Network-Based Disease Candidate Gene Prioritization: Towards Global Di usion in Heterogeneous Association Networks

Abstract

Disease candidate gene prioritization addresses the association of novel genes with disease susceptibility or progression. Networkbased approaches explore the connectivity properties of biological networks to compute an association score between candidate and diseaserelated genes. Although several methods have been proposed to date, a number of concerns arise: (i) most networks used rely exclusively on curated physical interactions, resulting in poor coverage of the Human genome and leading to sparsity issues; (ii) most methods fail to incorporate interaction con dence weights; (iii) in some cases, relevance scores are computed as local measures based on the direct interactions with the disease-related genes, ignoring potentially relevant indirect interactions. In this study, we seek a robust network-based strategy by evaluating the performance of selected prioritization strategies using genes known to be involved in 29 di erent diseases.

Keywords

• protein-protein interaction
• network
• random walk
• disease candidate genes
• prioritization

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Biomarkers play a crucial role in modern medical practice as a means of improving accuracy in diagnosis, prognosis and treatment. In particular, research has been actively devising associations of novel genes with disease susceptibility or progression, relying on high-throughput technologies and the proliferation of accessible resources of biological data to enable large-scale genome-wide studies.

Most computational methods proposed for disease gene prioritization aim to identify putative candidates based on their similarity with genes known to be involved in the occurrence of a particular phenotype, according to: intrinsic properties, functional annotations, coherent transcriptional responses via expression data analysis, orthologous relations with genes from model organisms or even co-occurrence in the literature [22]. Alternative strategies adopt a systemic approach and explore the topology of biological networks, including protein-protein interactions, regulatory data or metabolic pathways. These approaches rely on the assumption that genes co-occurring in a particular network substructure or interacting tend to participate together in related biological processes to identify novel genes based on their linkage with the known disease genes [22].

Integrative network-based analysis has been addressed [ 8,11,15,16,20,23,26 ], combining knowledge from distinct resources in association networks to unravel novel disease genes. However, most of these approaches rely solely on physical interactions [ 8,23 ], potentially inferred via orthologous relations with model organisms [26], often resulting in insu cient coverage of the Human genome. Others include additional interactions predicted from coexpression, pathway, functional or literature data, but still devise sparse networks [ 11, 15 ]. Although the risk for false positive interactions may rise, the integration of knowledge from heterogeneous sources generates denser networks which tend to be less biased toward a particular evidence, more robust to noise and thus able to perform better in the prioritization task [16].

Network-based prioritization methods further di er in how they de ne the ranking of the candidates from the known disease-related genes. Local measures are usually computed based on the direct links or shortest paths between the candidates and the disease-related genes [15, 16], while global strategies di use or smooth a disease-related signal through the network. In this work, we evaluate whether the latter should be preferred over the former, as the inclusion of indirect associations is able to compensate for missing linkage, ultimately mitigating sparsity and \small world" e ect issues [20], and global similarities have recently been shown to outperform local measures [15].

Random walks or di usion kernels arise as natural candidates for the diffusion approach and their application to prioritization has been proven e ective [ 6, 8, 15, 23 ]. Not only they compute fast using iterative methods, even for large networks [ 6 ], they are also able to straightforwardly establish a ranking of the candidates based on the global connectivity of the network. Nevertheless, some of the proposed methods [ 8, 15 ] ignore or fail to incorporate weights expressing the con dence on the evidence of every particular association [16]. Furthermore, their scores are based on the steady-state probability obtained after a large number of iterations or upon convergence. In this study, we assess the claim that limited di usion is usually su cient for ranking purposes [ 9, 10 ] and on our intuition which leads us to expect the prior knowledge to be somehow lost or of very little importance to the ranking after di using to a large extent.

Throughout this paper, we address the aforementioned topics by analyzing the performance of di erent prioritization strategies in three case studies: (i) Integrative heterogeneous protein association network vs integrative proteinprotein physical interaction network (PPPIN); (ii) Global ranking measure vs local ranking measure; (iii) Con dence weights, degree of di usion and parameter variation.

