A hub-attachment based method to detect functional modules from confidence-scored protein interactions and expression profiles Authors: Chia-Hao Chin 1,4, Shu-Hwa Chen 1, Chin-Wen Ho 4, Ming-Tat Ko 1,5, Chung-Yen Lin 1,2,3,5 1. Institute of Information Science, Academia Sinica, Taiwan 2. Division of Biostatistics and Bioinformatics, National Health Research Institutes, Taiwan 3. Institute of Fishery Science, College of Life Science, National Taiwan University, Taiwan 4. Department of Computer Science and Information Engineering, National Central University, Taiwan 5. Research Center of Information Technology Innovation, Academia Sinica, Taiwan

Outline Goal Method Experiment results

Detecting functional modules Identify functional modules by parsing Protein-Protein Interaction (PPI) networks into densely connected regions +

A more reliable PPI C1C1 C2C2 C3C3 C4C4 V1V V2V V3V V1V1 V2V2 V3V3 V1V1 V2V2 V3V3 V1V V2V V3V Pearson correlation threshold = 0.6 Gene expression data A PPI network

The overview of HUNTER An Example Module seeds generation Modules amalgamation Module seed growth module seeds grown modules final modules

Module seed generation Four cases for this stage input graph contain expression data UnweightedWeighted NoCase 1Case 2 YesCase 3Case 4

Module seed generation(1/4) Case 1 : –Input data is an unweighted graph. Find a maximum connected component of the subgraph induced by v's neighbors. v The Union of the vertex set of a maximum connected component and vertex v is a module seed. Union vertices of this sugraph and vertex v. This is a maximum connected component of the subgraph induced by v's neighbors. This is the subgraph induced by v's neighbors. It is composed of three connected components.

A q-connected module A vertex set U  V is q-connected if the probability is at least q for all W  U with at least one edge that connects W with U \ S. [Ulitsky et. al. 2009] a b c p( {a}, {b, c} ) = 1 - (1-0.8)*(1-0.6) = 0.92 p( {a, b}, {c} ) = 1 - (1-0.8)*(1-0.7) = 0.94 p( {a, c}, {b} ) = 1 - (1-0.6)*(1-0.7) = 0.88 If q = 0.9, then this graph is not q-connected.

q-connected We call a set of vertices U ⊆ V q-connected if, for all U’ ⊂ U, the probability that at least one edge connects U’ with U\U’ is at least q. Let E(U, W) denote the event that at least one edge connects a node from W ⊂ U with a node from U\W. Then U is q-connected if and only if P( E( U, W) ) > q for every W ⊂ U. V U W WU\W P( E( U, W) ) > q

U is q-connected if and only if < 1– q for every W ⊂ U. Assuming edge appearances are independent, we get

Find a maximum q-connected component algorithm Input data –Graph G=( V(G), E(G), p ), where p is a edge-weight function. –Threshold q Initial value –G’ = ( V(G), E(G), w ), where w = -log( 1- p(e) ) –t = -log( 1- q ) –max-q-connected component   Max-q-connected(G’) –If |V(G’)| > | V(max-q-connected component) | then If min-cut-value(G’)  t then –max-q-connected component  G’ else –(G’ 1, G’ 2 ) = min-cut-partition(G’) –Max-q-connected(G 1 ’) –Max-q-connected(G 2 ’)

Find a maximum q-connected component algorithm Input data –Graph G=( V(G), E(G), p ), where p is a edge-weight function. –Threshold q Initial value –G’ = ( V(G), E(G), w ), where w = -log( 1- p(e) ) –t = -log( 1- q ) –max-q-connected component   –candidate max-q-connected component C   Max-q-connected(G’) –Push G’ into C. –If |V(G’)| > | V(max-q-connected component) | then If min-cut-value(G’)  t then –max-q-connected component  G’ else –(G’ 1, G’ 2 ) = min-cut-partition(G’) –Max-q-connected(G 1 ’) –Max-q-connected(G 2 ’)

P i Proof Proof by contradiction –Assume candidate max-q-connected component C = { C 1, C 2,…, C k } S is a max-q-connected component, and S  C. ∵ S is a max-q-connected component, and S  C. ∴  C i  C i contains S, and  C j contains S, |V(C i ) |  |V(C j ) | ∵ S is q-connected ∴ min-cut-value(S)  t …(1) ∵ C i is not q-connected ∴ min-cut-value(C i ) < t …(2) ∵ C i is the minimum graph in C that contain S. ∴ min-cut-value(S)  min-cut-value(C i ) …(3) ∵ (1), (2) and (3) ∴ t  min-cut-value(S)  min-cut-value(C i ) < t (contradiction)  Q.E.D. S

Module seed generation(2/4) Case 2 : –Input data is a weighted graph. Find a maximum q-connected component of the subgraph induced by v's neighbors. v This subgraph is q-connected, and the vertex set of it is a module seed If a threshold q = 0.9, then this induced subgraph is not q-connected. If a threshold q = 0.9, then this induced subgraph is q-connected. If a threshold q = 0.9, then this induced subgraph is not q-connected. Is this subgraph q-connected? Find a maximum q-connected component of the subgraph induced by v's neighbors.

