Predicting genetic interactions with random walks on biological networks
© Chipman and Singh; licensee BioMed Central Ltd. 2009
Received: 10 July 2008
Accepted: 12 January 2009
Published: 12 January 2009
Several studies have demonstrated that synthetic lethal genetic interactions between gene mutations provide an indication of functional redundancy between molecular complexes and pathways. These observations help explain the finding that organisms are able to tolerate single gene deletions for a large majority of genes. For example, system-wide gene knockout/knockdown studies in S. cerevisiae and C. elegans revealed non-viable phenotypes for a mere 18% and 10% of the genome, respectively. It has been postulated that the low percentage of essential genes reflects the extensive amount of genetic buffering that occurs within genomes. Consistent with this hypothesis, systematic double-knockout screens in S. cerevisiae and C. elegans show that, on average, 0.5% of tested gene pairs are synthetic sick or synthetic lethal. While knowledge of synthetic lethal interactions provides valuable insight into molecular functionality, testing all combinations of gene pairs represents a daunting task for molecular biologists, as the combinatorial nature of these relationships imposes a large experimental burden. Still, the task of mapping pairwise interactions between genes is essential to discovering functional relationships between molecular complexes and pathways, as they form the basis of genetic robustness. Towards the goal of alleviating the experimental workload, computational techniques that accurately predict genetic interactions can potentially aid in targeting the most likely candidate interactions. Building on previous studies that analyzed properties of network topology to predict genetic interactions, we apply random walks on biological networks to accurately predict pairwise genetic interactions. Furthermore, we incorporate all published non-interactions into our algorithm for measuring the topological relatedness between two genes. We apply our method to S. cerevisiae and C. elegans datasets and, using a decision tree classifier, integrate diverse biological networks and show that our method outperforms established methods.
By applying random walks on biological networks, we were able to predict synthetic lethal interactions at a true positive rate of 95 percent against a false positive rate of 10 percent in S. cerevisiae. Similarly, in C. elegans, we achieved a true positive rate of 95 against a false positive rate of 7 percent. Furthermore, we demonstrate that the inclusion of non-interacting gene pairs results in a considerable performance improvement.
We presented a method based on random walks that accurately captures aspects of network topology towards the goal of classifying potential genetic interactions as either synthetic lethal or non-interacting. Our method, which is generalizable to all types of biological networks, is likely to perform well with limited information, as estimated by holding out large portions of the synthetic lethal interactions and non-interactions.
Remarkably, only 18 percent of S. cerevisiae genes are known to be essential for viability [1, 2], as determined by single gene deletions for nearly all of the predicted 6, 000 genes. Similarly, genome-wide RNAi knockdown experiments conducted in C. elegans produced non-viable phenotypes for 10% of the 18, 000 tested genes . The remaining genes that are not required for viability under laboratory conditions are termed "non-essential," though their status more likely reflects the extent to which individual genes can compensate for one another in the event of a null mutation. The concept of genetic buffering [4, 5] has received support from recent studies utilizing high-throughput methods (SGA, dSLAM) [6–10] to systematically implement double null mutations for large sets of gene pairs. One major finding of these systematic studies is the prevalence of synthetic sick or lethal (SSL) interactions. SSL interactions are revealed when two genes that are not essential for viability as single loss-of-function mutants combine to form a double mutant with a lethal phenotype.
A key finding in one of the original system-wide studies conducted by Tong et al.  is that genetic interactions tend to run orthogonal to physical interaction. In light of this observation, several recent studies have sought to model this phenomenon in the context of biological networks [11–13]. Kelley and colleagues  used probabilistic models to validate the observation that genetic interactions are often oriented orthogonally to physical interactions, and therefore can be modeled as "between-pathway" interactions. This interpretation is consistent with the theory that genetic buffering confers robustness to molecular complexes and pathways functioning in parallel. The authors also found that, in some cases, genetic interactions may overlap with physical interactions, and can therefore be modeled as "within-pathway" models. This is consistent with an earlier finding that 1 percent of gene pairs exhibiting a SSL interaction also share a physical interaction , which is 35 times more frequent than would be expected by chance. Protein complexes enriched for genetic interactions tend to indicate that a particular complex is essential, most likely due to a lack of buffering partners. Finally, Ye and colleagues  offer additional evidence supporting the notion that genetic redundancy can be interpreted at the complex level, as they use the congruence of synthetic lethal interactions, defined as the similarity in SSL partners in a genetic interaction network, to predict complex membership. A common theme developed in these studies is that genetic redundancy is to a large extent defined at the level of molecular complex, a property that can be exploited to predict novel interactions.
