Comparative analysis of protein interaction networks reveals that conserved pathways are susceptible to HIV-1 interception

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1 Comparative analysis of protein interaction networks reveals that conserved pathways are ssceptible to HIV-1 interception Xiaoning Qian 1, Byng-Jn Yoon 2 1 Department of Compter Science and Engineering, University of Soth Florida, Tampa, FL, USA 2 Department of Electrical and Compter Engineering, Texas A&M University, College Station, TX, USA Xiaoning Qian - xqian@cse.sf.ed; Byng-Jn Yoon - bjyoon@ece.tam.ed; Corresponding athor Abstract Backgrond: Hman immnodeficiency virs type one (HIV-1) is the major pathogen that cases the acqired immne deficiency syndrome (AIDS). With the availability of large-scale protein-protein interaction (PPI) measrements, comparative network analysis can provide a promising way to stdy the host-virs interactions and their fnctional significance in the pathogenesis of AIDS. Until now, there have been a large nmber of HIV stdies based on varios animal models. In this paper, we present a novel framework for stdying the host-hiv interactions throgh comparative network analysis across different species. Reslts: Based on the proposed framework, we test or hypothesis that HIV-1 attacks essential biological pathways that are conserved across species. We selected the Homo sapiens and Ms mscls PPI networks with the largest coverage among the PPI networks that are available from pblic databases. By sing a local network alignment algorithm based on hidden Markov models (HMMs), we first identified the pathways that are conserved in both networks. Next, we analyzed the HIV-1 ssceptibility of these pathways, in comparison with random pathways in the hman PPI network. Or analysis shows that the conserved pathways have a significantly higher probability of being intercepted by HIV-1. Frthermore, Gene Ontology (GO) enrichment analysis shows that most of the enriched GO terms are related to signal transdction, which has been conjectred to be one of the major mechanisms targeted by HIV-1 for the takeover of the host cell. 1

2 Conclsions: This proof-of-concept stdy clearly shows that the comparative analysis of PPI networks across different species can provide important insights into the host-hiv interactions and the detailed mechanisms of HIV-1. We expect that comparative mltiple network analysis of varios species that have different levels of ssceptibility to similar lentivirses may provide a very effective framework for generating novel, and experimentally verifiable, hypotheses on the mechanisms of HIV-1. We believe that the proposed framework has the potential to expedite the elcidation of the important mechanisms of HIV-1, and ltimately, the discovery of novel anti-hiv drgs. Backgrond Acqired immne deficiency syndrome (AIDS), one of the most destrctive pandemics in recorded history according to the statistics from the World Health Organization (WHO) [1], has killed more than 25 million people since it was first recognized in Hman immnodeficiency virs type one (HIV-1) has been fond to be the casative pathogen of AIDS [2, 3]. HIV-1 is a lentivirs, a slow retrovirs that is responsible for long-dration illness with a long incbation period. HIV-1 has 9 genes which encode p to 19 proteins de to post-translational cleavage [4]. By reverse transcription from viral RNA to host-integrable DNA, the virs can become active and replicate to case rapid T cell depletion, immne system collapse, and opportnistic infections that mark the advent of AIDS [5]. Althogh advances in antiviral therapy and management of opportnistic infection for AIDS have remarkably improved the general health, the expensive cost and adverse effects of the available drgs have motivated many researchers to explore novel avenes to anti-hiv-1 drg discovery. With the increasing coverage of HIV-1 and hman protein interactions in the literatre [6 11], a hman/hiv-1 interactome has been created [12], which can play a critical role in better nderstanding the virology and pathology of this infectios disease and developing new therapetics. In addition to this, the availability of large-scale biological networks, inclding protein-protein interaction (PPI) networks, has led to the introdction of systems biology approaches for novel HIV-1 drg discovery [13, 14]. In [13], Balakrishnan et al. proposed to find alternative pathways to circmvent the HIV-1 intercepted pathways based on the efficiency and robstness of biological processes. The main goal was to generate new hypotheses regarding HIV-1 2

