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Department of Chemistry and the Skaggs Institute of Chemical Biology, The Scripps Research Institute, La Jolla, California 92037, USA
Reprint requests to: Jeffery W. Kelly, Department of Chemistry and the Skaggs Institute of Chemical Biology, The Scripps Research Institute, 10550 N. Torrey Pines Rd., BCC506, La Jolla, CA 92037, USA; e-mail: jkelly{at}scripps.edu; fax: (858) 784-9610.
(RECEIVED February 15, 2001; FINAL REVISION April 18, 2001; ACCEPTED April 19, 2001)
Article and publication are at http://www.proteinscience.org/cgi/doi/10. 1101/
| Abstract |
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-turn possibly disengages Asn31, allowing it to make up to three hydrogen bonds with the backbone in strand 1 and loop 2. The synergistic mutations A20R/L30Y in combination with the remotely located mutation D34T add together to create a hYap WW domain that is significantly more stable than any of the protein structures on which the design was based (Pin and FBP28 WW domains). Keywords: WW domain; protein design; homology-based; sequence alignment; structure comparison; protein stability; side-chain interactions
| Introduction |
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We chose the WW domain to test this design approach because of our keen interest in understanding the forces that stabilize ß-sheet structure. This domain represents the shortest sequence (3840 amino acids) that forms a monomeric three-stranded single-layer ß-sheet that folds and unfolds cooperatively without cofactors or disulfide bonds (Sudol 1996; Koepf et al. 1999b; Crane et al. 2000). It appears in >170 proteins and mediates proteinprotein interactions by interacting with proline-containing ligands (Sudol and Hunter 2000). Two high-resolution crystal structures, including a 1.35-Å structure of the peptidyl-prolyl cis-trans isomerase (Pin) WW domain (Ranganathan et al. 1997; Huang et al. 2000), and several NMR structures, including the human Yes-associated protein WW domain (hYap) bound to a proline-rich ligand (Macias et al. 1996), as well as the formin-binding protein (FBP28) WW domain (Macias et al. 2000) are available from the Protein Data Bank. WW domains contain two strictly conserved tryptophan residues spaced 2022 amino acids apart in the sequence for which they are named, as well as a highly conserved C-terminal proline residue. Previous studies on the hYap WW domain show that the N-terminal tryptophan (Trp17) is critical for the folding of the protein, whereas the C-terminal tryptophan (Trp39) is essential for ligand binding (Macias et al. 1996; Koepf et al. 1999a). Despite the similarities in the tertiary structures of the WW domains, both experimental studies and molecular dynamics simulations show that the thermodynamic stabilities of these small proteins can differ dramatically (Ibragimova and Wade 1999; Macias et al. 2000). For example, the hYap WW domain (57 residues) has a Tm of 51°C, whereas FBP28 (37 residues) and Pin (34 residues) exhibit higher thermal stabilities with Tm's of 62° and 58°C, respectively (M. Jäger and J.W. Kelly, unpubl.). Several shorter constructs of the hYap WW domain are either less stable than the 57-mer or are unfolded (E. Koepf and J.W. Kelly, unpubl.). It was reported that the side chain of an isoleucine residue at position 7 covers a hydrophobic patch in the hYap WW domain and is important for its stability (Macias et al. 1996).
Structural information from WW domain proteins identifies two segregated hydrophobic clusters, one on each side of the three-stranded ß-sheet. The first cluster of the hYap WW domain is composed of the side chains of the N-terminal Trp (W17) as well as those of Pro14, Phe29, Asn31, Thr38, and Pro42. Cluster 2 resides on the ligand-binding face and is more hydrophobic, involving the side chains of residues Glu18, Ala20, Tyr28, Leu30, His32, Thr37, and Trp39. Most of the residues in these two clusters are semi-conserved among WW domains. Figure 1
lists the sequences of the WW domains from hYap, Pin, and FBP28, as well as the consensus sequence generated using the SMART server (http://smart.embl-heidelberg.de) (Schultz et al. 1998, 2000) based on 166 globular proteins, containing >200 nonredundant WW domain sequences.
