Dear Eiso,

Sounds like we are getting somewhere.

Three points:

1) It sounds like using minimum distance instead of r-6 average might
make sense. We could then get rid of the latter, unless somebody wants
it.

Comments, anyone?


2) As you say, r-6 sum is really an NOE intensity translated into a funny
unit. It is the right thing for NOE violation analysis and restrained
dynamics. For anything where you think in terms of actual distances (that
includes getting a feel for what is going on with your restraints), you
(also) need something else.


3) The more sophisticated proposals at the end are worth looking at. What
happens (and when) would depend on exactly how easy it is to identify the
various cases, and on how much time we have in our schedule. The only
potential problem is that it would be a bit hard for the average user to
figure out exactly what was going on.

Yours,

Rasmus

---------------------------------------------------------------------------
Dr. Rasmus H. Fogh                  Email: [log in to unmask]
Dept. of Biochemistry, University of Cambridge,
80 Tennis Court Road, Cambridge CB2 1GA, UK.     FAX (01223)766002

On Fri, 10 Nov 2006, eiso wrote:

> Dear Rasmus and Tim,
>
> I hope I don't annoy you too much but I'm still convinced
> that r^-1/6 averages are the not the thing that one should be
> interested in. IMHO there is 'One Best Way To Do It', and I hope I
> can persuade you of my point of view, especially since the concept
> Resonance Object in the CCPN datamodel make it relatively easy to
> do it right.
>
> I agree that it's a complicated situation with different kinds
> of distances, distance averages, different kinds of ambiguities.
> Let's not make it overly complicated by confusing inexperienced
> users with flawed concepts like r^-1/6 averages.
>
> The r^-1/6 sum should be seen as a convenient representation of the NOE
> intensity (measured or calculated) in a familiar unit. When there are
> contributions from multiple pairs to the NOE, these contributions always add up
> and are never averaged.
>
> During typing this I realized there *is* a use case for r^-1/6 averages
> and that is ensemble and/or time-averaging. But then the averaging is only
> over distances between identical pairs in different models, and never over the
> different components of a distance restraints. (and for time averaging r^-1/3 is
> supposed to be better.
>
> Could it be that where you say you want to use the r^-1/6 average
> of a set of distances, you are really interested in the _minimum_
> distance of a number of possibilities, not actually in any kind of average
> over those possiblilites?
>
>
> If you want to evaluate vdW clashes between two groups of atoms (perhaps resonance
> objects)
> you want the minimum distance between the individual atoms, because that is
> the number that determines whether there's a violation. It's best to
> view vdW clashed this entirely separate from NOE analysis.
> In case of a prochiral ambiguity of two e.g. methyl groups, it's also a
> minimum distance that is the relevant number, but now it actually the minimum
> of several r^-1/6 sum distances.
>
>
> there are a few short comments in between your text and an example of what
> I think should be the default below.
>
>
>
> Rasmus Fogh wrote:
>  > Dear Eiso,
>  >
>  > In answer to your questions:
>  >
>  > The problem with the r^-1/6 sum is that it does not correspond to any
>  > distance. It is what the distance would have been if there had been only
>  > one proton. That is the correct value to compare to the distance
>  > constraint (which also does not correspond to any real distance in cases
>  > with multiple assignment). But if I want to get an idea about what is
>
>  > going on, it is nice to have at least the option of finding out how far
>  > away things are in reality. Tim had an example with prochiral methyl
>
> the r^-1/6  average also does not correspond to any distance in 'reality',
> certainly not more than the sum, which at least corresponds to a distance
> derived from the data. [idem for the geometric average]
>
>  > groups: r^-1/6  average 4.2A, r^-1/6 sum 1.8A. Now, if those methyl groups
>  > were really 1.8A apart they would be in van der Waals contact. They are
>  > not.
>
> if you want to evaluate vdW clashes, just look at the individual distances
> or the minimum distance if it's between groups with multiple atoms
> no special reason here for the r^-1/6 average/sum, geometric average or any other
> average to be relevant
>
>  >
>  > By all means use r^-1/6 sum as the default, I would say, but leave r^-1/6
>  > average as an alternative for tables and display. What you use for your
>  > dynamics calculations is another matter.
>
> ok let's focus on the analysis of distances. I hope we agree that
> r^-1/6 average distance restraints should not be used in stucture calculations
>
>  >
>  > Yours,
>  >
>  > Rasmus
>  >
>
>
> Tim Stevens wrote:
>  >>>As I remember r^-1/6 sum is used in all calculations, constraint lists,
>  >>>etc. r^-1/6  average is used in (some of?) the menus and in the structure
>  >>>viewer. I thought that was actually deliberate. The reason would be that