3 targeted pathways and their effects on varios moleclar fnctions, which will help s better nderstand the mechanisms of HIV-1 takeover of the host cell and find ways to circmvent it. The stdy was based on crated signal transdction pathways obtained from mltiple pathway databases. One practical problem of this pathway-based approach is that the crrently known pathways cover only a limited nmber of hman proteins, hence it may exclde important HIV-1 targets from the analysis. Moreover, many crated pathways in pblic databases overlap with each other, which may introdce bias in the analysis. On the other hand, Lin et al. [14] proposed comparative stdies of host-virs protein interactions across hman (Homo sapiens) and other animal models that may be invaded by similar lentivirses that case immnosppression or immnoproliferation, inclding three mammalian species: chimpanzee (Pan troglodyte), rhess macaqe (Macaca mlatta), and mose (Ms mscls). All these animal models have been extensively stdied to nderstand the HIV-1 host-virs interplay [15, 16]. Comparative stdies of host-virs interactions may provide new insights into why different species have different ssceptibility to HIV-1, which may lead to the development of potential therapetics in the long rn. Motivated by these works, we propose a novel framework for stdying hman/hiv-1 interactions, based on comparative analysis of the hman PPI network and the PPI network of other species that are ssceptible to lentivirs invasion. It has been shown that the comparative analysis of PPI networks of different species can identify conserved pathways that carry essential celllar fnctionalities [17 36]. Frthermore, HIV-1 has to be a minimalist in order to srvive, and for this reason, it has been believed to target these essential pathways that are conserved across species [13, 37]. As a reslt, the comparative analysis of PPI networks may be sed to generate new hypotheses that will be sefl in improving or nderstanding of the mechanisms of HIV-1 takeover of the host cell, and ltimately, for developing effective therapetics for AIDS. Reslts and Discssion Conserved pathways are ssceptible to HIV-1 attacks Or main goal in this paper is to validate the following hypothesis: Essential biological pathways that are conserved across different species that are ssceptible to lentivirses, have a high probability of being intercepted by HIV-1. To validate the above hypothesis, we first aligned the Homo sapiens PPI network with the Ms mscls PPI network to find conserved pathways (Figre 1). The Ms mscls network was chosen as it is the 3

4 HIV-1 genes gag pol env tat rev nef vif vpr vp (A) 4 8 v 6 v 3 v 4 v 1 v 7 v 9 v 2 v 5 v 8 HMM-based local network alignment Deletion (B) 1 v 3 Insertion v Insertion v v Deletion vs. (C) Homo sapiens PPI network Ms mscls network 9 v 9 Figre 1: Overview of the proposed approach: (A) Illstration of the Homo sapiens and Ms mscls PPI networks along with HIV-1 interactions. The dashed line that connects two nodes i and v j indicate that the corresponding proteins are orthologos. The solid lines represent protein-protein interactions. In the Homo sapiens network, the proteins are colored based on the HIV-1 proteins that can bind to them. Proteins with mltiple colors are ssceptible to mltiple HIV-1 proteins, while proteins with no color have no known interactions with HIV-1 proteins. Note that the Ms mscls network is not colored. (B) The top-scoring alignment between two similar paths and v. Colored nodes represent matched proteins. (C) An example of a randomly extracted pathway in the Homo sapiens network. largest animal network nder lentivirs stdy that is available from pblic databases. This will allow s to redce the bias that may arise from sing smaller networks. For identifying conserved pathways, we sed a local network alignment method based on hidden Markov models (HMMs), which we recently proposed in [36]. The HMM framework can natrally integrate both the seqence similarity of the proteins across different species and the interaction reliability between the proteins within the same PPI network into the scoring scheme for finding conserved pathways. The HMM-based local alignment method allows flexible nmber of consective insertions and/or deletions, and it can deal with a large class of path isomorphism. More importantly, the comptational complexity for finding the best matching pathways grows linearly with respect to the size of each network, making it sitable for finding long conserved pathways in large PPI networks. We ran the HMM-based local alignment algorithm to find conserved pathways both with and withot gaps. Since the Ms mscls network is still qite sparse (see Methods), the nmber of conserved pathways depends on whether we allow gaps and how long the pathways can be. Typically, we have fewer conserved pathways when we search for long pathways with no gaps allowed. Next, we extracted 3, random pathways of different sizes (L = 16, 32, and 64) by performing a random walk on the Homo sapiens network (see Methods). Then we compared the HIV-1 ssceptibility of the conserved pathways with that of the random pathways in the Homo sapiens PPI network, by sing the 4

