Revealing Biological Modules via Graph Summarization

1
Revealing Biological Modules via Graph
Summarization

• Saket Navlakha
• Computer Science Department
• Center for Bioinformatics and Computational
  Biology
• University of Maryland, College Park, USA
• Joint work with Michael C. Schatz and Carl
  Kingsford

2
Introduction

• High-throughput methods are producing lots of
  protein interaction data for many organisms
• Analyze networks and recover complexes or
  proteins involved in the same biological process
• Common approach
• Partition network into clusters or modules
• Use modules to predict annotations

Yeast protein interaction network
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Module-assisted predictions
?
Module Finding Algorithm
?
e.g. Newman 2003 King et al. 2004
Bader and Hogue 2003 Blatt et al. 2006
van Dongen 1998
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Our module-finding approach

• Want modules with proteins having similar
  cellular roles
• Similar interaction partners implies similar
  cellular roles
• Similar interaction partners also implies
  redundancy in the graph
• Redundancy implies compressibility!

Compressed Rep.
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Graph Summarization (GS)
Goal produce compressed representation of input
graph G
Corrections
Summary
h
G
(a,h)
X a,b,c
Y d,e,f,g
d
a
(c,i)
e
(c,j)
b
Modules
-(a,d)
f
c
g
j
i
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GS representation
Cost 14 edges
d
e
f
g

• Summary S highlights dominant trends, easy to
  visualize
• Supernode ? set of nodes with common neighbors
• Identifies bipartite cores, cliques, stars, etc.
• Corrections C exception/unusual edges
• Handles noise
• Minimize total cost S C
• (based on MDL principle)

a
b
c
Summary
X d,e,f,g
Y a,b,c
Corrections
Cost 5(1 superedge 4 corrections)
7
Greedy GS
Cost reduction 11 to 6

• Bottom-up, iterative merging
• Start with S G
• At every step, merge pair which maximally reduces
  cost
• If no pair reduces cost, stop

b
c
a
d
e
h
f
g
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Application to yeast network

• Network IntAct 5,492 proteins, 40,332
  interactions
• Complexes MIPS 266 leaf level
• Biological Process GO 182 terms Myers et al.
  2006
• Comparisons
• Graph Summarization
• Markov Clustering Alg.
• Molecular Complex Detect. Alg.
• Newman Modularity

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Module-assisted predictions

• Test quality of modules (supernodes)
• Compute hypergeometric enrichment of modules
• Use modules for annotation prediction (complexes,
  biological processes)

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1. Annotation Enrichment
Graph summarization ? larger variety of
annotations enriched in some module (P lt 0.001)
(A lower of GS modules are enriched for some
annotation, but not indicative of predictive
performance.)
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2. Making predictions

• Cross-validation (leave one out)
• Module-assisted annotation transfer schemes

Majority
Hypergeometric
Plurality
transfer the statistically enriched annotations
transfer if gt 50 annotated proteins have the
annotation
transfer the most common annotation(s)
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Complexes Biological
Processes
All GS predictions are Pareto optimal
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Conclusion

• Graph Summarization is good for annotation
  prediction
• Confirmed on complexes and biological processes
• Preferable to MCL, MCODE, NSP
• Advantages
• MDL-based graph compression, no parameters
• Module proteins which have similar interaction
  partners
• Generalizes bipartite cores, cliques, stars
  handles noise
• More in paper
• Similar results for high-confidence network
• Also used GS corrections to predict co-complexed
  pairs using only topology, fared favorably
  against Defective Cliques Yu et al. 2006
• Many unique predictions made by each algorithm

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Acknowledgements
Nisheeth Shrivastava

• Michael C. Schatz

Research Scientist Bell Labs Research,
India
PhD student University of Maryland
Rajeev Rastogi
Carl Kingsford
VP and Head Yahoo Research, India
Assistant Professor University of Maryland
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Additional slides
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Enrichment of Modules

• Want modules to contain proteins dominantly with
  the same complex or biological process
• Measure enrichment via hypergeometric P-value
• n nodes in the network
• m nodes in M
• f nodes in network annotated with F
• k nodes in M annotated with F
• Threshold 0.001

