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

0.5838

-7.3556

-6.3511

-5.5312

3.69893

-5.2571

-3.3368

3.2723

-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

0.553838

-7.32156

-6.315511

-5.506312

3.6539866

-5.252571

-3.365368

3.23673

-1.366879

-5.506312

-0.66434

0.53838

-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

0.553838

-7.321556

-6.315511

3.685398

-5.252571

-3.365368

3.236723

-1.366879

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

0.553838

-7.321556

-6.315511

3.685398

-5.252571

-3.365368

3.236723

-1.366879

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

0.55338

-7.3215

-6.3151

3.6398

-5.252571

-3.3653

3.23672

-1.36679

2.1373

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

-7.321556

-6.315511

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?

-0.66434

0.5538

-7.3215

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3.6853

-5.252571

-3.365368

3.26723

-1.366879

-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?

-0.664347

0.553838

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3.685398

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3.236723

-1.366879

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