Genecentric: a package to uncover graph-theoretic structure in high-throughput epistasis data

When two non-essential genes are simultaneously deleted, sometimes a surprising phenotype emerges compared to the phenotype of the deletion mutants of the single genes. When studying the yeast genome, often this can be quantified in terms of the growth rate of the double deletion mutant, compared to the growth rate of its component single deletion mutants, termed epistasis [1]. Recent SGA [2], dSLAM [3] and E-MAP [4] technology produces high throughput weighted epistasis values for large collections of double knockouts.

A variety of algorithmic methods have been proposed to infer functionally meaningful relationships between genes based on the structure of their epsistatic genetic interactions [5-10]. In particular, we consider the generalized “Between Pathway Model” (or BPM) as studied by Leiserson et al[5]. As discussed in [5], this involves finding pairs of sets of genes, where the sum of the epistasis values between genes in different sets, minus the sum of the epistasis values between genes in the same set, is as negative as possible. This is a generalization of an unweighted BPM model studied by Ma et al. [11] and Brady et al. [12], which was a simplification of the original BPM model introduced by Kelley and Ideker [13]. Other versions of BPMs, in different settings or criteria, have been studied [9, 14, 15].

Leiserson et al. [5] presented a randomized algorithm based on maximal graph cuts to generate these putative generalized BPMs from weighted epistasis data. They showed that the BPMs produced by their method were biologically enriched when their method was run on several different yeast E-MAP and SGA data sets [8, 16]. We now present a full implementation, Genecentric, of this algorithm that is fast, easy to use, well documented and open source. In addition, Genecentric has an extension that performs GO enrichment analysis using FuncAssociate’s web service API [17].

Genecentric implements a randomized algorithm to generate putative generalized BPMs as described in Leiserson et al[5].

Algorithm

Genecentric takes as input a file with genetic interaction data and outputs a list of pairs of sets of genes corresponding to the putative generalized BPMs. The genetic interaction data must be in a tab-delimited format where each row corresponds to a gene pairing and that pairing’s interaction score. Specifically, the first column contains the first gene identifier, the second column contains the second gene identifier, and the third column contains the interaction score.

We’ll now brielfy recap the algorithm described in Leiserson et al[5]. (Figure 1 provides a graphical representation of the algorithm.) First, the input genetic interaction data is used to create M random bipartitions, where the vertices correspond to genes and an edge between genes corresponds to its interaction score. Second, each random bipartition is transformed into a LocalMaxCut by iteratively modifying it until every vertex in the graph satisfies the following property: the sum of its edges to other vertices in the same partition is greater than the sum of its edges to other vertices in the other partition. Third, every unique gene g in the interaction data generates a bipartite subgraph (called a BPM) from this set of M bipartitions. Namely, one partition of the BPM includes g and every gene from the M bipartitions that is in the same partition as g at least C% of the time. The other partition of the BPM includes every gene from the M bipartitions that is in the opposing partition as g at least C% of the time. Finally, the set of all BPMs from all the genes is pruned, either to remove BPMs whose partite sets are too small or too large (see parameter settings, below), or to remove substantially overlapping BPMs generated from different genes g from the set.

Since a couple of the steps in the aforementioned algorithm involve many independent calculations, Genecentric parallelizes those computations automatically using the multiprocessing module included in the Python standard library. Therefore, large data sets can be used to generate BPMs in reasonable time. Genecentric was able to produce BPMs for a data set containing 1,685,210 genetic interactions in a few hours on an AMD 48 core Linux machine with default parameters. On a smaller data set (220,116 genetic interactions), Genecentric produces BPMs in under a minute on the same 48 core machine.

We ran Genecentric on the same E-MAP dataset as discussed in the Leiserson et al. paper [5], and showed that it produced comparable results (though note that results will not be 100% identical, because, as discussed above and in their paper, results wobble slightly over different randomized runs of the algorithm). We set out next to show that Genecentric with default or nearly default parameters can be run “out of the box” to produce meaningful results that corrolate well with the biological literature on other datasets as well. In particular, a recent study [18] produced an E-MAP dataset of 374 genes involved in various aspects of plasma-membrane biology, including endocytosis, signaling, lipid metabolism and eisome function. We ran Genecentric on this E-MAP dataset using all default parameters except the weights were squared, as Leiserson et al. [5] recommends for E-MAP data, and C was lowered from.9 to.8 in order to produce more BPMs (22 instead of 6). Since default parameters were used, GO enrichment was computed by FuncAssociate with a genespace consisting of only genes from the E-MAP data set. Of these 22 BPMs, 7 exhibited GO enrichment in both gene sets, according to the Genecentric FuncAssociate GO module, whereas an additional 8 exibited GO enrichment in one gene set of the BPM. These enrichment rates, while good, are still somewhat below the percentage enrichment reported for the ChromBio E-MAP dataset in [5], perhaps because the component genes in this plasma-membrane E-MAP data set are not all as well studied, and thus fewer functional annotations are yet known.

