Residual structure within the disordered C-terminal segment of p21^{Waf1/Cip1/Sdi1} and its implications for molecular recognition

Abstract

Probably the most unusual class of proteins in nature is the intrinsically unstructured proteins (IUPs), because they are not structured yet play essential roles in protein-protein signaling. Many IUPs can bind different proteins, and in many cases, adopt different bound conformations. The p21 protein is a small IUP (164 residues) that is ubiquitous in cellular signaling, for example, cell cycle control, apoptosis, transcription, differentiation, and so forth; it binds to approximately 25 targets. How does this small, unstructured protein recognize each of these targets with high affinity? Here, we characterize residual structural elements of the C-terminal segment of p21 encompassing residues 145–164 using a combination of NMR measurements and molecular dynamics simulations. The N-terminal half of the peptide has a significant helical propensity which is recognized by calmodulin while the C-terminal half of the peptide prefers extended conformations that facilitate binding to the proliferating cell nuclear antigen (PCNA). Our results suggest that the final bound conformations of p21 (145–164) pre-exist in the free peptide even without its binding partners. While the conformational flexibility of the p21 peptide is essential for adapting to diverse binding environments, the intrinsic structural preferences of the free peptide enable promiscuous yet high affinity binding to a diverse array of molecular targets.

Introduction

Many proteins adopt a well-defined tertiary structure under physiological conditions, and this structure largely determines protein function. However, there is a class of proteins known as intrinsically unstructured proteins (IUPs) that also play specific roles in protein-protein recognition. Some well-known examples include the phosphorylated kinase-inducible domain (pKID) of the cAMP responsive element binding protein (CREB),¹ the transcriptional activation domain (TAD) of p53,² and the GTPase-binding domain (GBD) of the Wiskott-Aldrich syndrome protein (WASP).³ Spectroscopic studies suggest that these IUPs are not completely random, but can exhibit residual secondary structural preferences. For example, NMR studies demonstrated that the linker helix of p27^Kip1 has a nascent secondary structure in its free state⁴ although it is largely unstructured in solution.⁵ It is increasingly apparent that residual structure of IUPs plays crucial roles in molecular recognition.^6–8 In this regard, it has been suggested that the classic protein structure-function paradigm for IUPs be re-assessed and that protein function for these systems can be understood using a formalism that models the IUP structure as an ensemble of distinct conformations.^6,9,10

p21^{Waf1/Cip1/Sdi1} (hereafter referred to as p21) is an IUP involved in the regulation of the cell cycle.¹¹ p21 was first identified as a cyclin-dependent kinase (Cdk) inhibitor¹² that mediates the G1/S arrest¹³ and later was found to function in apoptosis,¹⁴ differentiation,¹⁵ transcription,¹⁶ DNA synthesis control¹⁷ and stem cell self-renewal.¹⁸ The C-terminal region of p21, which is unique among the Cip/Kip family of Cdk inhibitors, interacts with a large array of proteins, including the proliferating cell nuclear antigen (PCNA),^19,20 calmodulin (CaM),²¹ SET,²² c-Myc,²³ and the E7 oncoprotein of human papilloma virus 16 (HPV-16).¹⁷

How does p21, a small protein of 164 residues, physically recognize so many structurally dissimilar proteins without sacrificing binding affinity? The binding diversity of the C-terminal segment of p21 has been attributed to its ability to acquire different conformations upon binding to distinct targets.²⁴ Although the far UV CD spectra suggest that residues 145–164 (p21(145–164)) is unstructured, this peptide adopts a well defined structure having a helical N-terminal region and an extended strand C-terminal region when bound to PCNA.²⁵ Based on previous examples of CaM-substrate binding²⁶ and CD measurement of mutant p21(145–164),²⁴ p21(145–164) is likely to acquire a helical conformation when bound to CaM.

