structures2 (1)

7/31/2019 structures2 (1)

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NMR data do not uniquely define a 3Dprotein structure (single set of

coordinates)

Restraints are ranges of allowed distances, angles etc. rather thansingle values, reflecting the fact that the experimental data contain

uncertainties both in measurement and interpretation.

Only a limited number of the possible restraints are observableexperimentallydue to peak overlap/chemical shift degeneracy, lack of

stereospecific assignments, etc.

View of protein structure as a single set of atomic coordinates mayitself be physically unrealistic!proteins are dynamic molecules


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The NMR Ensemble

NMR methods not calculate a single structure, but rather repeat a structurecalculation many times to generate an ensemble of structures

The structure calculations are designed to thoroughly explore all regions ofconformational space that satisfy the experimentally derived restraints

At the same time, they often impose some physical reasonableness on thesystem, such as bond angles, distances and proper stereochemistry.

The ideal result is an ensemble whichA. satisfies all the experimental restraints (minimizes violations)

B. at the same time accurately represents the full permissible conformationalspace under the restraints (maximizes RMSD between ensemble members)

C. looks like a real protein


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The NMR Ensemble

At right, an ensemble of 25

structures for Syrian hamster prionprotein(only the backbone isshown)

Liu et al.Biochemistry (1999) 38, 5362.

The fact that NMRstructures are reportedas ensembles givesthem a fuzzyappearance which isboth informative andsometimes annoying


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NMR structures include hydrogen

coordinates

X-ray structures do not generally include hydrogen atoms in atomiccoordinate 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 andhydrogen bond restraints often explicitly include the positions ofhydrogen atoms. Therefore, these positions are reported in the PDBcoordinate files.


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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 pushedin a different initial direction each time using a random-numbergenerator.


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DG--Distance geometry

In distance geometry, one uses the nOe-derived distance restraints togenerate a distance matrix, which one then uses as a guide incalculating a structure

Structures calculated from distance geometry will produce the correct

overall fold but usually have poor local geometry (e.g. improper bondangles, distances)

hence distance geometry must be combined with some extensiveenergy minimization method to generate physically reasonable

structures


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rMD--Restrained molecular dynamics

Molecular dynamics involves computing the potential energy Vwith respect to the atomic coordinates. Usually this is defined asthe sum of a number of terms:

Vtotal=Vbond+ Vangle+ Vdihedr+ VvdW+ Vcoulomb+VNMR

the first five termshere are real energy terms corresponding tosuch forces as van der Waals and electrostatic repulsions andattractions, cost of deforming bond lengths and angles...thesecome from some standard molecular force field like CHARMMor AMBER

the NMR restraints are incorporated into the VNMRterm, which isa pseudoenergy or pseudopotential term included torepresent the cost of violating the restraints


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Pseudo-energy potentials for rMD

Generate fake energy potentials representing the cost of violating thedistance or angle restraints. Heres an example of a distance restraintpotential

KNOE(rij-rij1)2 ifrijr

ij

u

0 ifrijl


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Example of nOe pseudopotential

rijl rij

u

0

VNOE potentialrisessteeplywith degree

of violation


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SA-Simulated annealing

SA is essentially a special implementation of rMD and usessimilar potentials but employs raising the temperature of thesystem and then slow cooling in order not to get trapped in localenergy minima

SA is very efficient at locating the global minimum of the targetfunction


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Dealing with ambiguous restraints

often not possible to tell which atoms are involved in a NOESYcrosspeak, either because of a lack of stereospecific assignments orbecause multiple protons have the same chemical shift

sometimes an ambiguous restraint is included but is expressedambiguously in the restraint file, e.g. 3 HA --> 6 HB#, where the #

wildcard indicates that the beta protons of residue 6 are notstereospecifically assigned. This is quite commonly done forstereochemical ambiguities.

it is also possible to leave ambiguous restraints out and then try toresolve them iterativelyusing multiple cycles of calculation. This is

often done for restraints that involve more complicated ambiguities, e.g.3 HA-->10 HN, 43 HN, or 57 HN, where three amides all have the sameshift.

can also make stereospecific assignments iteratively using what arecalled floating chiralitymethods


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A B

C

9.52 ppm

4.34 ppm

4.34 ppm

Due to resonance overlap

between atoms B and C,an NOE crosspeakbetween 9.52 ppmand 4.34 ppm couldbe A to C or A to B--this restraint is ambiguous

But if an ensemble generated withthis ambiguous restraintleft out shows that A is neverclose to B, then the restraint mustbe A to C.

Example of resolving an ambiguityduring structure calculation

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3-4

range of interatomicdistances observedin trial ensemble


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Iterative structure calculation withassignment of ambiguous restraints

source:

http://www.pasteur.fr/recherche/unites/Binfs/aria/

there are programs suchas ARIA, with automaticroutines for iterativeassignment of ambiguous

restraints. The key tosuccess is to makeabsolutely sure therestraints you start withare right!

start with some setof unambiguous NOEsand calculate an ensemble


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Acceptance criteria: choosingstructures for an ensemble

typical to generate 50 or more trial structures, but not all will convergeto a final structure that is physically reasonable or consistent withthe experimentally derived NMR restraints. We want to throw suchstructures away rather than include them in our reported ensemble.

these are typical acceptance criteriafor including calculated structuresin the ensemble: no more than 1 nOe distance restraint violation greater than 0.4 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, CC=O) and all heavy atoms (i.e.everything except hydrogen) are typically reported, e.g.

bb 0.6 heavy 1.4

sometimes only the more ordered regions are included in the reportedRMSD, 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 ensemble RMSD

two major ways of calculating RMSD of the ensemble:

pairwise: compute RMSDs for all possible pairs of structures in theensemble, 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 calculatethe mean of these RMSDs

pairwise will generally give a slightly higher number, so be awarethat these two ways of reporting RMSD are not completely equal.Usually the Materials and Methods, or a footnote somewhere in thepaper, will indicate which is being used.


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Minimized average structure

a minimized average is just that: a mean structure is calculated fromthe ensemble and then subjected to energy minimization to restorereasonable geometry, which is often lost in the calculation of a mean

this is NMRs way ofgenerating a single representative structure fromthe data. It is much easier to visualize structural features from aminimized average than from the ensemble.

for highly disordered regions a minimized average will not beinformative and may even be misleading--such regions are sometimesleft out of the minimized average

sometimes when an NMR structure is deposited in the PDB, there willbe separate entries for both the ensemble and the minimized average.

It is nice when people do this. Alternatively, a member of the ensemblemay be identified which is considered the most representative (oftenthe one closest to the mean).


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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-rangerestraints you have, meaninglong-range in the sequence: |i-j|> 5, where iandj 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 stereospecificassignments, e.g. b hydrogens; Leu, Val methyls


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Assessing Structure Quality

NMR spectroscopists usually run their ensemble through the programPROCHECK-NMR to assess its quality

high-resolution structure will have backbone RMSD ~0.8 , heavyatom RMSD ~1.5

low RMS deviation from restraints (good agreement w/restraints) will have good stereochemical quality:

ideally >90% of residues in core (most favorable) regions ofRamachandran 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

precision ofstructure (RMSD)

agreement ofensemble structureswith restraints (RMS)

calculated energies

sometimes also see listings of Ramachandran statistics, deviations

from ideal covalent geometry, etc.

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