Methods

A protein-protein association network can be described as a weighted undirected graph, a special case of a weighted directed graph, de ned as G = (V; E), where V is the set of vertices and E is the set of edges. Each vertex in V and edge in E correspond to a gene and an association between two genes, respectively. Let A and D denote the adjacency and diagonal matrices of G, respectively. Auv is the weight w(u; v) of the edge (u; v) between source u and target v. Also, Duu = P(u;v)2E Auv; 8u 2 V , that is, the sum of the weights of the edges for which u is the source. Prioritizing disease candidates thus formulates as obtaining a ranking on V given a set S 2 V of seed genes. For the local scoring scheme Endeavour's measure was used [ 2 ]. As global network-based strategies, the PageRank with priors and Heat Di usion random walks were applied: an initial signal expressing the relevance of the genes in the context of the disease in the form of a preference vector, p(0), is di used over the network by performing a limited number of iterations, N . 2.1

Endeavour's Measure: Intersection of Interactors Endeavour computes a local network-based measure, whereby the score of each gene is computed as the overlap between the sets of genes interacting with the seed genes and those interacting with the candidate gene itself [ 2 ]: Sv =

X (u;v)2E intSeeds(u) intSeeds(u) = 1 , if 9z 2 S : (u; z) 2 E 0 , otherwise 2.2

Heat Di usion and PageRank with Priors Heat Di usion is a discrete approximation of the heat kernel [28] rst introduced in [ 9 ], in which the rate of di usion is controlled by a non-negative parameter, the heat di usion coe cient t. The iterative equation is given by p(i+1) = v 1 t N p(i) + t v N

X (u;v)2E p(i) u

Auv : Duu PageRank with priors is an extension of the original PageRank algorithm to consider the original probability distribution of the scores [25]. A parameter , called \back probability" expresses the probability of jumping to the initial node at each iteration. The iterative equation is p(i+1) = v p(0) + (1 v )

X

Results

Evaluation sudies were performed using Human data from the STRING database [ 12 ] and a PPPIN from Entrez Gene [ 1 ] as representatives of protein-protein heterogeneous association and physical interaction networks, respectively. 620 genes known to be related with 29 diseases were used as prior knowledge to prioritize candidates in a leave-one-out cross-validation scheme. 3.1

Data and Preprocessing Networks The STRING database [ 12, 18 ] integrates physical interactions and predicted associations based on knowledge obtained from heterogeneous sources of transcriptional, functional, metabolic, literature and orthology data. For a fair comparison with Endeavour, we downloaded and parsed version 7.1 of STRING [18], including evidences from MINT [ 7 ], HPRD [19], BIND [ 4 ], DIP [27], BioGRID [ 5 ], KEGG [ 13 ] and Reactome [24] databases. Associations from STRING v8.2 [ 12 ] were also retrieved to assess to which extent the additional knowledge integrated from IntAct [ 14 ], PID [21] and GO [ 3 ] protein complexes would improve the prioritization performance relative to the previous release. A PPPIN was downloaded from the NCBI Entrez Gene FTP repository [ 1 ]. 130797 Human interactions were selected from 448534 entries, for which both interactant genes were tagged with tax ID 9606. From these, 4611, 51275 and 74911 were originally from BIND [ 4 ], BioGRID [ 5 ] and HPRD [19], respectively. Genes' identi ers followed Entrez Gene nomenclature. Preprocessing of these networks involved ltering redundant edges and devising an explicit representation of a directed graph. In the case of the STRING releases, original weights were used to express the con dence of every association, while in the PPPIN all edges were attributed weight 1. STRING v7.1 contained 16050 genes and 698534 unique associations. STRING v8.2 covered 17448 Human genes with 1256016 non-redundant associations. Finally, the PPPIN had 47873 physical interactions between 10175 genes. Seed sets 620 disease genes were selected from the OMIM [17] database spanning 29 disease-speci c sets, with an average of 21 genes per set. As genes were identi ed according to Ensembl nomenclature, the seeds could be directly used with STRING. For the PPPIN, however, we performed a conversion between Ensembl and Entrez Gene identi ers. A mapping was parsed from a le downloaded from the NCBI Entrez Gene FTP repository [ 1 ] and used to generate the corresponding seed sets using Entrez Gene names. Additionally, we ltered the genes absent from at least one of the networks or for which the conversion between Ensembl and Entrez did not succeed. In total, 94 seed genes were lost (14 with no conversion, 80 absent from the PPPIN). A single occurrence of a gene with several Entrez aliases happened. In this case, only the alias present in the PPPIN was kept. For validation purposes, seed sets containing randomly selected genes were generated. The number of seeds in each set was randomly chosen in the range [5; 100] and the genes were randomly selected from the Human STRING v8.2 network. 546 genes were retrieved. 3.2