In this study, we combine NMR measurements of free p21(145–164) with molecular dynamics (MD) simulations to obtain models for the unfolded ensemble of the free peptide at a physiologically relevant temperature and pH. We found that the N-terminal half of the peptide has a significant amount of residual helical structure and the C-terminal half has a preference for extended conformations in the unbound state of p21(145–164). NMR dipolar coupling measurements of the CaM – p21(145–164) complex indicate that the peptide is helical when bound to CaM, which in turn suggest that the region of the peptide with helical preference is likely to interact with CaM. On the other hand, the C-terminal loop-like region of the peptide adopts an extended conformation when bound to the PCNA.²⁵ Our results show that the structure adopted by p21(145–164) upon binding to CaM or PCNA already exist in the free peptide in significant population and suggest that the pre-formed structural elements of p21(145–164) contribute to its binding specificity.

Results

Residual secondary structure in p21(145–164) detected by NMR spectroscopy

The ¹H-¹⁵N HSQC spectrum of ¹⁵N-labeled p21(145-164) (Fig. 1) showed poor dispersion (< 1 ppm) of amide proton chemical shifts, consistent with a largely unstructured peptide as observed by far-UV CD spectroscopy.²⁴ To investigate whether there is any residual structure in p21(145–164), we measured ¹³C^α and ¹H^α chemical shifts, as well as the 3-bond ³J_HN-Hα coupling constants. The ¹³C^α and ¹H^α chemical shift values are very sensitive to local conformation and thus their deviations from the values of random coil, known as secondary chemical shifts, are indicative of secondary structure.²⁷ Secondary shift analysis is the most widely-used method for detecting residual structural elements in largely unstructured polypeptide chains.^28–30 The ¹³C^α secondary chemical shift of p21(145–164) [Fig. 2(A)] shows that the N-terminal half of the peptide, encompassing residues Met147-Lys154 is partially helical on average, while its C-terminal half shows a preference for extended conformations. In agreement with the ¹³C^α shifts, the ¹H^α secondary shifts [Fig. 2(B)] are consistent with an increased propensity for helical conformation for the N-terminal segment Thr148-Arg155. However, the ¹H^α shifts for the C-terminal half of the peptide are not characteristic enough to draw any conclusions on the secondary structure preferences. Independent from the chemical shifts, the deviations of the ³J_HN-Hα coupling constants from random coil values [Fig. 2(C)] also suggest helical tendency of the N-terminal half of the peptide, Thr145-Lys154.

Figure 1.

The ¹H-¹⁵N heteronuclear single quantum correlation (HSQC) spectrum of the ¹⁵N-labeled p21(145-164) recorded at ¹H frequency of 500 MHz, pH 6.5, and 30°C. All of the backbone ¹H^N and ¹⁵N are assigned except for Arg156.

Figure 2.

NMR measurements of residual secondary structures of p21(145-164). (A) Deviation of ¹³C^α chemical shifts of p21(145-164) from the random coil values.³¹ Δ¹³C^α = ¹³C^α (p21)-¹³C^α (random coil). (B) Same as in (A) for the ¹H^α chemical shifts. (C) Deviation of the ³J_HN-Hα coupling constants of p21 (145-164) from random coil values.³² Δ³J_HN-Hα = ³J_HN-Hα (p21)-³J_HN-Hα (random coil). Data are not available for Arg156 (indicated by *). (D) Secondary structure prediction based on the consensus among the prediction programs AGADIR, APSSP2, HNN, JUFO, nnPredict, Prof, and PSIpred (Supp. Info. Table S1). Shaded and dotted boxes represent the helical and extended conformations, respectively.

The experimental chemical shifts and scalar coupling constants together indicate that the N-terminal half of the peptide is helical, on average, under physiological conditions. While the ¹³C^α chemical shifts of residues Leu157-Lys163 suggests that this region is extended on average [Fig. 2(A), Supp. Info. Table S1], the ¹H^α secondary shifts [Fig. 2(B)] and the ³J_HN-Hα deviations [Fig. 2(C)] are less conclusive. Our result is consistent with the secondary structure prediction of p21(145–164) based on the consensus among 7 different prediction programs [Fig. 2(D)], including AGADIR,³³ APSSP2,³⁴ HNN (http://npsa-pbil.ibcp.fr/cgi-bin/npsa_automat.pl?page = npsa_nn.html), JUFO,³⁵ nnPredict.^36,37 and PSIpred.³⁸

Modeling the unfolded state of p21(145–164) with MD simulations

NMR measurements for unfolded proteins correspond to ensemble averages over a number of structurally dissimilar states and therefore do not provide information about the underlying distribution of conformers in the ensemble. To further our understanding of the conformers that make up the unfolded ensemble, we used molecular dynamics (MD) simulations to generate structural ensembles which agree with our experimental data.

