Solving NMR Structures II: Calculation and evaluation

1
Solving NMR Structures IICalculation and
evaluation

• What NMR-based (solution) structures look like
• the NMR ensemble
• inclusion of hydrogen coordinates
• Methods for calculating structures
• distance geometry, restrained molecular
  dynamics, simulated annealing
• Evaluating the quality of NMR structures
• resolution, stereochemical quality, restraint
  violations, etc

2
NMR data do not uniquely define a 3D protein
structure (single set of coordinates)

• Restraints are ranges of allowed distances,
  angles etc. rather than single values, reflecting
  the fact that the experimental data contain
  uncertainties both in measurement and
  interpretation.
• Only a limited number of the possible restraints
  are observable experimentally
• due to peak overlap/chemical shift degeneracy,
  lack of stereospecific assignments, etc.
• View of protein structure as a single set of
  atomic coordinates may itself be physically
  unrealistic!
• proteins are dynamic molecules

3
The NMR Ensemble

• NMR methods not calculate a single structure, but
  rather repeat a structure calculation many times
  to generate an ensemble of structures
• The 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 (maximizes RMSD between ensemble
  members)
• C. looks like a real protein

4
The NMR Ensemble
The fact that NMR structures are reported as
ensembles gives them a fuzzy appearance which
is both informative and sometimes annoying
At right, an ensemble of 25 structures for Syrian
hamster prion protein(only the backbone is shown)
Liu et al. Biochemistry (1999) 38, 5362.
5
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.

6
Methods for structure calculation

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

7
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.

8
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

9
rMD--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

10
Pseudo-energy potentials for rMD

• 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
11
Example of nOe pseudopotential
VNOE
potential rises steeply with degree of violation
0
rijl riju
12
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

13
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

14
Example of resolving an ambiguityduring
structure calculation
A
9-11 Å
9.52 ppm
B
4.34 ppm
3-4 Å
range of interatomic distances observed in trial
ensemble
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 left out shows that A is never close to
B, then the restraint must be A to C.
15
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/
16
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

17
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.

18
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.

19
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).

20
How many restraints do we need 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, e.g. b hydrogens
  Leu, Val methyls

21
Assessing Structure Quality

• NMR spectroscopists usually run their 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

22
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.