In addition to the aforementioned studies that used physical interaction data to model synthetic lethal interactions, recent work has demonstrated that synthetic lethal interactions can be leveraged to resolve molecular complexes [8, 14–16]. In one study, Collins et al. utilized genetic interaction data to provide finer resolution on the molecular function of 743 genes involved in various aspects of S. cerevisiae chromosome biology. The authors constructed an epistatic miniarray profile (eMAP) from an exhaustive test of pairwise interactions, from which they were able to characterize the extent to which physically interacting proteins act coherently in a common function. The results from this study suggest that genes that have been systematically tested to interact physically are more likely to form a stable complex if they share common genetic interactions. Similarly, St. Onge et al. implemented 650 double deletion experiments corresponding to an exhaustive pairings of 26 genes related to DNA repair. By measuring the fitness of the double deletion strains in the presence of DNA damaging chemicals, the authors were able to detect previously unknown functional relationships and pathway orderings . Thus, these studies collectively suggest that physical interaction data can be used to model genetic interactions, and, conversely, genetic interaction data can be leveraged to provide greater resolution to molecular complexes and pathways that have been inferred from systematic protein-protein interaction and gene co-expression data.
Despite the considerable benefits of high-throughput methods such as SGA and dSLAM, the adoption of SSL screens into the standard toolbox of molecular geneticists would impose considerable cost and time requirements. For example, in order to experimentally map out pairwise gene interactions for the S. cerevisiae genome, an exhaustive search would mandate (6, 000 × 6, 000)/2 = 18 million double null experiments. In the case of C. elegans, one would need to implement (20, 000 × 20, 000)/2 = 200 million experiments to cover all pairwise interactions. This understates the complexity of such an undertaking, as experimentalists need to account for varying culture conditions and hypomorphic alleles for essential genes. Considering these practical limitations, computational techniques that predict genetic interactions are of potential value in providing molecular biologists with leading candidates for pairwise interactions. Towards this goal, Roth and colleagues  reported success using topological information in conjunction with functional genomic information, which was used to build a decision tree-based classification system. Interestingly, it was not the functional genomic data but the 2-hop network characteristics that conferred the strongest predictive power. 2-hop network motifs capture the relationship between a pair of genes, e.g. A-B, and a third gene, C. In this example, genes A and B share a physical interaction, while genes A and C are synthetic lethal. The 2-hop scheme would suggest that genes B and C might also be synthetic lethal. Building on this concept, we apply random walks on biological networks to expand genome coverage and prediction accuracy. Furthermore, we incorporate SSL interactions as well as all experimentally validated non-interactions into our algorithm for measuring topological relatedness, resulting in increased prediction accuracy. Our method is capable of detecting SSL relationships for both the "between-pathway" and "within-pathway" topologies (see "Approach"). We report considerable performance gains in predicting SSL gene interactions as characterized by ROC curves.
Our technique is initiated by performing random walks on the individual biological networks, producing proximity matrices for each of the networks. Subsequently, the proximity matrices are combined with the genetic interaction data during the procedure for measuring the topological relatedness between two genes, which is run separately on both the synthetic sick or lethal genetic interaction dataset and the dataset of experimentally tested non-interactions. As a result of this procedure, there are two variables for each biological network (SSL interactions and non-interactions), which are ultimately incorporated into the decision tree classifier as a feature vector to predict genetic interactions.