Our method, energy-minima mapping and weighting (EMW), associates a statistical weight with each structure that corresponds to the probability that the given protein samples that conformation. The application of EMW presented here is similar to that previously described³⁹ and relies on obtaining NMR chemical shift data for a free peptide in solution, and optimizing structural ensembles containing energetically favorable conformations of that peptide to minimize the error between the calculated chemical shifts and the experimentally measured values. The resulting ensembles agree with the experimental values, while also fulfilling physical constraints imposed by the potential energy function.

As the construction of an unfolded ensemble is an underdetermined problem, there may be several ensembles that agree with any given set of experimental constraints. Therefore EMW does not strive to construct one ensemble that models the unfolded state of p21(145–164). Instead, we generate multiple ensembles that are all consistent with a given set of experimental data, and focus our analysis on local structural motifs that are present across different ensembles.

EMW was used to construct 250 ensembles using absolute ¹³C^α chemical shifts. The 250 ensembles were then ranked according to their ability to reproduce experimentally determined amide nitrogen chemical shifts, which were not used in the optimization procedure. The 10 ensembles best able to reproduce amide nitrogen chemical shifts were chosen for further analysis.

Calculated ¹³C^α chemical shifts for these 10 ensembles were in excellent agreement with experiment [Fig. 3(A)]. Moreover, secondary Cα chemical shifts from each of the 10 ensembles were also in excellent agreement with the experimental secondary shift values [Fig. 3(B)]. Experimentally determined nitrogen chemical shifts were all within 1.5 ppm of the experimental values; that is, the error associated with backbone carbon and nitrogen chemical shift predictions⁴⁰ (Supp. Info. Table S2). To further explore whether these models adequately represent the unfolded state of p21(145–164), we also computed ¹Hα, Cβ and ¹⁵N absolute chemical shifts for each model and compared these data to the corresponding experimental result. Calculated ¹Hα absolute chemical shifts were all within 0.2 ppm of the experimental result, well below the error associated with SHIFTX predictions of proton shifts⁴⁰ (Supp. Info. Table S2). Similarly, calculated Cβ chemical shifts were all within 1.5 ppm of the experimental values; that is, the error associated with backbone heavy atom chemic shift predictions⁴⁰ (Supp. Info. Table S2). We note that while the ¹⁵N chemical shift errors are the largest, all are less than 1.5 ppm and the SHIFTX error associated with ¹⁵N predictions is ∼2.4 ppm.⁴⁰ Lastly, we calculated scalar 3-bond J-coupling constants from the each of the 10 ensembles and compared these data to the corresponding experimental values.⁴¹ Calculated J-coupling constants for p21^146–164 had rms errors within 1 Hz from the experimental values. When the C-terminal residue (residue 164) is excluded, the rms error for the non-terminal residues (p21^146–163) have an rms error of 0.77 Hz relative to the experimental values (Supp. Info. Table S3). For comparison, prior predictions of scalar J-coupling constants yield an average rms error of 0.73 Hz when the crystallographic structure of the target protein is known, suggesting that even if one knew the precise structure of the protein of interest, an error near 0.73 Hz would not be unexpected.⁴¹ In summary, although only Cα chemical shifts were used to create the ensembles, the ensembles themselves have calculated values that are in reasonable agreement with ¹Hα, Cβ, and ¹⁵N chemical shifts, and scalar J-coupling constants. The final set of ensembles consists of heterogeneous sets of structures (Supp. Info. Fig. S1).

Figure 3.