>  >>>the r^-1/6 sum of a restraint to e.g. a methyl group would be clearly
>  >>>shorter than the distance between any two individual protons. For a
>  >>>methyl-methyl restraint it is even worse.
>  >>
>  >>why is that bad? what do you need the individual proton-proton
>  >>distances for except for calculation the -1/6 sum? which is the
>  >>quantitity that should be compared with the distance that is
>  >>determined from the NOE.
>  >
>  >
>  > The r^-1/6 sum assumes physical ambiguity, i.e. multiple contributions.
>  >
>  > This is not always the case.
>
> very true.
>
>  >
>  > As an example, take a constraint between two non-stereospecifically
>  > resolved prochiral methyl groups. Using a real structure, for 12LeuHdb* -
>  > 42ValHga*, the NOE sum is 1.850 and the NOE mean is 3.362. In this case
>
> yes , the ratio between the two is fixed for a certain the number of atoms
> in each group:     1.85*(1/(6*6))^(-1/6) =  3.36167
>
>
>  > there is logical ambiguity and there really is only one contribution
>  > between two methlys. Using an NOE sum here is misleading at best.
>
> not more misleading than the average I would say. If one of the distances is
> exactly equal to the upperbound (so the agreement between model and data is perfect)
> the r^-1/6 average will still give a violation w.r.t the upperbound.
>
> for a 2.0 A NOE and one of the pairs at 2.0A and one at 3.0A
> sum :  ( 1/2.0^6 + 1/3.0^6 )^-1/6 == 1.972
> ave :  (( 1/2.0^6 + 1/3.0^6 )/2)^-1/6 == 2.213
> so the r^-1/6 average calculated from the model violates the restraints.
>
> If the NOE sum is violated, then it follows that there must a violation
> if the assignments were known. This does not hold for the average.
>
> Isn't it actually the minimum distance (of the 4 sum averaged distances) that
> is the most interesting figures in this case?
>
>  >
>  > Also I might just want to do a seeminly simple thing and know an
>  > approximation to a real distance. Say if comparing to a crystal structure.
>
> For a resonance with equivalent protons the r^-1/6 sum should be used.
>
> For a case of multiple (for prochiral type ambiguities mutually exlusive)
> possibilities the minimum distance is the relevant number.
>
> Only in the case comparing your data with an ensemble of multiple models
> r^-1.6 averages over the same pair distances in each model makes sense.
>
>  >
>  > Sure, we can have the default as NOE sum if that's what people are doing
>  > most often. But Analysis should not be so restrictive and dictatorial to
>  > assume that all people would only be interested in working in ARIA-space
>  > at all times.
>  >
>
> It's not so much ARIA or not, but supplying the correct approach as the default to
> compare distances in the protein model to distances from the NOEs.
>
> CANDID works the same way btw.
>
>  > I think Igor's suggestion was a good one, and the two options will stay.
>  > This also gives the opportunity to not be restricted to the NOE. There are
>  > other kinds of distance relationships that are used in NMR, thinking
>  > initially about solid state and HADDOCK-like constraints.
>
> This is a bit vague. HADDOCK exlusively uses the sum, (as it should)
> Could you give one specific example where the average would be better than the sum
> or the minimum?
>
>  >
>  > T.
>  >
>
> For your example above, I would calculate the distances in the following way:
>
>   12LeuHdb* - 42ValHga*,
>
> there are (3+3)*(3+3) = 36 individual interproton distances. between
> methylgroups these are not interesting
>
> first apply r^1/6 sum for the equivalent methyl protons, so that we are left
> with the distances between groups of protons that correspond to a resonance
>
> 12LeuHD1# 43ValHG1#  3.45A
> 12LeuHD2# 43ValHG1#  1.85A
> 12LeuHD1# 43ValHG2#  3.01A
> 12LeuHD2# 43ValHG2#  4.59A
>
> these are the only `distances` that are interesting when evaluating NOEs
> assume that the 2nd possibility is correct, so the model is in perfect
> agreement with the NOE data.
>
> Now if you insist on capturing the distances corresponding  this in one number
> now the numbers:
>
> r^1/6 sum : 1.826 - too short but at least no violated.
> r^1/6 ave : 2.300 - (averaging of 4 distances) this distance violates
>                      the restraint by 0.3 A
> r^1/6 ave : 3.317 - (averaging over 6*6 distances, close to your 3.362A)
>                      violation even worse.
>
> minimum   : 1.85  -  bingo!
>
> so the minimum is the most useful figure in this case and the sum is only
> slightly worse; both sum and the minimum will never be violated in a correct model
>
> In order to produce the 4 numbers above,
> the datamodel needs to differentiate between the following cases. I'm assuming
> that it can already do that.
>
> 1. ambiguity because of equivalent protons (methyl, flipping aromatic ring protons)
>     there is not really an ambiguity here. all protons contribute equally. it's just easy
>     to evaluate a static model with an ambiguous restraint.
>
> 2. prochiral ambiguity  (exclusive OR type) -> use minimum
>
> 3. ambiguity because of overlap between non-equivalent protons
>     (could be a combination of 2 and 3) -> use sum
>
>
>
> hope you made it up to this point....
>
> kind regards,
>
> Eiso
>