Recent papers 234 have used the yeast-two-hybrid technique and literature surveys to identify and assemble over 7000 non-redundant protein-protein interactions among more than 4000 proteins. While two-hybrid screens efficiently identify fusion proteins that are able to interact, the biological significance of the interaction for native proteins acting in vivo generally requires verification, because the technique is susceptible to a high rate of false positives 8. To assess the possible contribution of false-positive protein-protein interactions to the combined interaction dataset, we analyzed the connectivity of each protein and found that a small fraction of proteins had a very high number of interactions (highlighted in red, Fig. 2). With these highly connected proteins included in our data set, NetSearch generates 17 million candidate signaling pathways of length seven or less, 95% of which involve one of these twenty-two highly-connected proteins. We excluded the highly interacting proteins from the interaction dataset based on their nonspecific inclusion in the predicted pathways and evidence of their susceptibility to systematic error. This yielded an interaction map that contains 5560 interactions among 3725 proteins, an average of three interactions per protein.

Using the NetSearch algorithm, this protein interaction network was queried for paths up to length eight that begin at membrane proteins and end at transcription factors. The search generated approximately 4.4 million candidate pathways of length eight or less whose biological plausibility was assessed using gene expression data.

To score the pathways, we first used a k-means algorithm to cluster all yeast genes into clusters based on their expression profiles. NetSearch then assigned each pathway a statistical score 10 according to the number of pathway members that clustered together. For example, a path with six members in one cluster would score higher than a path that only had five members in that cluster. Cluster size influenced path scoring such that a path that had three members from a cluster of 30 elements would score higher than a path that had three members from a cluster of 100 elements. Also, a path with four elements in one cluster and three elements in a second cluster would score higher than a path that had four elements in cluster one, but no more than two elements in cluster two.

Pathways were scored using NetSearch's 'sumprob' scoring metric: Assuming N proteins total and a partitioning of proteins into k clusters C₁, C₂,...C_k, with N₁, N₂,...N_k members, respectively, and a pathway p of L proteins p₁→p₂→...→ p_L, where c_p(i) = number of proteins in p in cluster C_i, the sumprob score is computed as follows:

prob_p(i) scores a pathway for a cluster C_i such that pathways which are more concentrated in C_i have higher scores. The summation in prob_p(i) computes the cumulative hypergeometric probability of pathway p containing c_p(i) or more members of C_i. prob_p(i) assesses co-clustering of pathway members in the single cluster C_i. sumprob(p), the sum of prob_p(i) values over all clusters for which c_p(i) >= 2, is a simple measure of co-clustering across the entire collection of available clusters. The rationale for the restriction c_p(i) >= 2 is that without it a pathway could get a high score simply from having single members in one or more rare clusters, in which case the score would no longer reflect co-clustering.

The exact composition of paths discovered using NetSearch depend on the parameters used in path drawing and path scoring. To ensure that NetSearch reproducibly generates statistically significant, biologically plausible paths, we combinatorially varied every parameter value in the path-drawing and path-scoring algorithms, and selected parameter combinations that generate the most statistically significant pathways. Statistical significance was measured by drawing pathways from membrane proteins to DNA-binding proteins through the experimentally determined protein-interaction map (henceforth called "real pathways") and comparing these pathways with pathways drawn through control interaction maps that were created by randomizing all pairwise interactions in the original dataset. (The randomization procedure was performed three times and statistics were calculated on the average output of these runs. Paths produced using these interaction maps are henceforth referred to as "random pathways"). We ultimately chose parameters that maximized the number of high-scoring pathways produced with real interactions, while minimizing high-scoring pathways from the randomized interactions.

The parameters we varied included the number of clusters into which the genes were grouped, the microarray expression datasets used in clustering, the maximum path length, and the scoring metric. Expression data were clustered into 12, 25, 50, 100 and 250 clusters, and NetSearch best discriminated between real pathways and random pathways when genes were grouped into 25 clusters. Three S. cerevisiae expression datasets were examined individually, including the "Compendium" set, composed of expression profiles in response to 300 diverse mutations and chemical treatments 5; the "MAPK" set, composed of 56 conditions chosen to probe the behavior of MAPK signal transduction 6; and the "Cell Cycle" set, composed of 77 conditions relevant to the cell cycle 7. Combinations of these datasets were also examined, for a total of five different sets that allowed us to compare the utility of data that probes specific biological processes, such as MAPK signaling or the cell cycle, and that which probes the state of the cell more broadly, such as the Compendium set and the combined sets. The composite data set that combined all three individual sets (for a total of 433 conditions) provided the best discrimination between real pathways and random pathways, although the other sets performed comparably.