5 25 15 (A) (B) (C) 15 2 Nmber of pathways Nmber of hman proteins interacting with HIV Figre 2: The nmber of proteins that interact with HIV-1 proteins in conserved pathways (with no gaps) and randomly extracted pathways. (A) The histograms for pathways of size L = 16. (B) The histograms for pathways of size L = 32. (C) The histograms for pathways of size L = 64. predicted hman/hiv-1 interactome map in [12]. Nmber of proteins in the pathways that are intercepted by HIV-1 Based on the identified conserved pathways and the randomly extracted pathways, we first compted how many proteins within each pathway can be intercepted by HIV-1, by mapping the predicted hman/hiv-1 interactions in [12] onto these pathways. Figre 2 shows the histogram of the nmber of HIV-1 interacting proteins in conserved pathways as well as the histogram for random pathways. From the figre, there is a clear distinction between the two types of histograms. Typically, the separation between the two histograms increases with the length of the pathways. We can clearly see that highly conserved pathways are more ssceptible to HIV-1 interception, in general. Next, we considered conserved pathways that have been identified by the HMM-based local network alignment algorithm by allowing gaps. We compared the histograms for these pathways to the histograms for random pathways. These reslts are shown in Fig. 3. We can see that the histograms show similar trends as in Fig. 2, bt the separation between the two types of histograms is smaller in this case. This might be de to the fact that the HMM-based algorithm may find less conserved pathways when we allow gaps. To evalate the statistical significance of the difference between conserved and random pathways, we estimated the p-vale of the nmber of HIV-1 interacting proteins for every conserved pathway. The detailed process for compting the p-vales is described in Methods. Basically, it comptes the statistical significance of the nmber of HIV-1 interacting proteins in each conserved pathway with respect to the 5

6 (A) (B) (C) 1 1 Nmber of pathways Nmber of hman proteins interacting with HIV Figre 3: The nmber of proteins that interact with HIV-1 proteins in conserved pathways (with gaps) and randomly extracted pathways. (A) The histograms for pathways of size L = 16. (B) The histograms for pathways of size L = 32. (C) The histograms for pathways of size L = 64. baseline distribtion, which is estimated from the histogram of the nmbers of HIV-1 interacting proteins in randomly extracted pathways. Figre 4(A) shows the plot of p-vales for conserved pathways of varios lengths and with no gaps allowed. Conserved pathways with gaps show a similar trend (reslts not shown). As we mentioned earlier, the nmber of conserved pathways decrease as the pathway size L gets larger. In the figre, the conserved pathways are sorted based on their alignment scores compted by the HMM-based local alignment method [36] (see Methods). The alignment score reflects the degree of conservation between the aligned pathways. We can see that highly conserved pathways are generally more ssceptible to HIV-1 interception. In fact, sch pathways typically contain more proteins that can be intercepted by HIV-1 proteins. Total nmber of hman/hiv-1 protein interactions within one pathway To frther validate or hypothesis, we checked the total nmber of hman/hiv-1 interactions within each pathway. Again, we sed the predicted hman/hiv-1 interactome in [12] to cont the total nmber of hman/hiv-1 interactions within each pathway. Figre 4(B) shows the p-vale of the total nmber of HIV-1 interactions within every conserved pathway (with no gaps). As before, the baseline distribtion was estimated sing the histogram of the total nmbers of HIV-1 interactions in randomly extracted pathways. Note that, for long conserved pathways (L = 64), the p-vales are always below.3. These reslts show that the difference in ssceptibility to HIV-1 interception between the conserved and random pathways is statistically significant. 6

