Automatically Assembling the Building Blocks of Cellular Circuitry

Transcription

1 Motivation Automatically Assembling the Building Blocks of Cellular Circuitry T. M. Murali April 20, 2006

2 Motivation Features of the Wiring iagram iagram is multi-modal. iagram is incomplete. Changes from organism to organism with evolutionary pressures acting as constraints. Wiring iagram is static. Not all interactions in the cell are active at all times. Set of active interactions changes with time, signals from other cells, environmental changes, attacks from pathogens,....

3 Motivation ynamic Views of the Cellular Wiring iagram Measure molecular concentrations in different conditions. Most common type of measurement is gene expression.

4 Motivation ynamic Views of the Cellular Wiring iagram Measure molecular concentrations in different conditions. Most common type of measurement is gene expression. Overlay gene expression data on the wiring diagram to obtain a dynamic view. Compare dynamic views for different conditions. How does the cellular network rewire itself under different conditions?

5 Motivation Previous Research ate hubs and party hubs. Purely topological changes in regulatory network structure across a small number of conditions Luscombe et al., Nature Most previous work focusses on rewiring at the level of single nodes or edges. Existing methods focus on the hierarchical organisation of modules in the universal network Ravasz et al., Science 2002; Tanay et al., PNAS, 2004.

6 Approach Overall Pipeline: Stage 1 Protein protein interaction networks Transcriptional regulatory networks Metabolic pathways Heat shock Form Universal network Experiments Cold shock Osmotic shock Sporulation Compute active networks Rapamycin

7 Approach Overall Pipeline: Stage 2 Compute NetworkLegos H C O H C O S R Active networks for each condition H C S R Network legos Network formulae sag 1. Automatically combine active networks via set-theoretic expressions. 2. Each expression is associated with a set of cell states (and their active networks) and has two interpretations: 2.1 A boolean formula that relates (the active networks of) a subset of the cell states using intersection and difference operations on graphs. 2.2 A network lego, a sub-network obtained by combining the active networks associated with the expression as decreed by the operators in the expression.

8 Approach Toy Example of Network Legos a c e a c e a c e b d b d b d Cell state A Cell state B Cell state C

9 Approach Toy Example of Network Legos a c e a c e a c e b d b d b d Cell state A Cell state B Cell state C a c A B C b d NetworkFormula NetworkLego

10 Approach sag H C O H C O S R H C S R Network legos Network formulae sag Each binary expression tree for a formula is a directed graph. sag is the AG formed by the union of all these trees. Leaves of the sag are the cell states (and the associated active networks). Each internal node of the sag is a formula recursively built by

11 Approach Novel Features of Our Approach Combined representation of biological processes using formulae and network legos. A formula relates different cellular states or perturbations by explicitly denoting their participation in a formula via intersections and differences. Each formula corresponds to a network lego, a functional module of coherently interacting genes in the universal network. sag puts all cell states/conditions in context with respect to each other in a hierarchical representation.

12 efinitions Basic efinitions Given two graphs G 1 and G 2, the intersection G 1 G 2 is the graph induced by the edges that occur in both. Their difference G 1 G 2 is the graph induced by the edges that occur in G 1 but not in G 2.

13 efinitions Problem Setting nput: U is the universal network of interactions. For each cell state s, A s U is the set of all interactions active in s. A is the set of all active networks. Output: A set of formulae and associated network legos The sag formed by the union of all the formulae The statistical significance and functional enrichment of each formula (network lego).

14 efinitions efinition of Network Legos and Formulae a c A B C b d NetworkFormula NetworkLego Each network lego L associated with a set A L of active networks. efine network legos and formulae recursively in parallel:

15 efinitions efinition of Network Legos and Formulae a c A B C b d NetworkFormula NetworkLego Each network lego L associated with a set A L of active networks. efine network legos and formulae recursively in parallel: 1. f N A, then N is a network lego with A N = {N}.

16 efinitions efinition of Network Legos and Formulae a c A B C b d NetworkFormula NetworkLego Each network lego L associated with a set A L of active networks. efine network legos and formulae recursively in parallel: 1. f N A, then N is a network lego with A N = {N}. 2. f L and M are network legos, then L M is a network lego with A L M = A L A M.

17 efinitions efinition of Network Legos and Formulae a c A B C b d NetworkFormula NetworkLego Each network lego L associated with a set A L of active networks. efine network legos and formulae recursively in parallel: 1. f N A, then N is a network lego with A N = {N}. 2. f L and M are network legos, then L M is a network lego with A L M = A L A M. 3. f L and M are network legos, then L M is a network lego with A L M = A L A M.

