1. Automated Drawing of 2D chemical structures Kees Visser

2. Overview  Introduction  Previous works  Algorithm of Boissonnat, Cazals and Flötotto  Algorithm of Fricker, Gastreich and Rarey  Conclusion

3. Introduction  Molecule graphs: Connected Undirected Even length edges Planar Restricted angles between edges Double bonds

4. Introduction  Skeletal formula hydrogen atoms removed Only functional groups left

5. Introduction  Applications Drug design Pharmacology

6. Previous works  1974: Zimmerman and Feldman Uses a library of basic structures Lacks generality

7. Previous work  1983: Shelby Heuristic for positioning of atoms Good method Heuristic quite involved and missing information

8. Previous Work  1993: D. B. Hibbert Genetic algorithm Angles are fixed following the valence of the atoms Drawing evaluated by the distance between non-adjacent atoms

9. Algorithm of Boissonnat, Cazals and Flötotto  Overview: Definitions and Assumptions Drawing conventions and constraints Algorithm outline Cycle and block detection Computing the supertree Drawing the molecules

10. Algorithm of Boissonnat, Cazals and Flötotto  Definitions and assumptions Molecules only have induced cycles of at most length A, where A is typically 6 A molecule family is a set of molecules M = {M 1,M 2,M 3...M n } sharing a connected subgraph T called the template. For a molecule M k the connected subgraphs of M k \T are called its appendices and are denoted T ti, i.e. M k = T U {T t1, T t2,...., T tk }. The graphs are assumed to be having planar drawing.

11. Algorithm of Boissonnat, Cazals and Flötotto  Drawing conventions and constraints Drawing must be planar Restrictions on edge angles

12. Algorithm of Boissonnat, Cazals and Flötotto  Algorithm outline Cycle and block detection in molecules Computing the supertree Drawing the molecules using the supertree

13. Algorithm of Boissonnat, Cazals and Flötotto  Cycle and block detection in molecules Traversing each appendix with a BFS Find the non-tree edges Find the cycle with the non-tree edge Adjacent cycles are grouped to a block

14. Algorithm of Boissonnat, Cazals and Flötotto  Computing the supertree Make a supertree of each pair of molecules Make a supertree out of each pair of supertrees Optimal result is not guarenteed

15. Algorithm of Boissonnat, Cazals and Flötotto  Computing the supertree for 2 molecules Identify common substructures Topological embedding

16. Algorithm of Boissonnat, Cazals and Flötotto  Computing the supertree from 2 trees Adapting algorithm by Gupta and Nishimura  Using dynamic programming  Presence of cycles cause NP-hardness Remove the cycles

17. Algorithm of Boissonnat, Cazals and Flötotto  Removing the cycles Hiding an edge  The edge to hide is not uniquely determined which results in non optimal result Reducing a cycle to 1 node  Only complete blocks of cycles can be matched Hybrid method

18. Algorithm of Boissonnat, Cazals and Flötotto  Drawing the first molecule Breadth-first-order to draw using a permutation  Largest subtree  Longest chain Cycles and blocks are drawn at once In case of conflicts backtrack to a different permutation  Drawing the rest Using the most successful method of placing used before.

19. Algorithm of Boissonnat, Cazals and Flötotto  Conclusion Correct and readable result in general If no drawing can be found, resulting to the original database drawings

20. Algorithm of Fricker, Gastreich and Rarey  Overview Automated structure diagram generation Extension to drawing combinatorial libraries Drawing under directional constraints

21. Algorithm of Fricker, Gastreich and Rarey  Automated structure diagram generation Divide the molecule into small pieces, e.g. drawing units Draw a unit Add its adjacent units to the drawing queue Iterative drawing of the units on the drawing queue, checking for collisions and adding the adjacent pieces to the drawing queue

22. Algorithm of Fricker, Gastreich and Rarey  Dividing the molecule into small drawing units Cycles form ring drawing units The a-cyclic parts are divided into drawing units by finding the longest chains  Faster then atom by atom  Bends only introduced in case of overlap

23. Algorithm of Fricker, Gastreich and Rarey  Drawing the units Starting with the longest chain unit Chain units  A chain is drawn starting at a previously drawn piece with a zigzag layout with alternating 30 degree around the main chain direction Ring units  Ring units are first divided into a set of shortest cycles  Starting from the connecting bond, rings are successively attached until the whole ring system is drawn

24. Algorithm of Fricker, Gastreich and Rarey  Checking for collisions Plane sweep algorithm Collision detected  Identify all drawing units involved  Try to rotate whole drawing units  In case of atoms with multiple outgoing bonds Change the order of the bonds at the atom Change the angle pattern of the bonds at the atom  Selective Bonds to terminal atoms shortened  Rotations within chain drawing units  Selective bonds between the colliding atoms are stretched

25. Algorithm of Fricker, Gastreich and Rarey  Post processing The overall structure is re-oriented to the standard layouts.  Remarks Variations of bond lengths are minimized but it is not assured that the lengths do not differ.

26. Algorithm of Fricker, Gastreich and Rarey  Extension to drawing combinatorial libraries Same orientation of the common core structure increases usefulness.  The algorithm: Draw the molecule with the largest substituent first. For each following molecule Create the layout for the common core using the information from the first molecule Every substituent leaving the common core is added to the drawing queue with its direction Use the algorithm explained earlier Only bond shrinking and stretching allowed

27. Algorithm of Fricker, Gastreich and Rarey  Drawing under directional constraints Consistent layouts for similar molecules without a significant common substructure User or computer generated directional constraints to guide the drawing 8 logical directions, e.g. north, north-east, east, south-east, etc.

28. Algorithm of Fricker, Gastreich and Rarey  Drawing under directional constraints Phase 1, direction tree  Root of the tree is a node with a direction constraint  Nodes are called ring nodes if they point to a ring  Each node gets local drawing rules Each rule contains a vector with orientations Each orientations consists of one orientation for the node itself and one or more for each child node with respect for the tree.

29. Algorithm of Fricker, Gastreich and Rarey  Drawing under directional constraints Phase 2:  Mark all orientations and drawing-rules as either valid or invalid compared to the user- defined directions  Breadth-first manner  Calculate the valid orientations

30. Algorithm of Fricker, Gastreich and Rarey  Drawing under directional constraints Phase 3:  Much like the earlier discussed algorithm  Drawing unit selected on what makes the longest chain of bonds  Using the direction tree

31. Algorithm of Fricker, Gastreich and Rarey  Conclusion Worst case a rather inefficient algorithm Variable bond lengths differ from standards Results depend on user constraints  Possible improvements Ignoring impossible user constrains Variable importance for certain user constraints Favouring nodes pointing to important constraints

32. Algorithm of Fricker, Gastreich and Rarey  Feature tree-based Creation of Directional user constraints Automated directional user constraints

33. Conclusion  Few publications  Interesting algorithms  Difficult problem  More work to be done

34. Question?