Solving NMR structures II: Calculation and evaluation

1
Solving NMR structures IICalculation and
evaluation

• The NMR ensemble
• Methods for calculating structures
• distance geometry, restrained molecular
  dynamics, simulated annealing
• Evaluating the quality of NMR structures
• resolution, stereochemical quality, restraint
  violations, etc

2
Calculating NMR structures

• so weve talked some about getting qualitative
  structural information from NMR, for instance
  certain secondary structures have characteristic
  nOes and J-couplings associated with them
• weve also talked about the concept of explicit
  distance or dihedral angle or hydrogen bond
  restraints from nOe and J-coupling data etc.
• how might we use such restraints to actually
  calculate a detailed, quantitative
  three-dimensional structure at a high level of
  accuracy and precision?

3
In NMR we dont get a single structure

• the very first thing to recognize is that our
  input restraints do not uniquely define a
  structure at infinitely high precision
  (resolution) and accuracy--we can never have
  enough restraints, determined at high enough
  accuracy and precision, to do that!
• rather, a set of many closely related structures
  will be compatible with these restraints--how
  closely related these compatible structures are
  will depend on how good/complete our data are!
• the goal of NMR structure determination is
  therefore to produce a group of possible
  structures which is a fair representation of this
  compatible set.

4
The NMR Ensemble

• repeat the structure calculation many times to
  generate an ensemble of structures consistent
  w/restraints
• ideally, the ensemble is representative of the
  permissible structures--the RMSD between ensemble
  members accurately reflects the extent of
  structural variation permitted by the restraints

ensemble of 25 structures for Syrian hamster
prion protein
Liu et al. Biochemistry (1999) 38, 5362.
5
Random initial structures

• to get the most unbiased, representative
  ensemble, it is wise to start the calculations
  from a set of randomly generated starting
  structures

6
Calculating the structures--methods

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

7
DG--Distance geometry

• In distance geometry, one uses the nOe-derived
  distance restraints to generate a distance
  matrix, from which one then calculates 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 good structures

8
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

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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
10
SA-Simulated annealing

• SA is very similar to 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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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
• possible to resolve many of these ambiguities
  iteratively during the calculation process
• can generate an initial ensemble with only
  unambiguous restraints, and then use this
  ensemble to resolve ambiguities--e.g., if two
  atoms are never closer than say 9 Å in any
  ensemble structure, one can rule out an nOe
  between them
• can also make stereospecific assignments
  iteratively using what are called floating
  chirality methods
• there are now automatic routines for iterative
  assignment such as the program ARIA.

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Criteria for accepting structures

• typical to generate 50 or more structures, but
  not all will converge to a final structure
  consistent with the restraints
• therefore one uses acceptance criteria for
  including calculated structures in the ensemble,
  such as
• 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, such as having multiple residues
  with backbone angles in disallowed regions of
  Ramachandran space or simply having high
  potential energy in rMD simulations

13
Precision of NMR Structures (Resolution)

• judged by RMSD of 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.

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Reporting 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.

15
Minimized average

• 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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What 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

17
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
• 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.