18 efinitions efinition of Network Legos and Formulae a c A B C b d NetworkFormula NetworkLego Each network lego L associated with a set A L of active networks. efine network legos and formulae recursively in parallel: 1. f N A, then N is a network lego with A N = {N}. 2. f L and M are network legos, then L M is a network lego with A L M = A L A M. 3. f L and M are network legos, then L M is a network lego with A L M = A L A M. 4. Require A L A M = to prevent trivial formulae. Skip statistical significance

19 efinitions Statistical Significance of a Network Lego The size σ(l) of a network lego is the number of edges in L. σ(l) depends on the number of networks in A that are combined in the corresponding formula. t is not appropriate to compare different network legos based on their sizes.

20 efinitions Statistical Significance of a Network Lego The size σ(l) of a network lego is the number of edges in L. σ(l) depends on the number of networks in A that are combined in the corresponding formula. t is not appropriate to compare different network legos based on their sizes. To put all network legos on an equal footing, we compute the statistical significance of each network lego.

21 efinitions Statistical Significance of a Network Lego The size σ(l) of a network lego is the number of edges in L. σ(l) depends on the number of networks in A that are combined in the corresponding formula. t is not appropriate to compare different network legos based on their sizes. To put all network legos on an equal footing, we compute the statistical significance of each network lego. Suppose we observe a network lego with k edges. What is the probability that we will observe a network lego with k or more edges if the active networks were constructed at random?

22 efinitions Statistical Significance of a Network Lego The size σ(l) of a network lego is the number of edges in L. σ(l) depends on the number of networks in A that are combined in the corresponding formula. t is not appropriate to compare different network legos based on their sizes. To put all network legos on an equal footing, we compute the statistical significance of each network lego. Suppose we observe a network lego with k edges. What is the probability that we will observe a network lego with k or more edges if the active networks were constructed at random? We compute the statistical significance of a network lego under the null hypothesis that 1. each network N in A is formed by selecting each edge in N uniformly at random without replacement and 2. each network N in A is selected independently from the other networks in A.

23 efinitions Statistical Significance: a Simple Case Consider the formula L = A B, where A, B A.

24 efinitions Statistical Significance: a Simple Case Consider the formula L = A B, where A, B A. For an edge e U, let X e be a binary random variable denoting the event that e is selected in L under the null hypothesis.

25 efinitions Statistical Significance: a Simple Case Consider the formula L = A B, where A, B A. For an edge e U, let X e be a binary random variable denoting the event that e is selected in L under the null hypothesis. X e = 1 if and only if e is selected in A and in B.

26 efinitions Statistical Significance: a Simple Case Consider the formula L = A B, where A, B A. For an edge e U, let X e be a binary random variable denoting the event that e is selected in L under the null hypothesis. X e = 1 if and only if e is selected in A and in B. Pr(X e = 1) = σ(a) σ(b) σ(u) σ(u). This probability is equal for all edges e U. enote the probability by p L.

27 efinitions Statistical Significance: Another Simple Case Consider the formula M = A B.

28 efinitions Statistical Significance: Another Simple Case Consider the formula M = A B. For an edge e U, let X e be a binary random variable denoting the event that e is selected in M = A B under the null hypothesis.

29 efinitions Statistical Significance: Another Simple Case Consider the formula M = A B. For an edge e U, let X e be a binary random variable denoting the event that e is selected in M = A B under the null hypothesis. X e = 1 if and only if e is selected in A but not in B. Pr(X e = 1) = σ(a) σ(u) 1 σ(b). σ(u) This probability p M is equal for all edges e U.

30 efinitions Statistical Significance: the General Case Extend these arguments to formulae involving more than two networks in A.

31 efinitions Statistical Significance: the General Case Extend these arguments to formulae involving more than two networks in A. Consider the formula H = L M. By definition, any network in A appears either in L or in M or in neither.

32 efinitions Statistical Significance: the General Case Extend these arguments to formulae involving more than two networks in A. Consider the formula H = L M. By definition, any network in A appears either in L or in M or in neither. An edge e is selected in H if and only if e is selected in L and in M.