7 p vale for nmber of HIV interacting proteins L=16 L=32 L=64 (A) p vale for total nmber of HIV interactions L=16 L=32 L=64 (B) p vale for average HIV interaction score L=16 L=32 L=64 (C) Conserved pathways in a descending order based on the alignment score Figre 4: Statistical significance of the interactions between HIV-1 and the conserved pathways (with no gaps). (A) The p-vales of the nmber of hman proteins that interact with HIV-1 proteins within conserved pathways with different sizes (L = 16: red, L = 32: ble, L = 64: green). (B) The p-vales of the total nmber of predicted hman/hiv-1 interactions within conserved pathways. (C) The p-vales for the average predicted interaction scores within conserved pathways. HIV-1 interaction score of conserved pathways Finally, we evalated the HIV-1 interaction score for conserved pathways based on the scoring scheme in [12]. For this evalation, we mapped the prediction scores of hman/hiv-1 interactions onto the conserved pathways and compted their average. In a similar way, we compted the average HIV-1 interaction score for each random pathway and estimated the distribtion of these average scores. Then we compted the p-vales of the average prediction scores for all the conserved pathways. These p-vales are shown in Fig. 4(C) for the conserved pathways with different lengths. By comparing the reslts in Fig. 4(C) and those shown in Fig. 4(A,B), we can clearly see that there exist considerable correlation between these reslts. This is especially interesting, if we consider the fact that or approach does not se any extra data except for the PPI networks, while the prediction algorithm in [12] is obtained by integrating the information from varios sorces, sch as gene expression, domain and motif identification, tisse distribtion, fnctional annotation, sbcelllar localization and hman network featres, and HIV-1 s mimicry of hman protein binding partners. GO term enrichment analysis We also performed a Gene Ontology (GO) term enrichment analysis [38] sing GO::TermFinder [39]. We took the top 2 conserved pathways of size L = 64 and checked their GO terms. Table 1 shows some of the enriched GO terms, whose adjsted p-vales are smaller than 2.e 7. 1 Examples of highly enriched GO terms inclde: signaling pathway, signal transdction, cell commnication, phosphate metabolic 1 The complete enrichment analysis reslts can be fond at xqian/hiv/. 7

8 process, response to stimls, response to stress, protein modification process, reglation of immne system process, which are pathways that are widely known to be ssceptible to HIV-1 interception [2, 3, 12, 13]. There are also more specific GO terms that are enriched, sch as hemopoietic or lymphoid organ development and lymphocyte proliferation. Interestingly, the pathogenesis of HIV-associated lymphomas has been conjectred to case the complication of HIV infection as reported in [4]. From all the proteins covered by the top 2 conserved pathways, we have listed ten hman proteins with the largest nmber of predicted HIV-1 interactions in Table 2. We also selected eight hman proteins that are not known to be intercepted by HIV-1, which are shown in bold face in Table 2.. We have also listed their associated ontology keywords or GO terms based on the UniProt database. 2 We note that many of these proteins are related to the aforementioned biological processes and they might be nidentified targets of HIV-1. Frther stdy on these proteins may lead to a better nderstanding of the biological mechanisms of HIV-1. Reslts sing crated hman/hiv-1 protein interactions In order to ensre that the obtained reslts are biologically meaningfl, we frther validate or hypothesis by testing the HIV-1 ssceptibility sing the crated hman/hiv-1 protein interaction data in the Hman Protein Interaction Database (HPID) [41]. These hman/hiv-1 interactions were reported in the literatre and crated by experts and can provide another spporting evidence that pathways which are conserved across species have a high probability of being attacked by HIV-1. As in or previos experiments, we conted the nmber of HIV-1 interacting proteins in conserved pathways (withot allowing gaps) and compared it to the nmber of HIV-1 interacting proteins in random pathways. The reslting histograms are shown in Fig. 5. We can see that the histograms show similar trends as in Fig. 2, bt the nmbers of interacting hman proteins are relatively smaller and the separation between the histograms of the conserved pathways and the random pathways is less significant. This is expected since the HPID crated interactions are sparser compared to the predicted interactions in [12] and smaller nmber of proteins in the Homo sapiens PPI network have been mapped with the HIV-1 interactions. We have also compared the total nmber of hman/hiv-1 interactions in conserved pathways with that in random pathways. The reslting histograms are shown in Fig. 6. Figre 7 plots the compted p-vales of both the nmber of the HIV-1 interacting proteins and the total nmber of hman/hiv-1 interactions within every conserved 2 8

9 Table 1: Selected GO terms enriched in the top 2 conserved pathways of size L = 64 with adjsted p-vales. Gene Ontology terms signaling pathway signaling signal transdction reglation of celllar process signal transmission signaling process reglation of biological process biological reglation intracelllar signaling pathway intracelllar signal transdction cell proliferation phosphate metabolic process system development enzyme linked receptor protein signaling pathway developmental process anatomical strctre development organ development cell srface receptor linked signaling pathway response to endogenos stimls celllar response to stimls response to stimls protein modification process reglation of metabolic process response to hormone stimls cell commnication reglation of biosynthetic process Ras protein signal transdction response to stress RNA biosynthetic process celllar macromolecle biosynthetic process reglation of transferase activity immne system development reglation of immne system process hemopoietic or lymphoid organ development hemopoiesis nerogenesis lekocyte differentiation lymphocyte proliferation Adjsted p-vales 1.39e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e e-7 9

