An allosteric conduit facilitates dynamic multisite substrate recognition by the SCFCdc4 ubiquitin ligase

The ubiquitin ligase SCFCdc4 mediates phosphorylation-dependent elimination of numerous substrates by binding one or more Cdc4 phosphodegrons (CPDs). Methyl-based NMR analysis of the Cdc4 WD40 domain demonstrates that Cyclin E, Sic1 and Ash1 degrons have variable effects on the primary Cdc4WD40 binding pocket. Unexpectedly, a Sic1-derived multi-CPD substrate (pSic1) perturbs methyls around a previously documented allosteric binding site for the chemical inhibitor SCF-I2. NMR cross-saturation experiments confirm direct contact between pSic1 and the allosteric pocket. Phosphopeptide affinity measurements reveal negative allosteric communication between the primary CPD and allosteric pockets. Mathematical modelling indicates that the allosteric pocket may enhance ultrasensitivity by tethering pSic1 to Cdc4. These results suggest negative allosteric interaction between two distinct binding pockets on the Cdc4WD40 domain may facilitate dynamic exchange of multiple CPD sites to confer ultrasensitive dependence on substrate phosphorylation.

W D40 domains, and the related Kelch b-propeller domains, mediate protein interactions in many contexts and together form the largest domain family in the human genome 1 . WD40 domain proteins are a predominant class of substrate receptor in the ubiquitinproteasome system, found in F-box proteins and other subunits of the cullin-RING (CRL) ubiquitin ligases [2][3][4] . The WD40 domain of the yeast F-box protein Cdc4 (Cdc4 WD40 ) recognizes substrates via phosphorylated motifs termed Cdc4 phosphodegrons (CPDs). One of the best characterized Cdc4 substrates is the cyclin dependent kinase inhibitor Sic1, which is targeted for ubiquitination and degradation in late G1 phase upon its phosphorylation by Cln-Cdc28 kinase activity 5,6 . Sic1 is phosphorylated at 9 low-affinity CPD sites (K d B10-100 mM) that all bear mismatches to the optimal CPD sequence (I/L-I/L/P-pT-P-oKR44, whereo4 indicates a disfavoured residue) 7 . Phosphorylation on between 4 and 6 low-affinity CPD sites generates a high-affinity Sic1-Cdc4 interaction (K d B1 mM) 7,8 . This requirement for multisite phosphorylation sets a threshold that converts a graded increase in Cln-Cdc28 activity into switch-like elimination of Sic1 6,8 . Responses that transform graded inputs into sharply thresholded outputs are referred to as 'ultrasensitive' 9,10 , and often result from multisite phosphorylation 11,12 .
Nuclear magnetic resonance (NMR) analysis suggests that multiple Sic1 low-affinity CPD sites interact with Cdc4 in a dynamic equilibrium to generate an overall high-affinity interaction 13,14 . The structure of a high-affinity singly phosphorylated CPD bound to Cdc4 revealed that the P0 phosphorylated residue occupies a deep arginine-rich pSer/Thr binding pocket in the WD40 domain, and that adjacent subpockets confer sequence selectivity at P À 2, P À 1, P þ 1 and P þ 2 CPD positions 7 . A distal basic surface in Cdc4 and its human orthologue Fbw7 can also simultaneously engage a second phosphorylated residue at the P þ 4 position to increase affinity [15][16][17] , or conversely antagonize the interaction of CPDs with C-terminal basic residues 7 . However, this secondary phosphate-binding site is dispensable for Sic1 degradation in vivo 8 . Dimerization of the SCF Fbw7 complex also contributes to the recognition of some multisite phosphorylated substrates 18 , and catalytic efficiency of the SCF Cdc4 complex 19 . Cln-and Clb-CDK may act in a processive multi-phosphorylation cascade on Sic1 to facilitate Cdc4 recognition through generation of appropriate CPD sites 16 . Recognition of the Ash1 transcriptional repressor by Cdc4 depends on three closely-spaced CPD sites that form a redundant diphosphodegron 20 . Other substrates, including Far1, Gcn4, Cln2 and Cln3 for Cdc4 in yeast and cyclin E, c-Myc and Mcl1 for Fbw7 in humans, also may depend on multisite phosphorylation 2,21,22 . These various interaction modes illustrate the tunability of the Cdc4/Fbw7 system for substrate elimination.
The phenomenon of allostery, whereby ligand binding at one site alters interactions at a physically distant site, allows for complex control of protein function [23][24][25] . A biplanar dicarboxylic acid compound called SCF-I2 allosterically inhibits Cdc4 WD40substrate interactions by binding to a site 25 Å away from the main CPD pocket 26 . SCF-I2 elicits this allosteric effect through structural changes that occlude the P À 2 region of the CPD pocket. Enigmatically, SCF-I2 is 10-fold less potent towards full-length Sic1 compared to a singly phosphorylated high-affinity CPD of similar affinity for Cdc4. The SCF-I2 site and associated allosteric infrastructure appear to be conserved through evolution 27 .