33 efinitions Statistical Significance: the General Case Extend these arguments to formulae involving more than two networks in A. Consider the formula H = L M. By definition, any network in A appears either in L or in M or in neither. An edge e is selected in H if and only if e is selected in L and in M. p H = p L p M

34 efinitions Statistical Significance: the General Case Extend these arguments to formulae involving more than two networks in A. Consider the formula H = L M. By definition, any network in A appears either in L or in M or in neither. An edge e is selected in H if and only if e is selected in L and in M. p H = p L p M Similarly, if H = L M, then e is selected in H if and only if e is selected in L but not in M. p H = p L (1 p M )

35 efinitions Statistical Significance: the General Case Extend these arguments to formulae involving more than two networks in A. Consider the formula H = L M. By definition, any network in A appears either in L or in M or in neither. An edge e is selected in H if and only if e is selected in L and in M. p H = p L p M Similarly, if H = L M, then e is selected in H if and only if e is selected in L but not in M. p H = p L (1 p M ) n both cases, we can compute p H by recursively computing p L and p M.

36 efinitions Statistical Significance: Completing the Analysis For a formula H, p H is the probability that an edge will be selected in H under the null hypothesis. The number of edges in H is σ(h) = e U X e.

37 efinitions Statistical Significance: Completing the Analysis For a formula H, p H is the probability that an edge will be selected in H under the null hypothesis. The number of edges in H is σ(h) = e U X e. σ(h) has mean σ(u)p H and variance σ(u)p H (1 p H ).

38 efinitions Statistical Significance: Completing the Analysis For a formula H, p H is the probability that an edge will be selected in H under the null hypothesis. The number of edges in H is σ(h) = e U X e. σ(h) has mean σ(u)p H and variance σ(u)p H (1 p H ). The statistical significance of H is Pr( σ(h) σ(h)).

39 efinitions Statistical Significance: Completing the Analysis For a formula H, p H is the probability that an edge will be selected in H under the null hypothesis. The number of edges in H is σ(h) = e U X e. σ(h) has mean σ(u)p H and variance σ(u)p H (1 p H ). The statistical significance of H is Pr( σ(h) σ(h)). t is possible to estimate Pr( σ(h) σ(h)) using Chernoff bounds. We use the Central Limit Theorem: the distribution of σ(h) is approximately normal.

40 efinitions Statistical Significance: Completing the Analysis For a formula H, p H is the probability that an edge will be selected in H under the null hypothesis. The number of edges in H is σ(h) = e U X e. σ(h) has mean σ(u)p H and variance σ(u)p H (1 p H ). The statistical significance of H is Pr( σ(h) σ(h)). t is possible to estimate Pr( σ(h) σ(h)) using Chernoff bounds. We use the Central Limit Theorem: the distribution of σ(h) is approximately normal. efine the z-score z(h) of H to be z(h) = σ(h) σ(u)p H) σ(u)ph (1 p H ).

41 efinitions Statistical Significance: Completing the Analysis For a formula H, p H is the probability that an edge will be selected in H under the null hypothesis. The number of edges in H is σ(h) = e U X e. σ(h) has mean σ(u)p H and variance σ(u)p H (1 p H ). The statistical significance of H is Pr( σ(h) σ(h)). t is possible to estimate Pr( σ(h) σ(h)) using Chernoff bounds. We use the Central Limit Theorem: the distribution of σ(h) is approximately normal. efine the z-score z(h) of H to be z(h) = σ(h) σ(u)p H) σ(u)ph (1 p H ). The z-score of each formula is normally distributed with mean 0 and variance 1.

42 Algorithm Problem Complexity Number of potential formulae is exponential in the number of active networks.

43 Algorithm Problem Complexity Number of potential formulae is exponential in the number of active networks. For any threshold on statistical significance, we can construct a set of active networks for such that every possible intersection-only formula involving at least two networks has p-value at most the threshold.

44 Algorithm Problem Complexity Number of potential formulae is exponential in the number of active networks. For any threshold on statistical significance, we can construct a set of active networks for such that every possible intersection-only formula involving at least two networks has p-value at most the threshold. To make the problem tractable, we focus on constructing highly statistically significant formulae. Use the z-score as the measure for driving the algorithm.

45 Algorithm ntersection-only Algorithm: Overview Only allow the operator.

46 Algorithm ntersection-only Algorithm: Overview Only allow the operator. Algorithm is a version of bottom-up hierarchical clustering.

47 Algorithm ntersection-only Algorithm: Overview Only allow the operator. Algorithm is a version of bottom-up hierarchical clustering. nput: U is the universal network of interactions. For each cell state s, A s U is the set of all interactions active in s. A is the set of all active networks. Output: The sag formed by the union of all the formulae.