Comparison of experimental Cα chemical shifts and Cα chemical shifts calculated using the “worst” model; that is, the model with the highest rms difference between the calculated and experimental result. (A) Relationship between experimental and calculated absolute Cα chemical shifts. (B) Comparison of experimental and calculated Cα secondary chemical shifts.

To identify local conformations preserved across ensembles, all structures were clustered based on the rms backbone deviation of contiguous six-residue subsequences in p21(145–164). A characteristic length of six residues was chosen as the local region size for this analysis since a crystal structure of a bound state of p21(145–164) contained local structured regions approximately six residues in length.⁴² Clustering all contiguous six residue segments resulted in 225 distinct clusters. Each cluster is representative of a local conformation within p21(145–164). The total weight associated with a given cluster in an ensemble is given by the sum of the weights of all structures in the cluster. A given cluster is said to be preserved across all 10 ensembles if it has a non-zero weight in each ensemble. Using this definition, only 5.8% of the clusters were preserved across all ensembles.

A preserved structural motif that is present in all independent ensembles is likely required to reproduce the experimental data. Consequently, we consider such locally preserved structures to represent local conformational preferences. Structures of conserved local conformations offer a more detailed view of ensemble characteristics than ensemble averaged experimental secondary chemical shifts.

Conformational preferences for p21(145–164) are shown in Figure 4. Several points are clear from Figure 4. First, every residue in p21(145–164) is found in a six-residue segment that has an extended conformation. Hence, the simulations predict that each residue can adopt an extended state in solution, including the N-terminal residues that have positive secondary Ca chemical shifts [Fig. 2(A)]. What distinguishes the N-terminus is the fact that these residues can also adopt helical conformations (see Fig. 4). Three conserved N-terminal helical clusters were found, corresponding to preformed helical states in the unfolded ensemble, in the six-residue regions corresponding to residues 147–152, 148–153, and 149–154. Residues 153–158 can also adopt a loop/turn conformation in solution. Lastly, the simulations predict that residues 159–163 have a distinct preference for only extended states.

Figure 4.

Conserved six-residue structural motifs. Helical conformations are colored purple and extended regions are shown in cyan. The region corresponding to a turn is colored yellow.

It was previously reported that residues (146–151) in PCNA-bound form of p21(139–160) forms a 3₁₀ helix, while the C-terminal region spanning residues 152–160 adopts an extended strand which hydrogen bonds to a neighboring β strand in PCNA [Fig. 5(A,B)].⁴² We sought to determine whether comparable local conformational preferences are predicted for the unfolded ensemble representing the unbound state. We find that the six residue subsequence ranging from residues 147 to 152 can adopt a helical conformation in solution and that the subsequence consisting of residues 155–160 adopts an extended state, suggesting that there local structural preferences in the unfolded ensemble similar to those adopted by the bound form of p21(139–160) [Fig. 5(C)].

Figure 5.

(A) X-ray crystallographic structure of a p21 model peptide (residues 139–160) bound to PCNA [PDB ID 1AXC.⁴³ The helical region (p21 residues 146–151) is highlighted in purple, while the extended C-terminus (p21 residues 152–160) is depicted in cyan. Only residues of p21 included in our model peptide (145–160) are shown. (B) Structure of the p21 model peptide alone. (C) Comparison of corresponding local conformational preferences in models of the unbound form of p21(145–164). Regions for which models of the unbound form include local conformations which match the bound form crystal structure are indicated.

Helical mode of p21(145–164) binding to Ca²⁺-calmodulin from NMR dipolar couplings

Based on CD measurements of mutant p21(145–164)²⁴ and the previous knowledge of CaM-binding peptides,²⁶ we expected p21(145–164) to be helical upon binding to CaM. Previously, at least 180 CaM recruitment signaling (CRS) motifs were identified and classified based on the spacing of the hydrophobic residues of CRS that make major hydrophobic interaction with CaM.²⁶ However, p21 peptide contains no sequence that conforms to any of these known CRS motifs.

