Download Fast Molecular Shape Matching Using Contact Maps

Fast Molecular Shape Matching Using Contact
Maps
Jesmin Jahan Tithi
Student No. 04090565
Department of Computer Science and Engineering
Bangladesh University of Engineering and Technology, Dhaka-1000
[email protected]
October 9, 2009
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Outline of the talk
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Introduction
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Outline of the talk
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Introduction
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Problem Definition
Fast Molecular Shape Matching Using Contact Maps
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Outline of the talk
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Introduction
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Problem Definition
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Previous Results
Fast Molecular Shape Matching Using Contact Maps
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Outline of the talk
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Introduction
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Problem Definition
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Previous Results
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Solution for Two Dimension
Fast Molecular Shape Matching Using Contact Maps
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Outline of the talk
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Introduction
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Problem Definition
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Previous Results
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Solution for Two Dimension
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Staircase and self-avoiding walk
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Outline of the talk
JJT, BUET
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Introduction
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Problem Definition
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Previous Results
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Solution for Two Dimension
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Staircase and self-avoiding walk
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Stack and self-avoiding walk
Fast Molecular Shape Matching Using Contact Maps
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Outline of the talk
JJT, BUET
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Introduction
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Problem Definition
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Previous Results
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Solution for Two Dimension
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Staircase and self-avoiding walk
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Stack and self-avoiding walk
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Overall algorithm
Fast Molecular Shape Matching Using Contact Maps
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Outline of the talk
JJT, BUET
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Introduction
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Problem Definition
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Previous Results
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Solution for Two Dimension
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Staircase and self-avoiding walk
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Stack and self-avoiding walk
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Overall algorithm
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Solution for Three Dimension
Fast Molecular Shape Matching Using Contact Maps
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Outline of the talk
JJT, BUET
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Introduction
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Problem Definition
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Previous Results
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Solution for Two Dimension
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Staircase and self-avoiding walk
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Stack and self-avoiding walk
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Overall algorithm
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Solution for Three Dimension
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Future Directions
Fast Molecular Shape Matching Using Contact Maps
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Outline of the talk
JJT, BUET
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Introduction
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Problem Definition
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Previous Results
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Solution for Two Dimension
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Staircase and self-avoiding walk
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Stack and self-avoiding walk
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Overall algorithm
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Solution for Three Dimension
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Future Directions
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Conclusions
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Introduction
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Problem: Computing the similarity of two protein structures
by measuring their contact-map overlap.
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Introduction
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Problem: Computing the similarity of two protein structures
by measuring their contact-map overlap.
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Contact Map Overlap: Contact-map overlap abstracts the
problem of computing the similarity of two polygonal chains
as a graph-theoretic problem.
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Introduction
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Problem: Computing the similarity of two protein structures
by measuring their contact-map overlap.
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Contact Map Overlap: Contact-map overlap abstracts the
problem of computing the similarity of two polygonal chains
as a graph-theoretic problem.
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Best Known Algorithm: In 2D (R 2 ), it is O(n3 logn).
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Motivation of Protein Structure Comparison
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Proteins, a polymer consisting of a long chain of amino acid
residues −− > machines and building blocks of living cells.
Inter-atomic forces between residues bend and twist the chain
causes the folded state of the protein.
3-dimensional structure of a protein has a crucial influence on
its function−two proteins that are similar in their
3-dimensional structure will likely have similar functions
(Leach, 1996).
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Problem Definition
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The contact-map of a protein is a graph, which represents the
three dimensional structure of the protein by modeling the
neighborhood of each residue by edges (or contacts) to the
neighbors.
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Problem Definition
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The contact-map of a protein is a graph, which represents the
three dimensional structure of the protein by modeling the
neighborhood of each residue by edges (or contacts) to the
neighbors.
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Contact-map overlap measures the similarity between two
proteins (in the lattice model) based on the pairwise distances
of the Cα −atoms of each protein.
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Problem Definition
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The contact-map of a protein is a graph, which represents the
three dimensional structure of the protein by modeling the
neighborhood of each residue by edges (or contacts) to the
neighbors.
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Contact-map overlap measures the similarity between two
proteins (in the lattice model) based on the pairwise distances
of the Cα −atoms of each protein.
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Two protein structures are considered similar if there is a
mapping of vertices from one to the other such that the
pattern of the neighborhoods is similar for a large number of
mapped vertices.
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Self-avoiding walk and Contact-map
The protein backbone is mapped to a non-self-intersecting path on
an integer grid Z .
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Previous Results
This problem is NP-hard!
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Goldman et al.(1999): 3-approximation algorithm with O(n6 )
running time if the contact-maps are derived from
self-avoiding walks on a 2-dimensional lattice.
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Previous Results
This problem is NP-hard!
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Goldman et al.(1999): 3-approximation algorithm with O(n6 )
running time if the contact-maps are derived from
self-avoiding walks on a 2-dimensional lattice.
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Lancia et al.(2001): Branch-and-bound method (based on a
linear programming relaxation) for the contact-map overlap
problem in R 3 .
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Partial and Complete Contact Map Overlap
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Stack, Queue and Staircase
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Staircase and Decomposition
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Algorithm
The overall algorithm is similar to the one described in Goldman et
al. (1999). Given two two-dimensional contact maps G1 and G2,
we first decompose G1 into two 2-stacks and two 2-staircases.
Each 2-staircase is then decomposed into two 1-staircases in linear
time. We then compute the maximum overlap of G2 with these six
graphs and take the maximum of them. This gives a
6-approximation of ν(G 1, G 2) and µ(G 1, G 2) .
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3D Case
Decompose G1 or G2 into at most σ stacks and staircases, in
O(snlogn) time. The contact- map overlap of each stack or
staircase can be computed in polynomial time.
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conclusion
Especially in computer aided drug design, a critical problem of
virtual screening, aimed at identifying the drug-like molecules likely
to have beneficial biological properties, is comparing molecular
shapes. An alternative virtual screening technique consists of
searching a molecular database for compounds that most closely
resemble a given query molecule
Conclusion
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