10 Table 2: UniProt accession nmbers of selected proteins in the top 2 conserved pathways of size L = 64 with protein names and the associated top ontology keywords and GO terms listed by UniProt IDs Protein names Gene Ontology terms P4637 Celllar tmor antigen p53 apoptosis; host-virs interaction; DNA damage response; protein tetramerization P17612 camp-dependent protein kinase hormone-mediated signaling pathway; catalytic sbnit α intracelllar protein kinase cascade P28482 Mitogen-activated protein kinase 1 Ras protein signal transdction; cell cycle; transcription; interspecies interaction between organisms; chemotaxis; synaptic transmission P27361 Mitogen-activated protein kinase 3 Ras protein signal transdction; interspecies interaction between organisms P5412 Transcription factor AP-1 SMAD protein signal transdction; positive reglation by host of viral transcription; transforming growth factor (TGF) β receptor signaling pathway P6241 Tyrosine-protein kinase Fyn T cell receptor signaling pathway; interspecies interaction between organisms P6493 Cell division protein kinase 1 anti-apoptosis; cell division; mitosis Q15796 Mothers against decapentaplegic SMAD protein complex assembly; homolog 2 intracelllar signaling pathway; palate development; transcription; TGF β receptor signaling pathway P64 Retinoblastoma-associated protein Cell cycle; Host-virs interaction; androgen receptor signaling pathway; myoblast differentiation P449 RAF proto-oncogene serine/ Ras protein signal transdction; threonine-protein kinase cell proliferation; protein amino acid phosphorylation O14512 Sppressor of cytokine signaling 7 Ubl conjgation pathway; reglation of growth; negative reglation of signal transdction P1721 Mast/stem cell growth factor male gonad development; receptor transmembrane receptor protein tyrosine; kinase signaling pathway P15884 Transcription factor 4 cerebral cortex development; reglation of smooth mscle cell proliferation; transcription P1641 Cytotoxic T-lymphocyte protein 4 immne response; negative reglation of reglatory T cell differentiation P29597 Non-receptor tyrosine-protein intracelllar protein kinase cascade; kinase TYK2 peptidyl-tyrosine phosphorylation Q1348 GRB2-associated-binding protein 1 cell proliferation; epidermal growth factor receptor signaling pathway; inslin receptor signaling pathway Q1553 Son of sevenless homolog 2 apoptosis; reglation of Rho protein ; signal transdction; small GTPase mediated signal transdction Q96TE Cdk inhibitor p27kip1 cell cycle arrest 1

11 2 18 (A) 25 (B) 6 (C) Nmber of pathways Nmber of hman proteins interacting with HIV Figre 5: The nmber of proteins that interact with HIV-1 proteins based on the HPID interaction data in conserved pathways (with no gaps) and randomly extracted pathways. (A) The histograms for pathways of size L = 16. (B) The histograms for pathways of size L = 32. (C) The histograms for pathways of size L = 64. Nmber of pathways (A) (B) (C) Nmber of hman/hiv-1 interactions Figre 6: The total nmber of hman/hiv-1 protein interactions based on the HPID interaction data in conserved pathways (with no gaps) and randomly extracted pathways. (A) The histograms for pathways of size L = 16. (B) The histograms for pathways of size L = 32. (C) The histograms for pathways of size L = 64. pathway (with no gaps). Both reslts show that the predicted ssceptibility of conserved pathways in the Homo sapiens PPI network and the Ms mscls PPI network to HIV-1 interception is statistically significant. Conclsions Local network alignment can effectively identify conserved pathways that are biologically meaningfl [36]. If HIV-1 is a minimalist in order to srvive and therefore targets essential pathways [13], as other virses do, it is natral to expect that essential pathways that are conserved across different species shold be highly vlnerable to HIV-1 attacks. Or analysis based on comparing the Homo sapiens PPI network and the Ms mscls PPI network indicates that or conjectre is indeed tre. This proof-of-concept stdy 11