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The small size of the WW domain, combined with available sequence and structural information, makes it an ideal model for studying sequence, structure, and function relationships as they relate to a three-stranded ß-sheet structure. Our goal was to reengineer the relatively unstable hYap WW domain to afford a more thermostable ß-sheet by introducing point mutations based on analysis of both sequence and structure of WW homologs. Mutations were introduced to utilize stabilizing forces such as solvation energy, hydrogen bonding, electrostatic interactions, and van der Waals interactions. Both structural and sequence homologies were considered in the redesign of semi-conserved residues in the two hydrophobic clusters and their surrounding residues.
| Results |
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50% consensus but are not highly conserved. Because the WW domain is composed of a single-layer ß-sheet, most of the core residues are partially exposed. In the first cluster, Trp17 dominates the hydrophobic interactions, as demonstrated from earlier work on hYap (Koepf et al. 1999b). An examination of the peripheral region of this cluster employing the 1.35-Å resolution crystal structure of the Pin WW domain suggests that the side chain of Asn26 plays an essential stabilizing role by forming three hydrogen bonds to the protein backbone (Fig. 2B
bond relative to Asn26 in the Pin WW domain (Asn31 of hYap has a
2 angle of -9.4° compared with
2 of -64.7° for Asn26 in Pin WW domain). This is possibly the result of the strong dipole attraction between the side-chain NH of Asn31 and the negatively charged carboxylate group on the Asp34 side chain. As a result, the Asn31 side-chain amide NH in the wild-type hYap WW domain points toward the side chain of Asp34, interfering with hydrogen-bonding interactions between the Asn31 side chain and the protein backbone (Fig. 2A
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The mutation A20R increases electrostatic and hydrophobic interactions in the second hydrophobic cluster
In the Pin WW domain crystal structure, Arg14 (which is equivalent to Ala20 in hYap; Fig. 4A
) forms a salt bridge with Glu12 (which corresponds to a Glu18 in the hYap sequence), which further forms a hydrogen bond with His27 (which corresponds to His32 in hYap; Fig. 4B
). Such a hydrogen-bonded network motif is conserved over a large number of proteins. Introduction of Arg at position 20 in hYap should result in formation of a salt bridge with Glu18, with the latter interacting with His32 as well. Therefore, Glu18 can act as a "networking" residue connecting amino acid side chains from different strands in the ß-sheet structure. In addition, the n-propyl side-chain substructure of Arg20 buries more hydrophobic solvent-accessible surface area (
ASAap) against Leu30 (in comparison to Ala20; Fig. 4A
), which should increase
Gu, on the basis of the correlation between increased positive
ASAap and increased
Gu (Murphy and Freire 1992; Jiang et al. 2000). Structural comparisons of the second hydrophobic cluster (the ligand-binding site) reveal that the hYap cluster (Fig. 4A
) is more exposed than is the cluster in the Pin (Fig. 4B
) and FBP28 WW domains, especially at position 30. The buried surface area at this position is 99.0 Å2 for Leu30 in hYap, 141.4 Å2 for Phe25 in Pin, and 138.0 Å2 for the equivalent Tyr22 position in FBP28 (Fig. 1
). The introduction of A20R mutation onto the first strand of hYap should increase solvation energy (hydrophobic interactions) by burying the isobutyl group of Leu30 against the n-propyl substructure in Arg, as suggested by molecular modeling using an optimized set of dihedral angles for the Arg side chain. The amphiphilic side chain of A20R can also bury more surface area against the side chain of Tyr28 in the folded hYap WW domain structure. It is important to point out that the choice of the A20R mutation was based mainly on the consideration of structural homology and not on sequence homologies (Fig. 1
). As a matter of fact, this position was assigned to be Tyr in a designed WW prototype protein, which shows a Tm of 44°C (Macias et al. 2000).
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Tyr mutation at position 30 would complement the increased hydrophobic cavity created by the A20R mutation. The A20R/L30Y double mutation should be synergistic because this arrangement not only greatly increases the buried surface area of the Tyr30 side chain but also reduces the possible conformational space available to the Arg20 side chain, therefore reducing the chain entropy for the arginine side chain. Hence, these mutations should contribute more to stability than additivity would predict.