Module seed generation(3/4) Case 3 : –Input data is composed of an unweighted graph and gene expression data. Find a maximum connected component of the subgraph induced by v's neighbors, where the Pearson correlation of any pair of vertices is greater than a threshold. v In this subgraph, the Pearson correlation of each pair of vertices is greater than a threshold, and the vertex set of it is a module seed A blue dashed line means its Pearson correlation is less than a threshold t = 0.6 A green dashed line means its Pearson correlation is larger than a threshold t = 0.6 Check each subgraph by using gene expression data.

Module seed generation(4/4) Case 4 : –Input data is composed of a weighted graph and gene expression data. Find a maximum connected component of the subgraph induced by v's neighbors, where the Pearson correlation of any pair of vertices is greater than a threshold. v The vertex set of this subgraph is a module seed. A blue dashed line means its Pearson correlation is less than a threshold t = 0.6 A green dashed line means its Pearson correlation is larger than a threshold t = 0.6 This induced subgraph is not q-connected We check whether this subgraph is q-connected. We check each subgraph by using gene expression data. This subgraph is q-connected.

Module growth After creating a module seed, we join the neighbors of the module seed if most of their adjacent nodes also belong to the module seed. v w A module seed v w A grown module

Module amalgamation we merge any two modules if they have too many common proteins grown module 1 grown module 2 A final module

Stage 1: Module seed generation

Find q-connected component

Stage 2: Module seed growth

Stage 3: Modules amalgamation

Functional Group Verification Using Gene Ontology  Gene Ontology Three separate ontologies: Biological Process Molecular Function Cellular Component Organized as a DAG describing gene products (proteins and functional RNA) GO Annotation A GO term is associated with a gene or gene product to form a GO annotation.

p-value Given a gene ontology and term t, the p-value is the probability of observing x or more proteins in the cluster c. –N: the number of proteins annotated to a term of the GO ontology. –M: the number of proteins annotated to the GO term t. –n : the number of proteins of the cluster c. –x : the number of proteins of the cluster c which are annotated to the GO term t. N M n x

F-measure For each method, we measured –Sensitivity: the fraction of annotations that are enriched in at least one module at p-value < [Ulitsky et.al. 2009]. –Specificity: the fraction of modules enriched with at least one annotation at p-value < [Ulitsky et. al. 2009].

We compare our method with three newly developed methods CEZANNA [Ulitsky et. al. 2009] CMC [Liu et. al. 2009] Core [Leung et. al. 2009]

Check experiment results by GO

Check experiment results by golden standard databases p-value: Given a golden standard database and complex g, the p-value is the probability of observing x or more proteins in the cluster c. –N: the number of proteins in a golden standard database. –M: the number of proteins in a complex g of the golden standard database. –n : the number of proteins of the cluster c. –x : the number of proteins of the cluster c which also belong to the complex g. N M n x

Check experiment results by golden standard databases

RNA Polymerase I RNA Polymerase III RNA Polymerase II Common module for RNA polymerase I, II, III Common module for RNA polymerase I, III Common regulatory unit for RNA polymerase I, II TFIIF for RNA polymerase II A cluster of our prediction on yeast PPI

Threshold q-connected –We set q as 0.95 corresponds to an "error probability" of correlation threshold t –Initiation A complete graph given a cutoff threshold –Remove those edges whose Pearson correlation are less or equal than the threshold cutoff threshold = 0.6

Clustering coefficient k i : degree of node i E i : edges between neighbors of node i’s The density of the network surrounding node i, characterized as the number of triangles through i. i The center node has 8 (grey) neighbors There are 4 edges between the neighbors C = 2*4 /(8*(8-1)) = 8/56 = 1/7 K is the number of nodes whose degree are larger than 1.

A threshold for Pearson correlation The authors conjectured that the removed links are likely to be noise as long as the difference between the observed clustering coefficient and its randomized counterpart increases monotonically [Elo et. al. 2007]. A threshold r 0 = 0r 1 = 0.01r 100 = 1 threshold C( r i ) – C 0 ( r i ) the first local maximumC*

References Elo LL, Jarvenpaa H, Oresic M, Lahesmaa R, Aittokallio T: Systematic construction of gene coexpression networks with applications to human T helper cell differentiation process. Bioinformatics 2007, 23(16): Liu G, Wong L, Chua HN: Complex discovery from weighted PPI networks. Bioinformatics 2009, 25(15): Leung HC, Xiang Q, Yiu SM, Chin FY: Predicting protein complexes from PPI data: a core-attachment approach. J Comput Biol 2009, 16(2): Ulitsky I, Shamir R: Identifying functional modules using expression profiles and confidence-scored protein interactions. Bioinformatics 2009, 25(9):

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