12 p vale for nmber of HIV interacting proteins L=16 L=32 L=64 (A) p vale for total nmber of HIV interactions (B) (B) Conserved pathways in a descending order based on the alignment score Figre 7: Statistical significance of the interactions between HIV-1 and the conserved pathways (with no gaps) according to the crated interactions in HPID. (A) The p-vales of the nmber of hman proteins that interact with HIV-1 proteins within conserved pathways with different sizes (L = 16: red, L = 32: ble, L = 64: green). (B) The p-vales of the total nmber of predicted hman/hiv-1 interactions within conserved pathways. that we present clearly shows that the comparative network analysis of different species can provide important insights into the mechanisms of hman/hiv-1 interactions. We believe that frther stdies based on aligning the networks of varios species that are ssceptible to similar lentivirses will lead to breakthroghs in HIV research. For example, althogh chimpanzees are the hman s closest relative in natre, AIDS is rarely life-threatening to them [14]. Identifying the main reasons for this difference in HIV-1 ssceptibility may lead to the development of novel therapetics for this highly destrctive disease. Balakrishnan et al. [13] proposed a heristic way to search for alternative pathways that can circmvent HIV-intercepted pathways, whose ltimate goal is to identify potential drg targets. In a similar way, comparative network analysis may also be sed to identify alternative pathways in the PPI network, by qerying known HIV-intercepted pathways in the hman PPI network. Althogh comparative network analysis is still at an early stage and is not yet as matre as comparative seqence analysis, it can take direct advantage of the large-scale interaction measrements that have become available these days and it has the potential to generate experimentally verifiable hypotheses on the biological mechanisms of HIV-1, which may lead to the identification of better drg targets and innovative AIDS therapetics in the ftre. Methods Protein-protein interaction (PPI) networks We have obtained both the Homo sapiens and Ms mscls protein-protein interaction (PPI) networks from the open platform NATALIE 3, managed by the Knowledge Management in Bioinformatics grop of the Hmboldt-Universität Berlin. Both networks were obtained from several open databases [42 47] as

13 described in [24, 48]. The Homo sapiens network has 34, 979 interactions among 9, 695 proteins, and the Ms mscls network has 3, 116 interactions among 3, 247 proteins. The similarity between proteins in the two networks were determined based on protein seqences, protein domain information (InterPro domains) and fnctional annotations (GO annotations) [48 51]. Pairs of similar proteins in the two networks were identified based on a minimm protein identity threshold of α =.4 as in [24, 48]. Hman-HIV interaction data As mentioned in [13], there are several types of interactions between HIV-1 proteins and hman proteins, inclding direct physical interactions that are reported in the literatre, indirect interactions reported in the literatre, and interactions that have been manally annotated by experts [12, 41]. However, many HIV-1 virologists do not agree pon the majority of these interactions [13]. For this reason, we focs on the hman/hiv-1 interactome in [12] in or analysis, which has been comptationally predicted by integrating varios types of protein featres. The hman/hiv-1 interactome data can be obtained from the athors website. 4 For frther validation, we also performed similar analysis based on the crated hman/hiv-1 protein interactions in HPID [41]. Identification of conserved pathways throgh local network alignment To align the Homo sapiens and Ms mscls PPI networks, we sed the local network alignment algorithm based on hidden Markov models (HMMs) [35, 36]. Let s represent the Homo sapiens and Ms mscls PPI networks as G h = (U, D) and G m = (V, E), respectively. U = { i } and V = {v i } represent the sets of nodes, where each node represents a protein in a given network. D = {d ij } and E = {e ij } are the sets of edges, where each edge represents the interaction between the connected proteins. For the orthologos protein pairs in the Homo sapiens and Ms mscls PPI network that have been predicted based on the method in [48], we define the node similarity score s(, v) between a pair of proteins U and v V as follows: { 1, if and v are orthologos s(, v) =, otherwise. (1) The interaction reliability scores between two nodes are binary for both PPI networks. For example, the interaction score w h ( i, j ) between i and j in the Homo sapiens network is defined as: {, if interaction between i and w h ( i, j ) = j exists;, otherwise. (2) 4 oznr/hiv/hivppi.html 13

