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Genecentric: Finding Graph Theoretic Structure in High-Throughput Epistasis Data . Andrew Gallant, Max Leiserson , M. Kachalov , Lenore Cowen , Ben Hescott Tufts University . Protein-protein interaction. High-throughput Interaction Data: aka ‘The Hairball’. What we want:. What we have:. - PowerPoint PPT Presentation
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Genecentric: Finding Graph Theoretic Structure in High-Throughput Epistasis Data
Andrew Gallant, Max Leiserson, M. Kachalov, Lenore Cowen, Ben Hescott
Tufts University
Protein-protein interaction
High-throughput Interaction Data: aka ‘The Hairball’
What we want:
What we have:
Question: Can we infer anything about "real" pathways from the low-resolution graph model of pairwise interactions?
The hairball: A simple graph modelvertices ↔ genes/proteins
edges ↔ physical interactions or
genetic interactions
simplifications:
• undirected
• loses temporal information
• difficult to decompose into separate processes
• conflates different PPI types into one class of "physical interactions"
1)Physical interactions2) Genetic Interactions (epistasis)
Interaction types
• We distinguish here between two types of interaction:
– physical interactions
• genetic interactions
Genetic interactions (epistasis)
Only 18% of yeast genes are essential (the yeast dies when they’re removed).
For the rest, we can compare the growth of the double knockout to its component single knockouts.
Genetic interactions (epistasis)
• For non-essential genes, we can compare the growth of the double knockout to its component single knockouts
Picture: Ulitsky
Nonessential Genes
– Some genes are non-essential because they are only required under certain conditions (i.e. an enzyme to metabolize a particular nutrient).
– Other genes are non-essential because the network has some built-in redundancy.
• One gene (completely or partially) compensates for the loss of another.
• One functional pathway (completely or partially) compensates for the loss of another.
Redundant pathwaysand synthetic lethality
Kelley and Ideker (2005):Between-Pathway Model (BPM)
In reality, the data are very incomplete:Between-Pathway Model (BPM)
Kelley and Ideker (2005)
• Goal: detect putative BPMs in yeast interactome• Method:
1) find densely-connected subsets of the physical protein-protein interaction (PI) network (putative pathways)
2) check the genetic interaction (GI) network to see if patterns in density of genetic interactions correlate with these putative pathways
3) check resulting structures for overrepresentation of biological function (gene set enrichment)
and Ulitsky and Shamir (2007)
Kelley and Ideker (2005)and Ulitsky and Shamir (2007)
(1) (2)
(3)
enriched for function X
enriched for function Y
Kelley and Ideker (2005)
• Problems:– Sparse data limits the potential scope of discovery
– independent validation is difficult
and Ulitsky and Shamir (2007)
Further work on this problem:
Synthetic lethality:– Ulitsky and Shamir (2007)– Ma, Tarrone and Li (2008) – Brady, Maxwell, Daniels and Cowen (2009) – Hescott, Leiserson, Cowen and Slonim (2010)
Epistasis (weighted) data: -- Kelley and Kingsford (2011) -- Leiserson, Tatar, Cowen and Hescott (2011)
So: what is the right way to generalize BPMs to edge weights?
Quantitative interaction data
-0.6347
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3.69893
-5.2571
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-1.3668
E-MAP, Epistatic Miniarray Profile
Data is scalar (-22 to 15)
Synthetic Lethal, < -2.5 Synthetic Sick, -2.5 < x < 0
Synthetic Rescue, >+2.5Allevating 0<x< 2.5
SGA, Synthetic Genetic Array(smaller weights, -1.1 to 0.8)
New methods generates high-throughput data for genetic interactions.
Want most negative weight across
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-7.32156
-6.31511
3.68398
-5.25271
-3.36536
3.23723
-1.36879
2.73
What is the Quality of a BPM?
Once we obtain a candidate BPM we can score it using interaction data.
Sum interactions within
Sum interactions between
Take the difference andnormalize to create aninteraction score
-0.664347
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2.13473
0.13342
Genecentric takes the perspective of each gene in turn
What is the ‘best’ candidate BPM that contains node g?
Consider a diverse set of GLOBAL partitions that try to MAXIMIZE our objective function over the whole graph. Which genes are consistently placed in the same (opposite) partition as g?