The large size of the Cdc4 complex previously precluded determination of substrate interaction effects on the WD40 domain. Here we investigate substrate-Cdc4 interactions by NMR analysis of assigned methyl groups in the isolated Cdc4 WD40 domain. Unexpectedly, we find that the CPDs of an extended phosphorylated Sic1 substrate directly contact the SCF-I2 allosteric site. On the basis of this data and the inhibitory effect of SCF-I2 on the CPD pocket, we predicted that extended multisite CPDs might engage the WD40 domain through both pockets in a mutually antagonistic manner, and then confirmed this hypothesis using fluorescence-binding data. Consistent with this negative allosteric effect, NMR analysis reveals smaller chemical shifts in the P À 2 sub-pocket for extended multisite CPDs compared with short CPD-containing peptides. Mathematical modelling suggests that interactions at the primary and allosteric pockets may enhance the ultrasensitive dependence of the Sic1-Cdc4 interaction on Sic1 phosphorylation. This negative allosteric binding mechanism helps explain the conundrum of how multiple low-affinity sites can generate a rapidly exchangeable yet high-affinity Sic1-Cdc4 interaction.

Results
Characterization of isolated Cdc4 WD40 . We determined the effects of substrate binding on the isolated WD40 domain of Cdc4 (Cdc4 WD40 ), which is more amenable to NMR due to its size (40 kDa) than the minimal Cdc4-Skp1 complex (B70 kDa). The N-terminal targeting region of Sic1 (residues 1-90, called Sic1 1-90 ), which contains 7 of the 9 Sic1 CPD sites and is sufficient for Cdc4 binding 28 , was phosphorylated to completion by Cln2-Cdc28-Cks1 kinase (called pSic1). We used isothermal titration calorimetry (ITC) to determine the affinity of Cdc4 WD40 for pSic1 and SCF-I2 ( Supplementary Fig. 1a-c). The K d value for pSic1-Cdc4 WD40 was 0.8±0.12 mM, similar to the 0.6 mM value determined for pSic1-Cdc4-Skp1 by intrinsic tryptophan (Trp) fluorescence 13 . The K d value for SCF-I2 binding Cdc4 WD40 was 0.6 ± 0.02 mM, concordant with the B2 mM K i value determined for SCF-I2-Cdc4-Skp1 by a fluorescence polarization competition assay 26 .
NMR resonances for Cdc4 WD40 were highly broadened, with millisecond-microsecond timescale motion likely playing a significant role. Although addition of a CycE phosphopeptide or SCF-I2 sharpened resonances ( Supplementary Fig. 1d,e), backbone assignment was not possible. However, as Cdc4 WD40 methyl resonances were sharper due to the favourable properties of methyls 29,30 , we analysed Ile-d1-[ 13 CH 3 ] and Met-e-[ 13 CH 3 ] (IM)-labelled samples (Fig. 1a). Cdc4 WD40 contains 24 Ile and 5 Met residues distributed throughout the WD40 domain. Three Ile (Ile573, Ile716 and Ile385) and 1 Met (Met590) are adjacent to the arginine-rich CPD binding pocket on Cdc4 and another 9 Ile residues lie in close proximity to both the CPD and the allosteric pockets. Point mutations of 15 Ile to Val or Met to Val enabled assignment of 12 Ile and 1 Met methyls in Cdc4 WD40 (Fig. 1b).
Perturbation of Cdc4 WD40 methyl resonances. Unlabelled CycE phosphopeptide, pSic1 or various phosphopeptides derived from Sic1 and Ash1 were titrated into IM-labelled Cdc4 WD40 samples and chemical shift perturbations and changes in line shape were observed as a function of ligand concentration. Ligand interactions are expected to broaden NMR spectra due to slowed tumbling, exchange between free and protein/peptide-bound states, and dynamic exchange within the bound state (Supplementary Note 1). Upon titration of CycE phosphopeptide into IM-labelled Cdc4 WD40 , large chemical shift perturbations (420 Hz combined 1 H/ 13 C shifts, see Methods, Fig. 1c,d, Supplementary Fig. 2a) were observed for Ile396 P , Ile573 P , Met590 P and Ile716 P (where P indicates a residue close to the primary CPD binding pocket) and Ile654 (which lies between the primary CPD and allosteric inhibitor pockets). We also observed a smaller but still significant chemical shift perturbation on Ile385 P . These NMR results are consistent with engagement of the primary CPD pocket by CycE (Fig. 1d).
Titration of unlabelled pSic1 into IM-labelled Cdc4 WD40 resulted in large chemical shift perturbations for residues Ile385 P , Ile396 P and Met590 P in the primary CPD pocket, as for CycE. Perturbations around the CPD pocket induced by pSic1 matched expectations from X-ray structures of CycE and pSic1 phosphopeptide-Cdc4 complexes 7,8 (Fig. 1d,f). We also observed differences for pSic1 binding compared to CycE, including smaller chemical shift perturbation for Ile716 P and no change for Ile573 P . In contrast to CycE, pSic1 elicited extensive chemical shift perturbations on blade 5 (Ile577 A , Ile594 A and Ile596 A , where A indicates a residue close to the allosteric inhibitor binding pocket) and blade 6 (Ile654) of Cdc4 WD40 , precisely around the SCF-I2 allosteric binding site ( Fig. 1f; Supplementary  Fig. 2b).
