Subject: Re: CCL:conformational isomers

From: [email-masked] (Graham Hurst)
Date: Wed, 22 Feb 1995 23:32:59 -0500

At 02:47 PM 2/22/95 -0800, Marvin Waldman <[email-masked]> wrote:
>On Tue, 21 Feb 95 4:08:12 EST, Dongchul Lim wrote:
>
>> Is there a simple way of testing if two given conformational isomers
>> are equivalent?

[good stuff deleted]

>The ideal/correct solution would be to
>compare both the energy as well as all combinations of RMS comparisons
>of topologically equivalent atoms until the RMS difference found
>for a given comparison pair fell below some threshold.  I am not
>aware of a software package that has actually implemented such
>an algorithm, and would be very interested to hear about one that
>does.

The Conformational Search module of the ChemPlus set of extensions
for HyperChem uses energy and RMS compairisons of topologically
equivalent atom pairings.

I've been following this discussion with some interest.  When I
wrote the Conformational Search module of ChemPlus, I implemented
the following tests to compare for equivalent conformations that
might result from the search.  The comparisons available are (in
the order that the program can optionally execute them) are:

1. Changed chirality (R or S) of chiral centers with 4 bonded
   neighbours. (Chiral centers are determined by HyperChem.)

2. Energy (from HyperChem) within a user adjustable range.

3. Varied torsions within a user adjustable range.  This test is
   turned off by default, since it doesn't handle topologically
   equivalent dihedral angles.

4. R.M.S. deviation for a least-squares overlay of atoms.  As Marvin
   Waldman pointed out, one needs to compare with all topologically
   equivalent permutations of atom order and this option (discussed
   further below) is available in ChemPlus.  A subset of atoms can
   also be specified for the comparision.

I initially included an option for comparison of inertial moments
(suggested earlier by Leif Norskov <[email-masked]>) but I abandoned it
because it seemed too sensitive a measure, with suitable tolerances
varying widely with the number of atoms.

If the option to use equivalent atoms in the RMS comparison is
turned on, the program generates all equivalent atom order
permutations.  The algorithm I used for this is basically brute
force, O(N!) at worst, but being able to compare element type
and number of bonds for each topological "node" allows considerable
trimming of the paths.  Further trimming results from only considering
a subset of atoms (eg. no hydrogens or only backbone atoms) so
that permutations of ignored atoms are unnecessary (assuming
equivalent sets are either all included or all excluded).

>So, the bottom line answer to the question, is: No, I don't think
>there is a SIMPLE way to do this.

I agree!  It took me about a month to puzzle out and implement an
algorithm for generating equivalent atom orders!  As Valery
Golender <[email-masked]> pointed out, the conformational
isomer problem is a specific instance of isomorphism of 3D objects.

Cheers,

Graham

P.S. If you want more ChemPlus or HyperChem product info, please
send email to [email-masked], not to me because I don't work
there anymore.
-------
Graham Hurst, PhD <[email-masked]> or <[email-masked]>
Cambridge, Ontario, Canada

---

From: Matt Stahl <[email-masked]>
Date: Thu, 23 Feb 1995 07:26:43 -0700 (MST)

Greetings,
	The problem of duplicate conformer removal certainly is 
challenging, especially to anyone doing extensive conformational 
searches.  The "easy" method of detection is to compare a unique 
identifier based on atomic coordinates.  Shape descriptors such as the 
sum of interatomic distances, or the sum of all triangles in a molecule 
provide a single number to identify a conformation.  In this sense, 
energy is also a "shape descriptor" because it is simply a function 
operated on a set of coordinates.  As pointed out by Dr. Waldman, there 
is always the possibility of ambiguity when using this kind of 
descriptor.  I have seen cases in larger bicyclo alkanes where very 
different conformations had the same mechanics energy to the 5th or 
6th decimal place!
	There are several matters that must be addressed with regard to 
comparing conformations.  Rms fitting may not be the best measure of 
similarity when comparing long acyclic chains because of the 'torque' 
effect.  Torsional comparisons certainly have valid applications.  In 
general, rms fits work well with the exception of the problems of 
automorphism and enantiomeric coordinates.  Generating enantiomers is 
trivial.  Simply multiply all of the x, y, or z coordinates by -1 to 
generate the mirror image.  Automorphisms can be more of a problem.  They 
can be discovered by connectivity matrix manipulations (see 
balasubramanian in j. chem. inf. comp. sci. may/june 1994).  A much 
quicker approach is to effectively do an atom-by-atom max common 
substructure search using comparisons of atom types.  Once the 
automorphisms are discovered they can be used in both torsional and rms 
comparisons.
	Pat Walters and i have written a program called Padre (Population
Analysis and Duplicate REmoval) that will read multi-structure files,
automatically generate the automorphisms (and enantiomers if desired), and
do rms or torsional comparisons and identify duplicate conformers.  It
will also map rings onto each other and compare all possible overlays.  
Padre is FAR from completion, but the features currently implemented are 
solid.  Please contact me directly if you are interested in this software.

sincerely,
matt

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Mr. Matthew Stahl			| 
Department of Chemistry			| I'd rather be right half of the
University of Arizona			| time than half right all the
Tucson, AZ  85721			| time.
[email-masked]		|	-Malcom S. Forbes
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~