Volume 1 Chapter 7 Exhaustive Fragment Location

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7.11 Topological Symmetry and Fragment Location

Some complete molecular structures in the CSD exhibit topological (molecular) symmetry in their 2D representations. However, many substructural fragments are small and symmetric. This has consequences for the 3D search process itself, and for the relative ordering of the geometrical parameters generated by QUEST3D.

Consider the cyclohexane fragment shown below. It is specified as a 2D query with the atoms enumerated in some way, perhaps cyclically as shown. The 2D query has plane symmetry D6h.

(a) Multiple mappings of 2D search query for cyclohexane due to D6h topological symmetry of fragment

Substructure searching in QUEST3D proceeds via an atom-by-atom, bond-by-bond matching of the query chemical connectivity against the chemical connectivity of a succession of database entries, which we shall call 'target' molecules.

Query atom 1 can map on to any one of six possible atoms in the cyclohexane target and the completion of the substructure search by atom/bond matching can occur in either a clockwise or counter-clockwise direction from each starting point.

This procedure will give rise to 12 independent and totally equivalent mappings of the query to each target. Essentially, there are 12 different and topologically equivalent enumerations of the query atoms (see above).

In its exhaustive fragment location mode QUEST3D will locate all equivalent mappings of a target fragment to the query substructure but will normally choose the first mapping to satisfy the search request.

The equivalent enumerations of the fragment define its Atomic Permutational Symmetry Group (APSG). In 3D, each enumeration corresponds to one of the permutational isomers of the fragment.

In general, the symmetry of the 3D fragment will be lower than the topological symmetry of its 2D representation.

Thus a cyclohexane ring exists in a number of ideal forms, e.g. chair (D3d), boat(C2v), etc. However, in the real target structures most rings will only approximate these symmetries and, indeed, can deviate from them quite significantly in some cases.

These considerations lead to problems in the display and search of geometrical parameters for topologically symmetric fragments.

Imagine that we define the conformation of cyclohexane using the cyclically ordered set of torsion angles tau1 - tau6 indicated in the diagram. QUEST3D will perform a particular mapping of the target atoms to the query, and then use the associated x,y,z-coordinates to calculate tau1 - tau6. However, there is no guarantee that these angles will represent the same permutational isomer in each target, since the particular mapping chosen by the program is not unique.

(b) GSTAT instruction set for tabulating tau1 - tau6 and Cremer-Pople puckering parameters.

RFA 0.001 0.080
AT1 C 2
AT2 C 2
AT3 C 2
AT4 C 2
AT5 C 2
AT6 C 2
BO 1 2
BO 2 3
BO 3 4
BO 4 5
BO 5 6
BO 6 1
DEF TAU1 6 1 2 3
DEF TAU2 1 2 3 4
DEF TAU3 2 3 4 5
DEF TAU4 3 4 5 6
DEF TAU5 4 5 6 1
DEF TAU6 5 6 1 2
The result is that a final tabulation of tau1 - tau6 will order these items in one of the 12 possible ways given by the APSG, as illustrated in the table below. Ways of handling this problem in data analysis have been introduced into GSTAT (see Volume 4 of the CSD System Documentation: October 1992 Edition), and the methodology will be introduced into QUEST3D as soon as practicable.

(c) GSTAT output table for instruction set (b) showing random permutational isomers located by GSTAT

 Nfrag  Refcod        TAU1  TAU2      TAU3    TAU4    TAU5    TAU6      Q2    PHI3      Q3
    63  BABXUX     -71.994   1.721  70.736 -73.630   2.225  70.155   0.996   1.814  -0.004
    69  BAPOCM10    70.352  -1.203 -71.729  71.315   1.711 -70.764   0.985 179.843  -0.020
   114  BEVZOR       5.235 -78.111  72.850   0.174 -69.785  64.376   0.967 296.501  -0.018
   121  BEWNOG     -65.846  70.060  -1.047 -72.544  72.773  -4.658   0.983  62.584  -0.022
   131  BIGDUQ      72.708 -70.487  -0.588  71.129 -68.715  -2.548   0.964 238.473  -0.012
   134  BIWDUG       4.684  68.206 -73.248   1.756  70.861 -75.603   0.959 122.576  -0.013

At a more fundamental level, the presence of permutational isomers must be catered for in the 3D search process itself. Thus, we might choose to select boat form cyclohexane fragments by restricting tau1 and tau4 to be close to zero, and tau2, tau3, tau5, tau6 to be close to + or - 60deg. as appropriate. If the QUEST3D search operated only on the first permutational isomer located (see table above) then very large numbers of hits would be omitted.

As a direct consequence of its exhaustive mode of fragment location QUEST3D performs searches over all permutational isomers in order to decide whether a set of geometrical constraints is satisfied or not.

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Volume 1 Chapter 7 Atomic Overlap in Multiple Fragment Situations.