In order to confirm the helical mode of p21(145–164) binding to Ca²⁺-CaM, two types of residual dipolar couplings (RDCs), ¹D_NH and ¹D_CαHα, were measured for Ca²⁺-CaM in complex with p21(145–164) in a liquid crystalline medium containing 18 mg/mL filamentous phage Pf1. RDCs have been successfully used to determine the binding mode of CaM-interacting peptide to Ca²⁺-CaM.^44,45 The experimentally measured RDCs of CaM in complex with p21(145–164) were fitted to the free Ca²⁺-CaM structure [Fig. 6(A)] and CaM/peptide complexes using the singular value decomposition (SVD) method.⁴⁶ The measured RDCs show very poor agreement with the dumbbell-shape crystal structure of the free Ca²⁺-CaM [Fig. 6(A)] because the conformation of Ca²⁺-CaM bound to p21(145–164) is very different from that of free Ca²⁺-CaM. Among the 13 CaM/peptide complexes tested (see Supp. Info. Table S4), including the complexes that show different types of binding mode, the best correlation was obtained for CaM/CaMKII complex that belongs to the 1–10 class⁴⁷ [Fig. 6(B)]. This suggests that p21(145–164) adopts a known CaM-binding mode (possibly the 1–10 class) in which the CaM-interacting region is helical.

Figure 6.

Determination of the CaM/p21 binding mode using RDCs. Best-fitting of observed backbone RDCs of the Ca²⁺-CaM/p21(145-164) complex to (A) the free Ca²⁺-CaM crystal structure (PDB code: 1EXR) and (B) the crystal structure of Ca²⁺-CaM/CaMKII (PDB code: 1CDM). All RDCs are normalized to ¹D_NH.

Discussion

The NMR data and molecular dynamics simulations are used to explain the binding promiscuity and specificity of p21(145–164) mediated protein-protein signaling. The binding promiscuity can be attributed to the structural plasticity, or unstructured nature of the peptide, which allows it to adapt to the distinct structural environments of many different target proteins. A fundamental question remains-if the peptide is largely unstructured, how does it bind multiple proteins with high affinity?

We first examined the residual structure of p21(145–164) in solution and compared locally preferred conformations to regions of structure in bound forms of p21(145–164). The crystal structure of p21(139–160) bound to PCNA shows that residues Ser146 – Tyr151 of p21 forms a 3₁₀-helix which is involved in hydrophobic interaction with PCNA, whereas residues His152 – Ser160 of p21 adopt an extended β-strand conformation which interacts with PCNA.²⁵ We have shown the helical preference of the N-terminal region of the p21(145–154) which corresponds to the helical region of the PCNA-bound structure. The chemical shifts and scalar couplings for residues Arg155-Lys163 show no sign of residual helical structure and the MD simulations suggest that the helical and extended portions of p21 that bind PCNA exist in the free state prior to binding (see Fig. 5). The recognition for PCNA in this case comes from the fact that residues His152-Ser160 of p21 have a preference for conformational arrangements which readily expose the positively charged residues for specific interactions with PCNA. In the extended, uncoiled conformation of the p21 peptide, residues Arg155 and Arg156 readily interact with the negatively charged Asp122 and Asp29 of PCNA, respectively.

In addition, the NMR structure of Cdk4-bound p21(141–160) also includes a helical region (residues 149–156).⁴⁸ Similarly, model ensembles of the unbound state generated by EMW suggest that the region corresponding to residues 149–154 can adopt helical conformations (see Fig. 4).

We then examined the mechanism of recognition between p21 and Ca²⁺-CaM. Although the NMR resonances of the p21(145–164) peptide bound to CaM are extremely broad due to chemical exchange, the resonances of CaM are much less affected by the peptide and thus allow accurate structure measurement. An extensive set of RDCs measured for CaM bound to the p21(145–164) peptide indicates a CaM-substrate interaction mode in which the substrate adopts an α-helical conformation. For the free p21(145–164) peptide, the NMR chemical shifts and scalar couplings together show that residues 147–154 have significant helical propensity, and MD simulations suggest that the N-terminal region has a strong preference for helical conformations while helical structure is absent in the C-terminal region. We believe the residual helical segments observed in the free p21(145–164) peptide is responsible for its initial recognition with Ca²⁺-CaM. The helical structure is then stabilized by the binding. Overall, the structural propensities of the free p21(145–164) peptide correlate well with the different structures adopted by p21 upon binding to different targets. This observation suggests that pre-existing residual conformations of p21 provide the initial recognition for the target proteins. Binding then further stabilizes these residual conformations. The p21 peptide provides an interesting example of how residual structural elements of an IUP are involved in specific and diverse protein-protein signaling.