Evaluation Measures and Experimental Setting Evaluation measures Ideally, in a leave-one-out cross-validation scheme, we would expect the prioritization strategy to rank the left-out gene known to be related with the disease at the top. Under this assumption, we assess the performance of the scoring methods overall and per disease based on four evaluation measures: the number of left-out genes ranked in the top 10 and 20 positions, the Area under the ROC curve (AUC) score, and the mean average precision.

For a given combination of di usion parameter and number of iterations N , n rankings are generated (one per left-out gene). The AUC score is given by SAUC ;N = n

Pn r(N) k=1 mk(kN) ; n where r(N) is the ranking position of the kth left-out gene in the kth ranked list k and m(kN) is the number of ranked genes in the kth list.

Mean average precision (MAP) is an evaluation measure that combines precision and recall. Essentially, MAP averages the precisions computed by truncating the list after each of the relevant entities is found. Only one relevant entity must be found, the left-out gene. Thus, precision at rank r is either 0, before it has been found, or 1r . Moreover, in our setting the ranked lists contain equal number of genes, allowing us to simplify our MAP score for n lists with the same size to: SMAP ;N =

Pn 1 k=1 r(N)

k n Experimental setting In each validation run, one di erent gene was deleted from the set of seed genes and added to 99 randomly selected candidate genes. A ranking method was then applied to compute a score for every gene in the network. Finally, the ranking of the 100 candidate genes was de ned according to the retrieved scores. In the case of the Heat Di usion, the scores of the seed genes were initialized to 1. For PageRank, an initial seed score of 1=jSj was used. Performance was assessed by computing AUC and MAP scores, and counting the number of left-out genes ranked in the top 10 and top 20 positions, both overall and per disease. We sought the best performance of each method using several combinations of parameters. Heat di usion coe cients t and back probabilities of 0.1, 0.3, 0.5, 0.7 and 0.9 with 2, 5, 10, 15 and 20 iterations using STRING and 2, 5, 10, 20, 100 iterations using the PPPIN were tried. In the case studies, results are shown only for the parameter settings which achieved the best performance in each case. We further ranked the randomly generated seed sets using the leaveone-out cross-validation in STRING v8.2 to assess whether the Heat Di usion method was able to take advantage of the information contained in the seed sets to improve the identi cation of the left-out seeds. Overall, AUC and MAP scores of 0.501 and 0.05 were achieved and only 57 and 92 genes were ranked in the top 10 and 20 positions. Similar results were obtained per seed set (data not shown), in accordance with what would have been expected for random seed sets. 3.3 Heat Di usion and PageRank with priors achieved similar results in both networks (Table 1). For this reason, we abstain ourselves of comparing the results of both random walks, considering the results equivalent when applied to the same network. Throughout this section, we will always refer to one of them as a representative of a global measure. A brief description of the prioritization performances obtained for each case study follows.

Method Network Parameters AUC MAP TOP 10 TOP 20 #BRM #BRN HeatDi usion STRING8 t = 0:3; N = 10 0:962 0:711 484 502 26% 68% PageRank STRING8 = 0:7; N = 2 0:961 0:693 485 502 20% 69%

HeatDi usion PPPIN

PageRank PPPIN Global measure vs Local measure A network-based global ranking was obtained using the Heat Di usion method with t = 0:3; N = 10, while Endeavour [ 2 ] was used to score the genes using its local measure. Both rankings were based on STRING v7.1, the version included in Endeavour. Overall, the random walk global measure outperformed the local interaction overlap in all evaluation measures (see Table 2), that is, the higher number of left-out genes was ranked on the top positions, also achieving better ranks in general, using the latter.

