Targets of Cdk1p in S. cerevisiae contain clusters of matches to the CDK consensus
CDK substrates in S. cererevisiae
are often phosphorylated at multiple serine or threonine residues, some of which match the full (henceforth 'strong') consensus S/T-P-X-R/K, whereas others match a minimal (henceforth 'weak') consensus S/T-P. For example, the amino-terminal region of Cdc6p (Figure ) is a direct target of Cdk1p (also known as Cdc28p) [14
], and contains three strong and one weak CDK consensus. In order to test whether these observations could be used to predict new substrates, we first compared the number of matches of each motif per residue in a set of 12 Cdk1p targets known from low-throughput biochemical and genetic experiments (compiled by Ubersax and coworkers [11
]; henceforth referred to as 'known' targets; see Table and Figure ) with the number in the genome. We find a highly significant, more than ninefold enrichment of the strong consensus (Figure , left side) but not for a scrambled version (P-R/K-X-S/T) of the consensus (Figure , right side), indicating that the enrichment is not due to simple compositional effects. For the weak consensus (after masking the strong consensus), we also find enrichment over the genome and not for a scrambled consensus (after masking the weak and strong consensus), but it is less striking (less than twofold; Figure ).
Figure 1 Clustering of consensus motifs in S. cerevisiae CDK targets. (a) Schematics of characterized S. cerevisiae CDK targets. Blue and green symbols indicate matches to the strong and weak CDK consensus, respectively. The thick black bar below indicates the (more ...)
CDK target sets used in this study
Figure 2 Enrichment of matches to the CDK consensus in CDK substrates. (a) The protein sequences of well characterized ('known') CDK targets (gray bars) are highly enriched for matches to the CDK strong consensus relative to the genome (black bars) but not for (more ...)
Because we were concerned that the discovery of the known targets may have been biased by the observation that they contained many matches to the strong consensus, we also computed these frequencies for the 18 proteins out of a set of 198 randomly chosen genes from S. cerevisiae
identified as Cdk1p targets in a high-throughput assay [11
] (henceforth referred to as 'unbiased positives'; see Table ). We found similar results in this unbiased positive set, although the enrichment of strong matches was just under fourfold in this case and the enrichment of weak matches was less than 1.5-fold (Figure ). That the fold enrichment is somewhat less in this set is consistent with some of the enrichment in the known set being due to bias in their discovery, but also with some false-positive findings being picked up in the kinase assay. Nevertheless, this rules out the possibility that the enrichment of matches in bona fide
CDK substrates is only the result of a bias.
Examination of phosphorylated residues in CDK target proteins reveals that they are often found 'clustered' in one region of the primary amino acid sequence (Figure ). We sought to test whether this apparent clustering was due simply to a uniform overall enrichment of consensus matches in these proteins, or whether it was a preference for the consensus matches to occur near each other. We modeled the number of residues until a strong or weak match was identified using a bivariate geometric distribution (see Materials and methods, below). We then performed a likelihood ratio test (LRT) between the hypothesis (H1
) that the spacings were drawn from a mixture of a high-density 'cluster' component and a low-density 'background' component, and the hypothesis (H0
) that the spacings were simply the result of a single uniform density component (Figure ). In order to compare these models, we maximized the likelihood under each hypothesis using expectation-maximization (EM) [18
] (see Materials and methods, below) and computed the likelihood ratio statistic:
Figure 3 Modeling the distribution of spacing distances between matches to the CDK consensus. Fit of one (black trace) or two multivariate geometric components (blue and red traces) to the observed spacings (thin black trace) in the 'known' targets. The 'known' (more ...)
Where data represents the observed spacings and corresponding (strong or weak) consensus matches. Because H0 corresponds to the case of H1 with the parameters of the two components constrained to be equal, we expect the LRT statistic (Λ) to be χ2 distributed with three degrees of freedom (see Materials and methods, below).