Our data suggest that p21's binding promiscuity is explained by the fact that its target selects the appropriate preformed p21conformation. This “conformational selection” mechanism has been described for a number of proteins and therefore may represent a general method that enables proteins to bind structurally dissimilar targets.^49–52 This is to be contrasted with an induced fit mechanism, where the association of two proteins leads to concomitant binding and folding.^53–55 For proteins that associate via induced fit, binding and folding are coupled.⁵⁵ One difference between conformational selection and induced fit is that conformational selection presupposes that the protein conformation, which is complementary to a given binding partner, exists in solution even when the binding partner is absent. By contrast, this need not be the case with induced fit; that is, complementary protein conformations are formed when the protein of interest interacts with its binding partner. Hence information as to what mechanism is at play for any given protein may be obtained from an analysis of the conformational thermodynamics of the protein of interest in the absence of its binding partner. Consequently, methods that combine both experiment and simulation to provide insight into the conformational thermodynamics of IUPs like p21, may provide insight into the binding mechanism of a number of disordered systems.

Methods

Cloning, protein expression and purification

The peptide p21(145–164) was expressed as a C-terminal in-frame fusion to the trpLE protein containing the N-terminal 9-His tag. A pair of Asp-Pro residues was engineered between trpLE and p21(145–164) for acid catalyzed cleavage to release the p21 peptide from the fusion protein. The expression vector was constructed by inserting the DNA fragment of p21(145–164) into the C264 vector, a gift from Dr. M.E. Call, Harvard Medical School, Boston.

Escherichia coli strain BL21 (DE3) that express the trpLE-fused p21(145–164) were cultured in M9 minimal media for isotope labeling. The cell cultures were grown at 37°C to OD₆₀₀ of 0.6–0.8 before overnight induction at 25°C with 0.4 mM IPTG. Inclusion bodies were dissolved with a buffer containing 50 mM Tris, pH 8.0, 0.2 M NaCl, 6 M guanidine HCl, 10 mM imidazole. The cleared solution was bound to Ni²⁺ affinity column (Sigma) and eluted in 50 mM Tris, pH 8.0, 0.2 M NaCl, 6 M guanidine HCl, 400 mM imidazole. The eluted fusion protein was dialyzed against water to remove guanidine HCl. The precipitant was pelleted by centrifugation at 3000 rpm for 30 min. Incubation of the pellet in 0.1 N HCl at 37°C for 3 days released the p21(145–164) peptide from the trpLE fusion partner. The released peptide was dialyzed against water, lyophilized, and purified by reverse-phase HPLC on a C18 column (Grace-Vydac) with a gradient of water containing 0.1% trifluoroacetic acid (TFA) to acetonitrile containing 0.1% TFA. The resulting peptide was lyophilized and dissolved in 100 mM KCl, 10 mM CaCl₂, pH 6.5.

CaM was expressed and purified as previously described.⁵⁶ Isotropic NMR samples were prepared in 100 mM KCl, 10 mM CaCl₂, pH 6.5 in 93% H₂O/7% D₂O. The aligned sample contained 18 mg/mL filamentous phage Pf1 (Asla Labs, Riga, Latvia), 100 mM KCl, 10 mM CaCl₂, and 1 mM sodium azide, pH 6.5 in 93% H₂O/7% D₂O.

