Subject: Re: CCL:RMS FIts and Symmetries

From: Gregory Nikiforovich <[email-masked]>
Date: Wed, 10 May 1995 08:44:01 -0500 (CDT)

On Fri, 5 May 1995, James A Given wrote:

>   I have what I hope is a common problem. We are generating ligand
> conformations for use in drug design. The ligands we use can
> contain groups with various symmetries, e.g., benzene rings.  
> Does anyone know how to take such symmetries into account when 
> calculating RMS fit? 
> 
>   As a simple example of the problem that arises, imagine a 
> molecule with a plane of symmetry through its center. If the 
> molecule is flipped over and then superposed with the original, 
> the RMS calculation of the difference between the two should be zero. But a naive
> calculation of the RMS will not give zero, because the
> pairing of atoms induced by the superposition is not the
> identity pairing, i.e., the atom marked '1' in the original
> will not be coincident with the atom marked '1' in the copy. 

	The real trick is that in drug design you will have an "important"
	and "unimportant" atoms (or functional groups). So the only RMS what
	matters would be related to the "important" groups (i.e.: aromatics,
        H-bond donors/acceptors, ionized groups, etc.). In reality, you
	wouldn't encounter situations with the clear symmetry for the
	"important" groups. (Though, there are exceptions, like the symmetric
	HIV protease inhibitors.) On the other hand, if you are worried about
        non-coincidence of your atom "1" to a copy atom "1", what is the
        difference, if both atoms are the same, as in benzene case ?

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Gregory V. Nikiforovich                                   Phone (314) 935-4677
Research Professor                                        Fax   (314) 935-4979
Center for Molecular Design                            E-mail address:
Washington University                                  [email-masked]
Lopata Hall, Box 1099
St.Louis, MO 63130

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From: [email-masked] (Graham Hurst)
Date: Wed, 10 May 1995 23:43:24 -0400

>Does anyone know how to take such symmetries into account when 
 
 [Snip]

>  Is there provision in standard software packages for handling this
>problem?

The conformational search program that I wrote which is part of
the ChemPlus set of extensions for HyperChem optionally handles
this problem, without the need to specify equivalent pairs.

If the option is turned on, the program initially permutes atom
indices to find topologically equivalent atom orders. Although in
the worst case this would require comparing N! permutations, in
practice the program avoids generating permutations where the
elements or coordination don't match that of the initial atom
order. The permutations that it does generate are topologically
compared to the orginal and those that match are retained for use
in RMS comparisons. The program can also neglect hydrogens or
only consider specified atoms to further reduce the dimensionality.

Thus for cyclohexane with hydrogens ingored, it would use 12
permutations of the atom order for RMS comparisons.

I'm not sure if the program suits your purposes, since it doesn't
actually report the RMS differences. Rather it uses RMS deviations
(after faster initial screening comparisons) to determine whether
a produced conformation is equivalent to any already found. The
"match" thresholds and tests are user adjustable.

At 11:38 AM 5/10/95 -0400, Peter Shenkin wrote:

>There are several ways of doing this.  The way MacroModel/BatchMin
>does it is to define equivalence pairs of atoms;  for example,
>if you have a phenyl group attached at the 1-position, two equivalence
>pairs would be defined: 2-6 (the equivalent ortho positions) and 3-5
>(meta). When calculating an RMS, our software would do it four times
>for this ring, trying both possibilities for each pair, and would take
>the lowest result.
>
>Clearly, this could be done more smartly:  we could have a mechanism
>to say that 2 and 3 (ortho and meta on one side of the ring) correspond
>to 6 and 5 on the other, respectively;  then we would have to
>calculate the best rigid-body superposition and residual RMS only
>two times, instead of three.

For ChemPlus/HyperChem, one doesn't need to specify the equivalent
atom pairs. One checks the "Use equivalent atom orders" option in
a dialog box, and for this case it would only do up to two RMS
comparisons. (If the first was within a specified threshold it
wouldn't bother with the second.)

I'm curious to know if any other programs can systematically determine
and use equivalent atom orders for RMS comparisons...

Cheers,

Graham
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Graham Hurst, PhD <[email-masked]> or <[email-masked]>
Cambridge, Ontario, Canada