48 Algorithm ntersection-only Algorithm: Steps 1. Add each network in A as a formula to.

49 Algorithm ntersection-only Algorithm: Steps 1. Add each network in A as a formula to. 2. For every pair (F, G) of formulae in, insert the z-score z(f G) into a priority queue Q.

50 Algorithm ntersection-only Algorithm: Steps 1. Add each network in A as a formula to. 2. For every pair (F, G) of formulae in, insert the z-score z(f G) into a priority queue Q. 3. Repeatedly extract z-scores in decreasing order from Q until it becomes empty.

51 Algorithm ntersection-only Algorithm: Steps 1. Add each network in A as a formula to. 2. For every pair (F, G) of formulae in, insert the z-score z(f G) into a priority queue Q. 3. Repeatedly extract z-scores in decreasing order from Q until it becomes empty. 4. Suppose the next z-score corresponds to the formula F = G H.

52 Algorithm ntersection-only Algorithm: Steps 1. Add each network in A as a formula to. 2. For every pair (F, G) of formulae in, insert the z-score z(f G) into a priority queue Q. 3. Repeatedly extract z-scores in decreasing order from Q until it becomes empty. 4. Suppose the next z-score corresponds to the formula F = G H. 5. f G or H already has a parent in, do not consider F any further.

53 Algorithm ntersection-only Algorithm: Steps 1. Add each network in A as a formula to. 2. For every pair (F, G) of formulae in, insert the z-score z(f G) into a priority queue Q. 3. Repeatedly extract z-scores in decreasing order from Q until it becomes empty. 4. Suppose the next z-score corresponds to the formula F = G H. 5. f G or H already has a parent in, do not consider F any further. 6. Otherwise, insert F into as the parent of G and H. 7. For every formula L F, if A F A L =, insert the z-scores of F L into Q.

54 Algorithm Complete Algorithm: Steps 1. Add each network in A as a formula to. 2. For every pair (F, G) of formulae in, insert the z-score z(f G) into a priority queue Q. 3. Repeatedly extract z-scores in decreasing order from Q until it becomes empty. 4. Suppose the next z-score corresponds to the formula F = G H. 5. f G or H already has a parent in, do not consider F any further.

55 Algorithm Complete Algorithm: Steps 1. Add each network in A as a formula to. 2. For every pair (F, G) of formulae in, insert the z-score z(f G) into a priority queue Q. 3. Repeatedly extract z-scores in decreasing order from Q until it becomes empty. 4. Suppose the next z-score corresponds to the formula F = G H. 5. f G or H already has a parent in, do not consider F any further. 6. Otherwise, insert F, F 1 = G H and F 2 = H G into as the parents of G and H. and F For every formula L F, if A F A L =, insert the z-scores of F L, F 1 L, and F 2 L into Q.

56 Algorithm Post-processing the sag Compute functional enrichment of each network lego. Only keep formulae that are significant at the 0.01 level. Find true network legos: one that is more statistically significant than any of its descendants in the sag.

57 Algorithm Are Network Legos Building Blocks? f network legos are building blocks, they must be components of multiple active networks. f we remove an active network and repeat the computation, we should obtain almost the same set of network legos.

58 Algorithm Are Network Legos Building Blocks? f network legos are building blocks, they must be components of multiple active networks. f we remove an active network and repeat the computation, we should obtain almost the same set of network legos. Stability Analysis (based on Segal et al., Nature Genetics, 2004): 1. For each active network N A, compute the sag N for the set of active networks A {N}. 2. For each network lego L in, compute the most similar network lego L in N using the set-similarity measure. and store this measure with the pair σ(l, N). 3. Given a similarity threshold t, for each network lego L in, compute the fraction of networks in A such σ(l, N) t.

59 Results atasets Used Analysed data for S. cerevisiae and H. sapiens. Focus on some results for H. sapiens. H. sapiens: Wiring diagram has 9352 nodes and edges Edges in wiring diagram are protein-protein interactions (Ramani et al., Genome Biology, 2005; Rual et al., Nature, 2005; Stelzl et al., Cell, 2005, BN, HPR, REACTOME, Co-citation, Orthology) and promotor motif-based interactions (Xie et al., Nature 2005).

