Delineating functional principles of the bow tie structure of a kinase-phosphatase network in the budding yeast

Abstract

Background: Kinases and phosphatases (KP) form complex self-regulating networks essential for cellular signal processing. In spite of having a wealth of data about interactions among KPs and their substrates, we have very limited models of the structures of the directed networks they form and consequently our ability to formulate hypotheses about how their structure determines the flow of information in these networks is restricted.

Results: We assembled and studied the largest bona fide kinase-phosphatase network (KP-Net) known to date for the yeast Saccharomyces cerevisiae. Application of the vertex sort (VS) algorithm on the KP-Net allowed us to elucidate its hierarchical structure in which nodes are sorted into top, core and bottom layers, forming a bow tie structure with a strongly connected core layer. Surprisingly, phosphatases tend to sort into the top layer, implying they are less regulated by phosphorylation than kinases. Superposition of the widest range of KP biological properties over the KP-Net hierarchy shows that core layer KPs: (i), receive the largest number of inputs; (ii), form bottlenecks implicated in multiple pathways and in decision-making; (iii), and are among the most regulated KPs both temporally and spatially. Moreover, top layer KPs are more abundant and less noisy than those in the bottom layer. Finally, we showed that the VS algorithm depends on node degrees without biasing the biological results of the sorted network. The VS algorithm is available as an R package ( https://cran.r-project.org/web/packages/VertexSort/index.html ).

Conclusions: The KP-Net model we propose possesses a bow tie hierarchical structure in which the top layer appears to ensure highest fidelity and the core layer appears to mediate signal integration and cell state-dependent signal interpretation. Our model of the yeast KP-Net provides both functional insight into its organization as we understand today and a framework for future investigation of information processing in yeast and eukaryotes in general.

Keywords: Biological properties; Functional principles of cell behaviour; Kinase-phosphatase signalling network; Network hierarchical structure; Saccharomyces cerevisiae; Topological properties; Vertex Sort algorithm.

Fig. 1

The pipeline used to assemble and to sort the KP-Net, and the KP-Net bow tie structure. a The steps followed to elucidate the KP-Net hierarchical structure starting from the different sources used to collect kinase-protein and phosphatase-protein interactions, passing through the data annotation procedure and filtering criteria applied to select high quality PDIs, to the assembly and sorting of the KP-Net by the VS algorithm. b The bow tie structure of the KP-Net showing how KPs are classified in top, core and bottom layers. Top layer KPs control core layer KPs; top and core layer KPs control bottom layer KPs and KPs in the three layers control proteins in the substrates layer formed of proteins that are not KPs and of KPs having no substrates. Numbers between parentheses represent number of nodes in each layer. Arrows represent directed interactions (red: phosphorylation, green: dephosphorylation and black: both). Percentages designate percentage of interactions within and between layers

Fig. 2

Depleted and enriched biological processes and cellular components in each of the KP-Net layers. Depleted and enriched (a) biological processes and (b) cellular compartments associated with KPs in each of the KP-Net layers (top: red; core: green; and bottom: blue). Nodes represent the different enriched and depleted GO terms. Colour gradients represent log₁₀ of P-values (log₁₀(P)) of enriched and depleted GO terms. Size of nodes indicates the specificity of each GO term (small: specific and large: general). Enriched GO terms are encircled with solid border, while depleted ones are encircled with a dashed border

Fig. 3

Topological and biological properties of KPs in the different layers of the KP-Net. Distribution of (a) in-degree and (b) out-degree of KPs in each layer of the KP-Net and percentage of KPs representing (c) hubs, (d) bottlenecks, (e) shared components between pathways (KPs involved in at least two pathways), and (f) essential genes in each layer of the KP-Net. The broken line in bar plots represents the expected mean of the corresponding percentage in each layer. Black diamonds in box plots designate the average of the corresponding property of KPs. Outliers were omitted from box plots to simplify data representation. P-values were calculated by comparing property means of two layers and the enrichment/depletion of a property within a layer using the RT (Methods) and HT, respectively. For description of the used datasets see Supplementary Materials in Additional file 1

Fig. 4

Biochemical and spatiotemporal modulators of KPs in the different layers of the KP-Net. Distribution of (a) the percentage of disordered regions, (b) the percentage of predicted linear binding motifs (LBM), (c) the maximum number of phosphosites within a predicted LBM, (d) the number of phosphosites acting as molecular switches in each KP in KP-Net layers and (e) the percentage of scaffold-associated KPs and (f) the distribution of the number of subcellular localizations in which a KP was detected for KPs in each of the three KP-Net layers. For description of box plots and bar plots, see Fig. 3 and for description of used datasets see Supplementary Materials in Additional file 1

Fig. 5

mRNA and protein turnover related properties of KPs in the different layers of the KP-Net. Distribution of (a) mRNA synthesis rate, (b) mRNA half-life, (c) mRNA abundance, (d) mRNA translation rate, (e) protein half-life, (f) protein abundance, (g) percentage of noisy mRNA KPs and (h) distribution of noise in KP protein abundance of KPs in the different layers of the KP-Net. A KP is considered to be noisy at the transcriptomic level, if the promoter region of its gene was predicted to contain a TATA-box consensus sequence. Protein noise was defined as the distance of coefficient of variation (CV) of protein abundance from a running median of protein abundance CV. For description of box plots and bar plots, see Fig. 3 and for description of used datasets see Supplementary Materials in Additional file 1

Fig. 6

The VS algorithm depends on node degrees to sort network nodes into three layers. The mean and its 95% confidence interval of the studied properties of KPs in the three layers of each of the five sets of the 1,000 random networks generated by: degree preserving randomization (DPR, red line), similar degree preserving randomization (SDPR, pink line), in-degrees preserving randomization (IDRP, blue line), out-degree preserving randomization (ODRP, green line) and degree non-preserving randomization (DNPR, black line). The black diamonds represent the mean of studied properties of KPs in the three layers of the KP-Net

Fig. 7

Stability of KP-Net layers and their overlap with subsampled/noisy network layers. a Stability of KP-Net layers on adding edges to the KP-Net. b Significance of the overlap between KPs in each layer of the KP-Net and noisy network layers on adding edges. c Stability of KP-Net layers on deleting edges from the KP-Net. d Significance of the overlap between KPs in each layer of the KP-Net and subsampled network layers on deleting edges. Stability was quantified using the Jaccard coefficient as a similarity measure between KPs belonging to KP-Net layers and those belonging to noisy/subsampled network layers. P-values in (b) and (d) were calculated using the HT. Colours designate the different layers of the noisy/subsampled networks (top: red, core: green and bottom: blue)