The random walk procedure with restarts is a computationally efficient method to profile the neighborhood of a node . A biological network, G, is represented by G = (V, E), where V represents the nodes (genes) and E represents the edges (significant linkages between genes). The restart node, s, takes on a restart probability, c = 0.2, and the procedure is run separately for each node in the biological network. Ultimately, V and E are translated into a column-normalized proximity matrix, P, which is subsequently used to solve for the stationary vector . The stationary vector represents the steady-state distribution of the neighborhood for a particular node. An overview of the procedure is provided below.
Input: The biological network G = (V, E);
a start node s;
restart probability c;
Output: The proximity matrix P;
Let (V) be the restart vector with value 0 for all of its entries except a 1 for the entry denoted as node s;
Let A be the column normalized adjacency matrix as defined by the edge matrix, E;
Initialize (V) = (V);
*Solve for: ;
*The stationary vector can be obtained by either solving for the dominant eigenvector or running iteratively until convergence. .
Algorithm for measuring topological similarity
We used version 3.5.7 of the Weka  machine learning software to classify gene pairs as either interacting (SSL) or non-interacting. Specifically, we used the J48 decision tree implementation provided with the package. We applied a 5-fold, stratified cross-validation scheme whereby four fifths of the instances are used for training and the other one fifth of the data is held out for testing (see above).
Scoring of gene pairs
Each gene pair is assigned a probability according to the leaf to which it is directed. Each leaf in the decision tree is associated with a probability according to the ratio of interacting pairs versus the total number of gene pairs assigned to that leaf during the training process. In order to generate ROC curves, we varied the threshold probability associated with the "SSL/interacting" class by a factor of 0.0001 over a range of 0 to 1, thereby generating 10, 000 data points for each ROC curve.
Results and discussion
We compared the performance of our random walk-based method to the leading methods of Wong et al.  and Zhong et al. . We note that while other existing studies have successfully modeled genetic interactions [11, 13], these techniques are not optimized for predicting novel interactions and are therefore not incorporated into our performance measurements. We first offer a comparison of the random walk method against the two established methods. Subsequently, for the random walk method, we show the predictive ability of each of the individual datasets in both S. cerevisiae and C. elegans, the added value provided by non-interaction data, and the robustness of our method under conditions where varying levels of information are held out. The performance gain associated with our method is present in both S. cerevisiae and C. elegans.
Comparison to established methods
Integrating the biological networks
Non-interaction data improves performance
Performance as a function of available information
In addition to measuring the area under the ROC curves, one may gain insight into the relative power of the respective methods by quantifying classification performance with varying levels of information, where the amount of "information" represents the fraction of interactions and non-interactions that are utilized by the procedure for measuring network relatedness. For example, in the case where 20% of the information is incorporated into the algorithm for measuring topological similarity, 4 out of 5 instances will be included in the algorithm.
Controlling for biases in the genetic interaction datasets
The performance of the Zhong et al. classifier was relatively weak compared to either of the two methods utilizing network topology. We suspect that the approach of Zhong et al., which uses Bayes' formula to derive a likelihood ratio to score gene pairs for each piece of evidence, would be better suited for predicting general functional relationships between genes. Indeed, Lee et al.  recently published work using a very similar framework to predict functional similarities between gene pairs. However, in contrast to Zhong et al., the authors used GO functionality as their training data, of which there is considerably more information that is better suited for measuring the degree to which proteins may function coherently. And we reiterate that, for the purpose of predicting genetic interactions, the random walk method offers the advantage of combining genetic interaction data with information regarding functional network topology.
While this study focuses on predicting genetic interactions, using random walks as a method for capturing properties of biological networks may be applied to other areas of bioinformatics. One potential application concerns the prediction of novel transcription factor-gene interactions, which was recently implemented using a 2-hop scheme . Additionally, our findings will hopefully encourage the reporting of non-interactions for all studies in reverse and forward genetics. We found that non-interactions considerably improve the performance of our classifier, and these gains represent a lower bound on the potential benefit, as non-interaction data was not available for some of the studies.