60 Results atasets Used Analysed data for S. cerevisiae and H. sapiens. Focus on some results for H. sapiens. H. sapiens: Wiring diagram has 9352 nodes and edges Edges in wiring diagram are protein-protein interactions (Ramani et al., Genome Biology, 2005; Rual et al., Nature, 2005; Stelzl et al., Cell, 2005, BN, HPR, REACTOME, Co-citation, Orthology) and promotor motif-based interactions (Xie et al., Nature 2005). 23 cancer-related gene expression data sets (Segal et al., Nature Genetics, 2004) spanning 92 distinct clinical conditions.

61 Results Overview of Results 92 clinical conditions yielded 298 active networks. Active networks for a single condition are edge disjoint.

62 Results Overview of Results 92 clinical conditions yielded 298 active networks. Active networks for a single condition are edge disjoint. We found 338 network legos. 227 network legos were significant at the 0.01 level and also more significant than all their descendants in the sag.

63 Results Overview of Results 92 clinical conditions yielded 298 active networks. Active networks for a single condition are edge disjoint. We found 338 network legos. 227 network legos were significant at the 0.01 level and also more significant than all their descendants in the sag. 141 statistically-significant network legos were functionally enriched in a total of 334 distinct functions. Enriched functions spanned processes involving NA replication, proteolysis, defense and immune response, cell proliferation, the cell cycle, and antigen processing.

64 Results Human Network Legos are Stable

65 Results Example of a Human Network Lego PTPRC C2 L3 L6ST C80 SPN C3Z C38 C58 FNG C4 Lung carcinoid (Lung cancer)_1 C28 LCK L4 L2 TGAL L7 FAS Lung carcinoid (Lung cancer)_2 L2RB L15 TGAM JAK3 Adenocarcinoma (Lung cancer)_1 Stage T1 (Lung cancer)_1 22 genes and 69 interactions. All interactions are supported by the literature. Enriched functions are signal transducer activity (p-value ), defense ( ), immune response ( ), and cell communication ( ).

66 Activated B like LBCL (B lymphoma)_2 Human mammary epithelial cells HMECs (Breast cancer)_4 Stimulated B cells (B lymphoma)_1 Normal lung tissue (Lung cancer)_3 Acute myelogeous leukemia (Leukemia)_6 Lung carcinoid (Lung cancer)_1 Primary blood mononuclear cells (B lymphoma)_2 Cell line (B lymphoma)_3 Epithelial cell line (NC60)_4 Activated B like LBCL (B lymphoma)_4 Atypical teratoid rhabdoid tumour CNS and other origin (Neuro tumors)_4 Adenocarcinoma periphery (Lung cancer)_1 iffuse large B cell lymphoma LBCL (B lymphoma)_3 Non small cell lung cancer (General compendium)_1 Estogen receptor (ER) positive breast cancer (Breast cancer)_2 Breast cancer (prognostic) relapse (Breast cancer)_2 nvasive liver tumor (Liver cancer)_5 Lung carcinoid (Lung cancer)_2 Acute lymphocytic leukemia ALL1 sub class (Leukemia)_4 Follicular lymphoma (B lymphoma)_2 Adenocarcinoma (Prostate cancer)_2 Small cell lung cancer (Lung cancer)_3 Squamous cell lung cancer (Lung cancer)_4 Normal lung tissue (Various tumors)_2 Melanoma (Various tumors)_1 Cell line (B lymphoma)_2 Acute lymphocytic leukemia ALL1 sub class (Leukemia)_6 Stage T2 (Lung cancer)_3 Acute lymphocytic leukemia MLL sub class (Leukemia)_2 Adenocarcinoma (Lung cancer)_1 Non classic malignant glioblastoma (Gliomas)_3 Renal tissue (Various tumors)_3 Acute lymphocytic leukemia ALL1 sub class (Leukemia)_3 Primary blood mononuclear cells (B lymphoma)_4 Stage T2 (Lung cancer)_1 Non small cell lung cancer (General compendium)_10 Activated B like LBCL (B lymphoma)_1 Adenocarcinoma extrapulmonary metastasis (Lung cancer)_2 p53 positive hepatocellular carcinoma (Liver cancer)_2 Stage T1 (Lung cancer)_1 Mesothelioma (Various tumors)_2 Adenocarcinoma (Prostate cancer)_4 Non small cell lung cancer (General compendium)_3 Breast cancer (prognostic) relapse (Breast cancer)_8 0.5hr immune stimulation (Stimulated PBMC)_1 Normal bladder tissue (Various tumors)_1 Grade 1 (Breast cancer)_1 Adenocarcinoma periphery (Lung cancer)_3 nvasive liver tumor (Liver cancer)_7 Adenocarcinoma extrapulmonary metastasis (Lung cancer)_3 Normal lung tissue (Lung cancer)_2 Normal prostate tissue (Prostate cancer)_6 Grade 3 (Breast cancer)_3 Mutated p53 tumor (Breast cancer)_4 Small cell lung cancer (Lung cancer)_2 iffuse large B cell lymphoma LBCL (B lymphoma)_5 After doxorubicin chemotherapy (Breast cancer)_1 Malignant glioblastoma (Various tumors)_3 Uterine tissue or cancer (Various tumors)_3 Normal prostate tissue (Prostate cancer)_3 iffuse large B cell lymphoma LBCL (B lymphoma)_4 T cells (Leukemia)_2 ead prognosis (Breast cancer)_2 Activated B like LBCL (B lymphoma)_5 Normal CNS tissue (Neuro tumors)_1 Malignant glioblastoma (Neuro tumors)_2 Unstimulated immune cells (Stimulated PBMC)_5 Adenocarcinoma extrapulmonary metastasis (Lung cancer)_4 Medulloblastoma (Neuro tumors)_6 Adenocarcinoma extrapulmonary metastasis (Lung cancer)_1 onomycin PMA stimulated immune cells (Stimulated PBMC)_1 Non small cell lung cancer (General compendium)_5 Colon cancer cell line (NC60)_2 Epithelial cell line (NC60)_2 Normal prostat Alive prognosis Acute myelogeous leukemia Normal tissue (Liver canc Results Example of a Human sag

