1. Algorithms for Comparing Molecule Conformations David Sehnal

2. Contents Motivation Algorithm –Outline –Optimal Translation –Quaternions –Optimal Rotation Implementation, Results & Applications

3. Motivation Three different conformations of cyclohexane (C 6 H 12 ):

4. Motivation (cont.)

5. Algorithm Outline Given sequences And Find transformation So that is minimized.

6. Optimal translation Superimposes centroids By expanding the relation for RSMD we obtain:

7. Optimal rotation Assuming both structures are in centroid coordinates we need to minimize Expanding previous sum yields Which is minimized when is maximized.

8. Quaternions The quaternions are members of a non- commutative division algebra first invented by William Rowan Hamilton. Quaternion is a number with and The set of unit quaternions is isomorphic to set of rotation matrices in 3D space.

9. Optimal rotation (cont.)

10. The algorithm

11. Implementation

12. Results

13. Results (cont.)

14. Applications The implementation will be used in projects of Bioinformatics department in ANF Data Advantages –Source code available –Batch-friendly interface –Speed

15. Thank you for your attention.