The allosteric binding pocket directly engages pSic1. We determined that all allosteric pocket residues exhibited fast-tointermediate timescale exchange dynamics (Fig. 2a,b), consistent with weak direct interaction, unlike the slow-intermediate exchange observed for some residues in the primary CPD pocket (see below). To identify potential contact residues between pSic1 and Cdc4 WD40 , we performed methyl cross-saturation experiments. Among the 13 assigned Ile and Met methyl resonances, only Ile396 P , Ile594 A , Ile596 A and Ile654 intensities were decreased significantly upon addition of pSic1 (Fig. 2c). Because cross-saturation exploits fast exchange between free and bound states 31 , we did not observe significant intensity changes for residues close to the primary CPD pocket due to slow exchange (Supplementary note 1). However, residues around a positively charged surface that includes Arg655 and Arg664 of the allosteric pocket were susceptible to cross-saturation (Fig. 2d,e). These results unambiguously identify the allosteric site as a direct second binding pocket on Cdc4 WD40 for CPD motifs, and eliminate the alternative possibility of indirect allosteric effects transmitted from binding at the primary CPD pocket. Arg655, Arg664 and Trp657 are the main determinants of SCF-I2 binding in the allosteric pocket 26 . Side chains of these residues form salt bridges and hydrogen bonds with the two SCF-I2 carboxylic acids and may likewise engage phosphates.
The allosteric pocket appears to be contacted only by extended multisite phosphopeptides (pSic1, Sic1 20pS69/pS76/pS80 ), but not short Sic1 10pT2/pT5 , Sic1 9pT45 , Sic1 9pT173 phosphopeptides ( Supplementary Fig. 3). We speculated that tethering of an extended substrate at the primary CPD pocket may increase local CPD concentration and drive interactions at the weaker-affinity allosteric site 32 . We used the program HADDOCK 33 to dock Sic1 20pS69/pS76/pS80 onto the allosteric pocket based on chemical shift perturbations and cross-saturation. One of the main simulated orientations placed one CPD in the allosteric pocket with potential contacts of another CPD at the primary binding pocket ( Supplementary Fig. 4a,b).
IM-labelled Cdc4 WD40 was also titrated with unlabelled SCF-I2. We observed large chemical shift perturbations close to the SCF-I2 binding pocket (Ile594 A , Ile596 A , Ile654 and Ile676) and also adjacent to the P À 2 sub-pocket of the CPD binding interface (Met590 P and Ile573 P ; Fig. 2f,g). These data confirm long-range structural effects on the CPD binding pocket caused by insertion of the inhibitor at the allosteric pocket 26 . SCF-I2 also had a smaller but still significant effect on Ile385 P and Ile716 P next to the P À 1 sub-pocket, not evident in the SCF-I2 bound crystal structure 26 . These results demonstrate that pSic1 and SCF-I2 have an overlapping binding surface on Cdc4 WD40 and would therefore be expected to compete for binding at this position 34 .
Role of the allosteric pocket in multisite recognition. We assessed the contribution of the allosteric pocket to substrate interactions by mutation of positively charged Arg655 and Arg664 residues, both of which are required for SCF-I2 inhibition 26 . We generated Arg655Gln and Arg664Gln substitution mutants to minimize disruptive steric effects on the allosteric pocket and WD40 domain. Mutation of either Arg residue resulted in four-to fivefold reduction in pSic1-Cdc4 WD40 affinity by in vitro Trp fluorescence (Fig. 3a, Table 1). Importantly, these mutations did not significantly reduce CycE-Cdc4 WD40 affinity, consistent with CycE not appreciably interacting with the allosteric pocket (Fig. 1c).
Previous mutational analysis of the allosteric pocket showed that Arg655Ala and Arg664Ala substitutions completely block SCF-I2 inhibition in vitro, but do not cause obvious growth or cell cycle defects in vivo 26 . As other nominally functional Cdc4 mutants are sensitive to Sic1 dosage and phosphorylation status 8 , we examined effects of additional Sic1 dosage on Arg655 and Arg664 mutants. While SIC1 overexpression had little impact on mutant strain growth rates ( Supplementary Fig. 4g), additional SIC1 dosage caused accumulation of cells with elongated buds and a concomitant G1 delay (Fig. 3b,c), consistent with a mild Sic1 elimination defect. These results suggest that, while not essential, the allosteric pocket facilitates Cdc4 substrate degradation in vivo.
Allosteric pocket binding weakens the primary CPD interaction. We compared affinities of Sic1 peptides phosphorylated either on Ser69 (Sic1 20pS69 ) or Ser80 (Sic1 20pS80 ) alone or together (Sic1 20pS69/pS80 ). NMR titration of the Sic1 20pS69/pS76/pS80 phosphopeptide perturbed chemical shifts in the primary and allosteric pockets ( Supplementary Fig. 3d), suggesting that Ser69-and/ or Ser80-containing CPDs can bind both pockets ( Fig. 4a,b) and that the two CPDs are distant enough to enable simultaneous binding (Fig. 4c). To test this model, we computationally docked the Sic1 20pS69/pS80 phosphopeptide onto Cdc4 WD40 at the primary and allosteric pockets, and found that the two sites can indeed simultaneously engage with no obvious energetic strain ( Supplementary Fig. 4c).
