Predicting domain-domain interactions using a parsimony approach Katia Guimaraes, Ph.D. NCBI / NLM / NIH

K. Guimaraes NCBI/NLM/NIH 2 The problem We have: A protein-protein interaction network, not necessarily very reliable. Domain composition of the proteins in the network. We want: Identify a set of putative domain interactions. Basic assumption: Protein interactions are mediated by domain-domain interactions.

K. Guimaraes NCBI/NLM/NIH 3 Related Work Association Method: Sprinzak and Margalit. J.Mol. Biol., Score(, ) = 4 Score based on the ratio: observed frequency (i,j) expected frequency (i,j) (Figure from Sprinzak and Margalit, 2001) P( )

K. Guimaraes NCBI/NLM/NIH 4 Related Work Maximum Likelihood Estimation (EM): Deng, Mehta, Sun, and Chen. Genome Res., GOAL: To assign a probability to each domain-domain contact so that the likelihood of the network is maximized. Repeatedly tries to adapt parameters to explain the observed network, until there is no change. Important feature of this method: Can take into account missing data so as to consider, for instance, false negatives.

K. Guimaraes NCBI/NLM/NIH 5 Related Work Domain Pair Exclusion Analysis (DPEA): Riley, Lee, Sabatti, and Eisenberg. Genome Biology, APPROACH: MLE is computed multiple times, with a given domain-domain interaction disallowed, in order to observe the impact of that in the likelihood of the protein interaction network. DPEA outperforms all previous prediction methods.

K. Guimaraes NCBI/NLM/NIH 6 Our Approach Our hypothesis: Interactions evolved in the most parsimonious way. So, we will try to explain the protein interactions using the “smallest-weighted” set of putative domain interactions. Ex: For this protein interaction network: Domain pair (, ) would suffice to explain all protein interactions.

K. Guimaraes NCBI/NLM/NIH 7 The intuition behind our approach If single-domain proteins interact, But the fact is that most proteins have multiple domains. the problem is trivial:

K. Guimaraes NCBI/NLM/NIH 8 What if there are multiple interacting proteins all with multiple domains? By parsimony principle  Domain pairs that are common in those protein interactions are the best candidates as putative mediators. In this example, pairs (, ) and (, ) represent the best choices.

K. Guimaraes NCBI/NLM/NIH 9 Modeling the problem as an LP For each domain pair D i D j create a variable x ij ≥ 0. For each protein interaction P m P n create a constraint: x ij P m P n i j  x ij  1 x ij  { P m, P n } For this network there will be six constraints.

K. Guimaraes NCBI/NLM/NIH 10 Modeling the problem as an LP From the set protein-protein interactions, identify the potential domain-domain contacts, a set of variables. Ex: We have 8 potential contacts: (, )   1 1

K. Guimaraes NCBI/NLM/NIH 11 Modeling the problem as an LP Since parsimonious evolution favors that domain pairs appearing in multiple interacting protein pairs are better candidates for mediating the contact, minimize the sum of all scores assigned to the variables. So, we have: Minimize  x ij Subject to:  x ij  1 x ij  {P m, P n } {P m, P n } interacting protein pair

K. Guimaraes NCBI/NLM/NIH 12 Modeling the reliability of the protein interaction network Large scale experiments are rather unreliable. Estimation: Protein interaction network reliability ~50% To model that: –Build 1000 protein interaction subnetworks where each edge is kept according to the network reliability. –Compute LP-scores for each x ij in each network k, x ij k –LP-score for each pair will be the average of the values obtained in all runs.

K. Guimaraes NCBI/NLM/NIH 13 The pw-score pw-score(i,j) = min (p-value (i,j), (1-r) w(i,j) ) pw-score is an indicator of the influence of: - Frequency of appearance of the domain pair - Number of witness in view of network reliability We use pw-score to filter our predictions.

K. Guimaraes NCBI/NLM/NIH 14 Dataset used Protein interaction network and domain contents compiled by Eisenberg’s group for [Riley et al., 2005] (DPEA) Protein interaction network originally obtained from DIP. - 26,032 protein-protein interactions (constraints) - 177,233 potential domain contacts (variables) Gold Standard Set = Subset of iPFAM

K. Guimaraes NCBI/NLM/NIH 15 Comparison with other methods We did two experiments to evaluate our method: 1. Enrichment of domain pairs in confirmed by crystal structure among topmost scored pairs 2. Prediction of interacting domain pair between two proteins containing at least one domain pair in the gold standard set.

K. Guimaraes NCBI/NLM/NIH 16 Enrichment of domain pairs in the gold standard set among topmost scored pairs PE method outperforms others in both coverage and accuracy. pw-score ≤ 0.01 pw-score ≤ 0.05

K. Guimaraes NCBI/NLM/NIH 17 EXPERIMENT 2 Prediction of interacting domain pair between two interacting proteins We use a more controlled dataset Protein pairs used in this experiment includes only those that contain at least one potential domain contact that is in the GSS (1,780 and not 26,032). Pm Pm PnPn Given an interacting protein pair, Identify which domain pair(s) mediates the protein interaction. We assume that: Every protein interaction is mediated by a domain pair in the gold standard set. For each one of the 1780 protein interacting pairs, check if the domain(s) with maximum score is (are) in gold standard set.

K. Guimaraes NCBI/NLM/NIH 18 Comparison of PPV in Mediating Domain Pair Prediction experiment Overall PPV around 75% PPV of PE is well above that of other methods in every class DPEA ~42% PPV estimations separated by classes, according to the # of potential domain contacts of the protein interaction.

K. Guimaraes NCBI/NLM/NIH 19 Predicting domain-domain interactions using a parsimony approach Katia Guimaraes, Raja Jothi, Elena Zotenko, and Teresa Przytycka Genome Biology, 2006

K. Guimaraes NCBI/NLM/NIH 20 The impact of many appearances of the same domain Domain pairs that appear very frequently may induce domain pairs with higher scores. Obviously, a frequent pair may actually interact. But we define a p-value to indicate that possibility.

K. Guimaraes NCBI/NLM/NIH 21 Estimating a p-value We randomize the network: Build 1000 protein interaction networks with: Same set of proteins, with same domain architectures n e edges selected at random ( n e = # edges in original protein interaction network.) –Compute LP-scores for each x ij in each network k, x ij k –p-value (x ij ) = # times LP-score (x ij k )  LP-score (x ij ) 1000

K. Guimaraes NCBI/NLM/NIH 22 The presence of Witnesses We recall the case of single domain interacting proteins: We call such interacting protein pairs witnesses. But since the edges of the network are not reliable, we may have false witnesses. We use an estimation on the chance that a false witness is present in the dataset: (1-r) w(i,j) r = reliability of network; w(i,j) = # witnesses of (i,j).

K. Guimaraes NCBI/NLM/NIH 23 Dataset used As input data we used the files compiled by Eisenberg’s group for [Riley et al., 2005] (DPEA) Protein interaction network originally obtained from DIP. - 26,032 protein-protein interactions - underlying 11,403 proteins - from 69 organisms. (This set generated 177,233 potential domain contacts.) Domain architectures of the 11,403 proteins were obtained by HMM, and include PFAM-B domains. Our LP had 177,233 variables and 26,032 constraints.