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

• 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

• 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

• 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 structuresfor Syrian hamster prion protein

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

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

Calculating the structures--methods

• distance geometry (DG)

• restrained molecular dynamics (rMD)

• simulated annealing (SA)

• hybrid methods

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

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

• 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-rij1)2 if rij<rij

l

KNOE(rij-riju)2 if rij>rij

u

0 if rijl<rij < rij

u VNOE =

where rijl and rij

u are the lower and upper boundsof our distance restraint, and KNOE is somechosen 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

• 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

• 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

Precision of NMR Structures (Resolution)

• judged by RMSD of ensemble of accepted structures

• RMSDs for both backbone (C, 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

• 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

• 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”

• 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 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-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. hydrogens; Leu, Val methyls

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 >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

precision ofstructure (RMSD)

agreement of ensemble structureswith restraints (RMS)

calculated energies

sometimes also see listings of Ramachandran statistics, deviationsfrom ideal covalent geometry, etc.