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Exploring Protein Folding Trajectories Using Geometric Spanners

Daniel Russel and Leonidas Guibas Stanford University. Exploring Protein Folding Trajectories Using Geometric Spanners. Goals. Existing work understanding protein structure Classification Comparison Matching Qualitative understanding of proteins motions We do not quite get there yet.

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Exploring Protein Folding Trajectories Using Geometric Spanners

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

  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 distanceand Euclidean distance

  5. Geometric Spanners • Vertexes are points • Edges have length • Expansion factor • Ratio between graph distanceand Euclidean distance

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

  7. 2CI2 Spanner: Helix backbone atom index ahelix backbone atom index

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

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

  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 1.5 1.75 2.0 2.5 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 some matching pairs initial frame edges final frame edges identical edges (identical edges coloredgreyormagenta)

  17. Another View backbone index Initial edges Final edges

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

  19. Strip Spanner Representation length start vertex

  20. Strip History brighten edge length frame index along backbone

  21. Segmenting Trajectories segmentdividers sample conformation

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

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