NMR spectroscopy

All NMR spectra were collected at 30°C on Bruker and Varian spectrometers operating at ¹H frequencies of 500 MHz or 600 MHz and equipped with cryogenic probes. The sequence-specific backbone assignments were accomplished using pairs of HNCACB/CBCA(CO)NH and HNCA/HNCACB on the ¹⁵N, ¹³C-labeled CaM in complex with unlabeled p21(145–164) and ¹⁵N, ¹³C-labeled p21(145–164), respectively. Two types of backbone RDCs, ¹D_NH and ¹D_CαHα, were measured on the ¹⁵N, ¹³C-labeled CaM in complex with unlabeled p21(145–164). The ¹H-¹⁵N RDCs were obtained from ¹J_NH/2 and (¹J_NH+¹D_NH)/2, which were measured at 600 MHz (¹H frequency) by interleaving a regular gradient enhanced HSQC and a gradient-selected TROSY, both acquired with 80 ms of ¹⁵N evolution. The ¹H-¹³C^α RDCs were measured at 600 MHz (¹H frequency) using the 3D CT-(H)CA(CO)NH without ¹H-decoupling.⁵⁷ Measurement of ³J_HN-Hα coupling constant for determining backbone ϕ angle was carried out on the ¹⁵N, ¹³C-labeled p21(145–164) using the 3D HNHA experiment.⁴¹ The ¹H chemical shifts were referenced directly to external 2,2-dimethyl-2-silapentane-5-sulfonic acid (DSS) in D₂O and ¹³C chemical shifts are indirectly referenced to 0 ppm proton using the method in ref.58.

Data processing and spectra analyses were done in NMRPipe,⁵⁹ CARA,⁶⁰ and Sparky (http://www.cgl.ucsf.edu/home/sparky). RDCs were extracted by subtracting isotropic couplings from the aligned couplings. Fitting of RDCs to structures was done by singular value decomposition,⁴⁶ using the program PALES⁶¹ The goodness of fit was assessed by both Pearson correlation coefficient (R) and the quality factor (Q).⁶² The ¹H-¹³C^α RDCs were normalized to the ¹H-¹⁵N RDCs by a scaling factor of 0.5.

Molecular dynamics simulations

Energy-minima mapping and weighting (EMW)

To construct an ensemble that represents the unfolded state of p21(145–164), we employ EMW method. Details of EMW are described in detail below.

Conformational sampling

The goal of conformational sampling was to generate a library of energy-minimized structures with representatives from all regions of conformational space accessible to the peptide. This was done using quenched molecular dynamics (QMD), as diagrammed in Figure S2 (Supp. Info.). To ensure that both compact and extended structures were adequately sampled, QMD was carried out at 50 different end-to-end distance constraints, spanning a range from 4 to 53 Å. At each distance constraint, a polar hydrogen model of an extended peptide having the sequence TSMTDFYHSKRRLIFSKRKP (p21(145–164)) was constructed using CHARMM, and a harmonic penalty was introduced to enforce the desired distance between ¹³C^α of T145 and ¹³C^α of P164. The structure was then minimized using 500 steps of steepest descent minimization followed by 10,000 steps of minimization using the Adopted Basis Newton Rhapson algorithm. Next, the structure was heated to 1000 K for 10 ps and allowed to equilibrate for 10 ps, before high temperature MD was run for 3 ns. Throughout the simulation, a Berendsen heat bath was used to maintain the temperature,⁶³ and the EEF1 energy function (a Gaussian solvent exclusion model for the solvation free energy) was used to assign energies.⁶⁴ The SHAKE algorithm was employed to hold bonds to hydrogen atoms fixed near their equilibrium values, allowing for a 2 fs time step during high temperature MD simulations.⁶⁵ The peptide's coordinates were saved after every 5000 steps (10 ps) of high temperature MD simulation, yielding 300 structures per end-to-end distance constraint. Thus, 15000 structures were created using high-temperature molecular dynamics.

With end-to-end distance constraints still in place, each of these structures was coupled to a Berendsen heat bath at 298 K and cooled for 40 ps, at which point the end-to-end constraint was removed and the system was minimized using 10000 steps of Adopted Basis Newton Rhapson minimization.⁶³ Cooling and equilibrating each structure before minimization gave the system a chance to escape shallow local energy minima, thereby making more stable structures accessible. The 15,000 structures obtained in this manner comprised our structure library.