We determined phosphopeptide binding affinities for wildtype and mutant (Arg664Gln) Cdc4 WD40 by Trp fluorescence (Supplementary Fig. 4d-f). Strikingly, the association constant for Sic1 20pS69/pS80 binding to wild-type Cdc4 WD40 , K a (p69,p80|wt) ¼ 1.42 Â 10 5 M À 1 , was about half that for Sic1 20pS69/pS80 binding to mutant Cdc4 WD40 , K a (p69,p80|mt) ¼ 2.67 Â 10 5 M À 1 (see Methods, Table 2). Despite the presence of two binding pockets on wild-type Cdc4 WD40 , binding was considerably weaker than for Cdc4 WD40 bearing only the primary CPD pocket. This result demonstrated negative allostery for a diphosphopeptide with sites that are sufficiently spaced to allow simultaneous contact with the primary and allosteric pockets. In contrast, if Cdc4 WD40 had two independent binding sites, the expected result would be higher affinity for the wild-type due to additive contributions of both sites. We also found that the Sic1 20pS69/pS80 K a (p69,p80|wt) ¼ 1.42 Â 10 5 M À 1 was smaller than the sum K a (p69|wt) þ K a (p80|wt) ¼ 2.07 Â 10 5 M À 1 for singly phosphorylated peptides binding to wild-type Cdc4 WD40 . This result is also in agreement with negative allosteric coupling between the primary and allosteric pockets, although other effects that weaken combinatorial interactions at different sites may also be operative 32 . Note that the negative effect of the allosteric site on Sic1 20pS69/pS80 diphosphopeptide binding is opposite to the decreased affinity of the allosteric site mutants for the larger pSic1 1-90 ligand. This apparent inconsistency is resolved by accounting for long-range electrostatic contributions from the four additional CPDs in pSic1 1-90 (see Supplementary note 4). Finally, we found that the doubly phosphorylated peptide (Sic1 20pS69/pS80 ) bound mutant Cdc4 WD40 with K a (p69,80|mt) ¼ 2.67 Â 10 5 M À 1 , approximately 1.7 times larger than the sum K a (p69|mt) þ K a (p80|mt) ¼ 1.56 Â 10 5 M À 1 for the singly phosphorylated peptides. This result is consistent with additional long-range electrostatic contributions from a second CPD in the absence of direct contact with Cdc4 (ref. 35).
Chemical shift perturbations in the primary CPD pocket. We then examined NMR chemical shift and line-shape perturbations  Ile596   M590   I676   I654   I596   I594   I573   Ile654   Ile396   90°I   le654   Ile596   396  553  565  573  577  586  590  594  596  654  676  716  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16  17  18   385   Peak #   396  553  565  573  577  586  590  594  596  654  676  716  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16   for signatures of negative allostery. Although populationweighted averaging and differential broadening due to exchange between states prohibits quantitative interpretation, qualitative comparisons are possible. First, we examined residues near the P À 1 sub-pocket lined by Trp717 and Val384 ( Supplementary  Fig. 5a). CycE led to Ile385 P chemical shift changes dependent on peptide concentration (fast exchange), whereas two peaks were observed for Ile716 P (slow-intermediate exchange; Supplementary Fig. 5b). The opposite was seen for pSic1 with Ile385 P in slow-intermediate and Ile716 P in fast exchange ( Supplementary Fig. 5c). These chemical shift perturbations demonstrate binding of both CycE and pSic1 in the P À 1 sub-pocket, albeit with some differences. A striking difference between pSic1 and CycE was evident for Met590 P and Ile573 P close to the P À 2 sub-pocket that binds hydrophobic residues of the CPD (Fig. 5a). For both CycE and pSic1, two peaks were observed for each residue reflecting slowintermediate exchange between free and bound states (Fig. 5b,c). However, the complexity of the NMR line-shapes suggested a dynamic equilibrium, possibly including partially engaged states. Met590 P is one of the most exposed side chains near the CPD pocket (Fig. 5a) and may be a general probe of substrate interactions. The loss of intensity and chemical shift perturbations for Met590 P in both CycE and pSic1 titrations were similar. In contrast, Ile573 P lies at the bottom of the P À 2 sub-pocket and should be sensitive to deep engagement (Fig. 5a). While Ile573 P was broadened and showed chemical shift changes in the presence of CycE (Fig. 5b), neither effect was significant for pSic1 (Fig. 5c). These results suggest that the P À 2 sub-pocket interacts less with pSic1 than CycE.
To investigate whether the apparent differential engagement of the P À 2 pocket by pSic1 and CycE was due to the absence of preferred hydrophobic residues in P À 2 positions of 8 of the 9 CPD sites of pSic1, titrations of pSic1 phosphopeptides (Sic1 10pT2/pT5 , Sic1 9pT45 , Sic1 9pT173 and Sic1 20pS69/pS76/pS80 ) were analysed. The binding of all phosphopeptides perturbed chemical shifts of Ile573 P ( Supplementary Fig. 3), as for CycE. The Sic1 20pS69/pS76/pS80 phosphopeptide actually had the smallest Ile573 P perturbation, about one third that of CycE. This was surprising since the Leu at the P À 2 position of the pSer76 site is a match to the Leu/Ile consensus; if the P À 2 position were the sole determinant of binding, we might expect the Sic1 20pS69/pS76/pS80 phosphopeptide to have the largest Ile573 P perturbation yet this was not the case. From these results, we concluded that the lack of consensus Leu/Ile residues in P À 2 positions of pSic1 CPDs cannot explain the apparent differences in pSic1 and CycE binding the P À 2 pocket, and instead suggested an allosteric effect might be at play.
