Download - Using Spanners to Describe Protein Structure Leonidas Guibas, Daniel Russel Stanford University
Using Spanners to Describe Protein Structure
Leonidas Guibas, Daniel Russel
Stanford University
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Outline
• Goal• Spanners of proteins• Trajectories• Future work
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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
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Outline
• Goal• Spanners of proteins• Trajectories• Future work
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A Geometric Spanner
A graph spanner formsa compact encoding of allproximities among the points
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Protein Structure Descriptors
• Detect and capture – Proximities – Global conformation– Large-scale changes
during motion
3-spanner of BBA5
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Static Shapes: Alpha Helix
…1VDF
Protein sequence
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Mostly Beta
hairpins
1IHV
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Outline
• Goal• Spanners of proteins• Trajectories• Future work
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Folding Steps
• Matching successive frames– Easy correspondence– Small conformation changes
• We want stable descriptions
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Matching Edges
• Edge from atom i to atom j– Interval (i,j)
• Find best bipartite matching
Spanner edges from successive MD frames
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Folding Trajectory
End of helix stabilizes
helix and strand adopt
final conformation
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Spanners are Unstable
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Edges Come and Go
White is -Green is -Cyan is -
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Some Do Not Fold
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Outline
• Goal• Spanners of proteins• Trajectories• Future work
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Future Work
• Motif finding/Matching– Induced patterns as intervals– 1D matching problem– Gaps Hard
• Statistical models
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Simplified Distance Matrices
• Cover distance matrix with rectangles• For each rectangle, the two
subsequences are well separated, geometrically
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Simplified Distances: α-helix
Distance Matrix WSP decomposition
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Simplified Matrix: Mostly β-strands
Distance Matrix WSP decomposition
hairpin