1H NMR spectroscopy
Well-dispersed chemical shifts were observed in the 1D proton NMR spectra (25°C), both in the amide proton region and in the upfield aliphatic region for all of the designed single- and multiple-mutation-containing WW domains, which is characteristic of structurally well-defined proteins. The amide regions of several representative WW variants are shown in Figure 5
. The indole N-H protons of Trp17 and Trp39 in the wild-type hYap WW domain exhibited chemical shifts of 10.48 and 10.16 ppm, respectively. A downfield chemical shift of the Trp39 indole resonance was observed for the A20R variant, reflective of a more deshielding environment for Trp39, which is not surprising because the mutation is on the same face as the tryptophan in hydrophobic cluster 2. Interestingly, all other variants showed downfield chemical shifts for Trp17 relative to that of wild-type hYap, indicating a more deshielding and perhaps less dynamic hydrophobic core around Trp17 in these variant proteins. This observation suggests that mutations on the opposite side of the ß-sheet of Trp17 have a global stabilizing effect.
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Gu) as well as the differences in free energies (
Gu) were calculated and compared at 65°C (Table 1a
Gu at 65°C, and thus a more accurate comparison can be made among all of the proteins. As expected, the stabilizing contribution of the D34T mutation was additive when introduced with the A20R or the A20R/L30Y mutations, because additivity is often observed when mutations are not in contact with each other (Dill 1997; Wells 1990). Additivity was not expected when both the A20R and L30Y mutations were introduced, because they bury their hydrophobic surfaces into each other in hydrophobic cluster 2. As shown in Table 1a
The thermal stability of the mutants was also measured at a high salt concentration (2 M NaCl), and the results are displayed in Table 1b
. The stabilizing influence (
Gu at 65°C) of the A20R mutation under high salt conditions was reduced to
65% of the effect in standard buffer (20 mM potassium phosphate, 100 mM NaCl at pH 7), indicating a favorable electrostatic contribution of the guanidiniumcarboxylate interaction involving the Arg20 and Glu18 side chains. The mutation designed to increase the solvation energy or hydrophobic interaction (L30Y) exhibited a more pronounced stabilizing effect in high salt, consistent with the effect of salt concentrations on increasing the hydrophobic effect (Jaenicke 2000). This effect could be the result of an extremely unfavorable denatured state wherein the hydrophobic side chains are exposed to aqueous solution where the high salt concentration strongly disfavors solvation. Not much variation in the stabilization derived from the mutation D34T was observed as a function of the salt concentration, as one would expect. The proteins with multiple mutations exhibit the expected balance between increased hydrophobic and decreased electrostatic contributions under high salt conditions.
Fluorescence-monitored GdnHCl denaturation
On the basis of the existence of a near-UV CD spectrum, our laboratory previously reported that the wild-type hYap WW domain is unfolded by chemical denaturants such as urea and GdnHCl to a non-random-coiled state, as opposed to the random-coiled denatured state afforded by thermal denaturation (no near-UV CD signal) (Koepf et al. 1999b). This behavior is exhibited by all the WW domain variants studied within, as is demonstrated in Figure 7A
for the A20R/L30Y/D34T triple mutant. Most of the thermostable variants discussed in this paper did not entirely lose their tertiary structure in 8 M urea; therefore, the stronger denaturant GdnHCl was employed. Tryptophan fluorescence was monitored to probe the environmental changes around the tryptophans and hence protein structural changes. When excited at 295 nm, the native state WW domain showed maximum emission wavelength (
max) around 343 nm. When we added 6 M GdnHCl, the
max red-shifted to 358 nm with a decrease in intensity, indicating increased exposure of the Trp residues to the surrounding solvent (Fig. 7B
). Fluorescence-based denaturation curves (GdnHCl) recorded at 4°C are shown in Figure 7C
. The designed WW domain variants showed different fluorescence intensity (345 nm) at both 0 and 6 M GdnHCl relative to that of the wild type (Fig. 7C
), an indication of the different environment around the Trp residues in the proteins, in both the folded and the chemically denatured states. Given that the denatured states afforded by chaotrope and thermal denaturation may be different (Fig. 7A
), the results shown in Table 2
(fitted to a two-state model using equation 1) should be considered only as an estimate for assessing stability. The chaotrope-derived stability may or may not be directly comparable to the thermal stability, depending on the extent of the differences in the denatured states, which are the subject of ongoing studies (Table 1a
). Table 2
indicates that the designed WW variants also exhibit increased stability, with the triple mutant (A20R/L30Y/D34T) being the most stable.
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| Discussion |
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50% consensus yet are not highly conserved) and their immediate structural neighbors. By combining both sequence and structural information, stabilizing single mutations and multiple mutations were identified with a high success rate.