The allosteric inhibitor SCF-I2 is known to cause occlusion of the P À 2 sub-pocket due to re orientation of a main chain Tyr residue 26 . Both pSic1 and Sic1 20pS69/pS76/pS80 significantly perturbed residues on blade 5 (Ile594 A , Ile596 A and Ile577 A ) and also caused unexpectedly small chemical shift perturbations at Ile573 P relative to CycE. We speculate that this NMR effect reflects decreased binding at the P À 2 sub-pocket due to negative allosteric modulation of the primary CPD pocket upon simultaneous binding of another CPD site in the extended Sic1 multisite degrons (Fig. 4d-f).
Interactions of Ash1 with Cdc4 WD40 . We then investigated binding of IM-labelled Cdc4 WD40 to unlabelled phosphopeptides derived from Ash1 residues 283-299. Singly phosphorylated peptides around pThr286, pThr290 and pSer294 sites have affinities for Cdc4 of 0.9, 4.1 and 6.5 mM, respectively, and  the triphosphorylated peptide has an affinity of 0.07 mM (ref. 20). Ash1 9pT290 significantly perturbed residues close to the primary CPD pocket but not residues near the allosteric pocket (Fig. 6a,b). Ash1 9pS294 had much less effect on the P À 1 sub-pocket than Ash1 9pT290 since Ile385 P and Ile716 P did not show significant perturbations (Fig. 6a,c). Since the P À 1 and P À 2 positions for the Thr290 and Ser294 sites match the CPD consensus ( Supplementary Fig. 2c), the observed difference for the P À 1 sub-pocket likely reflects the weaker affinity of pSer versus pThr for the P0 sub-pocket 6 . Consistently, a pSic1 phosphopeptide containing pSer at P0 (Sic1 20pS69/pS76/pS80 ) also minimally perturbed the P À 1 sub-pocket ( Supplementary Fig. 3).
In contrast to the lower affinity Ash1 CPD motifs, Ash1 9pT286 led to two peaks for Ile385 P , Ile396 P , Ile573 P , Ile586 A , Ile594 A and Ile596 A resonances in the fully saturated complex, diagnostic of two bound-state conformations (Supplementary Fig. 6a). In one of these, chemical shift perturbations for Ile573 P , Ile594 A and Ile596 A were much greater than for other residues (Fig. 6a,d). Titration with the Ash1 18pT286/pT290/pS294 triphosphopeptide resulted in similar chemical shift perturbations as for Ash1 9pThr286 but with slightly smaller shifts for Ile396 P and Ile586 A (Fig. 6a,e, Supplementary Fig. 6b). The magnitude of shifts for residues in the allosteric pocket for these Ash1 peptides was significantly larger than for pSic1 (Fig. 1e), suggesting that Differential effects of SCF-I2 on Ash1 CPDs. Using fluorescence polarization 26 , we found that SCF-I2 was 10-fold more potent for inhibiting Ash1 18pT290/pS294 binding than Ash1 18pT286/pT290 or Ash1 18pT286/pT290/pS294 peptides (Fig. 6f,g, Table 3). However, since the Ash1 18pT286/pT290/pS294 bound equally well to wild-type versus Arg655Gln or Arg664Gln Cdc4 WD40 ( Supplementary  Fig. 6c), we concluded the pThr286 CPD exerted an indirect allosteric effect on the SCF-I2 binding pocket. HADDOCK docking of Ash1 phosphopeptides to Cdc4 WD40 based on chemical shift perturbations was used to provide a model for allosteric transmission. In these models, the P À 2 sub-pocket of Cdc4 was occupied by the P À 2 prolines of pThr290 and pSer294 CPDs but by the P À 3 tryptophan of the pThr286 CPD, possibly due to predicted pi-pi interactions with Tyr594 ( Supplementary  Fig. 6d). Since SCF-I2 binding causes residue rearrangements near the CPD pocket, including Leu634, Val 635 and Tyr594 ( Supplementary Fig. 6e), interaction between the P À 3 tryptophan and Tyr594 may inhibit such rearrangements, thereby more effectively outcompeting SCF-I2 than other CPDs. These prominent indirect effects of the pThr286 Ash1 CPD on the allosteric pocket are in contrast to the minimal effects of CycE on the allosteric site and the direct allosteric site contacts made by CPDs in extended multisite ligands. The contributions of the allosteric pocket in Cdc4 may thus be modulated in a substratespecific manner.
Biophysical model for dynamic site exchange. The above results suggested that dynamic exchange of the CPDs may be facilitated through negative allosteric communication between the primary and allosteric pockets. Binding of one CPD to the primary pocket would tether other CPDs in close proximity to Cdc4, and thereby enhance interactions with the low-affinity allosteric pocket (Fig. 7a, i and ii). In contrast to simple two-site binding, however, CPD binding to the allosteric pocket also weakens the CPD interaction with the primary pocket (Fig. 7a, iii), facilitating disassociation and subsequent rebinding to the primary pocket, possibly involving a previously non-engaged CPD (Fig. 7a, iv).
