Despite the apparent importance of disorder in mediating important protein functions 4 , our knowledge is still limited in terms of its specific functional roles. The yeast GI network offers a new opportunity for global insights into the role of disorder in protein function 9 . Briefly, GIs are defined as pairs of genes whose combined mutation or deletion leads to an unexpected double mutant phenotype. Here we limit our attention to negative interactions; these are interactions in which the double mutant is significantly less fit than would be predicted by the fitnesses of the single mutants. Interestingly, it has been observed that the number of GIs of a gene (GI degree) is correlated with the percentage of disordered regions in the gene product 9 (Figure 1a). GI degree is also correlated with different measures of multi-functionality (number of gene ontology (GO) annotations, phenotypic capacitance 10 and chemical-genetic sensitivity 11 ), suggesting that the presence of disordered regions may underlie the highly pleiotropic roles of some proteins.

The relationship between disorder and multi-functionality appears to depend on whether a gene is a hub in the GI network (that is, the gene is associated with a large number of GIs). Specifically, within the set of the GI hubs (> 90 percentile in GI degree), disorder of the gene product is a strong predictor of multi-functionality (r = 0.22, P < 10^-12; Figure 1b), suggesting it is able to distinguish highly functionally versatile GI hubs from genes with more limited functional roles that simply exhibit a large number of GIs. However, this trend is absent on the set of non-GI hubs (< 50 percentile in GI degree) where there is no significant correlation between the amount of disorder and the number of annotated functions (r = -0.02, P > 0.3). This stark difference suggests that disorder plays a highly functional role on the set of proteins that have many GIs while disorder outside these genes is either less functional or simply of a markedly different nature. A similar distinction can be observed for protein-protein interactions: disorder is significantly correlated with protein-protein interaction degree on GI hubs (r = 0.16, P < 3 × 10^-3; Figure S1 in Additional file 1) while no such correlation holds on non-GI hubs (r = -0.01, P > 0.5). Thus, the GI network appears to provide a clear means of defining a set of proteins where the disorder plays a key functional role.

Despite their seeming functional importance, disordered regions of proteins have previously been associated with swiftly evolving, less conserved sequences, presumably because of lower structural constraint 12 . We were intrigued by this property because, in general, GI hubs exhibit significantly lower rates of evolution (for example, measured by the dN/dS ratio) and tend to be conserved more broadly across species 9 . Indeed, we found that even among GI hubs, disordered proteins have significantly elevated rates of evolution. This trend is consistent outside the hubs as well (Figure 1c). However, disordered GI hubs are just as conserved phylogenetically as measured by their appearance across the yeast clade (Figure 1d). Thus, while the amino acid sequences tend to evolve faster for disordered GI hubs, they appear to be as phylogenetically constrained at the gene level as other GI hubs. Interestingly, outside of GI hubs, this is not true: non-GI hubs that are disordered tend to be less conserved across the yeast clade compared to their structured counterparts (Figure 1d). These observations relating disordered proteins to the GI network raise an interesting paradox. While the presence of disordered regions appears to be directly connected to their importance in the genetic network, there appears to be little evolutionary sequence constraint on these regions.

The counter-intuitive evolutionary pressure on disordered proteins motivated us to undertake a comparative analysis of disordered regions across the yeast clade. We hypothesized that functionally important disordered regions, such as those present in GI hubs, would be conserved as disorder across species (that is, also disordered, even if the underlying amino acid sequence was different) independent of rate of evolution. We therefore assessed the conservation of disorder on the residue level, which was also recently addressed by Chen et al. 13 14 . Specifically, we predicted which residues were disordered for all Saccharomyces cerevisiae genes and their orthologs in the 23 species of the yeast clade using DISOPRED2 2 , an algorithm that has been shown to predict disordered regions reliably 15 . For each disordered residue, we defined a measure of conserved disorder as the percentage of orthologs in which that residue is disordered as well (Figure 2). We operationally define conserved disordered residues as those with greater than 50% of disorder conservation.

Consistent with the general observations by Chen and co-workers 13 14 , we found that there is a surprisingly high rate of conservation of disordered regions: over 50% of disordered regions are conserved through 90% of the orthologs considered. Notably, disorder is conserved in many regions even where the specific amino acids are not conserved in the same regions, which explains the elevated dN/dS that has been previously associated with disorder 12 (Figure 2). However, consistent with the stability of disorder across the yeast clade, we find that changes of amino acids in disordered regions are biased towards hydrophilic residues associated with disordered regions and away from hydrophobic residues (Figure S2 in Additional file 1). This result suggests that, despite a high evolutionary rate at the sequence level, there is substantial evolutionary pressure to keep these regions disordered.

