Efficient Algorithms for Detecting Signaling Pathways in Protein Interaction Networks

1
Efficient Algorithms for Detecting Signaling
Pathways in Protein Interaction Networks

• Jacob Scott, Trey Ideker,
• Richard M. Karp, Roded Sharan

RECOMB 2005
2
Outline

• Motivation
• Theoretical foundations
• Biological extensions
• Implementation
• Validation techniques
• Results from yeast

3
Motivation

• Post-genomics, want to understand organisms
  protein-protein interaction network
• Model network as a probabilistic graph, with edge
  weights representing probabilities
• Interested in protein signaling cascades
• Show up as simple paths in the graph
• Want to find biologically interesting paths
  efficiently
• Score paths, with high scores reflecting
  importance
• Extended graph algorithms provide speed
• Automated modelling of signal transduction
  networks as baseline (Steffen et al 2002)

4
Theoretical Foundation

• Finding long, simple paths is NP-Hard
• Reduce from TSP
• Once we find these paths, want the best
  (lightest) ones
• Need for paths to be simple is what drives
  hardness
• Color-Coding is a randomized, dynamic-programming
  based algorithm for finding paths of fixed length
• Developed by Alon et al (1995)
• Randomly color graph and require paths be
  colorful (exactly one vertex of each color)
• Number of colors length of paths
• A colorful path is always simple

5
Color-Coding

• Colorful paths can be found with dynamic
  programming
• Key point a colorful path of length k contains a
  colorful path of length k-1.
• Store path information at each node for each
  subset of k colors
• Only 2k color subsets, rather than O(nk) node
  subsets
• Runtime is O(2kkm) ltlt O(knk) brute force
• Space is O(2kn) ltlt O(knk) brute force

6
Coloring Example
II
I

• Two different colorings on toy graph, k3
• In coloring I, W(A,RGB) is built C-gtBC-gtABC
• In coloring II, W(A,RGB) is built G-gtBG-gtABG
• ABC is not colorful in coloring II

7
Monte Carlo Details

• A colorful path is simple, but a simple path may
  not be colorful under a given coloring
• Solution run multiple independent trials
• After one trial, for paths of length k,

8
Adding Biology

• Color-Coding gives an algorithmic basis, now
  introduce biologically motivated extensions
• Can set the start or end of path by type
• E.g. screening by Gene Ontology categories
• Can force the inclusion of a protein on the path
  by giving it a unique color
• Using counters, can specify path must contain
  between x and y proteins of a given type
• Computational cost multiplicative in y per counter

9
Adding Biology - Segmented Paths

• Pathways may be ordered
• Signaling pathways going from the membrane, to
  nuclear proteins and finally transcription
  factors
• Assign each protein an integer label based on
  biological information, build path out of ordered
  sequences of labeled proteins
• Now only need to constrain color collisions among
  proteins with the same label
• If path length is about equally split among
  labels, probability of correct coloring rises
• Modifications allow for inability to assign
  proteins to unique labels

10
Adding Biology - More Structures

• Modifications to the Color-Coding recurrence
  allow for the discovery beyond simple paths
• Example Two-terminal series-parallel graphs
• Capture parallel signaling pathways

Example two-terminal series-parallel graph
11
Generating Edge Weights

• So far, have glossed over how weights
  (probabilities) on the protein graph are assigned
• Here, use our previous work, generate logistic
  function of three variables (for a pair of
  proteins)
• Number of times interaction between them was
  experimental observed
• Pearson correlation coefficient of expressions
  (for corresponding genes)
• Their small world clustering coefficient
• Used training data from MIPS (gold standard) for
  training our relative weighting
• Taking log of weights makes path score additive

12
Application

• Tested our simple path implementation with the
  yeast interaction network
• 4,500 vertices, 14,500 edges
• Based on interaction data from Database of
  Interacting Proteins (Feb 2004)
• Runtimes varied from minutes (length 8) to under
  two hours (length 10)
• Much faster than brute force for longer paths
  (14x for paths of length 9)
• Focus on paths from membrane proteins to
  transcription factors

13
Validation Techniques

• Three methods of validation
• Two statistical
• Functional enrichment p-value based on how many
  proteins in the path are similar (by GO category)
• Weight p-value compares weights of paths to those
  found when the protein graph undergoes random
  degree-preserving shuffling
• Lastly, search for expected pathways
• MAP-Kinase, ubiquitin-ligation

14
MAP-Kinase and Ubiquitin-Ligation

• Concentrated on three MAPK pathways (same as
  Steffen et al)
• Pheromone response
• Filamentous growth
• Cell wall integrity
• Looked for shorter (length 4-6)
  ubiquitin-ligation pathways
• Started at a cullin, ended at an F-Box
• High functional enrichment under ubiquitin GO
  category

15
Statistical Results (CDFs)

• 100 best paths of length 8 _at_ 99.9 success
• 100 normal, 2000 random paths used for weight
  p-value

16
MAPK Recovery Results

• Cell wall integrity pathway in yeast

MID2 RHO1 PKC1 BCK1 MKK1/2 SLT2 RLM1
B) Best path of length 7 found from MID2 to RLM1
MID2 ROM2 RHO1 PKC1 MKK1 SLT2 RLM1
C) Pheromone response signaling pathway in yeast
D) Best path of length 9 found from STE2/3 to
STE12
17
Additional MAPK Recovery Results
Pheromone response pathway assembly network
REM1
STE50
FAR1
GPA1
CDC24
STE3
STE4/18
STE12
FUS3
STE7
DIG1/2
CDC42
STE11
AKR1
KSS1
STE5
Pheromone response signaling pathway in yeast
18
Conclusion

• Presented efficient, color-coding based
  algorithms for finding simple paths
• Added biological extensions, other structures
• Integrated our well-founded reliability scores
• Applied our algorithms to yeast
• Shown 60 of discovered pathways were
  significantly enriched
• Recovered known MAP-Kinase, ubiquitin-ligation
  pathways

19
Simple vs. Segmented CDFs
Segmented 72
Simple 54
p-value (functional enrichment)
20
References

• Steffen, M., Petti, A., Aach, J., Dhaeseleer,
  P., Church, G. Automated modelling of signal
  transduction networks. BMC Bioinformatics 3
  (2002) 3444
• Alon, N., Yuster, R., Zwick, U. Color-coding. J.
  ACM 42 (1995) 844856