Subject: Problem with Kabsch measure for RMSD on planar molecules

From: Paul Darwen <[email-masked]>
Date: Thu, 18 Jul 2002 10:36:17 +1000 (EST)

I have a problem with the Kabsch method of measuring root-mean-square
distance (RMSD) between molecules, as described in Kabsch 1978, Acta 
Cryst A34:827-828.

As far as I can make out, the Kabsch method works so long as three 
or more planes are needed to intersect all the atoms.  This means 
that if a molecule happens to (say) be in a single flat plane, then 
the Kabsch method chokes. 

For example, consider a molecule that's two carbon rings joined by 
a bridge.  This makes it flat.  

Below are two Sybyl2 copies of this molecule, but rotated and translated.
Their root-mean-square distance (RMSD) after alignment should be zero. 

But running Tinker's "superpose" program will align them lengthwise, 
but they're still rotated about the lengthwise axis and not aligned.  
The same thing happens in VMD if you try to align them with the script 
   /usr/local/lib/vmd/scripts/vmd/rmsd.tcl
Both of these incorrectly return an RMSD that's way more than zero. 

Has anyone written an RMSD measure that copes with planar molecules
like this?  If you can run the following two molecules through your 
align-and-measure-RMSD routine and get zero for an answer, I'd be 
grateful for a copy.  

__________________________________________________________________

Paul Darwen                          www.protagonist.com.au/darwen
Protagonist Pty Ltd                      [email-masked]
Brisbane 4064 Australia                     Phone: +61-7-3377-0304

--------------- This is the first of two molecules ---------------

@<TRIPOS>MOLECULE
Bridge bond between two carbon rings
      22      23       1
SMALL
NO_CHARGES

@<TRIPOS>ATOM
       1   C1           1.304260    1.349055   -0.389125   C.2 
       2   C2           1.980455    0.216229   -0.145061   C.2 
       3   C3           1.892984   -0.380446    1.046579   C.2 
       4   C4           1.123138    0.166682    1.990862   C.2 
       5   C5           0.447667    1.299539    1.744975   C.2 
       6   C6           0.512887    1.932896    0.546310   C.2 
       7   H7          -0.161845    1.681260    2.577240   H   
       8   H8           1.043615   -0.318373    2.979753   H   
       9   H9           2.448954   -1.312367    1.248134   H   
      10   H10          2.614125   -0.227590   -0.933089   H   
      11   H11          1.432842    1.773440   -1.395729   H   
      12   C12         -0.113409    3.725645   -0.903027   C.2 
      13   C13         -0.788738    4.858585   -1.148921   C.2 
      14   C14         -1.558584    5.405739   -0.204656   C.2 
      15   C15         -1.646220    4.808998    0.986939   C.2 
      16   C16         -0.970147    3.676100    1.230993   C.2 
      17   C17         -0.178748    3.092243    0.295605   C.2 
      18   H18         -1.098820    3.251664    2.237563   H   
      19   H19         -2.279900    5.252856    1.774946   H   
      20   H20         -2.114383    6.337763   -0.406164   H   
      21   H21         -0.709092    5.343685   -2.137780   H   
      22   H22          0.496097    3.343872   -1.735268   H   

@<TRIPOS>BOND
       1       1       2       1
       2       1       6       1
       3       1      11       1
       4       2       3       1
       5       2      10       1
       6       3       4       1
       7       3       9       1
       8       4       5       1
       9       4       8       1
      10       5       6       1
      11       5       7       1
      12       6      17       1
      13      12      13       1
      14      12      17       1
      15      12      22       1
      16      13      14       1
      17      13      21       1
      18      14      15       1
      19      14      20       1
      20      15      16       1
      21      15      19       1
      22      16      17       1
      23      16      18       1

@<TRIPOS>SUBSTRUCTURE
       1            ****       1

--------------- This is the second of two molecules ---------------

@<TRIPOS>MOLECULE
Bridge bond between two carbon rings
      22      23       1
SMALL
NO_CHARGES

@<TRIPOS>ATOM
       1   C1           0.054840    0.525138   -1.730657   C.2 
       2   C2           1.112013   -0.267815   -1.962393   C.2 
       3   C3           2.327386    0.082664   -1.533765   C.2 
       4   C4           2.474774    1.233137   -0.871667   C.2 
       5   C5           1.416448    2.024847   -0.640943   C.2 
       6   C6           0.167392    1.700650   -1.061558   C.2 
       7   H7           1.626775    2.952893   -0.089236   H   
       8   H8           3.475262    1.532683   -0.512794   H   
       9   H9           3.197548   -0.569107   -1.724045   H   
      10   H10          0.978844   -1.216950   -2.510944   H   
      11   H11         -0.908118    0.160964   -2.117910   H   
      12   C12         -0.802543    3.687019   -0.155836   C.2 
      13   C13         -1.859722    4.479966    0.075891   C.2 
      14   C14         -3.075096    4.129477   -0.352705   C.2 
      15   C15         -3.222482    2.979014   -1.014814   C.2 
      16   C16         -2.164151    2.187340   -1.245587   C.2 
      17   C17         -0.915090    2.511520   -0.824932   C.2 
      18   H18         -2.374444    1.259272   -1.797273   H   
      19   H19         -4.223035    2.679500   -1.373569   H   
      20   H20         -3.945250    4.781258   -0.162414   H   
      21   H21         -1.726500    5.429133    0.624380   H   
      22   H22          0.160424    4.051217    0.231410   H   

@<TRIPOS>BOND
       1       1       2       1
       2       1       6       1
       3       1      11       1
       4       2       3       1
       5       2      10       1
       6       3       4       1
       7       3       9       1
       8       4       5       1
       9       4       8       1
      10       5       6       1
      11       5       7       1
      12       6      17       1
      13      12      13       1
      14      12      17       1
      15      12      22       1
      16      13      14       1
      17      13      21       1
      18      14      15       1
      19      14      20       1
      20      15      16       1
      21      15      19       1
      22      16      17       1
      23      16      18       1

@<TRIPOS>SUBSTRUCTURE
       1            ****       1

--------------- End of the second of two molecules ---------------