1. Exploring Protein Folding Trajectories Using Geometric Spanners Daniel Russel and Leonidas Guibas Stanford University

2. Goals ● Existing work understanding protein structure – Classification – Comparison – Matching ● Qualitative understanding of proteins motions – We do not quite get there yet

3. Outline ● Overview of spanners ● Properties of interest ● Displaying trajectories ● Future work

4. Geometric Spanners ● Vertexes are points ● Edges have length ● Expansion factor – Ratio between graph distance and Euclidean distance

5. Geometric Spanners ● Vertexes are points ● Edges have length ● Expansion factor – Ratio between graph distance and Euclidean distance

6. 2CI2 Spanner Expansion factor is 2 backbone atom index spanner edges

7. 2CI2 Spanner: Helix  helix backbone atom index

8. 2CI2 Spanner: Strands parallel strands antiparallel strands backbone atom index

9. 2CI2 Spanner: Tertiary Structure tertiary interactions backbone atom index

10. Outline ● Overview of spanners ● Properties of interest ● Displaying trajectories ● Future work

11. Combinatorializes Structure ● Picks a few pairs per set of adjacencies

12. Other Properties ● Regular structure of helices and strands ● Local meaning for edge

13. Family of Descriptors ● Vary expansion factor ● From distance matrix to sparse ● Linear for many values 1.51.752.02.5 3.0

14. Outline ● Overview of spanners ● Properties of interest ● Displaying trajectories ● Future work

15. Protein Folding Trajectories ● Input: Protein trajectories – Currently small proteins, later larger – Nanosecond timescales, later millisecond – Tens or hundreds of folding trajectories – Many non-folding ● Want to understand – Individual trajectories – Structure of conformation space

16. Processing Spanners ● Edges move slightly between frames ● Tracked edge initial frame edges final frame edges identical edges (identical edges colored grey or magenta) some matching pairs

17. Another View Initial edges Final edges backbone index

18. Smoothing ● Birth and death events ● Persistent edges ● Gaps time persistent edges Tracked edge Birth Death

19. Strip Spanner Representation start vertex length

20. Strip History edge length index along backbone frame brighten

21. Segmenting Trajectories sample conformation segment dividers

22. Example: BBA5 Native state (1)(3) (2)

23. Outline ● Overview of spanners ● Properties of interest ● Displaying trajectories ● Future work

24. Sidechains ● Breaks the ordering of nodes ● How many points?

25. Comparing Motions ● Compare pairs of trajectories – Partial matches ● Cluster conformations – Find bottlenecks ● Cluster trajectories – Which are similar – Which are unique

26. Deeper Understanding ● Proteins → spanner ● Graph → proteins ● Spanner distances vs. conformation distances