-0.664347
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2.13473
0.13342
So we can extract a gene’s best BPM from a diverse set of good
global bipartitions
Idea for constructing the global
bipartitions: Maximal cut
Create a random bipartitionFor every vertex (gene) assign to a partition at random
Local search methodNow for each gene, v, consider its interaction scores
Unhappy vs happy vertices
FlipFlip to the other side to make it happy!
same(v) is now opposite(v) and opposite(v) is same(v)
some vertices could change to happy or unhappy
Important propertiesFlip will always terminate
- finite number of possible partitions
- weight between partitions decreases with each flip
- everyone is happy eventually
- local optimum
How we make a BPM from bipartitions
For every gene run weighted flip on the entire graph of interactions, M times (250 times)
Some genes will stay on same side for most runs.
Some genes will stay on the opposite side for most runs.
Most will switch sides among the different runs
-0.66434
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0.13342
BPM collection: Removing Redundancies
Sort by score, add to final output set if Jaccard index < .66 for all previously added BPMs
Remove BPMs that are too large or small
-0.664347
0.553838
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3.685398
-5.252571
-3.365368
3.236723
-1.366879
2.13473
0.13342
Take the difference and divide by the size
Numbers chosen to match previous studies
How do we measure results?
• FuncAssociate to measure gene set enrichment
Berriz, Beaver, Cenik, Tasan, Roth, “Next generation software for functional trend analysis,” Bioinformatics, 2009, 25(22): 3043-4.
Location of physical interactions
Our Results
Comparison to previous methods: yeast ChromBio E-MAP
Study#Modules / (%Enriched) #BPMs
Enriched Same
Function
Enriched Same or Similar Function
Bandyopadhyay et al. 37 (35) 96 41 (43%) 53 (55%)
Ulitsky et al. 43 (43) 111 43 (39%) 71 (64%)
Kelley et al. 40 (40) 98 35 (36%) 52 (53%)
Genecentric 112 (103) 58 39 (67%) 43 (74%)
How does Gencentric work with various data?
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3.6853
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3.26723
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-7.22314-6.31511
-0.55672
0.253228
-2.404421
4.51368
-3.355371
-6.63178
1.23711
-1.687991
E-MAP(Cell Cycle)
E-MAP(s. pombe)
SGA
E-MAP(MAP-K)
-0.22314-0.91511
0.253228
0.404421
-0.687991
0.983123
0.54278
-0.22565-5.7225
1.2833
-7.137271
5.22163
-3.12363
Genecentric on Various Data Sets
Data Set #BPMs
Enriched Same
Function
Enriched Same or Similar Function
Collins et al.(Cell Cycle) 58 39 (67%) 43 (74%)
Fiedler et al.(MAP-K) 5 0 (0%) 4 (80%)
Tong et al. (SGA) 149 8 (5%) 17 (11%)
Roguev et al, (S. pombe) 16 1 (6%) 1 (6%)
Consider physical interactions -0.66434
0.5538
-7.3215
-6.31511
-5.506312
3.6853
-5.252571
-3.365368
3.236723
-1.366879
genetic interactions
Physical Interactions-0.66347
0.55838
-7.3556
-6.3111
3.5398
-5.25371
-3.33368
3.2723
-1.3689
2.13473
Physical interactions in Local Cut BPMS
Data Set
PIswithin
Pathways
Expected by chance within
PIsbetween
Pathways
Expected bychance
between
Collins et al. 172 20 18 20
Fiedler et al. 13 1 1 1
Tong et al. 147 41 17 39
Modifying the weights
How does alleviating interaction data affect the results?
Do extreme weights affect the quality of the results?
Does a continuum of possible weights change the results?
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Local Cut Weight VariantsWeight scheme #BPMs
Enriched Same
Function
Enriched Same or Similar Function
Unchanged 58 39 (67%) 43 (74%)
No alleviating 26 17 (65%) 19 (73%)
Large values capped 68 4 (6%) 6 (9%)
Alleviating +1 Aggravating -1 30 3 (10%) 7 (23%)
Genecentric: try this at home
• Project name: Genecentric• Project homepage:
http://bcb.cs.tufts.edu/genecentric• Operating system: platform independent• Programming language: Python• Other requirements: Python 2.6 or higher• License: GNU Public License (GPL 2.0)
Gencentric parameters
• Set M (number of randomized bipartitions) default 250
• Set C (consistency of same side/opposite side for inclusion in g’s BPM) default 90%
• Set J (Jaccard index, how much overlap before similar BPMs are pruned) default .66
• Do you want a min or max size module? (default 3-25)
• FuncAssociate parameters: genespace, p-value
Genecentric works out of the box
• “New” E-MAP of plasma membrane genes from Aguilar et al. in 2010.
• 374 genes including those known to be involved in endocytosis, signaling, lipid metabolism, eisome function.
