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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.
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.
Flexible protein alignment without prior hinge knowledge
FlexProt - algorithm
detects automatically flexibility regions,
exploits amino acid sequence order.
FlexProt Algorithm
Input: two protein molecules A and B, each two protein molecules A and B, each being represented by the sequence of the being represented by the sequence of the 3-D coordinates of its 3-D coordinates of its CC atoms.atoms.
Task: largest flexible alignment by largest flexible alignment by decomposing the two molecules into a decomposing the two molecules into a minimalminimal number of rigid fragment pairs number of rigid fragment pairs having similar 3-D structure.having similar 3-D structure.
Detection of Congruent Detection of Congruent Rigid Fragment PairsRigid Fragment Pairs
Joining Rigid Joining Rigid Fragment PairsFragment Pairs
Rigid Rigid Structural ComparisonStructural Comparison
ClusteringClustering(removing ins/dels)(removing ins/dels)
FlexProt Main Steps
j
i+1
j+1
i
j-1
i-1
vi-1 vi vi+1
wj-1 wj wj+1
Fragkt(l) = vk … vi ... vk+l-1
wt … wj … wt+l-1
RMSD (Fragkt(l) ) <
Detection of Congruent Rigid Fragment Pairs
k
t
k+l-1
t+l-1
RMSD Computation
VVii …...…... VVi+li+l
WWjj ...…...… WWj+lj+l
VVkk …...…... VVk+mk+m
WWtt ...…...… WWt+mt+mPP== Q=Q=
P U Q
RMSD( P U Q ) in O(1) time
NOT O( |P|+|Q| )
RMSD( P )RMSD( P )
RMSD( Q )RMSD( Q )
Detection of Congruent Detection of Congruent Rigid Fragment PairsRigid Fragment Pairs
Joining Rigid Joining Rigid Fragment PairsFragment Pairs
Rigid Rigid Structural ComparisonStructural Comparison
ClusteringClustering(removing ins/dels)(removing ins/dels)
FlexProt Main Steps
Graph Representation •The fragments are in ascending order.The fragments are in ascending order.
•The gaps (ins/dels) are limited.The gaps (ins/dels) are limited.
•Allow some overlapping.Allow some overlapping.
W
+ Size of the rigid fragment pair (node b)
- Gaps (ins/dels)
- OverlappingPenalties
a b
Optimal Solution?
•““All Shortest Paths” All Shortest Paths” O(|E|O(|E|**|V|+|V||V|+|V|22) (for DAG) ) (for DAG)
W_i
W_k
W_t
W_m
W_n
•““Single-source shortest paths”Single-source shortest paths” O(|E|+|V|) O(|E|+|V|)
Detection of Congruent Detection of Congruent Rigid Fragment PairsRigid Fragment Pairs
Joining Rigid Joining Rigid Fragment PairsFragment Pairs
Rigid Rigid Structural ComparisonStructural Comparison
ClusteringClustering(removing ins/dels)(removing ins/dels)
FlexProt Main Steps
Clustering (removing ins/dels)
T1
T2
If joining two fragment pairs gives small RMSD (T1 ~ T2) then put them into one cluster.
Detection of Congruent Detection of Congruent Rigid Fragment PairsRigid Fragment Pairs
Joining Rigid Joining Rigid Fragment PairsFragment Pairs
Rigid Rigid Structural ComparisonStructural Comparison
ClusteringClustering(removing ins/dels)(removing ins/dels)
FlexProt Main Steps
Motivation
Prediction of biomolecular recognition.
Detection of drug binding ‘cavities’.
Molecular Graphics.
Connolly’s 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.
Connolly’s MS algorithm - cont.
Convex, concave and saddle patches according to the no. of contact points between the surface atoms and the probe ball.
Outputs points+normals according to the
required sampling density (e.g. 10 pts/A2).
Critical points based on Connolly rep. (Lin, Wolfson, Nussinov)
Define a single point+normal for each patch.
Convex-caps, concave-pits, saddle - belt.