Method Network AUC MAP TOP 10 TOP 20

HeatDi usion (t = 0:3; N = 10) STRING v7.1 0:942 0:643 536 569 Endeavour STRING v7.1 0:806 0:326 393 464

Regarding the AUC scores per disease (see Table 3), the Heat Di usion method outperformed Endeavour in all diseases except Ehlers-Danlos syndrome (0.944 opposed to 0.948, respectively). This was also the only disease for which the number of genes ranked in the top 20 positions was higher using the local measure (Endeavour was able to rank one more gene in the top 20). However, the MAP score was better for the Heat Di usion method and, in fact, 9 of the 10 seed genes ranked in the top 10 positions by both methods scored higher using the global measure.

For the remaining diseases, Heat Di usion was always able to rank the same or a higher number of genes in both the top 10 and the top 20 positions. Regarding the MAP scores, Heat Di usion outperformed Endeavour in every disease and was able to rank all genes of both amyotrophic lateral sclerosis and Usher syndrome in the rst position.

Disease

Alzheimer's disease

amyotrophic lateral sclerosis anemia breast cancer cardiomyopathy cataract

Charcot-Marie-Tooth disease

colorectal cancer deafness diabetes dystonia Ehlers-Danlos syndrome emolytic anemia epilepsy ichthyosis leukemia lymphoma mental retardation muscular dystrophy myopathy neuropathy obesity

Parkinson's disease

retinitis pigmentosa spastic paraplegia spinocerebellar ataxia

Usher syndrome

xeroderma pigmentosum

Zellweger syndrome

Protein-Protein Associations vs Protein-Protein Physical Interactions Heat Di usion achieved better performance using STRING v8.2, with AUC score 0.962, opposed to 0.862 using the PPPIN (see Table 1). Furthermore, STRING enabled to rank more than 90% of the genes in the top 10 positions, while using the PPPIN less than 60% were in top 10. In a one-to-one comparison, Heat Di usion ranked 68% of the genes better using STRING, while only 11% of the ranks were better using the PPPIN. Table 4 compares the results obtained for the Heat Di usion method using STRING v8.2 with PageRank with priors in a PPPIN, one of the best performing strategies in [ 8 ], per disease.

Disease

Alzheimer's disease

amyotrophic lateral sclerosis anemia breast cancer cardiomyopathy cataract

Charcot-Marie-Tooth disease

colorectal cancer deafness diabetes dystonia Ehlers-Danlos syndrome emolytic anemia epilepsy ichthyosis leukemia lymphoma mental retardation muscular dystrophy myopathy neuropathy obesity

Parkinson's disease

retinitis pigmentosa spastic paraplegia spinocerebellar ataxia

Usher syndrome

xeroderma pigmentosum

Zellweger syndrome

Regarding the disease-speci c scores (see Table 4), the lowest AUC (and MAP) values for the combination Heat Di usion and STRING v8.2 were of 0.926 (0.727) for mental retardation, and 0.930 (0.476) for lymphoma, which are still good results. For ve diseases, namely amyotrophic lateral sclerosis, EhlersDanlos syndrome, spastic paraplegia, Usher syndrome and Zellweger syndrome, the heterogeneous association network approach was actually able to rank all the seed genes in the rst position of the ranking. On the other hand, the PageRank di usion in the PPPIN achieved AUC scores above 0.9 only for two diseases: colorectal cancer with 0.912 and xeroderma pigmentosum with 0.98. The lowest AUC and MAP scores were obtained for amyotrophic lateral sclerosis (0.53 and 0.028) and spastic paraplegia (0.49 and 0.083). The PPPIN strategy could not rank any of the seed genes for amyotrophic lateral sclerosis in the top 10 positions and only one was identi ed in the rst 20. Also, only one gene out of the 5 seeds for spastic paraplegia was ranked in the top 10/20. In this case, the performance for both diseases is comparable to the one obtained using the random seed sets (data now shown).

