An Efficient Algorithm for LargeScale Detection of Protein Families TRIBEMCL A' J' Enright, S' Van D

1
An Efficient Algorithm for Large-Scale Detection
of Protein Families (TRIBE-MCL)A. J. Enright, S.
Van Dongen and C. A. Ouzounis

• Fachseminar D Simmen
• 5. April 2008

2
Overview

• Motivation
• Proteins Problems
• Earlier solutions
• MCL
• Example
• Conclusion

3
Goals

• Understand MCL
• See why this works with proteins
• Understand the example

4
Motivation

• Why do we want to group proteins into families?
• Detection of protein families in large databases
  is one of the principal research objectives in
  structural and functional genomics
• Protein family classification can significantly
  contribute to
• the delineation of functional diversity of
  homologous proteins
• prediction of function based on domain
  architecture
• presence of sequence motifs
• comparative genomics
• Valuable evolutionary insights

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Proteins

• Linear Structure
• Made of amino acids peptide bonds
• Consists of one or more domain
• A domain is independent structure

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Problems

• Multi- domain structure of many protein families
• confounds grouping methods Shared Domain vs
  Biochemical Function
• result in the incorrect grouping of proteins
• Promiscuous Domains - Smaller, quite widespread
  protein modules
• Families based on such domains are unlikely to
  share a common evolutionary history

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Example P1
Families (A), (CD), (BEFH), (G)
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Earlier Solutions

• Attempted Solutions
• detection of individual domains
• using BLAST reports
• domain database dictionaries
• iterative sequence comparison
• manual intervention for family assignment of
  multi-domain proteins
• Drawbacks
• either too computationally intensive
• or somewhat inaccurate
• or not fully automatic

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Is there another way?

• Represent proteins a graph
• Protein as node
• Similarity as edge
• Higher similarity -gt shorter edge
• Ignores domains or the other problems statet
• Families are represented by clusters

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Clusters
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MCL

• Detect clusters in graphs
• Uses
• A markov matrix
• Expansion operation
• Inflation operation

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Markov matrix

• Represents a graph with the probabilites of
  changing from one node to another.
• Each column can be read as the probabilities of
  passing from the coresponding node to another
• Each column sums to one

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Markov chains

• Given an Markov matrix M we can compute the
  possibility to be in a point after one step
• To do this we have to compute MM

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Expansion

• corresponds to computing random walks of higher
  length (which means random walks with many
  steps)
• Premise Higher length paths are more common
  within clusters than between different clusters
• the probabilities associated with node pairs
  within a cluster will, in general, be relatively
  large
• Inflation will then have the effect of boosting
  the probabilities of intra-cluster walks and will
  demote inter-cluster walks

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Hadamard Product
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Inflation

• corresponds with taking the Hadamard power of a
  matrix (taking powers entry wise)
• followed by a scaling step, such that the
  resulting matrix is stochastic again
• ?r -gt Inflation Operator
• M -gt Stochastic matrix
• r -gt a real number (power coefficient) gt1
• Mij -gt probability of going from j to I
• For values of r gt 1, inflation changes the
  probabilities by favoring more probable walks
  over less probable walks

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All together

• MCL simulates random walks by expand and inflate
• As long as the matrix changes MCL continues with
  these steps

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Result

• The resulting matrix has to be intepreted as a
  graph
• The resulting matrix shows the clusters according
  to the chosen granularity
• The clusters look like stars with one node as
  center

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TRIBE MCL

• The actual Algortihm for Proteins
• BLASTp computes the similarities
• With these values a Markov matrix is created
• MCL runs on this matrix and returns a result

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Example P2

• Similarities between Proteins
• Based on E-Values given by BLASTb

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Example P3

• Corresponding Markov matrix

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Example P4

• r 5
• it 7
• A B C D E F G H
• A 1 0 0 0 0 0 0 0
• B 0 1 0 0 0 0 0 0
• C 0 0 1 0 0 0 0 0
• D 0 0 0 1 0 0 0 0
• E 0 0 0 0 1 0 0 0
• F 0 0 0 0 0 1 0 0
• G 0 0 0 0 0 0 1 0
• H 0 0 0 0 0 0 0 1

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Example P5

• r 1
• it 8
• A B C D
  E F G
  H
• A 0.0953 0.0953 0.0953 0.0953 0.0953
  0.0953 0.0953 0.0953
• B 0.1588 0.1588 0.1588 0.1588 0.1588
  0.1588 0.1588 0.1588
• C 0.0946 0.0946 0.0946 0.0946 0.0946
  0.0946 0.0946 0.0946
• D 0.0946 0.0946 0.0946 0.0946 0.0946
  0.0946 0.0946 0.0946
• E 0.1588 0.1588 0.1588 0.1588 0.1588
  0.1588 0.1588 0.1588
• F 0.1588 0.1588 0.1588 0.1588 0.1588
  0.1588 0.1588 0.1588
• G 0.0806 0.0806 0.0806 0.0806 0.0806
  0.0806 0.0806 0.0806
• H 0.1588 0.1588 0.1588 0.1588 0.1588
  0.1588 0.1588 0.1588

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Example P6

• r 1.1
• it 456
• A B C D E F
  G H
• A 0 0 0 0 0
  0 0 0
• B 0 0 0 0 0
  0 0 0
• C 0 0 0 0 0
  0 0 0
• D 0 0 0 0 0
  0 0 0
• E 0.5 0.5 0.5 0.5 0.5
  0.5 0.5 0.5
• F 0.5 0.5 0.5 0.5 0.5
  0.5 0.5 0.5
• G 0 0 0 0 0
  0 0 0
• H 0 0 0 0 0
  0 0 0

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Example P7

• r 2.1
• it 63
• A B C D E F
  G H
• A 1 0 0 0 0
  0 0 0
• B 0 0 0 0 0
  0 0 0
• C 0 0 1 1 0
  0 0 0
• D 0 0 0 0 0
  0 0 0
• E 0 0 0 0 0
  0 0 0
• F 0 1 0 0 1
  1 0 1
• G 0 0 0 0 0
  0 1 0
• H 0 0 0 0 0
  0 0 0

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Example P8
B
F
A
E
H
G
C
D
Famillies predicted (A), (CD), (BEFH), (G)
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Performance

• Examples of tests done so far

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Conlcusion

• Fast and remarkable accurate Algorithm
• Highly experimental
• MCL so far solution for ca 200 different
  applications

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Questions

• Questions?