Stabilizing forces provided by the mutations
The three mutationsD34T, A20R, and L30Ywere envisioned to stabilize the hYap WW domain by using different mechanisms. D34T possibly acts to disrupt the dipole attraction between the side chains of Asn31 and Asp34, allowing Asn31 to form what we expect to be two or three more hydrogen bonds with the protein backbone, by analogy with the Pin WW domain. Because Asn31 resides at the end of the central ß-strand, it is likely to be able to reach out to the protein backbone of both the first strand and the loop between the second and the third strands, analogous to Asn26 in Pin (Fig. 2B
).
Another possible stabilizing effect provided by the D34T mutation relates to the role this residue plays in stabilizing a
-turn. The conformation of residues His32 to Gln35 approximate a common
-turn motif consisting of an
r-
r-
r-
L loop ((Sibanda and Thornton 1985; Thornton et al. 1988; Efimov 1993; Gunasekaran et al. 1997; DeGrado et al. 1999). The first three residues of the loop form almost a full turn of an
-helix. As a result, the residue that proceeds this turn has a preference for side chains that can form a classical N-cap motif, such as Asn31 in hYap WW domain. However, Asp is the most preferred residue based on studies of the B1 IgG-binding domain (Zhou et al. 1996). This study also indicated a high frequency of occurrence of a Ser or Thr residue at position 3 in the
-turn (Zhou et al. 1996), corresponding to residue Asp34 in the wild-type hYap. The hydroxyl group from Ser or Thr generally accepts a hydrogen bond from an amide two residues in the C-terminal direction in sequence (thereby stabilizing the intervening residue in an
L conformation) while simultaneously forming a hydrogen bond to the N-capping residue. Therefore, it is also possible that the D34T mutation in hYap stabilizes the native structure of the protein simply because Thr is intrinsically favored over Asp at this position.
The D34T mutation in the hYap WW domain increased the Tm by 5°C and
Gu by 0.38 kcal mol-1 at 65°C (thermal unfolding) or 0.44 kcal mol-1 at 4°C (GdnHCl denaturation). Such an increase in stability could be the result of the putative importance of hydrogen bonding between a side chain and the protein backbone (Strop and Mayo 2000), or
-turn forming propensity at this position as suggested by a genetic and structural analysis (Zhou et al. 1996).
The surface mutation, A20R, stabilizes the protein both by increasing favorable electrostatic interactions with a nearby carboxylate group and by burying hydrophobic surface against the neighboring Leu30 side chain (Fig. 4
). Generally, placing charged groups on the surface of folded proteins to increase stability has been attributed to either improved electrostatic interactions in the folded state or the influence of charge on the ensemble of denatured states (Pace et al. 2000). In this case, we believe that the A20R mutation provides stabilizing forces beyond favorable electrostatic interactions in the folded state. There are at least two pieces of evidence to support this statement. First, the stabilizing effect of A20R was mostly retained in 2 M NaCl, indicating the existence of more substantial stabilizing forces than simply electrostatic interactions (Table 1
). Furthermore, a calculated increase in the solvent-buried hydrophobic surface area was observed for Leu30 and other hydrophobic residues in the second cluster, owing to the A20R mutation, which further contributes to solvation energy. Together, favorable electrostatic and hydrophobic interactions seem to explain the increase of 0.89 kcal mol-1 (65°C) or 0.87 kcal mol-1 (GdnHCl, 4°C) in thermodynamic stability and the 11.4°C increase in Tm relative to the wild type.
In the wild-type hYap WW domain structure, the side chain of Leu30 is partially exposed in the central strand, surrounded by the side chains of Glu18, Ala20, Tyr28, His32, and Thr37 in hydrophobic cluster 2. The L30Y mutation contributed only moderately to stability when the wild-type hYap WW domain was used as the host because the Leu
Tyr mutation only slightly increased the buried hydrophobic surface area of the protein, as confirmed by the small (2.9°C) increase in Tm for the L30Y mutant. However, when A20R hYap variant was used as the host, the Tyr side chain at position 30 becomes more extensively buried owing to the complimentary hydrophobic surface created by the extended Arg20 side chain. It is also possible that a highly favorable His-aromatic interaction between Tyr30 and His32 could contribute to stabilization in the folded state. The L30Y mutation introduced in the context of A20R WW sequence results in 40 Å2 increase in
ASA at position 30 alone, which should contribute favorably to both the
Gu and the Tm. Overall, the A20R/L30Y mutations raised the Tm of hYap WW domain by >22°C, the
Gu by 1.86 kcal mol-1 (65°C), and 1.76 kcal mol-1 (4°C, GdnHCl) relative to the wild type. This increase in thermodynamic stability is beyond the additive effects of both mutations as a result of molecular recognition between the two newly introduced side chains. It is worth pointing out that an A20Y/L30Y variant showed a 12°C increase in Tm (Ibragimova and Wade 1999), as opposed to the 22°C increase for the A20R/L30Y variant discussed here, underscoring the importance of favorable electrostatic interactions brought about by the Ala to Arg mutation.