Model optimization

A goal of this procedure is to find ensembles that represent the solubilized p21 peptide, where each ensemble consists of 15 structures and their associated weights. Accordingly, the optimization stage of EMW involved generating such ensembles by choosing structures from the conformational library generated in the first step and assigning weights to these structures. Experimentally determined ¹³C^α NMR chemical shifts for the peptide were used to determine what constituted an optimal ensemble; structures and weights were assigned to minimize the root mean square error between ¹³C^α chemical shifts computed from the model using SHIFTX and ¹³C^α chemical shifts that were experimentally measured.⁴⁰ We focused on the Cα chemical shifts for the model construction and used the remaining experimental data (¹³CO, ¹⁵N, Hα, scalar J-couplings) to screen the models to ensure that they could reproduce data that was not used to construct the model. Sequestering part of the experimental data (and not using it in model construction) helps to ensure that our models are not overly fit to a given set of experimental results.

Model generation was performed by minimizing an appropriate error function, f, given by:

1.1

where N is the number of structures in the ensemble (N = 15), X_i is the i^th structure, ω_i is the weight of the i^th structure, r is the number of residues in the peptide for which experimental chemical shift data is available (r = 18), (j) is the calculated Cα chemical shift of residue j in structure X_i, and (j) is the experimentally determined ¹³C^α chemical shift of residue j.

A simulated annealing protocol using a cooling schedule based upon that described by Nulton et al. was implemented.^66,67 Each ensemble was generated from an initial ensemble consisting of 15 Boltzmann-weighted structures chosen at random from the conformational library.⁶⁸ This initial ensemble was subjected to an iterative simulated annealing protocol that minimized the rmse between measured and predicted ¹³C^α chemical shifts. Each step of the annealing protocol consisted of carrying out Monte Carlo steps at a given value of the control parameter T, which is analogous to the temperature in physical systems, until the system had equilibrated.

A Monte Carlo step consists of perturbing the ensemble by replacing one conformer in that ensemble with a conformer from our structure library. Weights for all structures are then reassigned to minimize the overall error, f. The number of Monte Carlo steps for a given value of the control parameter, as well as the schedule used to decrease the overall temperature, is as described in a previous work.⁶⁷ Overall, 250 ensembles were generated using this simulated annealing protocol.

Model validation

The rmse between predicted nitrogen chemical shifts and measured nitrogen chemical shifts for each ensemble was calculated for each of the 250 models generated, and those ensembles in which this error was less than 1.5 ppm were taken to be valid models based upon their ability to predict experimentally measured amide nitrogen chemical shifts. Ten valid ensembles were found that reproduced the NMR chemical shift data well, due to the underdetermined nature of the problem, but we accounted for this by using all 10 of these independently generated, validated structural ensembles in our analysis and focusing on those structural motifs that were preserved across all of them. Calculated 3-bond scalar J-couplings were also computed using the Karplus relations as previously described.^41,69

Procedure for identifying conserved preformed structures

Two different methods were employed to find structural motifs that were present across all validated model ensembles of the unfolded state. Since studies have shown that bound states of p21(145–164) adopt helical conformations, we looked for evidence of preformed helical motifs in the unfolded ensemble. We then sought to identify other structural motifs suggested by the model ensembles.

Identification of conserved local structure by clustering

We sought to identify other types of local structural motifs in the peptide. To this end, all conformers were clustered based on local conformational preferences. Since the helical region in the crystal structure of PCNA-bound p21 is six residues in length, we defined the characteristic size of a local structural motif to be six residues. To account for all local motifs, every six residue subsequence of p21(145–164) was analyzed to find preserved conformations. This was accomplished by clustering based upon backbone atom RMS deviations within each six-residue window of interest. Clustering was carried out in MATLAB (© Mathworks) such that the maximum rmsd between any two structures was 2.5 Å. Clustering based on other window sizes (five, seven, and eight residues in length) was performed to ensure that analysis was relatively insensitive to the choice of window size. Clusters that were represented in all 10 ensembles were identified as preserved local structural motifs.