The kinase-phosphatase network (KP-Net)
The kinase interaction database (KID) provides the most detailed and specialized annotation of kinase-protein interactions; its annotation is based on 31 experimental categories including genetic, biochemical, physical and phenotypic experimental evidence [14]. However, phosphatase-protein interactions are not included in and many kinase-protein interactions are missing or partially annotated in this database. Hence, we collected these interactions from different sources, then, curated, annotated and scored the collected interactions according to the KID database pipeline with minor adjustments to annotate phosphatase-protein interactions (Fig. 1a and Additional file 1: Supplementary Methods) [2, 15–20]. The KID pipeline associates a confidence score to each interaction based on the extent to which the different experimental methods that validate an interaction contribute to identifying a true positive Kinase-protein interaction. To ensure that the interactions assembled in the KP-Net represent PDIs rather than simply Kinase-protein or phosphatase-protein interactions, we selected interactions having a confidence score ≥ 4.52 (corresponding to a P ≤ 5 × 10−2) and those validated by at least one biochemical experiment showing the occurrence of a PDI (in vitro kinase assay, in vivo or in vitro phosphosite mapping, mobility shift of phosphoproteins on gel or substrate trapping by a dead phosphatase catalytic domain). The assembled KP-Net contains 1,087 directed interactions (918 and 169 PDIs, respectively) implicating 616 proteins [101 kinases and 31 phosphatases, covering ~77% of these enzymes and 484 proteins, most of which are KP substrates that are not KPs, (Fig. 1a and Additional file 2)]. Similar to other biological networks, the KP-Net possesses a scale-free structure (P(K) ~ K-2.58 with a goodness-of-fit test P = 1.3 × 10−2) in which most KPs regulate few proteins and few KP hubs regulate a large number of proteins (Additional file 1: Supplementary Methods and Figure S1).
The KP-Net possesses a “corporate” hierarchical structure in the form of a bow tie with a strongly connected core layer
We assessed the amount of the hierarchical structure of the KP-Net by calculating its global reaching centrality (GRC), which represents a normalized average of the proportions of nodes accessible from each node in the network [21]. The closer the GRC is to 1, the more hierarchical the network is. The KP-Net has a moderate GRC of 0.61, suggesting that the KP-Net represents a hierarchical structure that could be placed between two extremes: (i) an autocratic structure comparable to a complete tree and (ii) a democratic structure in which collaborative regulation dominates and no hierarchy exists [5]. Bhardwaj et al. observed a similar moderate hierarchy in a co-phosphorylation network and described it as a corporate hierarchy [5]. Obviously, the KP-Net does not represent a complete tree, as it is enriched for many logic motifs that do not occur in trees: feed-forward loops (a structure in which a node regulates another node and together they regulate a third one), two node feedback loops (two nodes that regulate each other), and bi-fans (a structure in which two nodes regulate two other nodes) (P < 10−3, Methods). Moreover, the KP-Net does not represent democracies and encapsulates a hierarchical structure, as its GRC is significantly higher than that of Erdős–Rényi random networks (non-hierarchical networks) having the same number of nodes and edges as the KP-Net (P < 10−4, Methods). Interestingly, the GRC of the KP-Net is significantly smaller than that of random networks generated by degree preserving randomization (DPR, Methods). This result is not surprising, as the degree distribution of a network is essential to determine its organizational structure, meaning networks having same degree distributions will have similar organizational structures. Thus the GRC of the KP-Net was expected to be comparable to that of DPR networks, but it was found to be significantly smaller than the GRC of DPR networks, probably indicating enrichment for feedback loops that generally exist in KP-Nets.
Subsequently, we applied the VS algorithm to the KP-Net to elucidate the network hierarchical structure and the signal flow within the elucidated hierarchy. The VS algorithm is among the best network decomposition algorithms available. It was conceived and applied by Jothi et al. to the transcription regulatory network of the budding yeast Saccharomyces cerevisiae to elucidate the network hierarchical structure [5, 6, 8–11, 22]. The VS algorithm sorts nodes into different levels so that nodes in upper levels control those in lower levels [8]. It first transforms a cyclic graph to an acyclic one by collapsing each strongly connected component (SCC, a sub-graph where each node pair is related by two paths of opposite directions) into a super node and then it applies the leaf removal algorithm to the resulting graph and to its transpose. This generates global solutions in which a node could span a range of levels, reflecting the huge amount of missing data in and the dynamic nature of biological networks.