Regions in which disorder is highly conserved across the yeast clade exhibit a wide range of amino acid conservation rates (Figure 3). We reasoned that the degree of constraint on the precise underlying sequence (as opposed to the more general property of disorder) might highlight distinct subclasses of functional disorder. To test this hypothesis, we divided conserved disordered regions into those where the underlying amino acid sequence is also conserved ('constrained disorder'), and the regions where there appears to be selection on the structural property of disorder itself rather than the specific sequence ('flexible disorder'; Materials and methods; Figure 2). Disordered residues that were not conserved across the yeast clade were considered as a separate, third class ('non-conserved disorder'; Figure S3 in Additional file 1). It is important to note that these results do not depend on the disorder predictor algorithm and core results were qualitatively replicated using DisEMBL 16 instead of DISOPRED2 (Figure S4 in Additional file 1). Furthermore, the three classes also appear to be robust to various perturbations of the particular parameter choices of the method (Figures S5, S6, S7, and S8 in Additional file 1). In addition, flexible disorder was more robust to random simulated mutations (Figure S9 in Additional file 1), which is notable given the general fragility of disorder to mutation reported by 17 .

The three classes of disorder exhibit widely different properties (Figure 2b). First, while disorder is generally thought to be important in proteins with regulatory and signaling functions, we find that this is true only for flexible disorder. For instance, proteins enriched in flexible disorder have high phenotypic capacitance and are multifunctional. Moreover, they exhibit low-expression coherence, that is, are connectors in the cellular network, consistent with a regulatory role 18 . Finally, flexible disorder is highly correlated with occurrence of linear motifs and GI degree, also consistent with signaling or regulatory roles. The respective associations for all the above properties with either constrained or non-conserved disorder are much weaker and, in most cases, not significant, suggesting that the regulatory properties of disorder are best captured by flexible disorder. Secondly, disordered proteins have recently been found to be expressed at a low level and have tightly controlled expression 4 . We find this only true for proteins enriched in flexible disorder: flexible disorder is negatively correlated with gene expression level, while constrained disorder shows either a positive or no correlation depending on the inclusion of ribosomal proteins (Figure 4; Figure S7 in Additional file 1). Also, while genes enriched in non-conserved disorder appear to be expressed at a low level, there appears no evidence for tighter expression control as measured by half-life. Thirdly, a recent study found disordered proteins to exhibit high dosage sensitivity 5 . We again find that this is a hallmark of flexible disorder (Figure 4), whereas constrained disorder is only weakly associated with this property. Non-conserved disorder shows little or much weaker association with most of these features, suggesting that the functional hallmarks of this class are less obvious. Indeed, we find that proteins enriched for non-conserved disorder have less confident disorder as scored by DISOPRED2 (Figure S10 in Additional file 1). However, our inability to identify functional roles for non-conserved disorder does not preclude the possibility of its functionality.

Because of their recognized importance for signaling pathways, we next turned our attention towards phosphosites and linear motifs. It has been noted previously that phosphosites and other recognized linear motifs often appear in disordered regions of proteins 19 . As these motifs are crucial for signaling pathways, their occurrence in these regions certainly has strong functional consequences. In a detailed analysis at the residue level, we find that disorder conservation is strongly correlated with the placement of phosphosites (Figure 5a). In particular, we find that the relative density of phosphosites increases dramatically for residues with higher disorder conservation (Figure 5b). Conversely, the correlation of phosphosite density with amino acid conservation is weak (Figure 5c). Likewise, we find similar results for linear motif placement (Figure S11 in Additional file 1). In both cases, the partial correlation with conserved disorder, when controlling for amino acid conservation, remains strong, while the partial correlation between amino acid conservation and phosphosite or linear motif density disappears when controlling for conserved disorder. Conversely, neither linear motifs nor phosphosites show enrichment in residues that exhibit non-conserved disorder, which suggests that non-conserved disorder may not be functionally relevant in this context.

Given our comparative genome-based classification of disorder, we revisited our earlier observation regarding the correlation between protein disorder and multi-functionality on GI hubs. As described earlier, we observed that within the set of the GI hubs (> 90 percentile in GI degree), disorder of the gene product is a strong predictor of multi-functionality (r = 0.22, P < 10^-12; Figure 1b) while this trend does not hold on the set non-GI hubs (< 50 percentile in GI degree). Thus, we reasoned that the disorder present in GI hubs may exhibit different abundances across our classes. Indeed, we did find evidence that disordered regions tend to be significantly more conserved among GI hubs than non-hubs (P < 10^-6; Figure S12 and Table S1 in Additional file 1). Furthermore, flexible disorder appears to account for the correlation between disorder and multi-functionality observed among the GI hubs since controlling for flexible disorder destroys the correlation (P > 0.5), while a strong correlation is maintained when controlling for the level of constrained disorder (r = 0.15, P < 0.01).