We therefore computed the P
values for the LRT on the known targets, the set of 'unbiased positives', the remaining randomly chosen proteins that were found not to be targets of Cdk1p in the assay [11
] (henceforth referred to as 'unbiased negatives'; see Table ), and the 'known' targets using the scrambled consensus sequences (Table ). Consistent with the model that bona fide
targets contain clusters of consensus matches, rather than a simple overall enrichment, we could reject the overall enrichment hypothesis in the first two tests (P
= 1.2 × 10-9
= 1.6 × 10-4
, respectively), but not in the latter two negative controls (P
= 0.13 and P
= 0.15, respectively; see Table ).
Likelihood ratio tests for spatial clustering of CDK consensus matches
Methods to detect clustering in individual proteins
Having established statistical enrichment and tendency for consensus matches to cluster in the primary sequence of bona fide CDK targets, we developed a method to predict CDK targets based on these properties. For each protein, we sought to compare the likelihood of the observed matches and spacings given the genome frequencies (Hbg) with the likelihood under a two-component model (Hc), in which one component is the background genome model and the other is high-frequency 'cluster' component whose parameters are estimated from the protein of interest. This suggests ranking genes according to the following:
Because the weak CDK consensus matches the specificity of any proline-directed kinase, we were concerned that some of our predictions would not be specific to CDKs. In order to rule out these cases, we defined a 'nonspecific' model (Hns) as above, except that the frequency of strong matches in the high-frequency 'cluster' component was constrained to be less than or equal to the background genome frequency. We optimized the likelihood under each of these models for each protein (see Materials and methods, below) and ranked them by a classifier assuming uniform 'priors' over the various models:
This will assign lower scores to proteins that have clusters of only weak consensus matches. Cdc6p (Figure ), for example, has SLR = 7.28, and ranks 22nd in the genome.
Identifying optimal clusters
The mixture models we have employed thus far do not assume that the closely spaced matches fall in a single contiguous region of the primary sequence. We considered this appropriate because residues may be adjacent in the structure of the protein but not in the primary sequence. Nevertheless, we were also interested in identifying the continuous subregions of proteins that contain high densities of matches, such as the amino-terminal domain of Cdc6p (Figure ). We therefore also developed a method to identify the most significant 'cluster' of matches within each protein. While SLR (described above) measures 'clustering' in the whole protein, this method allows identification of a single optimal 'cluster'. This represents an alternate strategy to predict proteins that contain clusters of consensus matches - by explicitly identifying the clusters. We note that this does assume that the clustered matches occur in a contiguous region, and therefore, for example, in the case of Cdc6p (Figure ) the carboxyl-terminal matches would not contribute to the score.
To find optimal clusters, we counted the number of matches (n
) to the strong (s
) or weak (w
) consensus in each possible subregion of the protein of length l
. We then computed the probability of observing as many matches or more of each type using the binomial distribution, and combined these P
values by multiplying them together by assigning a P
value to their product using the Q-fast algorithm [19
]. We note that the subregion with the maximal score will begin and end with a match. There are therefore only N
- 1)/2 possible clusters to try, where N
) is the total number of matches in the entire protein. This means that proteins with many matches have more chances to obtain a high scoring cluster. We therefore correct for the total number of clusters searched by multiplying the P
value by this factor (a Bonferoni multiple testing correction). Thus, we define the following:
where Q [...] is the Q-fast algorithm, p(≥ x | l, f) is the binomial probability of observing x or more in l tries when the per try probability is f, and fsb and fwb are the per residue probabilities of observing strong and weak matches, respectively, in the genome. Once again we were concerned about the possibility of nonspecific clusters and therefore, when using SBN to predict CDK targets, we imposed the following heuristic; to be considered, subregions must contain at least one match to the strong consensus per 100 residues. For example, in the case of Cdc6p, this optimal cluster corresponds to the amino-terminal domain (Figure , bold residues) and has SBN = 8.38, ranking 61st in the genome.