Notably, engagement at the allosteric pocket provides a physical basis for tethering of Sic1 to Cdc4 upon transient disengagement from the primary CPD site. In an earlier model, we rationalized the physical basis for ultrasensitivity by through-space long-range interactions between a single positively charged binding pocket on Cdc4 and the collection of negatively charged phosphates on Sic1 (ref. 35). Given evidence for CPD engagement of the allosteric pocket, we sought to ascertain whether the hypothesized polyelectrostatic basis for ultrasensitivity would hold. We extended our mathematical model to three bound configurations, under the same simplifying assumption of equivalent CPD motifs as the original model 35 (Fig. 7b, Supplementary Fig. 7; see Supplementary note 3 for mathematical formulation). We refer to the single-point bound configurations with only the primary (P) pocket or only the allosteric (A) pocket engaged as P and A 0 , respectively, and the two-point bound configuration with both pockets engaged simultaneously as (P 0 ,A). In this model, despite conformational entropy loss for two-point binding 36 , the (P 0 ,A) configuration becomes more favourable than P or A 0 when the Sic1 net charge becomes negative because the average Sic1 to Cdc4 distance for (P 0 ,A) is smaller due to the constraint imposed on the Sic1 conformational ensemble by two-point binding, resulting in stronger electrostatic attraction between Cdc4 and non-contacting CPDs. This two-point contact model can lead to sharper ultrasensitive binding transitions than single-site models even though the transition midpoint remains essentially identical (Fig. 7c, Supplementary Fig. 7a). The critical role of noncontacting CPDs is underscored by considering an alternate model without long-range electrostatic contributions to binding, in which case ultrasensitivity is lost (Supplementary Fig. 7b). Note that the enhancement of ultrasensitivity by two-site binding does not rely on a precise degree of positive or negative allosteric coupling between the two Cdc4 sites but instead depends only on the existence of a two-site bound state to tether the Sic1 conformational ensemble closer to Cdc4 ( r 2 h io r 1 h i). Negative coupling is, however, required for a similar transition midpoint in the one-and two-site models ( Supplementary Fig. 7c). Comparing ultrasensitivity for different degrees of negative coupling between the two Cdc4 binding pockets, we found that as long as the bound Sic1 conformations are held closer on average to the Cdc4 for two-point than for one-point binding by B20% or more, ultrasensitivity is higher for the two-point model, even in the presence of substantial negative coupling ( Supplementary Fig. 7d). Thus, the proposed ultrasensitivity enhancement effect for the two-site model is robust.

Discussion
Multisite phosphorylation is often the basis for cellular decision-making 37 and can control kinase priming events 38 , substrate dephosphorylation, subcellular localization and signal integration 39 . Multisite phosphorylation can lead to either linear graded responses 40 or non-linear ultrasensitivity 6,11,12 . Sic1-Cdc4 is a well-studied example of an ultrasensitive interaction [6][7][8]13,14 . However, the molecular basis for Sic1 multisite-dependence has been elusive, in part because the consequences of substrate interactions on Cdc4 itself have never been investigated. Our assignment of 13 methyl groups positioned throughout the Cdc4 WD40 domain provides the first effective NMR probes for investigating substrate effects on Cdc4 WD40 . This approach enabled detection of unexpected direct binding interactions of  Sic1 CPDs to the previously described SCF-I2 allosteric pocket, a finding with major ramifications. First, the allosteric pocket tethers Sic1 near the primary CPD pocket, curtailing Sic1 diffusion away from Cdc4 and increasing Sic1 local concentration. Second, based on affinity measurements, engagement of the allosteric pocket by CPDs weakens other CPD interactions with the primary pocket, likely by inducing rearrangement of P À 2 sub-pocket residues analogous to the effect of SCF-I2. This negative allosteric effect facilitates the exchange of multiple CPD motifs, and increases the probability of rebinding another CPD site. The allosteric effect also explains the   decreased chemical shift perturbations in the P À 2 sub-pocket for extended multisite pSic1 substrates compared to short CycE and Sic1 phosphopeptides. Identification of the allosteric pocket as a second direct binding determinant adds complexity to the already intricate nature of multisite Cdc4 substrate interactions. Since the sequence composition of individual CPD motifs varies considerably, some may bind to the allosteric pocket with higher affinity. Because of negative allosteric coupling between the primary CPD and allosteric pockets, CPDs that preferentially bind the allosteric pocket may have complex effects on substrate recognition. As the primary CPD and allosteric pockets are separated by B25 Å, simultaneous engagement can only occur if CPDs are separated by at least 7 residues. In Sic1, all but two CPD pairs meet this requirement, making many binding scenarios possible. These subtleties may affect timing of substrate degradation and confer differential susceptibility to small molecule allosteric inhibitors. We speculate that non-phosphorylated motifs in extended substrates may also engage the allosteric site to further refine substrate recognition.
Different models have been proposed for Sic1-Cdc4 ultrasensitivity. One initial proposal posited that a potential second binding pocket on Cdc4 could tether Sic1 to increase local concentration 41 . However, a simple two-site model would be dominated by overly strong thermodynamic effects, rendering high-affinity interaction dependent only on two sites, not the multiple sites observed. A kinetic model argued that, if internal CPD motion exceeded overall Sic1 diffusion, the probability of rebinding should exhibit an ultrasensitive dependence on number of CPDs 42 , but the physical basis for this effect was unknown. An entropic model postulated that multisite phosphorylation could significantly reduce conformational entropy for unbound Sic1 to favour binding 43 , but further experiments revealed no substantial decrease in Sic1 conformational disorder upon phosphorylation 14 .
