1. Genecentric: Finding Graph Theoretic Structure in High- Throughput Epistasis Data Andrew Gallant, Max Leiserson, M. Kachalov, Lenore Cowen, Ben Hescott Tufts University

2. Protein-protein interaction

3. High-throughput Interaction Data: aka ‘The Hairball’

4. What we want: What we have: Question: Can we infer anything about "real" pathways from the low-resolution graph model of pairwise interactions?

5. The hairball: A simple graph model vertices ↔ 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"

6. 1)Physical interactions 2) Genetic Interactions (epistasis)

7. Interaction types We distinguish here between two types of interaction: – physical interactions genetic interactions

8. 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.

9. Genetic interactions (epistasis) For non-essential genes, we can compare the growth of the double knockout to its component single knockouts Picture: Ulitsky

10. 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.

11. Redundant pathways and synthetic lethality

12. Kelley and Ideker (2005): Between-Pathway Model (BPM)

13. In reality, the data are very incomplete: Between-Pathway Model (BPM)

14. 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)

15. Kelley and Ideker (2005) and Ulitsky and Shamir (2007) (1)(2) (3) enriched for function X enriched for function Y

16. Kelley and Ideker (2005) Problems: – Sparse data limits the potential scope of discovery – independent validation is difficult and Ulitsky and Shamir (2007)

17. 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)

18. So: what is the right way to generalize BPMs to edge weights?

19. 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, >+2.5 Allevating 0<x< 2.5 SGA, Synthetic Genetic Array (smaller weights, -1.1 to 0.8) New methods generates high-throughput data for genetic interactions.

20. Want most negative weight across 0.553838 -7.32156 -6.315511 -5.506312 3.653986 6 -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

21. 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 and normalize to create an interaction score -0.664347 0.553838 -7.321556 -6.315511 3.685398 -5.252571 -3.365368 3.236723 -1.366879 2.13473 0.13342

22. 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

23. 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

24. Create a random bipartition For every vertex (gene) assign to a partition at random

25. Local search method Now for each gene, v, consider its interaction scores

26. Unhappy vs happy vertices

27. Flip Flip 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

28. Important properties Flip will always terminate - finite number of possible partitions - weight between partitions decreases with each flip - everyone is happy eventually - local optimum

29. 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

30. 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

31. 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

32. Our Results

33. 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)9641 (43%)53 (55%) Ulitsky et al.43 (43)11143 (39%)71 (64%) Kelley et al.40 (40)9835 (36%)52 (53%) Genecentric112 (103)5839 (67%)43 (74%)

34. How does Gencentric work with various data? -0.66434 0.5538 -7.3215 -6.315511 -5.506312 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

35. Genecentric on Various Data Sets Data Set#BPMs Enriched Same Function Enriched Same or Similar Function Collins et al. (Cell Cycle) 5839 (67%)43 (74%) Fiedler et al. (MAP-K) 50 (0%)4 (80%) Tong et al. (SGA)1498 (5%)17 (11%) Roguev et al, (S. pombe) 161 (6%)

36. 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

37. Physical interactions in Local Cut BPMS Data Set PIs within Pathways Expected by chance within PIs between Pathways Expected by chance between Collins et al. 172201820 Fiedler et al. 13111 Tong et al. 147411739

38. 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 -7.321556 -6.315511 -5.506312 3.685398 -5.252571 -3.365368 3.236723 -1.366879

39. Local Cut Weight Variants Weight scheme#BPMs Enriched Same Function Enriched Same or Similar Function Unchanged5839 (67%)43 (74%) No alleviating2617 (65%)19 (73%) Large values capped684 (6%)6 (9%) Alleviating +1 Aggravating -1 303 (10%)7 (23%)

40. Genecentric: try this at home Project name: Genecentric Project homepage: http://bcb.cs.tufts.edu/genecentric 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)

41. 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

42. 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)

43. 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

44. 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

45. 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)

46. Co-authors and collaborators Ben Hescott Max Leiserson Diana Tartar Maxim Kachalov

47. thanks.

48. 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?

49. 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.

50. Delete a gene in pathway 1; see if changes in pathway 2 coherent

51. log10 ratio BPM Deleted Gene Pathway restriction Sort

52. 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.

53. 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

54. 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

55. 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

56. 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.

57. 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.

58. 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.

59. 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.

60. Results BPM dataset# paths hit knockouts # validated pathways % validated pathways Kelley-Ideker (05) 1601610% Ulitsky- Shamir (07) 36514% Ma et al. (08) 54611% Our results95923024%

61. 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.

62. A random-gene validation test couples the two pathways together