Of the 7 BPMs that exhibit enrichment in both gene sets, 6 have one set that contains the genes coding for proteins COG 5, 6, 7, and 8, and there is some additional overlap in some of the genes in these BPMs (recall that Genecentric with default pruning options will permit overlapping BPMs provided their Jaccard index is less than 0.66). Table 1 shows a list of these BPMs and corresponding GO enrichment terms. Figure 2 depicts one of these BPMs by showing edges for physical and genetic interactions between each pair of genes.

The proteins encoded by COG 5, 6, 7 and 8 constitute a structural component known of the conserved oligomeric Golgi (COG) complex, an important peripheral Golgi apparatus protein structure that has been most significantly implicated in retrograde trafficking [19] and has additional roles in supporting Golgi apparatus structure [20] and glycosylation [21]. It is a hetero-octamer consisting of two lobes, A and B, that are both comprised of four proteins, COG 1-4 for lobe A and COG 5-8 for lobe B. Recent studies have also identified COG 1 as the linking unit between the two lobes of the complex [22]. Four out of the eight COG proteins have significant homology with other organisms, including mammals, and studies have shown that mutation of COG proteins in humans can lead to a group of serious conditions known as congenital disorders of glycosylation [21, 23]. Deletions in COG 1-4 (Lobe A) in Saccharomyces cerevisiae cause severe growth defects, but COG 5-8 have been shown to be non-essential [22]. Additionally, the mutations that cause these severe growth defects are phenotypically distinct, indicating different roles for the different subunits of the COG complex [24, 25]. Other genes that occur multiple times in the same set as the COG proteins in the BPMs include PIB2, a protein that binds phosphatidylinositol 3-phosphate, involved in vesicle-mediated transport. Phosphatidylinositol-3-phosphate, together with small GTPases, is also an important factor for sorting in the endocytic pathway [26]. Other proteins were CCZ1, a protein involved in vaculolar transport and vesicle docking, ARF1, ARF3 and GCS1, where ARFs are GTPases of the Ras superfamily that regulate the formation of coated vesicles in intracellular trafficking [27, 28] are regulated by the GTPase activating protein GCS1 [29]. RIC1, a GTPase invovled in localization of trans-Golgi membrane proteins [30] and MRP8, whose function is not known, also appear.

On the opposite module of the BPMs containing COG proteins, frequently occuring genes include VPS35 and PEP8, components of the retromer complex needed for retrograde transport, as well as VPS17, a protein associated with proper vesicle formation. Additionally, the protein GOT1, which plays a role in secretory transport [31] was found, which further hints at the variable function of the COG complex and its subunits. The second module also contained the genes encoding for the ARL1, SYS1, and ARL3 proteins—which are involved in vesicle tethering at the Golgi apparatus [32]. It is interesting that, different from the datasets discussed in the Leiserson et al paper [5], a large percentage of the enriched BPMs contain the same COG complex. We don’t know if the popularity of the COG complex in our results is simply because of what annotation is known, something about the interaction of the algorithm with the distribution of the E-MAP weights, or multiple roles for the COG complex that make it especially able to compensate for multiple different biological processes.

A full list of Genecentric BPMs is provided in the Additional file 1.

We have introduced Genecentric, a package that can automatically accept a set of high-throughput genetic interaction data, and output generalized BPMs along with their enrichment values. Genecentric has several features that make using it both easy and fast:

Finally, we provided an extension to Genecentric that can perform Gene Ontology (GO) enrichment on a set of BPMs. Genecentric uses FuncAssociate’s web API to achieve this, and parameters like genespace, namespace and p-value are configurable on the command line.

Project name: Genecentric

Project home page: http://bcb.cs.tufts.edu/genecentric

Operating system(s): Platform independent

Programming language: Python

Other requirements: Python 2.6 or higher

License: GNU General Public License Version 2

Any restrictions to use by non-academics: No

This work was partially funded by the National Institutes of Health (grant 1R01GM080330 to LC).