR
  to assess its quality
• high-resolution structure will have backbone RMSD
  0.8 Å, heavy atom RMSD 1.5 Å
• low RMS deviation from restraints (good agreement
  w/restraints)
• will have good stereochemical quality
• ideally gt90 of residues in core (most favorable)
  regions of Ramachandran plot
• very few unusual side chain angles and rotamers
  (as judged by those commonly found in crystal
  structures)
• low deviations from idealized covalent geometry

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Structural Statistics Tables
list of restraints, and type
calculated energies
agreement of ensemble structures with restraints
(RMS)
precision of structure (RMSD)
sometimes also see listings of Ramachandran
statistics, deviations from ideal covalent
geometry, etc.
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Structure validation
XPLOR/CNS Consistency with data? convergence of
structure calculation (eg rmsd over all
atoms) restraint violations? Procheck
programme that analyses and evaluates a family of
structures i.e. is the structure consistent with
what we know about structure ? residue by
residue output covalent geometry dihedral
angles non-bonded interaction main chain
H-bonds stereochemistry chirality disulphide
bonds
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Example of Procheck results
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Cross validation

• Leaving out a percentage of experimental
  constraints. Recalculating structures and
  checking for consistency with unused data
• Can be done with same type of data eg NOE
• More often used with NOEs and RDCs

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Grx-C1?????

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• Amber????
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Grx-C1?????

• CANDID/CYANA??????(???)
• 2 CPU, 8??
• SANE-CYANA??,??????(???)
• ???????????NOE
• ???? 2CPU 1??
• 20-40???
• SANE-AMBER??,??????(???)
• ???? 20 CPU 15??
• 1030???

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• PDB 1Z7P(ensemble), 1Z7R(mean)
  http//www.rcsb.org/pdb

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Most favored regions () 88.8
Additionally allowed regions () 10.7
Generously allowed regions () 0.5
Disallowed regions () 0.0
RMSD All residues Regular secondary structure
Backbone heavy atoms 0.88 0.32
All heavy atoms 1.13 0.68
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?????

• NMRPipe ????http//spin.niddk.nih.gov/bax/softwa
  re/NMRPipe/
• NMRView ????http//www.onemoonscientific.com/nmr
  view/
• CYANA???? 500 Euro http//www.las.jp/prod/cyana/e
  g/
• TALOS????????????? (NMRPipe????)
• http//spin.niddk.nih.gov/NMRPipe/talos/
• SANE?????NOE????J Biomol NMR, 2001 19(4) 321-9
• Amber ?????????????? 400 http//amber.scripps.
  edu/
• PROCHECK-NMR ???????http//www.biochem.ucl.ac.uk/
  roman/procheck_nmr/procheck_nmr.html
• MOLMOL ???????http//hugin.ethz.ch/wuthrich/softw
  are/molmol/

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• Felix ???? http//www.accelrys.com/products/fel
  ix/index.html
• AZARA Free http//www.bio.cam.ac.uk/azara/
• PROSA (Free?) http//guentert.gsc.riken.go.jp/Sof
  tware/Prosa.html
• ????
• Felix ???? http//www.accelrys.com/products/feli
  x/index.html
• XEASY 200 http//hugin.ethz.ch/wuthrich/softwar
  e/xeasy/index.html
• Sparky Free http//www.cgl.ucsf.edu/home/sparky/
• CARA Free http//www.nmr.ch
• ????
• CNS Free http//cns.csb.yale.edu/
• XPLOR Free http//xplor.csb.yale.edu/xplor/
• XPLOR-NIH Free http//nmr.cit.nih.gov/xplor-nih/
  
• ????
• PyMol Free http//pymol.sourceforge.net/
• MolScript Free http//www.avatar.se/molscript/
• RasMol Free http//www.openrasmol.org/
• VMD Free http//www.ks.uiuc.edu/Research/vmd/