Because the D34T and A20R/L30Y stabilizing mutations are spatially segregated in the three-dimensional structure of the WW domain, making all three mutations in the same sequence should further stabilize the hYap WW domain in an additive fashion. Indeed, the A20R/L30Y/D34T variant has a Tm of 79.6°C (28°C higher than that of the wild-type protein), and a 
Gu of 2.54 kcal mol-1(65°C) or 2.46 kcal mol-1(4°C, GdnHCl) relative to the wild type. The fact that the relatively small changes in free energy give rise to such significant changes in Tm for this protein is not surprising, considering its small size (57 residues) and correspondingly low
H and
CP (Alexander et al. 1992).
Notably, the Tm (79.6°C) of the triple mutant hYap WW domain (A20R/L30Y/D34T) has far surpassed the stability of the FBP28 (Tm = 62°C) and Pin (Tm = 58°C) WW domains, on which most of the structural homology was based. This could be partly the result of the fact that the hYap WW domain under study is
2025 residues longer than the other two WW domain proteins. Several shorter versions of the hYap wild-type proteins were shown to be less stable (E. Koepf and J.W. Kelly, unpubl.). The two termini of the hYap protein meet on top of and cover the first hydrophobic cluster. This structural arrangement helps exclude solvent molecules. Although WW domains with fewer residues have their termini in close proximity, they do not provide as much shielding to the first hydrophobic cluster and therefore are likely to have lower stability in comparison to the 57-residue A20R/L30Y/D34T variant of the hYap WW domain.
The NMR spectra (Fig. 5
) reveal that all the stabilizing variants when combined exhibit more dispersed chemical shifts relative to wild-type hYap or single-site variants thereof, indicating subtle changes in protein structure and/or dynamics. For example, the Trp17 indole N-H in the A20R/L30Y/D34T WW variant has a proton chemical shift of 10.68 ppm, a 0.2-ppm downfield shift in comparison to that of the wild-type protein. Because Trp17 was shown previously to be essential for hYap WW domain folding (Koepf et al. 1999a), one should not be surprised to see a correlation between a better-structured and more extensive hydrophobic core around Trp17 and increased stability.
| Conclusion |
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-turn. The advantage of using structural information within a protein family is that it enables consideration of important side-chain interactions in the context of the protein structure (Thornton et al. 1993; Babbitt and Gerlt 2001), therefore allowing a much higher success rate in protein design than simply considering sequence homology. Overall, this approach presents a simple and effective way to engineer stable WW domains and is complementary to phage display or other combinatorial methods used to randomize portions of the sequence in search of stable or functional variants (Dalby et al. 2000; Toepert et al. 2001). | Materials and methods |
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Protein preparation
The sequence of the wild-type 57-residue hYap WW domain construct used for this study is GSMSFEIPDDVPLPAGWEMAKTSS GQRYFLNHIDQTTTWQDPRKAMLSQMNVTAPTS. All mutant DNAs were prepared with the QuickChange site-directed mutagenesis procedure from Stratagene (La Jolla, CA), using wild-type DNA as the template; the mutations were verified by DNA sequencing. The wild-type hYap WW domain and the mutants were expressed recombinantly in Escherichia coli and purified as described previously (Koepf et al. 1999b). Protein sequence integrity was confirmed by electro-spray ionization mass spectrometry, and purity was evaluated by analytical HPLC. The concentrations of all protein solutions were determined by absorbance at 280 nm, using an
= 11,000 M-1 cm-1 for wild-type, A20R, and D34T, and an
= 12,000 M-1 cm-1 for WW domains with the L30Y mutation. A standard buffer containing 20 mM potassium phosphate (pH 7), 100 mM NaCl, 0.02% NaN3 was used for all measurements, except those in high salt, for which 2 M NaCl was used.