The final input parameter that required evaluation was the maximum path length allowable for NetSearch paths. While short path lengths risk omission of key path members, longer path lengths increase the likelihood of including false-positive interactions. As a first step towards determining the optimal maximum path length, we examined the path lengths connecting every possible pair of the 3725 proteins in the interaction dataset, regardless of subcellular localization. The minimal path length between any two proteins chosen at random contains on average 7.4 members. Secondly, we examined the fraction of pathways with high coclustering ratios for various path lengths. Consistent with our finding that the average path length between any two proteins is 7.4, this fraction peaks at eight, which we set as our maximum, unless otherwise noted.

Using a maximum path length of eight, and 25 gene clusters from 433 conditions 567, NetSearch generated ~4.4 million pathways each for the real and randomized protein interaction datasets. From the experimental ("real") data, 4059 pathways had a coclustering score ≥ 16 (Fig. 3). At this cutoff, randomized interaction data produced on average only ~1% this number of pathways (32 pathways, P = 7 × 10^-6). However, we emphasize that NetSearch selects paths based on their rank relative to all paths between selected starting and endpoints. The absolute score depends on the particular expression data set used, and varies from network to network depending on the degree of coregulation in the cell under the conditions tested in the expression data.

The signaling network models generated by NetSearch for the pheromone response, cell wall integrity and filamentation pathways are depicted in Fig. 4. In each case, the starting protein (receptor, depicted in blue) and ending protein (transcription factor, depicted in red) were selected as inputs, and NetSearch draws all possible paths between these points. The size of each vertex is proportional to the sum of scores of the paths in which that protein is found, providing a useful visual clue to the potential importance of a protein in the given network. Comparison with Fig. 1 shows that NetSearch reproduced many of the essential elements of these MAPK pathways, while providing a detailed account of the experimentally determined interconnections among network elements. Of the three network models, the one generated for the pheromone response pathway originating at Ste3p (Fig. 4A) exhibited the highest co-clustering scores. Every protein NetSearch included in this network model has a description in the Yeast Proteome Database (YPD) 9 consistent with a known or plausible role in mating. Of the nineteen proteins we have included in our depiction of the pheromone response network, eighteen are annotated as playing a role in the fungal cell differentiation by MIPS 10. The probability that this selection would have occurred by chance was calculated with the hypergeometric distribution was found to be P = 5 × 10^-24. Our model does differ in several respects from the canonical pheromone response pathway depicted in Fig 1. It includes more members of the heterotrimeric G protein complex, including the alpha, beta, and gamma subunits, the GDP-GTP exchange factor, and the GTPase-activating protein (Gpa1p, Ste4p, Ste18p, Cdc24p, and Sst2p, respectively). It includes Far1p, a protein necessary for pheromone-induced cell cycle arrest in G1 11, Mpt5p, a protein necessary for recovery from cell cycle arrest 12, and Bem1p and Sph1, both of which are necessary for establishment of cell polarity during shmooing and budding 1314. In our protein-interaction map there is no direct interaction between a pheromone receptor (Ste2p or Ste3p) and any component of the heterotrimeric G protein complex (Ste4p/Ste18p/Gpa1p), so NetSearch drew indirect paths through Akr1p, a known inhibitor of signaling in the pheromone pathway 15. The predicted network does not include the GTPase Cdc42p (paths were instead drawn preferentially through its cofactor Cdc24p, which physically interacts with Ste4p) or Ste20p, because of missing interactions in the protein-interaction map.