Interestingly, the set of highly disordered GI hubs is also significantly enriched for protein interaction hubs that bind temporally disparate partners (singlish interface hubs as defined in 20 ) when compared with disordered non-hubs or non-disordered hubs (P < 10^-5; Figure S13 in Additional file 1). In fact, the distinction between flexible and constrained disorder can be used to differentiate between singlish-interface hubs and the so-called multi-interface hubs, which typically bind their partners simultaneously (as defined in 20 ): singlish hubs have more flexible disorder than multi-interface hubs (P < 10^-13), while there is no significant difference in terms of constrained-disorder (P > 0.1; Figure 6).

The above results indicate that flexible disorder and constrained disorder are markedly different phenomena based on a variety of physiological and phenotypic data. On the one hand, flexible disorder corresponds to what we refer to as 'classic disorder': these are intrinsically unstructured regions, which evolve rapidly and present short linear motifs to signaling domains or protein kinases. Flexible disorder is thus a central player in signaling, which is confirmed by a GO enrichment analysis - all top enriched terms are related to regulation, including transcription factors, chromatin modifiers, and signaling pathways and DNA binding proteins (Figure 7; Table S2 in Additional file 2).

In contrast, proteins with a high level of constrained disorder exhibit dramatically different functional characteristics. Constrained disordered proteins are enriched in genes involved in ribosome biogenesis or function, RNA binding and protein chaperone activity (Figure 7; Table S2 in Additional file 2). Some of these functions have been previously associated with conserved disorder 14 , but our analysis suggests they are even more specifically associated with regions that are under tight sequence constraint, which is not generally true of regions that have properties characteristic of 'classic' disorder.

Given the dichotomy in functions arising from the presence or lack of sequence constraint, we explored the positions of these regions with respect to predicted domains. We find that flexible disordered residues rarely reside inside structured domains, consistent with the idea that they would localize to loops to present highly flexible linear motifs to their signaling partners. Conversely, constrained disordered residues lie within domains significantly more frequently than flexible residues, though occurring well below the level of the genomic background (Figures S14 and S15 in Additional file 1). The particular domains in which constrained disorder residues are enriched confirmed the location of these regions within RNA-binding ribosomal proteins and protein chaperones (GroEL-like chaperone, ATPase, Translation protein SH3-like, AAA ATPase, core; Table S3 in Additional file 2).

The highly distinct functional and positional characteristics associated with these two classes of disorder suggest that they are very different phenomena. On the one hand, flexible disorder is closest to what is canonically understood as protein disorder, that is, these are structurally flexible, fast evolving sequences with involvement in signaling. A good example of flexible disorder is found in the serine-arginine protein kinase Sky1 (YMR216C), similar to human SRPK1, which regulates proteins involved in mRNA metabolism and cation homeostasis. The region containing residues 712-737, conserved for disorder across orthologs but not sequence, is located at the end of the kinase (Figure S16 in Additional file 1). This carboxy-terminal disordered loop interacts with the activation loop of the kinase 21 and is likely involved in the regulation of kinase activity. Likewise, the corresponding region exhibits flexible disorder in many of the related cyclin-dependent kinases 22 . For example, in Bur1, this region contains flexible disorder and also harbors multiple phosphosites and linear motifs, underlining its importance in signaling (Figure S17 in Additional file 1).

On the other hand, our results suggest that constrained disorder can often adopt fixed conformation. As has been previously suggested, some disordered proteins are likely to undergo disorder-to-order transitions upon binding of their targets 3 , and we speculate this is a hallmark of the constrained disorder class. In the case of ribosomal biogenesis and RNA-binding structural proteins, they become structured upon binding RNA. This imposes a high degree of local structural constraint on them, which results in elevated constraint on the actual amino acid sequence. For instance, in Rpl5 a region of constrained disorder can be observed immediately before an alpha helix that forms the carboxy-terminal end of the amino acid sequence (Figure S18 in Additional file 1). The role of this region was specifically investigated in 23 , and they report strong evidence for a disorder-to-order transition of this region upon the binding of Rpl5 to 5S rRNA. We also found an enrichment for constrained disorder among protein chaperones, where disordered regions appear to be involved in the binding of client proteins. For example, the HSP90 heat shock protein (HSC82/HSP82) contains long regions of constrained disorder (Figure S19 in Additional file 1). In particular, the constrained disordered region from 590-600 is conserved throughout the bacterial kingdom, is localized at the inner surface of the barrel-shaped protein and has been directly implicated in the chaperone activity of this protein. It has been previously speculated that this disordered region may play a role in entropy transfer and the refolding of clients through a disorder-to-order transition 24 . However, there is little direct experimental evidence about the precise role of disorder in chaperone function. We hypothesize that, in general, the tight sequence conservation of constrained disorder is required in regions that assume a structured conformation, even if this conformation is only assumed in a transient fashion as in the case of HSP90 or more permanently as in the case of Rpl5.

Throughout this paper, correlations were done using Pearson's correlation coefficient 33 and calculated using Matlab's corrcoef function. Error bounds are the 95% confidence interval.

In the following section, we describe the data sets used throughout to characterize aspects of disorder. Several of these features were previously described in 9 .