Con dence weights, number of iterations and di usion rate We assessed the contribution of STRING's weights expressing the degree of con dence in the associations between genes to the performance of the prioritization method by di using the initial preference vector using the ltered disease-speci c seed sets on the network after setting all associations' weights to 1. Although the resulting AUC and MAP scores (0.957 and 0.662) were not substantially di erent from the ones obtained using the con dence weights (0.962 ans 0.711), they actually re ected in less 9 genes ranked in the top 10 (data not shown). Overall, the number of genes in the top 20 was the same, with slight variations per disease. From the ve diseases achieving maximum performance in the di erentially association weighted setting, only for Ehlers-Danlos syndrome, spastic paraplegia and Zellweger syndrome these results could be maintained.

In both random walk approaches, the best results were achieved using a limited number of iterations. STRING v8.2 provided consistent and stable performance when varying the number of di usion steps. On the PPPIN, the best ranking was always obtained using two iterations. It would then stabilize for larger numbers of steps, although measuring considerably lower in the evaluation, since it was never able to rank more than 289 or 346 genes - out of 526 in the top 10 and top 20, respectively.

Regarding the parameter controlling the rate of di usion, the Heat Di usion method delivered quite similar performance for the set of heat coe cients tried: in STRING v8.2, resulting in AUC scores ranging from 0.960 to 0.962 for each di usion coe cient, considering equal number of iterations; in the PPPIN, AUC scores ranging between 0.859 and 0.862 with 2 iterations, N = 2, and between 0.766 and 0.771 using 5, 10, 20 and 100 iterations.These results indicate its robustness to variations in this parameter. For PageRank with priors, the impact of the back probability value was not neglegible. For the lowest back probabilities (0.01 and 0.05) the scores were unstable leading to considerable performance variations, even using STRING v8.2. For = f0:1; 0:3; 0:5; 0:7; 0:9g, the PageRank AUC scores in STRING v8.2 varied between 0.936 and 0.961 considering the results obtained using the same number of iterations. In the PPPIN, PageRank obtained AUC scores between 0.859 and 0.861 using 2 iterations and ranging between 0.758 and 0.775 using 5, 10, 20 and 100 iterations. 4

Conclusions

Prioritization results con rmed our hypothesis that networks integrating gene associations retrieved or predicted using data from heterogeneous sources should be in general more informative and potentially able to perform better in the identi cation of genes associated with a given disease when compared to networks containing only physical interactions. Advantages of the former are supported by three key observations: (1) associations derived from the combination of several types of evidence should be more reliable and accurate; (2) heterogeneous data integration enables a better coverage of the genome and larger network density, confering robustness to noise; (3) con dence weights can be devised in order to di erentiate associations and mitigate the impact of false positive associations, particularly when based on a limited number of sources.

Nevertheless, our analysis shows that heterogeneous association networks do not present su cient guarantee for maximum performance by themselves. In fact, the network-based score measuring the degree of relatedness of each candidate gene with a given disease based on a set of known disease-related genes proved to play a major role. Essentially, based on the results we could conclude that in comparison to neighborhood-limited scores a network-based measure able to capture global connectivity properties by considering indirect associations between genes is not only (1) more robust, as it compensates for the sparsity related to direct associations and tackles the \small world" e ect issue; but also (2) more informative, deriving a score based on a systemic view of the interactome. This claim has also been previously hinted at in [15, 16].

Propagation schemes tested in the computation of global network-based scores di used an initial preference vector expressing the distribution of the known disease-related genes through the network using random walks. These methods compute fast using iterative procedures, even for large networks. Furthermore, we could verify that in the context of prioritization in association or physical interaction networks the maximum performance can be achieved using only a limited number of iterations. Heat Di usion and PageRank with priors delivered high quality results and achieved similar performance under appropriate parameter settings, supporting the claim of equivalence [ 8, 25 ] for other approaches of the same kind, namely HITS with priors and K-Step Markov. The importance of con dence weights was inconclusive, as the di erence in performance exhibited by our experiments was residual. We believe, however, that appropriate association con dence weights may improve accuracy of network-based prioritization results.

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