Fig. 4B depicts the pheromone response network at several different score cutoffs, and demonstrates how higher co-clustering score cutoffs reduces the complexity of the protein-interaction map. NetSearch detects 354 paths of length eight from Ste3p to Ste12p, and incorporates 70 different proteins into those paths. The top graph in Fig. 4B shows the network constructed from all 354 paths (with each protein arranged on the perimeter of an ellipse for clarity). In the middle graph, all paths that scored below the median have been eliminated, leaving only 27 proteins. On the bottom of Fig. 4B, only the highest scoring paths (those used to construct the network in Fig. 4A) with 19 proteins, are depicted. Comparison of these networks indicates that most proteins are eliminated by simply excluding the pathways that score in the bottom half; further modifications to the cutoff affect the results incrementally. In setting a precise cutoff for pathway inclusion in the final network models, one seeks to strike a balance between the inclusion of false-positives and the omission of true-positives. We set the cutoff such that the top fifteen paths for each network were included.

The network model generated for the cell wall integrity pathway is depicted in Fig. 4C. Membrane proteins in particular may fail to produce interactions when forced into the nucleus by the requirements of the standard two-hybrid technique. We observed this to be the case for the cell wall integrity pathway, as neither Wsc1p, Wsc2p, Wcs3p or Mid2p were observed to interact in any of the high-throughput screens. To reconstruct this network, we therefore started with the momomeric GTPase Rho1p, and restricted our search to a length of seven because of the omission of the initial signal sensor. Of the 18 proteins included in this network model, all but Smd3p have descriptions consistent with a role in cell wall maintenance. NetSearch included both GTPase constituents of this pathway, Rho1p and Cdc42p, as well as associated GAPs and other interactors, including Rdi1p, Rga1p, and Gic2p. Other included network elements are Fks1p, the 1,3-βglucan synthase of which Rho1p is a subunit 16, the actin protein Act1p, and the proteins Bni1p, Bud6p, and Sph1p, which are associated with Rho-mediated signal transduction, actin filament organization, cell polarity establishment, and bud growth. Smd3p forms a complex with the Sm core spliceosomal proteins 17, and we are not aware of any role it may play in maintaining cell wall integrity. Its inclusion is most likely a result of its expression correlation with BUD6 in one of the microarray datasets, but it seems unlikely that the observed interactions of Smd3p with Spa2p and Slt2p have biological significance. In the NetSearch-generated model, Bck1p is downstream of Mkk1p because, although it interacts with both Mkk1p and Mkk2p, it has been shown specifically not to interact with Pkc1p in two-hybrid assays 18.

The network model for filamentous growth (Fig. 4D) involves 21 proteins, 20 of which are known to play a role in filamentous growth, or have functions consistent with that role, with the exception of Fus1p. As in the pheromone response and cell wall integrity network models, key components of the Ras GTPase are included, such as Cdc25p (the Ras guanine nucleotide exchange factor), Cyr1p (the Ras-associated adenylate cyclase), and Srv2p, which enables the activation of adenylate cyclase by Ras2p. Several proteins with roles in actin filament organization, cell polarity establishment, bud growth, and GTPase-mediated signal transduction are shared with the cell wall integrity pathway, including Bni1p, Spa2p, Bud6p, and Act1p. NetSearch depicts interactions between Abp1p and both Srv2p and Act1p, consistent with the function of Abp1 in tethering Srv2p to the cytoskeleton. The adenylate cyclase and associated proteins mentioned above, along with Hsp82p and Hsc82p, activate the cAMP pathway 19, a pathway that acts in parallel with the MAPK pathway to promote filamentation. Hsp82p is a chaperone protein known to interact with a number of signaling pathway components 20. It is required for activation of the pheromone signaling pathway 21, and for the general response to amino acid starvation 22. It may play a similar role in response to nitrogen (ammonia) starvation, a trigger for filamentation. Fus1p, included in our predicted network, does not have a documented role in filamentation; it is required for cell fusion during pheromone initiated mating. Its transcript levels are significantly upregulated in response to pheromone, but are unchanged in tec1Δ strains 6; that study notes, however, that in dig1Δ dig2Δ cells, fus1 is constitutively activated, and both mating and invasive growth are observed. Tec1p, conspicuously absent in our model, has not been observed to interact with any proteins in high-throughput two-hybrid screens.