Application of the VS algorithm to the KP-Net revealed a hierarchical structure in which KPs are sorted into 9 levels that we subsequently grouped into three non-overlapping layers: top, core and bottom (Additional file 1: Figure S2a). As in Jothi et al., we first identified KPs of the largest SCC and classified them as belonging to the core layer (19 KPs); we then classified KPs that regulate core layer KPs to the top layer (38 KPs) and those that are regulated by core layer KPs to the bottom layer (36 KPs) (Fig. 1b) [8]. Thirty-eight nodes, of which 33 KPs and five proteins that are not KPs, were excluded from further analysis, because the former are not connected to any KP and the latter are substrates of the excluded KPs (Additional file 1: Figure S2b). The three layers of the KP-Net generated a bow tie structure in which the core layer has relatively fewer nodes than top and bottom layers (Fig. 1b). It is important to note that the bow tie shape of the KP-Net represents an intrinsic property of this network and it is not the result of the application of the VS algorithm. More specifically it is not not the result of choosing the core layer as the SCC of the KP-Net. This is because by applying the VS algorithm in the same way, the hierarchical structure of the regulatory network elucidated by Jothi et al. do not have a bow tie shape (top, core and bottom layers contain 25, 64 and 59 nodes, respectively) [8].
Interestingly, KP-Net top, core and bottom layers regulate 235, 276 and 148 proteins, respectively, corresponding to 38, 45 and 24% of the KP-Net nodes, respectively. Although the core layer is ~2 times smaller in size than top and bottom layers, it regulates a number of substrates that is 1.2 and 1.9 times larger than that regulated by top and bottom layers, respectively, implying an essential role of the core layer in the KP-Net.
The three layers of the KP-Net have dissimilar biological roles and subcellular localizations
To unravel biological roles of the KP-Net layers, we performed a Gene Ontology (GO) enrichment/depletion analysis for KPs in each of these layers (Additional file 1: Supplementary Methods). We found that the KP-Net top layer is enriched mostly for signal regulation and transduction; interestingly, the core layer is enriched for signalling also, for metabolic processes, but mostly for cell cycle, organization processes related to cell cycle and decision-making (Additional file 1: Table S3), confirming the essential role of the core layer in the KP-Net; and the bottom layer is enriched for few GO terms, suggesting that it has a less specialized and more diverse biological roles (Fig. 2a). These results are in line with the findings of Bhardwaj et al. [5].
On another level, the top layer is depleted for, whereas the core layer is enriched for KPs located in the bud neck (Fig. 2b), a result that has been already observed by Cheng et al. [6]. We further found that the bottom layer is enriched for KPs located in the mating projection tip (Fig. 2b). The latter observations suggest that top layer KPs might remain in the mother cell to regulate signalling, while core layer KPs may be polarized towards the daughter cell to contribute to mitosis, and bottom layer KPs might reside in the cell projection to contribute in mating.
Strikingly, dephosphorylation is enriched in the top layer and depleted in the bottom layer of the KP-Net (Fig. 2a), suggesting that phosphatases are over-represented in signalling pathway upstream and depleted in downstream arms of signalling pathways. The latter results are consistent with dynamic phosphoproteomic studies showing that at least 50% of early responses to cell perturbations are dephosphorylation of phosphosites [23].
Phosphatases are less regulated by phosphorylation than kinases
Our findings confirmed our proposition that the top layer is enriched whereas the bottom layer is depleted for phosphatases (Additional file 1: Figure S3a, P = 2.2 × 10−5 and P = 4.1 × 10−4 respectively; hypergeometric test (HT)). In addition, we observed that 81% of the top layer phosphatases have a zero in-degree. Using high quality phosphoproteomic data annotated in the PhosphoGRID database, we also found that the number of phosphosites identified in phosphatase protein sequences is smaller than that identified in kinases (Additional file 1: Figure S3b, P = 2.3 × 10−3; randomization test (RT), Methods). These results suggest that phosphatases are less regulated by phosphorylation than kinases are. Our suggestion is also supported by the great variety of regulatory subunits controlling phosphatases [24] and by the large number of cellular mechanisms, other than phosphorylation, reported to regulate phosphatases, including phosphorylation of the regulatory subunits of phosphatases [25–30].