Assessing the classifiers
In order to assess whether these classifiers were capturing useful information about the recognition of substrates by CDKs, we computed the scores described above for each protein in S. cerevisiae
and compared them to the 'phosphorylation scores' reported for the 695 S. cerevisiae
proteins tested in the high-throughput Cdk1p assay [11
] (Table ). These proteins tested in that study fall into three groups: 198 randomly chosen proteins (containing the 'unbiased positives' and 'unbiased negatives' described above, henceforth referred to as 'unbiased'), all 385 S. cerevisiae
proteins that contain two or more matches to the strong CDK consensus (henceforth '2+'), and finally 137 proteins that contain one match to the strong consensus, and exhibit cell cycle transcript regulation (henceforth '1cc'). We note that although the last two groups were biased in different ways, as long as we treat them separately (condition on the bias) the proteins in each group can be treated as identical and independently distributed.
In the 'unbiased' and '2+' groups, we found a highly significant correlation (R > 0.3, P < 10-10) between the phosphorylation score in the assay and both of the cluster-based scores described above (Table ), such that proteins with higher scoring cluster are more likely to have high scores in the kinase assay.
Correlation between cluster score and position and phosphorylation in the kinase assay
Because in many cases we noted that the clusters seemed to occur near the carboxyl- or amino-terminus of the proteins (as in the case of the Cdc6p amino-terminal domain; Figure ), we computed the relative 'position' of the optimal cluster, where 0.5 is the midpoint of the protein and 0 is either terminus (see Materials and methods, below). Interestingly, we found that the position was negatively correlated (R < -0.2, P
< 0.01), with the results of the kinase assay in the same two groups of targets, such that proteins with clusters near their termini were more likely to be positive in the assay. It has also been noted that phosphorylation sites tend to fall in disordered or unfolded regions of proteins [20
]. Consistent with this, we found a significant correlation (R ≤ -0.19, P
< 0.01) between the 'foldedness' [21
] of the cluster and the score in the kinase assay, such that proteins containing clusters of matches in unfolded regions were more likely to be bona fide
substrates. In order to verify that these factors were independently correlated with the results of the assay (and not simply correlated with each other), we fit linear models of the likelihood ratio score, position and 'foldedness', and found that they all contributed significantly (P
< 0.02; Table ).
Predicting CDK substrates based on clustering of consensus matches
The correlations we observed suggested that clustering of consensus matches could be used to predict the targets of Cdk1p in S. cerevisiae
. Taking proteins defined as CDK targets or not in the high-throughput assay [11
] as positives and negatives, we computed receiver operating characteristic (ROC) curves for the three groups of proteins tested in the assay.
First, we compared the two classifiers described above to simply classifying based on the density of strong CDK matches in the protein. We found that although all were strong classifiers in the 'unbiased' set, the cluster-based methods performed better than a simple density (Figure ). In the low false-positive range, which is of most relevance to protein database searches, the score based on the likelihood ratio (SLR) seemed most effective. We also compared the methods on the '2+' set and found similar results (data not shown). We therefore used SLR for subsequent analyses.
Figure 4 ROC curves for prediction of CDK substrate proteins. (a) Comparison of classifiers suggests that cluster based methods SLR and SBN (filled squares and triangles, respectively) perform better than the density of strong matches (filled circles). (b-d) (more ...)
We next compared the predictive power of the cluster-based classifier (SLR
) with that of a specificity matrix-based approach (Scansite [23
]), and used the score of the best match to the Cdc2 matrix in each protein (see Materials and methods, below) as the predictor. Both our cluster-based method and the specificity matrix-based method were strong classifiers for the 'unbiased' set (Figure ); since most of these proteins contain no matches, many of the negatives can be ruled out simply based on the absence of a match to the consensus. For the '1cc' proteins, neither method has much power (Figure ). For the '2+' set (Figure ), however, we notice a considerable increase in sensitivity and specificity in the low false-positive region by using our cluster score. In the '2+' group, at false-positive levels near 5%, the matrix-based method performs similar to a random classifier, whereas the cluster-based method retains some power. Because each of these proteins has multiple matches to the consensus, most have high matrix match scores. The proteins in which there are multiple matches that are spatially clustered, however, are more likely to be bona fide
substrates for Cdk1p. We note that even in this set the overall predictive power is still relatively poor.
