Seeds and Weeds : Good/Bad Lists in Structure Generation

With the recent revival of the moleculegen (AMG) project, I've started to properly think beyond just simple generation of spaces from a formula. For example, there are 4 trillion or so C30H62 structures - which might take ... a while.

In any case, one useful feature would be to have good/bad lists of substructures (or 'nice' vs 'naughty' as I've been thinking of them. One simple approach I thought might work is to just start with the largest good substructure and generate from there. This can work :

C9H16 from 6-cycle

(By-the-way : all images done with John May's new Depict utility! It's wonderful to use :)

Which is great! Except that it doesn't always work. The problem is that leaves on the tree with a particular substructure might not have that substructure as a common parent in the tree. Consider these C6H8 structures generated from a 4-cycle:

C6H10 from 4-cycle

These are not all of them. Now we filter out using subgraph isomorphism (Asad's SMSD code) from the whole space:

Whole C6H10 space filtered by 4-cycle

So we get half of them by growing from a 'seed'. Now to think about filtering out the weeds...

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chalky

I wanted to show something that hints at the things that the new architecture can afford us: This is using a Java2D graphics Paint object to make it look like chalk...kindof. It's a very simplistic way of doing it by making a small image with a random number of white, gray, lightgray, and black pixels. edit: it doesn't look so good at small scales some tweaking of stroke widths and so on is essential.

1,2-dichlorocyclopropane and a spiran

As I am reading a book called "Symmetry in Chemistry" (H. H. Jaffé and M. Orchin) I thought I would try out a couple of examples that they use. One is 1,2-dichlorocylopropane : which is, apparently, dissymmetric because it has a symmetry element (a C2 axis) but is optically active. Incidentally, wedges can look horrible in small structures - this is why: The box around the hydrogen is shaded in grey, to show the effect of overlap. A possible fix might be to shorten the wedge, but sadly this would require working out the bounds of the text when calculating the wedge, which has to be done at render time. Oh well. Another interesting example is this 'spiran', which I can't find on ChEBI or ChemSpider: Image again courtesy of JChempaint . I guess the problem marker (the red line) on the N suggests that it is not a real compound? In any case, some simple code to determine potential chiral centres (using signatures) finds 2 in the cyclopropane structure, and 4 in the ...

The Gale-Ryser Theorem

This is a small aside. While reading a paper by Grüner, Laue, and Meringer on generation by homomorphism they mentioned the Gale-Ryser (GR) theorem. As it turns out, this is a nice small theorem closely related to the better known Erdős-Gallai (EG). So, GR says that given two partitions of an integer ( p and q) there exists a (0, 1) matrix A iff p* dominates q such that the row sum vector r(A) = p and the column sum vector c(A) = q . As with most mathematics, that's quite terse and full of terminology like 'dominates' : but it's relatively simple. Here is an example: The partitions p and q are at the top left, they both sum to 10. Next, p is transposed to get p* = [5, 4, 1] and this is compared to q at the bottom left. Since the sum at each point in the sequence is greater (or equal) for p* than q , the former dominates. One possible matrix is at the top left with the row sum vector to the right, and th...

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