KP-Net upper levels are the least regulated and KP-Net lower levels are the least to regulate other KPs
Top layer KP in-degrees are on average smaller than KP in-degrees in core and bottom layers (Fig. 3a, P < 10−4; RT, Methods). This observation is a direct result of the VS algorithm application (P = 10−3; degree non-preserving randomization (DNPR), Methods) to a network, but it agrees with organizational principles found in hierarchical systems in which members of upper levels are the least regulated (e.g. pyramid networks). In contrast, the out-degree of the bottom layer is significantly smaller than that of top and core layers (Fig. 3b, P = 3 × 10−3; RT, Methods). This finding is independent of the VS algorithm application (P = 0.7; DNPR, Methods) on a network and has been previously observed in the hierarchical structure of a yeast transcriptional regulatory network elucidated by a decomposition algorithm (Breadth-First Search) different than the VS algorithm [9]. Finally, the observed features related to node in- and out-degrees were implemented in two network decomposition algorithms, other than the VS algorithm, to classify nodes in top and bottom layers, respectively [5, 12].
The KP-Net core layer is enriched for essential genes, bottlenecks, and pathway-shared components
To better grasp our knowledge of signal flow in the KP-Net, we analysed the distribution of hubs, bottlenecks, pathway-shared components (KPs involved in at least two pathways) and essential genes in the three layers of the KP-Net. Hubs and bottlenecks are defined as the 20% of KPs in the KP-Net that have, respectively, the highest degree and the highest betweenness (fraction of shortest paths between all pairs of nodes that pass through a single node; this measure captures how much signalling passes through a node). The hubs are equally distributed among the three layers, reflecting the prevalence of parallel regulation as a principle emerging from the three layers of the KP-Net (Fig. 3c). Interestingly, the core layer is enriched for bottlenecks, pathway-shared components and essential genes (Fig. 3d–f, P = 4.3 × 10−5, P = 1.4 × 10−2 and P = 3.8 × 10−2, respectively; HT), suggesting that most of the signal integration and crosstalk between pathways occur in the core layer.
Molecular switches are enriched in KPs in core and bottom layers
Molecular switches represent phosphosites within or adjacent to linear binding motifs (LBM) which mediate “on demand” controls switching proteins between different functional states (on-off, specificity, cumulative and sequential switches) [31]. Given their fundamental role in controlling signalling networks, we investigated the distribution of KP molecular switches in the KP-Net hierarchy. We predicted protein disordered regions in KP protein sequences and LBMs within these predicted disordered regions using the IUPred and ANCHOR algorithms, respectively (Additional file 1: Supplementary Methods) [32, 33]. We then overlaid bona fide in vivo phosphosites from the PhosphoGRID database on top of KP protein sequences (Additional file 1: Supplementary Materials). We found that percentage of predicted disordered regions in KP proteins in core and bottom layers are on average higher compared to the top layer (Fig. 4a, P < 2.3 × 10−2; RT, Methods). The same trend is observed for: (i), the percentage of sequences predicted to contain LBMs (Fig. 4b, P < 2.1 × 10−2; RT, Methods); (ii), the number of phosphosites in KP sequences generally (Additional file 1: Figure S3c, P < 6.1 × 10−4; RT, Methods) and (iii), in the predicted LBMs particularly (Fig. 4c, P < 2.2 × 10−2; RT, Methods); and (iv), the number of potential molecular switches in each KP (Fig. 4d, P < 3.1 × 10−3; RT, Methods). Interestingly, our findings suggest that phosphorylation of KPs in lower layers could form molecular switches important for KP temporal regulation. Two out of many examples confirming our suggestions are: (1) the specificity switch in Hsl1 (core layer kinase and morphogenesis checkpoint regulator) leading to a G2 arrest essential for cell survival upon osmotic shock and (2) the on-switch in Swe1 (core layer kinase) maintaining Cdc28 in an inhibited form essential for entry of cells into mitosis [34, 35].
Core layer KPs employ scaffolding to prevent unwanted pathway crosstalk
It is well established that redirecting information flow within signalling networks is accomplished through interactions of KP with scaffold proteins and is required for the insulation of interconnected pathways [36]. Interestingly, the KP-Net core layer is enriched for pathway-shared components (Fig. 3e) and for LBMs (Fig. 4b), suggesting that core layer KPs that are shared between pathways associate with scaffold proteins through LBMs. Indeed, although core and bottom layers are enriched for potential LBMs, only the core layer is enriched for scaffold-associated KPs (Fig. 4e, P = 2 × 10−4; HT). This indicates that scaffolding is extensively employed at the core layer where most pathway crosstalk occurs (Fig. 3d–e), in order to prevent inappropriate cellular responses resulting from the activation of undesired pathways. For instance, the mitogen extracellular signal-regulated kinase kinase Ste11, a core layer kinase, is involved in three pathways: high osmolarity, filamentous growth and pheromone pathway. Association of Pbs2 (a MAPK kinase and a scaffold protein implicated in the HOG signalling pathway) and Ste5 (a pheromone-responsive MAPK scaffold protein) with Ste11 reorients signal flow by activating the HOG signalling pathway and the mating pathway, respectively; whereas, unavailability of both Pbs2 and Ste5 favours filamentous growth [37].