An important feature of these cluster based methods is that we can include weak matches to the consensus in our predictor. We found, however, that classifiers based on clustering only of strong matches also performed well (data not shown). In order to confirm that the weak matches were contributing to the clusters, we identified optimal clusters based only on the strong matches using a univariate version of the method described above (SBN
). We then compared the density of weak matches in these regions with the density of the scrambled weak consensus. We found enrichment of 2.1-fold and 1.4-fold in the 'known' targets and assay positives (all groups combined), as compared with 1.2-fold in the negatives (all groups combined; Figure ), indicating that weak matches are preferentially associated with clusters of strong matches. The size of these effects is not great, however, and therefore weak matches may not contribute much to the classification of individual proteins. Nevertheless, this supports the use of both the strong and weak consensus matches in this case, and is consistent with previous reports that weak sites can be important for function [12
] (see Discussion, below).
Figure 5 Weak CDK consensus matches co-cluster with strong matches. Gray and unfilled bars indicate frequencies of matches to the weak CDK consensus and to a scrambled version of it within regions identified as optimal clusters based on only strong matches. 'Known' (more ...)
Our aim here was not to explore the properties of these classifiers in detail, but rather to establish the potential of methods that take advantage of the propensity of the CDK motifs to cluster (see Discussion, below).
Defining a set of proteins containing clusters of CDK consensus sequences
Taken together, these results suggest that not all Cdk1p targets in S. cerevisiae contain clusters of consensus matches, but that there is some subset that can be predicted in this way. In order to estimate the number of CDK consensus cluster containing proteins that can be recognized based on sequence alone, we searched the genome for matches to scrambled versions of the strong and weak CDK consensus (P-R/K-X-S/T and P-S/T, respectively) and compared the distribution of likelihood ratio scores with those obtained using the real consensus sequences. Comparison of these distributions suggests a score threshold of 3.5 (Figure ). This yields an excess of 50 proteins, because there are 67 proteins above the threshold when the real consensus sequences are used, and 17 when scrambled consensus sequences are used.
Figure 6 Defining a set of CDK consensus cluster containing proteins. Comparison of the distribution of scores from a search of the S. cerevisiae genome using either the real CDK consensus motifs (gray area) or scrambled versions (unfilled area) suggests a threshold (more ...)
Of these 67 top predictions (ranked based only on sequence), 49 were positive in the kinase assay [11
] (all groups combined). This indicates at this threshold our cluster-based method yields a positive predictive value (PPV) of 73%, but it includes 18 false positives. Compared with the PPV of 49% (17/35) for the proteins identified by the matrix-based approach (Scansite [23
]) at the same false-positive level, our cluster-based approach has significantly greater PPV (P
= 0.017, by Fisher's exact test), which is consistent with the hypothesis that searching for clusters can strongly identify at least some subset of CDK targets. In order to examine further the properties of the clustered matches in these proteins, we identified the maximal scoring cluster using the method described above (SBN
). Consistent with our earlier observations, we found that for 36% (24/67) of these proteins the optimal cluster ended within 5% of the protein's length from either terminus, and that even if we masked the CDK matches, the optimal clusters were on average significantly less 'folded' that the whole proteins (-0.08 versus -0.0002, respectively; P
< 0.001, by Students' t
Predicting CDK targets among human proteins
Regulation of cell cycle progression by CDKs is thought to be an ancient feature of eukaryotic cells. Indeed, human CDK homologs were first identified based on their ability to rescue yeast mutants [24
]. We therefore sought to test whether clustering of consensus matches could also be used to predict CDK targets in humans.
We found 73 human proteins (see Materials and methods, below) that were listed as CDK, CDK1, or CDK2 targets in the phosphoELM database [26
]. Although we do not have a set of negative proteins (as for S. cerevisiae
), we can still compute an ROC curve by using the fraction of the genome above the threshold as an approximate false-positive rate. In doing so we assume that the fraction of proteins that are targets in the genome is negligible compared with the total number of proteins. This analysis (Figure ) suggests that our method has some predictive power at reasonably low false-positive levels; some subset of human CDK targets may also contain clusters of consensus matches and may therefore be predicted using our method.