• Genecentric was run with default E-MAP parameters, except C was lowered from .9 to .8 to produce more BPMs (22 instead of 6)
Genecentric on plasma membrane E-MAP : example BPM
• COG6 COG5 COG8 PIB2 COG7
• Intra-Golgi vesicle-mediated transport, protein targeting to vacuole
BPM2
• ARL1 VPS35 GET3 ARL3 SYS1 GOT1 PEP8 SFT2 MNN1 VPS17
• Protein transport, Golgi apparatus, endsome transport, vesicle-mediated transport
BPM1
Genecentric on plasma membrane E-MAP : example BPM
• SLT2 BCK1 CLC1
• Endoplasmic reticulum unfolded protein response
BPM2
• PEX1 PEX6 EDE1 SKN7 ERG4 ADH1 PEX15 ARC18 EMC33
• Protein import into peroxisome matrix, receptor recycling
BPM1
Biological Findings (cont.)
• Some complexes come up again and again– could they be global mechanisms of fault tolerance?
In Plasma Membrane; -- COG complex In Chrombio;
– SWR-C complex (Chromatin remodeling)– Prefoldin complex (Chaperone)– MRE11 complex (DNA damage repair)
Co-authors and collaborators
• Ben Hescott • Max Leiserson• Diana Tartar• Maxim Kachalov
thanks.
A Graph Theory Problem
• Our algorithm samples from the maximal bipartite subgraphs. With what distribution? Is it uniform? Proportional to the number of edges that cross the cut?? ???
• What are the properties of the stable bipartite subgraphs of the synthetic lethal network? Are they conserved across species?
Approach• Run the partitioning algorithm 250 times on
the yeast SL network (G).• For each gene g in G,
– Construct a set A consisting of g and all nodes in G which wind up in the same set as g at least 70% of the time.
– Construct another set B consisting of all nodes in G which wind up in the opposite set from g at least 70% of the time.
• We call the subgraph of G defined by A and B the “stable bipartite subgraph of g”, and designate it as a candidate BPM.
Delete a gene in pathway 1; see if changes in pathway 2 coherent
log10 ratio
BPM
Deleted Gene
Pathway restriction
Sort
Validation: Microarray Data
• Rosetta compendium (Hughes et al, 2000): -- contains yeast expression profiles of 276
deletion mutants: i.e. for each gene in the yeast genome,
measures how its expression levels change when particular gene g is deleted, as compared to wildtype yeast.
At step i: N to 1
Calculate weighted percent of genes in pathway seen so far and precent of genes not in pathway:
Score is max difference
• Using a permutation test we sample 99 random subsets of genes the same size as the pathway
• We calculate the cluster rank score for each of these 99 sets
• We sort the test plus the pathway score• The p-value is the percentile• A pathway is validated if its p-value is <=0.1
How to validate a pathway
Delete a gene in pathway 1; see if changes in pathway 2 coherent
We call a pathway “Validated” if its Cluster Rank Score has p-value < .1
Kelley-Ideker Histogram of the Lowest CRS per Pathway per BPM
This histogram displays all the CRS scores from all of the results from Kelley and Ideker’s BPMs bucketed according to their lowest p value score. The p value scores <= 0.10 indicate a validated BPM.
Ulitskyi Histogram of the Lowest CRS per Pathway per BPM
This histogram displays all the CRS scores from all of the results from Ulitskyi’s BPMs bucketed according to their lowest p value score. The p value scores <= 0.10 indicate a validated BPM.
Ma Histogram of the Lowest CRS per Pathway per BPM
This histogram displays all the CRS scores from all of the results from Ma’s BPMs bucketed according to their lowest p value score. The p value scores <= 0.10 indicate a validated BPM.
Brady Histogram of the Lowest CRS per BPM
This histogram displays all the CRS scores from all of the results from Brady’s BPMs bucketed according to their lowest p value score. The p value scores <= 0.10 indicate a validated BPM. Clearly, Brady’s BPMs are disproportionately represented in the lower p value range.
Results
BPM dataset # paths hitknockouts
# validated pathways
% validatedpathways
Kelley-Ideker (05)
160 16 10%
Ulitsky-Shamir (07)
36 5 14%
Ma et al. (08)
54 6 11%
Our results 959 230 24%
A Tantalizing Peek of What We can Do With More Data!
• A heat map of the differential expression of yeast genes in pathway 2 in response to the deletion of two different genes (SHE4 and GAS1) from pathway 1 in a validated BPM of Ma et al.
A random-gene validation test couples the two pathways together