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Alignment of Flexible Molecular Structures
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Motivation

• Proteins are flexible. One would like to align
  proteins modulo the flexibility.
• Hinge and shear protein domain motions
  (Gerstein, Lesk , Chotia).
• Conformational flexibility in drugs.

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Problem definition
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Flexible Geometric Hashing

• Exploit the fact that neighboring parts share the
  joint - accumulate mutual information at the
  joint.
• Achieve complexity of the same order of magnitude
  as in rigid alignment.

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Flexible protein alignment without prior hinge
knowledge

• FlexProt - algorithm
• detects automatically flexibility regions,
• exploits amino acid sequence order.

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Motivation
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Geometric Representation
3-D Curve vi, i1n
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Experimental Results
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Experimental Results
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FlexProt Algorithm

• Input two protein molecules A and B, each being
  represented by the sequence of the 3-D
  coordinates of its Ca atoms.
• Task largest flexible alignment by decomposing
  the two molecules into a minimal number of rigid
  fragment pairs having similar 3-D structure.

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(No Transcript)
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FlexProt Main Steps
Detection of Congruent Rigid Fragment Pairs
Joining Rigid Fragment Pairs
Rigid Structural Comparison
Clustering (removing ins/dels)
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Structural Similarity Matrix
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Detection of Congruent Rigid Fragment Pairs
i1
i-1
i
j-1
j1
j
vi-1 vi vi1 wj-1 wj wj1
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RMSD Computation
Vi ... Vil Wj ... Wjl
Vk ... Vkm Wt ... Wtm
P
Q
P U Q
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FlexProt Main Steps
Detection of Congruent Rigid Fragment Pairs
Joining Rigid Fragment Pairs
Rigid Structural Comparison
Clustering (removing ins/dels)
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How to Join Rigid
Fragment Pairs ?
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Graph Representation
Graph Node
Graph Edge
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Graph Representation

• The fragments are in ascending order.
• The gaps (ins/dels) are limited.
• Allow some overlapping.

W
a
b
Size of the rigid fragment pair (node b) - Gaps
(ins/dels) - Overlapping
Penalties
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Graph Representation

• DAG (directed acyclic graph)

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Optimal Solution ?
W_k
W_m
W_n
W_t
W_i

• All Shortest Paths
• O(EVV2) (for DAG)

• Single-source shortest paths
• O(EV)

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FlexProt Main Steps
Detection of Congruent Rigid Fragment Pairs
Joining Rigid Fragment Pairs
Rigid Structural Comparison
Clustering (removing ins/dels)
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Clustering (removing ins/dels)
T1
T2
If joining two fragment pairs gives small RMSD
(T1 T2) then put them into one cluster.
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FlexProt Main Steps
Detection of Congruent Rigid Fragment Pairs
Joining Rigid Fragment Pairs
Rigid Structural Comparison
Clustering (removing ins/dels)
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Correspondence Problem
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Molecular Surface Representation

• Applications to docking

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Motivation

• Prediction of biomolecular recognition.
• Detection of drug binding cavities.
• Molecular Graphics.

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1. Solvent Accessible Surface SAS2.
Connolly Surface
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Connollys MS algorithm

• A water probe ball (1.4-1.8 A diameter) is
  rolled over the van der Waals surface.
• Smoothes the surface and bridges narrow
  inaccessible crevices.

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Connollys MS algorithm - cont.

• Convex, concave and saddle patches according to
  the no. of contact points between the surface
  atoms and the probe ball.

• Outputs pointsnormals according to the
• required sampling density (e.g. 10 pts/A2).

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Example - the surface of crambin
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Critical points based on Connolly rep. (Lin,
Wolfson, Nussinov)

• Define a single pointnormal for each patch.
• Convex-caps, concave-pits, saddle - belt.

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Critical point definition
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Connolly gt Shou Lin
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Solid Angle local extrema
hole
knob
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Chymotrypsin surface colored by solid angle
(yellow-convex, blue-concave)