Transcript Chemical shifts and structure

Solving NMR structures II:
Calculation 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
Calculating NMR structures
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so we’ve talked some about getting qualitative structural information
from NMR, for instance certain secondary structures have
characteristic nOe’s and J-couplings associated with them
we’ve 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?
In NMR we don’t get a single structure
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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.
The NMR Ensemble
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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.
Random initial structures
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to get the most unbiased, representative ensemble, it is wise to start
the calculations from a set of randomly generated starting structures
Calculating the structures--methods
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distance geometry (DG)
restrained molecular dynamics (rMD)
simulated annealing (SA)
hybrid methods
DG--Distance geometry
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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
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
Pseudo-energy potentials for rMD
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Generate fake energy potentials representing the cost of violating the
distance or angle restraints. Here’s an example of a distance restraint
potential
KNOE(rij-riju)2 if rij>riju
VNOE =
0
if rijl<rij < riju
KNOE(rij-rij1)2 if rij<rijl
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 it’s somewhat permissible to violate restraints but it raises V
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
Ambiguous restraints
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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.
Criteria for accepting structures
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typical to generate 50 or more structures, but not all will converge to a
final structure consistent with the restraints
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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
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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
Precision of NMR Structures
(Resolution)
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judged by RMSD of ensemble of accepted structures
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RMSDs for both backbone (Ca, N, CC=O) and all heavy atoms (i.e.
everything except hydrogen) are typically reported, e.g.
bb 0.6 Å
heavy 1.4 Å
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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.
Reporting RMSD
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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.
“Minimized average”
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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 NMR’s 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).
What do we need to get a highresolution NMR structure?
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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-j|> 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
Assessing Structure Quality
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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 >90% 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
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.