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1. Enrichment of modules
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1. Module enrichment

• Graph Summarization
• Variety of enriched annotations (P lt 0.001)
• Less modules enriched, but not indicative of
  predictive performance

GS
GS
Complexes Biological
Processes
Complexes Biological
Processes
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2. Making predictions

• Leave one-out cross-validation
• Module-assisted annotation prediction

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2. Making predictions

• Leave one-out cross-validation
• Module-assisted annotation prediction for
  annotation A in module M
• Majority transfer annotation A if gt 50
  annotated proteins in module M have A
• Plurality transfer most common A in M
• Hypergeometric transfer all enriched A in M
• (P lt 0.001)

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High-Confidence Network

• High-throughput data known to be noisy
• IntAct edges, associated with gt 1 PubMed
  identifier
• 2,604 proteins
• 8,341 interactions
• Similar results for both complexes and biological
  processes

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Co-complexed Pairs
Cost 7 edges
a
b
h
i

• Corrections hint at missing or false edges
• -ve corrections co-complexed pair
• ve corrections false edge

c
d
Summary
Y a,b,c,d
i
h
Corrections
Cost 4(1 superedge 3 corrections)
(d,h)
(b,i)
-(a,c)
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Complex-Pair Prediction

• Compared with defective clique algorithm (DCC)
• Find two cliques of size at least k, overlapping
  on at least l nodes
• Predict missing edges

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Prediction Results

• Test set, co-complexed pairs
• Co-complexed gold standard set of MIPS complexes
• Not co-complexed proteins in different
  sub-cellular locations
• Results high confidence
• GS 66.7 precise, 224 correct predictions
• DCC 62.5 precise, 39 correct predictions
• GS also filters 3,331 edges, 97 accuracy
• Results unfiltered network
• Both perform poorly
• Too many false positive edges

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Comparison of Predictions

• Complexes, Majority
• ? useful to combine methods

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Reconstruction
R
X d,e,f,g

• Reconstruct G from R
• For all superedges (u,v) in S, insert all pair of
  edges between u-nodes and v-nodes
• For all ve corrections, insert edge (a,b)
• For all -ve corrections, delete edge (a,b)

i
h
Y a,b,c
j
C (a,h), (c,i), (c,j), -(a,d)
G
d
e
f
g
h
i
j
a
b
c
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How to compress?
Cost 14 edges
d
e
f
g

• Summary S(VS, ES)
• Each supernode x represents a set of nodes Ax
• Each superedge (x,y) represents all pair of
  edges pxy Ax x Ay
• Corrections C (a,b) a and b are nodes of G
• Compute edge cost
• Exy actual edges of G between Ax and Ay
• Cost without (x,y) Exy
• Cost with (x,y) 1 pxy Exy
• Choose the minimum

a
b
c
Summary
X d,e,f,g
Y a,b,c
Corrections
Cost 5(1 superedge 4 corrections)
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Greedy Algorithm

• Cost of merging nodes u and v into supernode w
• Cost of a superedge (u,x)
• c(u,x) minpux Eux1, Eux
• cu sum of costs of all its edges
• s(u,v) (cu cv cw)/(cu cv)
• Main idea iterative, bottom-up merging of nodes
• If s(u,v) gt 0, merging u and v reduces the cost
  of reduction
• Normalize the cost remove bias towards high
  degree nodes

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Greedy Algorithm
Cost reduction 11 to 6
bc
a

• s(u,v) (cu cv cw)/(cu cv)
• GREEDY algorithm
• Start with SG
• At every step, pick the pair with max s(.) value,
  merge
• If no pair has positive s(.) value, stop

d
ef
gh
C (h,d),(a,e)
b
bc
bc
c
a
a
a
d
d
d
e
e
e
h
h
f
gh
f
f
g
g
C (h,d)
s(b,c).5 cb 2 cc2 cbc2
s(g,h)3/7 cg 3 ch4 cgh4
s(e,f)1/3 ce 2 cf1 cef2