Download - Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University
![Page 1: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/1.jpg)
Using Spanners to Describe Protein Structure
Leonidas Guibas, Daniel Russel
Stanford University
![Page 2: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/2.jpg)
2
Outline
• Goal• Spanners of proteins• Trajectories• Future work
![Page 3: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/3.jpg)
3
Folding Processes for Macromolecules
• Folding is a continuous process• state of the fold is discrete
– proximities between groups of atoms– residue exposure to solvent
• We want to combinatorialize the folding process
![Page 4: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/4.jpg)
4
Outline
• Goal• Spanners of proteins• Trajectories• Future work
![Page 5: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/5.jpg)
5
A Geometric Spanner
A graph spanner formsa compact encoding of allproximities among the points
![Page 6: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/6.jpg)
6
Protein Structure Descriptors
• Detect and capture – Proximities – Global conformation– Large-scale changes
during motion
3-spanner of BBA5
![Page 7: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/7.jpg)
7
Static Shapes: Alpha Helix
…1VDF
Protein sequence
![Page 8: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/8.jpg)
8
Mostly Beta
hairpins
1IHV
![Page 9: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/9.jpg)
9
Outline
• Goal• Spanners of proteins• Trajectories• Future work
![Page 10: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/10.jpg)
10
Folding Steps
• Matching successive frames– Easy correspondence– Small conformation changes
• We want stable descriptions
![Page 11: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/11.jpg)
11
Matching Edges
• Edge from atom i to atom j– Interval (i,j)
• Find best bipartite matching
Spanner edges from successive MD frames
![Page 12: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/12.jpg)
12
Folding Trajectory
End of helix stabilizes
helix and strand adopt
final conformation
![Page 13: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/13.jpg)
13
Spanners are Unstable
![Page 14: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/14.jpg)
14
Edges Come and Go
White is -Green is -Cyan is -
![Page 15: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/15.jpg)
15
Some Do Not Fold
![Page 16: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/16.jpg)
16
Outline
• Goal• Spanners of proteins• Trajectories• Future work
![Page 17: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/17.jpg)
17
Future Work
• Motif finding/Matching– Induced patterns as intervals– 1D matching problem– Gaps Hard
• Statistical models
![Page 18: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/18.jpg)
18
Simplified Distance Matrices
• Cover distance matrix with rectangles• For each rectangle, the two
subsequences are well separated, geometrically
![Page 19: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/19.jpg)
19
Simplified Distances: α-helix
Distance Matrix WSP decomposition
![Page 20: Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University](https://reader036.vdocument.in/reader036/viewer/2022081506/56649f1b5503460f94c31715/html5/thumbnails/20.jpg)
20
Simplified Matrix: Mostly β-strands
Distance Matrix WSP decomposition
hairpin