Our polyelectrostatic model suggested that long-range interactions between the positively charged CPD pocket on Cdc4 and the cohort of negatively charged phosphates on Sic1 could yield an ultrasensitive transition once the overall Sic1 charge became negative 35 , analogous to other bulk electrostatic effects 44 . However, as many Sic1 lysines are dispensable for recognition 45 , charge balance alone may not explain ultrasensitivity. Regardless, it is necessary for all models that non-contacting CPDs contribute to binding such that the bound Sic1 population increases approximately exponentially with the number of phosphorylation events. Our modelling suggests that, if the allosteric pocket contributes significantly only for intermediate to large numbers of CPDs, then disabling the allosteric pocket will decrease the sharpness but not the midpoint of the ultrasensitive transition (Supplementary note 3). This predicted effect of an allosterically-coupled two-site interaction is generalizable to other mechanisms, including tethering 41 and transient kinetic trapping 42 . To our knowledge, this form of negative allostery involving multiple biding sites within the same extended protein ligand has not been reported previously. Importantly, it has implications for the Sic1 conformational distribution that future, more comprehensive models will need to quantitatively consider (Supplementary note 4).
Allosteric communication between binding sites may be a general feature of WD40 domains, which frequently contact more than one partner on different surfaces, in some instances mediating allostery. In one example, the transducin inhibitor phosducin binds the transducin WD40 domain to induce structural rearrangements between blades 6 and 7, creating a binding pocket for the farnesyl moiety of the partner Gg subunit 27 . Remarkably, the key allosteric pocket residues and main chain movements are virtually superimposable between transducin and Cdc4 (ref. 26). In another example, the transcriptional regulator WDR5 interacts with RbBP5 between blades 5 and 6 to allosterically regulate the methyltransferase activity of MLL1, which binds to an arginine-rich site on WDR5 (ref. 46). As shown here, binding of the same ligand to two different sites can also elicit allosteric communication and engender unusual protein recognition behaviour, vastly diversifying the output of simple binding events. Finally, we note that the Cdc4 allosteric infrastructure appears conserved in Fbw7 (ref. 26), which is a frequently mutated tumour suppressor in human cancer 22 . Since many Fbw7 substrates are multisite phosphorylated 22 , it will be of considerable interest to determine whether allosteric coupling influences Fbw7 substrate recognition, and whether substrate-selective Fbw7 allosteric inhibitors can be developed.

Methods
Protein production and purification. Cdc4 WD40 (residues 367-744) was expressed from pET-Sumo (Invitrogen), isolated by Ni-nitrilotriacetate (NTA) affinity chromatography, digested with Ulp protease, and further purified by Ni-NTA and Superdex 200 chromatography 8 47 and 100 mg l À 1 L-methionine (methyl-13 CH 3 ) 48,49 1 h before protein induction and was purified as described above 8 . Sic1 was expressed as a GST fusion protein in Escherichia coli BL21(DE3) codon plus cells. The GST-Sic1 protein was purified by using glutathione-Sepharose affinity chromatography. After digestion with TEV protease, GST was removed by using anion exchange chromatography. Sic1 was further purified to homogeneity by using a Superdex 75 column (Amersham Biosciences). Sic1 was then phosphorylated with immobilized Cln2-Cdc28 kinase from baculovirus-infected Sf9 cells 13 .
NMR spectroscopy. Assignment of Ile and Met residues in Cdc4 WD40 . All NMR experiments were performed at 10°C on Varian Inova 500 and 800 MHz spectrometers. Methyl-TROSY spectra were recorded on per-deuterated protein samples dissolved in 100% D 2 O, 50 mM Na 2 HPO 4 , pH 8.0, 150 mM NaCl, 2 mM DTT. In order to assign the methyl residues, a total of 15 Ile to Val or Met to Val point mutations were made (I385V, I573V, M590V, I716V, I676V, I594V, I396V,  I404V, I553V, I565V, I586V, I596V, I654V and I577V), which resulted in unambiguous assignment of 1 Met and 13 Ile residues. (I404V mutation led to a spectrum of very poor quality that could not be used for assignment.) All spectra were processed using the program NMRPipe 50 and the spectra were analysed using SPARKY (T.D. Goddard and D.G. Kneller, SPARKY 3 (University of California, San Francisco).
NMR chemical shift perturbations. To monitor the interaction of Cdc4 WD40 with different partners, 2D 13 C-1 H TROSY HMQC spectra were recorded at 10°C on 200 mM IM-Cdc4 WD40 sample for increasing concentrations of pSic1, CycE and Ash1 peptides and SCF-I2 inhibitor. Chemical shift changes that were greater than one standard deviation from the mean were considered significant. Chemical shift perturbations (CSPs) were calculated from the relations where Dd is the chemical shift change between the apo and the fully saturated states of the protein.
Methyl-utilizing cross-saturation experiment. The cross-saturation (CS) experiment was carried out as described in Takahashi et al. 31 on a 300 mM IM-labelled Cdc4 WD40 sample with 600 mM pSic in 100% D 2 O, 50 mM Na 2 HPO 4 , pH 8.0, 150 mM NaCl, 2 mM DTT buffer at 10°C. Saturation of the aromatic protons in Sic1 was done by a WURST-2 adiabatic pulse with a maximum radiofrequency (RF) amplitude of 0.19 kHz. The saturation frequency was set to 7.0 with a saturation time of 1.5 s. As the saturation scheme was highly selective for the aromatic proton region, the irradiation did not affect the intensity of the pSic1 amide region. However, to ensure that CS effects seen were not transmitted by spin diffusion, a control experiment was performed in which the saturation frequency was set to À 5 p.p.m. CS effects are presented as ratios of (I irr /I 0 ) with Cdc4 and (I irr /I 0 ) without Cdc4 [(I irr /I 0 ) Cdc4 /(I irr /I 0 ) woCdc4 ].