Fluorescence-monitored denaturation
Fluorescence measurements were performed on an Aviv Model ATF105 Automated Titrating Differential/Ratio Spectrofluorometer (Lakewood, NJ), using an automated titrator. All samples were excited at 295 nm with a bandwidth of 2 nm, whereas fluorescence emission was measured at 345 nm with a bandwidth of 6 nm. Sample solutions were stirred vigorously for 4 min after each addition of titrant by the instrument to ensure that the samples reached equilibrium. GdnHCl denaturation studies were conducted at 4°C . The WW domain samples (2 µM) in the standard buffer were titrated with 2 µM protein in 8 M GdnHCl, maintaining a constant volume of 2 mL. A two-state model was invoked with each WW domain studied to obtain free energy of unfolding (
Gu) (see Results) by using equation 1 (Pace and Scholtz 1997):
![]() | (1) |
where Fobs is the observed fluorescence emission intensity at 345 nm,
GuH2O is the free energy of unfolding in water (by extrapolation), and m measures the dependence of
Gu on denaturant concentration. The slope of the pretransition/posttransition baselines are given by mN and mU, respectively, whereas the intercepts of the baselines are given by FN and FU, respectively.
Circular dichroism spectroscopy
All circular dichroism (CD) experiments were conducted on an AVIV Model 202SF Stopped Flow Circular Dichroism Spectrometer equipped with a Peltier temperature-controlled cell holder. WW domains (50 µM) in a 0.1-cm pathlength Suprasil quartz cuvette (Hellma, Forest Hills, NY) were used for far-UV thermal denaturation studies. Samples were heated/cooled with 2°C steps (10°C/min) with a 2-min equilibration time at each temperature before data acquisition. Ellipticity change as a function of temperature was fitted according to equations 2 and 3:
![]() | (2) |
in which
![]() | (3) |
where
obs is the observed ellipticity at temperatures T (Kelvin), mN and mU are the slopes of the pretransition and posttransition regions, respectively, of which the intercepts are represented by
N and
U, respectively.
CP is the heat capacity, and
Hm is the enthalpy at the unfolding transition with a midpoint of Tm. The fraction of unfolded protein (
) at each temperature is calculated using equation 4:
![]() | (4) |
and the
Gu at 65°C (338°K) was calculated based on the fraction unfolded (
) by using equation 5:
![]() | (5) |
1H NMR Spectroscopy
All 1H NMR spectra were recorded on an AMX 600 MHz spectrometer. 3-(Trimethylsilyl) propionate-2,2,3,3,-d4 was used as internal chemical shift standard. Typically, spectra were acquired at 25°C at a concentration of 150 µM (pH 7). Water suppression was achieved using the Watergate pulse sequence.
Energy simulations
Molecular modeling was performed on an SGI Octane workstation, using the software package Insight II (Molecular Simulations, Inc., San Diego, CA). Energy calculations were performed using the Discover module within Insight II. Solvent-accessible surface area was calculated using the Connolly algorithm with a 1.4 -Å radius water probe (Connolly 1983).
Ligand binding
The proline-rich ligand EYPPYPPPPYPSG was synthesized using standard solid-phase peptide synthesis and purified via HPLC (Koepf et al. 1999a). Binding of the ligand to the hYap WW domain and variants thereof was measured using an automated titrator on an Aviv Model ATF105 Spectrofluorometer. Peptide ligand (1 mM) dissolved in buffer was titrated into a cuvette containing 2 mL of a 9 µM WW domain solution. Samples were vigorously stirred for 3 min after each addition of the ligand to enable equilibrium to be reached. Fluorescence emission was monitored at 345 nm by exciting the samples at 295 nm. After background subtraction, the emission intensity at 345 nm (Fobs) was plotted as a function of total ligand concentration added in the sample (Ltotal) and fitted according to equation 6:
![]() | (6) |
where Ffree and Fbound are the fluorescence intensity without ligand and with ligand fully bound, respectively. P0 is the protein concentration in the solution, while Kd is the dissociation constant associated with interaction of the WW domain and ligand.
| Acknowledgments |
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The publication costs of this article were defrayed in part by payment of page charges. This article must therefore be hereby marked "advertisement" in accordance with 18 USC section 1734 solely to indicate this fact.
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