14 The interaction reliability score w m (v i, v j ) between v i and v j in the Ms mscls network is defined in a similar way. In order to find the pathways that are conserved in both PPI networks, we first search for the best matching pair of paths = L ( i U) and v = v 1 v 2... v L (v i V) in the respective networks (Fig. 1) that maximizes a predefined pathway alignment score S(, v). The pathway alignment score S(, v) integrates the similarity score s( i, v i ) between the aligned nodes i and v i (1 i L), the interaction reliability score w h ( i, i+1 ) between i and i+1 (1 i L 1), the interaction reliability score w m (v j, v j+1 ) between v j and v j+1 (1 j L 1), and the penalty for potential gaps in the alignment. We denote the nmber of nodes in a pathway as L. In this paper, we search for conserved pathways of size L = 16, 32, 64. Based on the HMM framework [35, 36], we transform the problem of finding the best matching pair of paths to a problem of finding the optimal pair of state seqences in the two HMMs that jointly maximize the observation probability of a virtal path (see Fig. 1). We se two different types of settings for finding conserved pathways, where we do not allow gaps in the pathway alignment in one setting while we allow gaps in the other setting. In general, the two setting will yield different predictions. We can find the best matching pair of paths in the given networks sing dynamic programming. For this prpose, we first define the score for the most probable pair of a sbseqence paths of length t ( L) as follows: [ ] γ(t, j, l) = max γ(t 1, i, k) + w h ( i, j ) + w m (v k, v l ) + s( j, v l ). (3) i,k Next, we find the optimal pair of paths (, v ) [ ] S(, v ) = max S(, v),v = max γ(l, j, l), (4) j,l by compting the score (3) iteratively. As discssed in [35, 36], we can add axiliary states to the HMMs that represent the PPI networks to find gapped path alignments. Instead of finding only the best matching pair of paths, we can also search for the top k path pairs by replacing the max operator in (4) and (3) by an operator that finds the k largest scores. The comptational complexity of the described dynamic programming algorithm is only O(kLM 1 M 2 ) for finding the top k pairs of matching paths, where M 1 is the nmber of edges (i.e., interactions) in G h, and M 2 is the nmber of edges in G m. Note that the comptational complexity is linear with respect to each parameter k, L, M 1, and M 2. To avoid mltiple occrrences of the same protein in the conserved pathways that are predicted by the algorithm, we incorporate a look-back step into each iteration of the dynamic programming algorithm [36]. 14

15 Extraction of random pathways In order to extract random pathways from the Homo sapiens PPI network, we performed random walks on the network starting from a randomly selected node in network G h. We randomly walk on the network to choose a random pathway, ntil the size of the pathway reaches a pre-specified size L. Dring this random walk, we avoid visiting a node that has been previosly visited, so that the extracted random pathway contains only distinct nodes. Comparison between conserved pathways and random pathways To compare the HIV-1 ssceptibility of conserved pathways with that of random pathways, we compted the following vales: (1) The nmber of proteins within these pathways that have been predicted to be intercepted by at least one of the HIV-1 proteins according to the hman/hiv-1 interactome in [12]. (2) The total nmber of predicted hman/hiv-1 protein interactions within these pathways; (3) The average HIV interaction scores within pathways. We also compted the p-vales of the estimated reslts for conserved pathways, according to the process described in the next sbsection. Finally, for GO term enrichment analysis, we sed an open sorce software called the GO::TermFinder [39]. Compting p-vales In order to evalate the statistical significance of the estimated reslts in conserved pathways, we first extract a large nmber of random pathways (3, ) from the Homo sapiens PPI network, based on random walk. For each random pathway, we also estimate the indices of HIV-1 ssceptibility (i.e., the nmber of hman proteins intercepted by HIV-1; the total nmber of hman/hiv-1 interactions, the average interaction scores among the proteins in each pathway). Baseline distribtions of different indices are estimated from these reslts. We can either model the baseline distribtions sing Gmbel distribtions [52] or simply se histograms. The latter approach was adopted in this paper. Once we have estimated the baseline distribtions, we can compte the p-vales of the estimated reslts in conserved pathways according to the estimated distribtions. Athors contribtions Conceived and designed the experiments: XQ, BJY. Performed the experiments: XQ. Analyzed the reslts: XQ, BJY. Wrote the paper: XQ, BJY. 15

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