Molecular docking. Models for Cdc4 WD40 -Ash1 and Cdc4 WD40 -Sic1 20pS69/pS76/pS80 complexes were obtained using the molecular docking program HADDOCK 2.1 (ref. 51), based on chemical shift perturbations for Cdc4 WD40 . Active and passive residues were selected based on the strategy outlined in ref. 33 and see also Supplementary Note 2. Docked structures, corresponding to the 200 best solutions with the lowest intermolecular energies, were generated and clustered based on a backbone RMSD tolerance of 1.0 Å. The quality of the structural ensemble was assessed using the PROCHECK program 52 .
Isothermal titration calorimetry (ITC). ITC experiments were performed using VP-ITC and iTC200 microcalorimeters (MicroCal Inc., Northampton, MA) at 20°C with the sample cell containing 30 mM Cdc4 WD40 and the syringe loaded with 100 mM pSic1 or 200 mM SCF-I2. The samples were dialysed in buffer containing 50 mM Na 2 HPO 4 , pH 7.2, 150 mM NaCl, 2 mM b-mercaptoethanol. Runs were performed using 13-20 injections at an interval of 120 s and each binding experiment was repeated twice. Using the Origin software provided by MicroCal Inc., heat associated with each injection was integrated and thermodynamic parameters were extracted by fitting the data to a single-site binding model.
Yeast strains and cell culture. Wild type or mutant CDC4 (Arg655Gln, Arg664Gln, Arg655Gln/Arg664Gln) alleles under control of the native CDC4 promoter were introduced on a oCDC4 TRP CEN4 plasmid into a cdc4DHIS3 strain in either W303 (MATa ade2-1 can1-100 his3-11,15 leu2-3, 112 trp1-1 ura3 GAL11 psi þ ) or S288C (BY4741 MATa his3D1 leu2D0 met15D0 ura3D0) backgrounds. Each strain was also co-transformed with a oGAL1-SIC1 LEU CEN4 plasmid to allow conditional high level expression of SIC1. For microscopy and FACS analysis of DNA content, cells were grown to early log phase and induced overnight in selective galactose medium before imaging and staining with Sytox green dye 8 . For spot dilution assays, strains were cultured for one day in SC-Trp-Leu 2% raffinose liquid medium, then spotted in 10-fold dilutions onto SC-Trp-Leu 2% glucose or SC-Trp-Leu 2% raffinose 2% galactose plates and grown at 30°C for three days.
Intrinsic Trp fluorescence measurements. The binding affinities of three different peptides (Sic1 20pS69 , Sic1 20pS80 and Sic1 20pS69/S80 ) for wild-type and mutant (Arg664Gln) Cdc4 WD40 were measured by intrinsic Trp fluorescence-binding experiments. The measurements were carried out by using an ATF 105 spectrometer (AVIV Instruments, Lakewood, NJ) equipped with an automatic titrator. The binding of the peptide fragments were monitored by using intrinsic tryptophan fluorescence with an excitation wavelength of 298 nm and an emission wavelength of 366 nm. All measurements were performed in 50 mM Tris, 150 mM NaCl, 5 mM DTT, pH 7.5 at 20°C. The concentration of Cdc4 was 0.5 mM for all measurements 35 . Dissociation constants were determined by assuming 1:1 protein stoichiometry, given that the allosteric site interaction is not detectably perturbed by singly phosphorylated CPD peptides. Association constants were calculated using the formula K a ¼ 1/K d . Prism 4.0 software (GraphPad Software, San Diego, CA) was used for statistical analysis (non-paired Student t test), and P values o0.05 were considered significant. Each experiment was repeated at least three times.
Fluorescence polarization assay. Fluorescence polarization assays containing 0.21 mM Skp1-Cdc4 complex and 10 nM fluorescently labelled cyclin E-derived or Ash1-derived phosphopeptides in 10 mM HEPES (pH 7.5), 40 mM NaCl, 0.1 mg ml À 1 BSA and 1 mM DTT in a final volume of 23.5 ml per well were performed on an Analyst HT plate reader (Molecular Devices Corp., Sunnyvale CA). Samples were excited at 485 nm and emission was read at 535 nm (ref. 26).
Mathematical model. We developed a variation of the mean-field electrostatic model 35 . Whereas the original model assumed only one Sic1 binding pocket on Cdc4, the model here embodies both a primary (P) and an allosteric (A) binding pocket. Accordingly, the Sic1-Cdc4 bound state consisted of three different bound configurations. To provide rationalization for the present experimental data, contact energies associated with the two binding pockets were chosen to represent experimentally observed trends. Additional energetic parameters that were likely unrealistic were also considered to explore alternate hypothetical binding scenarios and to assess the robustness of the proposed mechanism. Details are provided in the Supplementary Note 3.
Data availability. The data that support the findings of this study are available from the corresponding author upon request.