Subject: Interproton distance averages

From: [email-masked] (Mark J Forster )
Date: Tue, 7 Dec 93 16:56:17 -0800

Dear Comp. Chemists,

G. Ravishanker recently asked: 

>       I have a question regarding averaging properties over an MD run -
> especially those that fluctuate a lot (specifically interproton distances
> in MD simulations).

Here is my $0.02

The correct way to average distances for comparison to NMR data
is a little complicated.
 
Distance estimates derived from NMR are most often derived from nuclear 
Overhauser effect (nOe) data. This is a problematic area because
of the transfer of magnetization in a molecule that gives rise to nOe 
data is not simply a function of the separation of the two spins. 
In reality the direct nOe transfer pathway only dominates at very
short mixing times, as the mixing time increases multiple step 
pathways become increasingly important - this is 'spin diffusion'. 

One (of many) approaches to dealing with spin diffusion is to 
record nOe data at multiple mixing times and try to deduce the 
initial slope of the nOe buildup. This leads to the cross relaxation
rate constant and it is this that is from which we may derive 'NMR
distances' for comparisons with MD or other simulation methods. 

The appropriate form of averaging is stongly dependent upon the
timescale of the molecular motions involved. For biological
macromolecules the timescale of molecular reorientation is 
of the order of nanoseconds. Thus a molecular dynamics run 
of (say) 100ps is only sampling motions that are much slower
than the molecular reorientation. Under such conditions the 
equations of J.Tropp (J.Chem.Phys., vol 72, p6035 1980) show
the correct form of averaging to be used. In essence it is
inverse r cubed averaging with an additional weighting due 
to angular functions (spherical harmonics) of the orientation
of the H-H vector. 

If the timescale of the conformational interchange is very much
slower than molecular reorientation but faster than the timescale
for the nOe buildup itself (which is of the order of seconds) 
then an inverse r sixth average will be appropriate.
Such a timescale would not be probed by MD but perhaps 
monte carlo or other stochastic schemes would be appropriate. 

If the conformational interchange is much slower than the 
nOe buildup then one will be observing nOes that are the 
average of those in each conformation, but it is likely this 
situation that distinct resonances will be observed for 
occurences of the two conformers.  
  
Some of these issues are discussed in that excellent text
'Neuhaus and Williamson: The nuclear Overhauser effect in
structural and conformational analysis, VCH (1989)'

I also have a paper appearing in J.Comp.Chem. (should be
out in February) that discusses these issues.

Finally I should mention that the NMRchitect product
>from Biosym Technologies (my employers) allows the computation of
various types of distance average for a family of molecular
conformation derived by MD or other means.

Hope this helps. 

Best Wishes       __________________________________________________________
Mark             /
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