Core layer KPs undergo more spatial organization changes than top and bottom layer KPs
Controlling spatial distribution of KPs plays an essential role in tuning KP activity and specificity towards their substrates [38, 39]. By superposing microscopic subcellular localization data of proteins in single cells under different stress conditions [40] on top of the KP-Net hierarchy, we observed that KPs in the core layer dynamically redistribute among more subcellular compartments than KPs in top and bottom layers (Fig. 4f, P < 1.6 × 10−3; RT, Methods). This indicates that core layer KPs might be subject to a more stringent control than top and bottom layer KPs to tightly restrict their localization. Hog1 is a relevant example of a core layer kinase that is translocated from the cytoplasm to the nucleus to trigger a wide transcriptional response on exposure to a high osmolarity stimulus [41]. Another typical example of tight localization control is Cdc14, a core layer phosphatase essential for mitotic exit, which after its sequestration in the nucleolus, is released to the nucleus and the cytoplasm where it associates with the spindle pole body during early anaphase [42].
Top layer KP proteins are more abundant and less noisy than bottom layer KPs of the KP-Net
Since KPs turnover determines their availability and thus their activity, we overlaid various information of KP turnover taken from the literature (Additional file 1: Supplementary Materials) on top of the KP-Net hierarchy [43–49]. While transcripts coding for core layer KPs are synthesized at a higher rate than top and bottom layers (Fig. 5a, P < 3.9 × 10−3; RT, Methods), mRNA of top layer KPs have longer half-lives than core and bottom layers (Fig. 5b, P < 4.6 × 10−3; RT, Methods). However, mRNA abundance has a similar trend to mRNA half-life, implying that mRNA degradation (the process that determines half-lives) is more important than synthesis rate in determining mRNA abundance (Fig. 5c, P < 1.8 × 10−2; RT, Methods). Similarly, mRNA of top layer KPs are translated at higher rates than core and bottom layers (Fig. 5d, P < 4.8 × 10−2; RT, Methods). However, half-lives of KP proteins are statistically comparable among the three layers of the KP-Net (Fig. 5e; RT, Methods), suggesting that proteins abundance should have the same trend as the translation rate of mRNA molecules. This is partially true, since top layer KP proteins are more abundant than the bottom layer (Fig. 5f, P = 3.3 × 10−2; RT, Methods), but not more abundant than the core layer. This discrepancy might be due to the fact that KP proteins in the core layer tend to have longer half-lives (mean values are reported; 95 min, Fig. 5e) than the top layer (69 min, Fig. 5e). On another level, percentages of noisy KP genes at the mRNA level are comparable among the three KP-Net layers (Fig. 5g; HT). Moreover, top layer KP proteins are less noisy than core and bottom layers in starving S. cerevisiae cells (Fig. 5h, P < 2.2 × 10−2; RT, Methods). Interestingly although, we observed significant relative differences in each of protein abundance and noise between KP-Net layers, notably proteins were abundant (Fig. 5f, top 5,336 molecules/cell, core 3,041 molecules/cell and bottom 2,436 molecules/cell) and not noisy (Fig. 5h, top -0.94 a.u., core -0.05 a.u. and bottom 0.12 a.u.) in the three layers of the KP-Net. Taken together, these results suggest that higher protein abundance coupled with lower protein noise in the three layers and in particular in the top layer, might confer high signalling fidelity to the KP-Net.
The VS algorithm depends on node degree to classify network nodes in three layers
As the findings of this study mainly result from the application of the VS algorithm, we asked whether the VS algorithm depends on a specific node property to sort nodes into three layers and whether these findings reflect the biology underlying the KP-Net. To address these questions, we generated five sets of 1,000 random networks produced using five randomization methods: degree preserving randomization (DPR), similar degree preserving randomization (SDPR), in-degree preserving randomization (IDPR), out-degree preserving randomization (ODPR), and degree non-preserving randomization (DNPR) (Methods). We then applied the VS algorithm on these random networks and plotted means of KP properties in each layer of the KP-Net (black diamonds, Fig. 6), means of KP properties in each layer of random networks (points joined by coloured lines, Fig. 6) and the 95% confidence interval of random network means (coloured vertical segments, Fig. 6).