67 Conclusions Features of our Approach 1. The combination of formulae, network legos, and sag appears to a novel representation of biological processes. 2. Computing active networks for each condition allows us to explicitly compare and contrast cell states via formulae and the sag. 3. Construct the sag by generalising bottom-up hierarchical clustering to graphs. 4. Computed network legos are statistically-significant, functionally-enriched, and stable.

68 Conclusions Future Research: Short Term 1. mprove network lego algorithm and statistics.

69 Conclusions Future Research: Short Term 1. mprove network lego algorithm and statistics. 2. Apply to other organisms. 3. Apply network lego without underlying wiring diagram. Problem: ActiveNetworks are very large and very dense to make sense of biologically.

70 Conclusions Future Research: Short Term 1. mprove network lego algorithm and statistics. 2. Apply to other organisms. 3. Apply network lego without underlying wiring diagram. Problem: ActiveNetworks are very large and very dense to make sense of biologically. 4. emonstrate that network legos indeed are building blocks by showing that a small number of network legos can be combined in different ways to recover the active networks.

71 Conclusions Future Research: Long Term We have not addressed a number of theoretical questions.

72 Conclusions Future Research: Long Term We have not addressed a number of theoretical questions. Complexity of generating good formulae. Conditions under which we can find good formulae efficiently. ncluding other types of operators in formulae. Efficient algorithms for enumerating all formulae. Alternative definitions of score. Formalising the notion of recovering active networks from network legos.

73 Conclusions Future Research: Long Term We have not addressed a number of theoretical questions. Complexity of generating good formulae. Conditions under which we can find good formulae efficiently. ncluding other types of operators in formulae. Efficient algorithms for enumerating all formulae. Alternative definitions of score. Formalising the notion of recovering active networks from network legos. Use network legos as the basis for discrete simulation of biological systems.

74 S. cerevisiae Wiring iagram Physical network 15,429 protein-protein interactions from the atabase of nteracting Proteins (P) protein-na interactions (Lee et al., Science, 2002). 6,306 metabolic interactions (proteins operate on at least common metabolite) based on KEGG. Genetic network 4,125 synthetically lethal/sick interactions (Tong et al., Science, 2004). 687 synthetically lethal interactions (MPS). Overall network has 32,416 (27,604 physical and 4,812 genetic) interactions between 5601 proteins (Kelley and deker, Nature Biotech., 2005).

75 Example of a S. cerevisiae Network Lego NH1 ATP1 ATP7 YGR043C ATP4 TKL2 HXK1 GLK1 ATP2 QCR6 COX4 RP1 CYB2 erisi diauxic shift COX8 GAL10 COR1 QCR2 SH4 GAL7 gasch raffinose vs reference SH2 HAP4 GAL1 COX13 SH3 QCR7 SH1 PCK1 CT1 gasch fructose vs reference gasch glucose vs reference N1 NE1