Subject: Re: Problem with Kabsch measure for RMSD on planar molecules

From: "Dr. Peter Bladon" <[email-masked]>
Date: Thu, 18 Jul 2002 13:01:24 +0100

Dear Paul,

I have adopted a different approach to the problem of aligning and/or 
comparing two structures.  The approach is detailed in the paper:
"A rapid method for comparing and matching the spherical parameter
surfaces of molecules and other irregular objects" J. Mol. Graphics,
1989,7,130.

The method is implemented in various forms in the Interchem suite of 
programs.  In INTERCHEM (for SGI machines) or INTERCHEM-PC (for 
Windows machines) there was no problem in aligning your two structures.
Although the rms residuals were not exactly zero the two structures
overlaid pretty well.  A more sever case would be exemplified by 
linear molecules such as acetylene.  Again there was no problem.

The software is available by following links from:
http://www.interprobe.co.uk/inter/interprobe.html

The software is free to academics but commercial enterprises are
expected to pay a fee.
Cheers

Peter Bladon

---

From: Xiang Lu <[email-masked]>
Date: Thu, 18 Jul 2002 11:59:11 -0400 (EDT)

Dear Paul:

Your problem arises because of the "non-equivalent" sequential numbering of
atoms between the two structures. Using RasMol (with -mol2 option), and with
"label %i" command, you will see the numbering of carbons atoms in your two
structures as follows:

              15-----16            05-----04    
             /         \          /         \   
            /           \        /           \  
#1         14           17------06           03 
            \           /        \           /  
             \         /          \         /   
              13-----12            01-----02    

              13-----12            05-----04    
             /         \          /         \   
            /           \        /           \  
#2         14           17------06           03 
            \           /        \           /  
             \         /          \         /   
              15-----16            01-----02    

The RMSD (using only C atoms) is 1.3285 A. If you simply swap (12<--->16)
and (13<--->15) in structure #2, you will get RMSD to be zeros, as you would
expect. 

If you would like to know more about ls-fitting between two structures and
ls-fitting of a plane to a set of atoms, with working examples, you might
find the following URL helpful:
             http://rutchem.rutgers.edu/~olson/jmb/ls_fit.html

Xiang-Jun

-- 
Dr. Xiang-Jun Lu            | Tel:   (732) 445 4619 (O)
Department of Chemistry     |
Rutgers University          | Fax:   (732) 445 5958
610 Taylor Road             | Email: [email-masked]
Piscataway, NJ 08854-8087   | URL: http://rutchem.rutgers.edu/~xiangjun/