DISCOVERING LARGER NETWORK MOTIFS

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DISCOVERING LARGER NETWORK MOTIFS

• Wooyoung Kim and Li Chen
• 4/24/2009
• CSC 8910 Analysis of Biological Network, Spring
  2009
• Dr. Yi Pan

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OUTLINE

• Project Topic
• Related Works
• Proposed Ideas
• Unsolved Problems

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PROJECT TOPIC

• Discovering Larger Network Motifs
• Given a biological network (PPI, transcriptional
  regulatory network, gene network, etc), find
  network motifs whose size is large (gt15)

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RELATED WORKS (1)

• Network Motif Discovery using subgraph
  enumeration and symmetry breaking
• motif size lt15
• Given a candidate subgraph, find all symmetry
  subgraphs in the graph, then evaluate it by
  checking the frequency.
• Problem How to find candidate subgraph?
• ? Proposed solution Cluster the whole network
  and find the representation at each cluster to
  claim that as candidate subgraphs.

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RELATED WORKS (2)

• Motif Discovery Algorithm
• Exact algorithm on motifs with a small number of
  nodes
• 1. Exhaustive Recursive Search (ERS) (motif
  size lt 4)
• 2. ESU starting with individual nodes and
  adding
• one node at a time until the required
  size k is
• reached. (motif size lt14)
• 3. Compact Topological Motifs

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RELATED WORKS (3)

• Approximate Algorithms
• Search Algorithm Based on Sampling (MFINDER)
• Rand-ESU
• NeMoFINDER
• Sub-graph Counting by Scalar Computation
• A-priori-based Motif Detection

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RELATED WORKS (4)

• Network Clustering
• Compact representation of network.
• Type I minimum number of clusters
• Type II maximum cohesiveness
• Aggregation of topological motifs (combining
  smaller network motifs to observe the whole
  structure)
• However, in our proposed solution, the clustering
  task is grouping similar network patterns
  together, not grouping similar nodes (sequence)
  together. Nor it is not used for aggregating
  motifs.

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PROPOSED IDEAS

• Given a graph G (V,E), and t (the size of
  desirable motif) and k (the number of motifs),
  find a network motif with size t.
• List all graph patterns with t (or larger than t)
  nodes.
• Represent the network as an adjacency matrix A
  (1, -1, 0)
• Scan A for all t x t sub-matrices
• Cluster the subgraphs into k clusters
• Use any numerical clustering algorithms including
  K-means, NMF, etc.
• Find a subgraph representation at each cluster.
• Use the symmetry breaking technique to find the
  representation.
• Each representation can be a candidate of network
  motif.

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UNSOLVED PROBLEMS

• How to cluster the graphs?
• The clustering algorithms to apply will be
  various based on what features we are using for
  the data.
• What type of clustering algorithm? Type I or type
  II?
• How to find the representation subgraph of each
  cluster?
• Should we consider network alignment first?
• Should we consider the sequence similarities as
  well?
• Will there be any relationship between sequence
  motif and network motif?
• Applying the sequence motif into vertex
  attributes matrix? ?compact topological motifs.
• Large network motif vs. small network motif

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DISCOVERING TOPOLOGICAL MOTIFS USING A COMPACT
NOTATION
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COMPACT NOTATION

• Main Idea
• A topological motif can be represented either
  as a motif or as a collection of location lists
  of the vertices of the motif. It works in the
  space of the location lists so as to discover
  motif.

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COMPACT NOTATION

• Method
• Step1 compute an exhaustive list of potential
  lists of vertices of motifs as compact
  location lists
• Step 2 enlarge the collection of compact
  location lists computed in the first step by
  including all the non-empty intersections, along
  with the differences.

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COMPACT NOTATION

• An Example
• Different color indicate different attribute

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COMPACT NOTATION

• G1s adjacency matrices

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COMPACT NOTATION

• Adjacency Matrix B1 (the conjugacy relationship
  of two lists is shown by ?)
• L l1, l2, l3, l4

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COMPACT NOTATION

• Initialization Step

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COMPACT NOTATION

• Iterative Step

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REFERENCES

• 1 Bill Andreopoulos, Aijun An, Xiaogang Wang,
  and Michael Schroeder. A roadmap of clustering
  algorithms finding a match for a biomedical
  application. Brief Bioinform, pages bbn058,
  February 2009.
• 2 Alberto Apostolico, Matteo Comin, and Laxmi
  Parida". Bridging Lossy and Lossless Compression
  by Motif Pattern Discovery. Electronic Notes in
  Discrete Mathematics, 21219 - 225, 2005. General
  Theory of Information Transfer and Combinatorics.
  
• 3 Giovanni Ciriello and Concettina Guerra. A
  review on models and algorithms for motif
  discovery in protein-protein interaction
  networks. Brief Funct Genomic Proteomic,
  7(2)147-156, 2008.
• 4 Jun Huan, Wei Wang, and Jan Prins. Efficient
  Mining of Frequent Subgraphs in the Presence of
  Isomorphism. Data Mining, IEEE International
  Conference on, 0549, 2003.
• 5 Michihiro Kuramochi and George Karypis.
  Finding Frequent Patterns in a Large Sparse
  Graph. Data Mining and Knowledge Discovery,
  11(3)243-271, November 2005.
• 6 Laxmi Parida. Discovering Topological Motifs
  Using a Compact Notation. Journal of
  Computational Biology, 14(3)300-323, 2007.

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REFERENCES

• 7 Radu Dobrin, Qasim K. Beg, Albert-Laszlo
  Barabasi, and Zoltan N. Oltvai. Aggregation of
  topological motifs in the escherichia coli
  transcriptional regulatory network. BMC
  Bioinformatics, 510, 2004.
• 8 McKay, B.D. Isomorph-free exhaustive
  generation. J. Algorithms, 26306-324, 1998
• 9 Middendorf, M., Zive, E., and Wiggins, C.H.
  Inferring network mechanisms the Drosophila
  melanogaster protein interaction network. PNAS,
  102 (9)3192-3197, Mar 2005.
• 10Grochow, J. A. and Kellis, M. Network motif
  discovery using subgraph enumeration and
  symmetry-breaking. In RECOMB 2007, Lecture Notes
  in Computer Science 4453, pp. 92-106.
  Springer-Verlag, 2007.

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• Thank you so much !