Figure 7 Predicting CDK targets in the human genome. (a) The fraction of proteins in known human CDK targets versus the fraction in the human genome (black bar) as the cutoff is varied. (b) Genes with clusters scoring more than 3.5 from a list of human cell-cycle (more ...)
To predict novel human CDK targets, we obtained a set of 112 human cell cycle genes (see Materials and methods) and identified those containing clustered consensus matches. Of the six proteins in this set with clusters scoring 3.5 or greater (Figure ), none were included in the 73 CDK targets in phosphoELM. Of these, BRCA2 was recently shown to be a CDK target [27
]. Of the other five, there is already evidence that three (RANBP2, CDC20, and CDC5L) are mitotic phosphoproteins, and there are varying degrees of evidence that they are bona fide
CDK targets [28
]. The other two (CDCA5/sororin and TPX2) are both degraded by the anaphase-promoting complex through direct interaction with K-E-N motifs [31
]. Interestingly, these K-E-N motifs are found among closely spaced CDK consensus matches in these proteins (Figure ). It is tempting to speculate that their anaphase promoting complex-dependent degradation is regulated through phosphorylation by CDKs, as has been suggested for human CDC6 [33
], and that these clusters represent regulatory modules (see Discussion, below). Regardless, that these human cell cycle proteins contain clusters of CDK consensus sequences, and that there is some evidence for CDK phophorylation for four of the six, suggests that cluster-based methods can be used to predict CDK targets among human proteins as well.
Clusters of consensus matches and cyclin specificity
CDKs are thought to gain target specificity by pairing with particular cyclins. For example, Cdc6p was found to be a specific target of Cdk1p:Clb5p [34
] and contains cyclin specific 'cy' motifs (R/K-X-L [17
]) in addition to CDK motifs (Figure , filled bars). We noted that of 14 Cdk1p:Clb5p specific targets identified in a recent study [34
], 72% (10) where among our strongest S. cerevisiae
> 3.5). Because, of the 143 proteins tested in that study, only 29% (42) were included in this set (SLR
> 3.5), 72% represents a highly significant enrichment (P
< 0.001, Fisher's exact test; Figure , left side). Interestingly, we also found that the clb5 specific proteins above our cutoff contained a higher proportion of strong matches to the CDK consensus; the clb5 specific clusters contained 43 strong and 18 weak matches (70% strong), which is significantly more than in the clusters in the rest of the proteins above the cutoff, where we find 217 strong and 343 weak (39% strong; P
< 0.001, by Fisher's exact test; Figure , right side). We speculate that this may be related to the lower overall activity of the Cdk1p-Clb5p complex [34
Figure 8 Clustering of CDK consensus matches and cyclin specificity. (a) The left side shows that clb5-specific CDK targets (unfilled bar) are more likely to score above the cutoff than other proteins assayed (gray bar), while the right side of panel a shows that (more ...)
In order to test directly whether 'cy' motifs were associated with the CDK clusters, we masked out the matches to the CDK consensus and compared the frequency of matches to the cy motif in the clb5 specific proteins with the frequency in the rest of the proteins above the cutoff (Figure ). Although the frequency of cy motifs in the entire proteins was significantly greater in the clb5-specific targets than in the other proteins (Figure , left side; P
= 0.014, by Fisher's exact test), the difference was greater and more significant when we considered only the regions identified as optimal clusters (Figure , right side; P
< 0.001, by Fisher's exact test). Futhermore, we note that the regions defined as the optimal clusters in the proteins that were not clb5 specific contain fewer matches to this motif than expected based on the genome frequency, perhaps related to the paucity of leucine residues near phosphorylation sites [20
]. These findings suggest that cy motifs tend to cluster with CDK motifs in clb5 specific targets. Thus, it may be possible to associate cyclin specificity with a specific composition of motifs, analogous to the 'regulatory codes' that have been proposed for some enhancers of transcription [35
] (see Discussion, below).