Strikingly, we observed that the distribution of all properties, except in-degrees, hubs and bottlenecks, of the three layers form a straight horizontal line for DNPR networks (Fig. 6, black line), showing that the VS algorithm produces a particular global signature (they peak at the core layer) in completely random networks for only these three properties that are all related to node degrees. Interestingly, the distribution of all properties in the DPR and SDPR networks (red and pink lines, Fig. 6) are the closest to each other when node degrees are similar to each other (DPR and SDPR cluster together in Additional file 1: Figure S4). Taken together, our observations suggest that the VS algorithm depends on node degree to sort network nodes in the different layers. Moreover, on clustering the five sets of randomized networks using the Euclidean distance between the different properties of their KPs, we found that ODPR networks are closer to DPR networks than IDPR networks (Additional file 1: Figure S4), suggesting that the VS algorithm depends on node out-degrees more than node in-degrees. However, the VS algorithm obviously depends also on node in-degrees, as any node with a zero in-degree will be automatically placed in the top layer. Therefore, the VS algorithm depends on both nodes in- and out-degrees. Nevertheless, although the VS algorithm depends on node degrees to classify network nodes into different layers, three observations suggest that KP biological properties are not associated with KP degrees and that they are not the result of a bias in the VS algorithm: (i) all biological properties showed a straight line distribution in completely random networks (Fig. 6, black line); (ii), most of the means of KP biological properties in KP-Net layers (black diamonds, Fig. 6) are outside of the 95% confidence interval of the means of the corresponding properties in random network layers; and (iii), most of the KP biological properties (12 out of 18) are neither associated with their in- nor with their out-degrees (Additional file 1: Supplementary methods).
Robustness of results and incompleteness of data
It did not escape our attention that the KP-Net that was assembled in this study represents a small snapshot of the whole phosphorylation network of the budding yeast. Therefore, we assessed the robustness of our results to missing interactions by generating noisy networks (adding edges to the KP-Net) and the robustness of our results to false positives by generating subsampled networks (deleting edges from the KP-Net) (Methods). We then assessed the stability of KP-Net layers using the Jaccard coefficient as a measure of similarity between KP-Net layers and noisy/subsampled network layers (Methods) [50]. Also, we assessed the significance of the overlap between KP-Net layers and noisy/subsampled network layers using the HT (Methods) [50]. We observed that the KP-Net is more robust to removing than to adding edges (Fig. 7a and c). Moreover, the more edges are added to and removed from the KP-Net, the more the three layers become unstable (Fig. 7a and c). However, in spite of this instability, all layers in noisy/subsampled networks significantly overlap with the KP-Net layers (Fig. 7b and d), showing that our findings are sufficiently robust to describe the KP-Net with our current knowledge. Finally, properties characterizing the KP-Net were retained to different degrees in the noisy networks (Additional file 1: Supplementary Methods and Figure S9), confirming that the characteristics of the KP-Net elucidated in this study represent the best of our knowledge to date about KP-Nets.
Using the KP-Net as a gold standard to predict kinases acting on substrates in the HOG pathway
Presently, one of the most active areas of research consists of linking each KP to its substrates. As an example, we attempted to predict the kinases that could phosphorylate substrates characterized by a change in their level of phosphorylation in cells exposed to osmotic shock. We used the KP-Net as a gold standard; we overlaid on top of it phosphorylation consensus motifs curated from the literature and proteins that undergo time-dependent phosphorylation or dephosphorylation following osmotic shock from Kanshin & Bergeron-Sandoval et al. [23]. We identified 57 interactions linking 19 kinases to 25 potential substrates (Methods and Additional file 3). The overlap between the predicted kinases in our study and the kinases that underwent changes in phosphorylation in Kanshin & Bergeron-Sandoval et al. was significant (P = 3.8 × 10−2; HT). This result suggests, first, that a significant number of the 19 kinases that we predicted to act on 25 potential substrates do undergo time-dependent changes in phosphorylation that may reflect their activation or deactivation in response to osmotic shock; second, that the interactions forming the KP-Net that was assembled in this study are of high confidence; and finally, that this same KP-Net could be used as a benchmark with other phosphoproteomic data to identify kinases and perhaps phosphatases that act on a set of substrates.
