KNOTFIND: A SIMPLE ALGORITHM FOR DETECTING KNOTS IN PROTEINS Firas Khatib, Carol Rohl

1. KNOTFIND: A SIMPLE ALGORITHM FOR DETECTING KNOTS IN PROTEINS Firas Khatib, Carol Rohl Department of Biomolecular Engineering Can you tell which of these two protein chains are knotted?

2. How can we tell if a protein chain is knotted? This was the highest scoring model using Rosetta’s automated server Robetta for Target 202 in the CASP6 blind prediction experiment. Can you tell which of these two protein chains are knotted? Unfortunately this model is knotted. Knotted Region

3. How can we tell if a protein chain is knotted? This was the model submitted by our group using the same alignment as Robetta. It is devoid of knots. Knot Free

4. Why Knots? • Knots in polypeptide chains have been found in very few proteins. [Nureki et al., 2002] • Only 8 knots have been found in over 2000 known protein structures. [Taylor, 2000, 2002] • We set out to write a program that checked modeled structures for knots.

5. Detecting Knots without Knot Theory • Joining the ends of a protein chain can create additional knots and cause other problems. • In daily life we often encounter knots without closed loops: telephone cords, ethernet cables, extension cords, headphones…etc. • We define such knots as: “pulling both ends results in a tangle that cannot be undone.”

6. Pulling Both Ends of the Chain Potential Knot This is 1Ni5A. How can we find out if it is knotted?

7. Pulling Both Ends of the Chain Simplifying

8. Pulling Both Ends of the Chain Simplifying

9. Pulling Both Ends of the Chain Simplifying

10. Pulling Both Ends of the Chain Rotating and moving Simplifying

11. Pulling Both Ends of the Chain Simplifying

12. Pulling Both Ends of the Chain Simplifying

13. Pulling Both Ends of the Chain Simplifying

14. Pulling Both Ends of the Chain Simplifying

15. Pulling Both Ends of the Chain Simplifying

16. Pulling Both Ends of the Chain Simplifying Simplifying

17. Pulling Both Ends of the Chain N and C termini connected. Therefore 1Ni5A has no knot.

18. The Knotfind Algorithm • This concept of “pulling the ends of the chain” was the basis for the Knotfind Algorithm. • Knotfind goes through the chain three residues at a time and simulates the pulling of the ends of the chain in an attempt to simplify it.

19. Example of our Algorithm First iteration through the chain

20. Example of our Algorithm Therefore this chain has no knots

21. Example of our Algorithm with a knot In this final stage, all triangles of three consecutive residues have line segments going through them. This chain cannot be simplified further, so this is a knot.

22. Localizing the Knot But once we know a knot exists, how do we find it?

23. Localizing the Knot Knotfind specifies the region that could not be simplified.

24. Localizing the Knot Using Knotfind we are able to locate the knotted region of the chain.

25. Knotfind Results on CASP5 Experiment After running Knotfind on all of Rosetta’s comparative modeling CASP5 decoy sets from University of Washington’s group: 4.8% of the decoys had knots. Total number of chains : 45,366 Total number of knots : 2,163 Why do comparative modeling techniques lead to knots in some modeled structures?

26. We noticed three types of knots • Two different loop regions linking with one another. • A loop region threading itself through the template. • A loop region knotting with itself: This occurs extremely rarely and is likely the result of a high gap penalty.

27. How can we prevent knots? • For CASP6 we filtered our loops: • Libraries of loops were filtered before being placed onto the template. • They were screened for knots with themselves as well as knots with the template. Target 262 The green region is a loop region that conflicted with the template. Because of this, we selected a different alignment for this target.

28. How did we prevent knots in CASP6? Both models used the same template, shown in blue Robetta’s best model knots itself with the template One of our knotted decoys that we discarded due to two conflicting loop regions

29. Knotfind Results after CASP6 After running Knotfind on all of Rosetta’s comparative modeling CASP6 decoy sets from UCSC: 1.1% of the decoys had knots. Total number of chains : 117,200 Total number of knots : 1,300 For CASP5, 4.8% of the decoys had knots.

30. Conclusions • The Knotfind algorithm is simple and fast. • Knot formation correlates with breaks in the chain. • Early filtering of loop libraries helps prevent the formation of knots. • Future work: detecting regions that may not define a knot but are unproteinlike (such as tied shoelaces) .

31. Acknowledgements Carol Rohl Josue Samayoa David Bernick Craig Lowe Matt Weirauch Paul Bourke Brian Raney Art Lyubimov Kevin Karplus