Skip to main content

Using the CDK's group module

There is a new module and package for the CDK that is currently under review. This is a short guide to how to use it - to help both reviewers and users.

The basic idea is that molecules can be considered as a kind of graph, and that one useful thing to calculate about such graphs is the automorphism group that preserves element labels and/or bond labels. To put it another way, calculating the symmetries of the molecule - although I should point out that it's not quite the same as the crystallographic symmetry groups.

As a simple example, consider these two molecules (1,4-cylohexadiene and 4h-pyran) :


They are numbered from 0-5 for programming convenience; on the right each molecule has a table of automorphisms written as permutations in cycle notation. It should be fairly obvious that - for example - the H-Flip sends atom 0 to atom 4, 1 to 3, and fixes 2 and 5. Only the H-Flip is an automorphism for 4h-pyran, due to the oxygen atom.

The code to do this is fairly short and really just involves creating an AtomDiscretePartitionRefiner and then calling the getAutomorphismGroup(IAtomContainer) method. This returns a PermutationGroup which stores the automorphisms. What you do with them then is up to you...

There is a corresponding class to find automorphisms of the bonds of an atom container. This may be less useful, but here is napthalene as an example:


Note that the bonds are numbered, not the atoms; also the two different double-bond arrangements are called a and b for reference. The a form has only the V-Flip automorphism that swaps bonds (1, 2), (3, 10) and so on.

Finally, what are the actual uses in chemistry for this? Well, one possibility is external symmetry numbers (interesting reference, actually) - as also mentioned in this post. Another is molecule generation; it's used heavily in AMG. A future possibility might also be using it in CIP or other chirality code.

Comments

Patrik Rydberg said…
There is already some related code in the CDK which does symmetry of atoms. You might be interested in this, it is the EquivalentClassPartitioner and the function getTopoEquivClassbyHuXu
gilleain said…
This comment has been removed by the author.
gilleain said…
Hmm. I thought it double-posted so I deleted the duplicate comment - and now it's gone..

Anyway, it was :

"Good point, Patrik - one of the strengths of the CDK is that it has multiple solutions. It's also one of the weaknesses!

There was also an ancient branch that had a class to find the symmetries from the 3D structure, that could be integrated somehow. It's a little difficult to make packages written by different authors to work neatly together without making large changes. Some sort of interface, perhaps... "

Popular posts from this blog

Generating Dungeons With BSP Trees or Sliceable Rectangles

So, I admit that the original reason for looking at sliceable rectangles was because of this gaming stackoverflow question about generating dungeon maps. The approach described there uses something called a binary split partition tree (BSP Tree) that's usually used in the context of 3D - notably in the rendering engine of the game Doom. Here is a BSP tree, as an example:



In the image, we have a sliced rectangle on the left, with the final rectangles labelled with letters (A-E) and the slices with numbers (1-4). The corresponding tree is on the right, with the slices as internal nodes labelled with 'h' for horizontal and 'v' for vertical. Naturally, only the leaves correspond to rectangles, and each internal node has two children - it's a binary tree.

So what is the connection between such trees and the sliceable dual graphs? Well, the rectangles are related in exactly the expected way:


Here, the same BSP tree is on the left (without some labels), and the slicea…

Common Vertex Matrices of Graphs

There is an interesting set of papers out this year by Milan Randic et al (sorry about the accents - blogger seems to have a problem with accented 'c'...). I've looked at his work before here.

[1] Common vertex matrix: A novel characterization of molecular graphs by counting
[2] On the centrality of vertices of molecular graphs

and one still in publication to do with fullerenes. The central idea here (ho ho) is a graph descriptor a bit like path lengths called 'centrality'. Briefly, it is the count of neighbourhood intersections between pairs of vertices. Roughly this is illustrated here:


For the selected pair of vertices, the common vertices are those at the same distance from each - one at a distance of two and one at a distance of three. The matrix element for this pair will be the sum - 2 - and this is repeated for all pairs in the graph. Naturally, this is symmetric:


At the right of the matrix is the row sum (∑) which can be ordered to provide a graph invarian…

Signatures with user-defined edge colors

A bug in the CDK implementation of my signature library turned out to be due to the fact that the bond colors were hard coded to just recognise the labels {"-", "=", "#" }. The relevant code section even had an XXX above it!

Poor show, but it's finally fixed now. So that means I can handle user-defined edge colors/labels - consider the complete graph (K5) below:

So the red/blue colors here are simply those of a chessboard imposed on top of the adjacency matrix - shown here on the right. You might expect there to be at least two vertex signature classes here : {0, 2, 4} and {1, 3} where the first class has vertices with two blue and two red edges, and the second has three blue and two red.

Indeed, here's what happens for K4 to K7:

Clearly even-numbered complete graphs have just one vertex class, while odd-numbered ones have two (at least?). There is a similar situation for complete bipartite graphs:

Although I haven't explored any more of these…