We presented a method based on applying random walks to biological networks to capture aspects of network topology that can be used to classify potential genetic interactions as either synthetic lethal or non-interacting. Our method, which is generalizable to all types of biological networks, is likely to perform well with limited information, as estimated by holding out large portions of the SSL interactions and non-interactions.
We chose to test the performance of our method on two well-studied model organisms, as it allows testing for consistency across organisms and their respective biological networks. The S. cerevisiae dataset is composed of 3 networks from GO, PPI and SSL interaction data. Co-expression, PPI, SSL, human homologs and yeast homologs comprise the C. elegans study (Table 1).
Genetic interaction data
Data on synthetic sick or lethal (SSL) interactions were aggregated from several studies. For S. cerevisiae, we collected 12, 397 synthetic lethal interactions from the 2.0.31 version of the BioGRID database . In addition to these interactions, we collected 9, 472 synthetic sick or lethal interactions from the Collins et al.  study. Note that this study provided a scoring matrix from which we counted scores that were < -3 as SSL. We also collected 97, 450 pairwise interactions that scored > 0, which we categorize as non-interactions. 563 SSL interactions and 17, 498 non-interactions were collected from a study conducted by Davierwala et al. . Lastly, we obtained 611, 509 non-interactions from the Tong et al.  study, for which the SSL interactions are already included in the BioGRID database.
For C. elegans, we obtained 1, 246 SSL interactions and 3, 771 non-interactions from the Byrne et al. study , which used RNAi knockdown to test for synthetic sickness or lethality. Similarly, Lehner et al.  generated 338 SSL interactions and 57, 306 non-interactions, also via RNAi knockdown. Finally, we incorporated 2, 279 hand-curated genetic interactions from wormbase version WS190. In total, there were 3, 863 SSL interactions and 58, 579 non-interactions for C. elegans.
Protein-protein interaction data
For S. cerevisiae, we used the high-confidence protein-protein interaction dataset generated by Batada et al. , which includes 9, 857 interaction pairs with representation from 4, 008 different genes. The authors produced the dataset by taking the intersection of multiple high-throughput protein interaction experiments. Specifically, the authors required that protein-protein interactions be present in two distinct experiments measured using two different experimental techniques (e.g. yeast two-hybrid, tandem mass spectrometry). Consequently, at the expense of lower coverage, we reduce the potentially negative impact of false positive protein-protein interactions on our classification scheme.
For C. elegans protein-protein interactions, we used the worm interactome  dataset, which covers 1, 371 interactions between 1, 136 proteins.
Homologs of C. elegans proteins
For C. elegans, we incorporated homologs of worm genes that are known to interact in other organisms (also termed "interologs"). These datasets were procured by Marcotte and colleagues . In total, there are 30, 098 interactions between 3, 145 genes of H. sapiens homologs and 56, 193 interactions between 2, 627 genes of S. cerevisiae homologs.
Co-expression network of C. elegans genes
For the co-expression network, we again included data procured by Marcotte and colleagues . The co-expression network prepared in their study includes 287, 130 interactions for 14, 491 genes.
Gene Ontology data for S. cerevisiae
Gene Ontology data  for S. cerevisiae was obtained from the project website. In order to construct a gene network for the GO data, we flattened out the information into pairwise interactions using the "has a" relationship rule implemented by Marcotte and colleagues . This produced a dataset of 66, 174 pairwise interactions with representation from 3, 515 genes.
Implementation of existing methods
We implemented the 2-hop characteristics from the Wong et al. method as described in the manuscript, which were subsequently incorporated into Weka's J48 decision tree classifier. We opted to exclude the functional information for two reasons: Figure 1 from Wong et al. indicates that the 2-hop characteristics provide nearly all of the predictive power, while the predictive ability of the functional information was very limited. Secondly, if desired, the random walk method can be complemented with other types of information, just as the 2-hop characteristics were in the Wong et al. study. In summary, both the random walk and 2-hop methods were applied to the same datasets, trained via 5-fold cross-validation with the aforementioned training sets, and scored with a decision tree classifier.
Zhong et al. method
AS and KC designed the experiment. KC implemented the software and carried out the experiments. Both authors read and approved the final manuscript.
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