Exploring the impact of polyproline II (P_II) conformational bias on the binding of peptides to the SEM-5 SH3 domain

Abstract

The left-handed polyproline II helical structure (P_II) is observed to be a dominant conformation in the disordered states of protein and small polypeptide chains, even when no prolines are present in the sequence. Recently, in work by Ferreon and Hilser, the energetics associated with Ala and Gly substitutions at a surface exposed proline site were determined calorimetrically by measuring the binding energetics of Sos peptide variants to the C-terminal Src Homology 3 domain of SEM-5. The results were interpreted as a significant conformational bias toward the bound conformation (i.e., P_II), even when the ligand is unbound. That study was not able to determine, however, whether the conformational bias of the peptides could be explained in terms other than that of a P_II preference. Here, we test, using a computer algorithm based on the hard sphere collision (HSC) model, the notion of whether a bias in the unbound states of the peptide ligands is specific for the P_II conformation, or if a bias to any other region of (φ, ψ) space can also result in the same observed binding energetics. The results of these computer simulations indicate that, of the regions of (φ, ψ) modeled for bias in the small peptides, only the bias to the P_II conformation, and at rates of bias similar to the experimentally observed rates, quantitatively reproduced the experimental binding energetics.

Proline residues preceded in sequence in a polypeptide chain by another proline residue are restricted significantly in available backbone dihedral angle space, and are observed typically with Phi (φ), Psi (ψ) values of approximately (−75, 145) when all involved prolines are in the trans isomer of their peptide bonds (Cowan and McGavin 1955; Okabayashi et al. 1968; Deber et al. 1970; Helbecque and Loucheux-Lefebvre 1982; Dukor and Keiderling 1991; Dukor et al. 1991). Surprisingly, this conformational state of polyproline, generally referred to as the polyproline II (P_II) conformation, is found to be a dominant structure in the unfolded states of polypeptide chains, even when no prolines are present in the sequence (Tiffany and Krimm 1968, 1972; Krimm and Tiffany 1974; Drake et al. 1988; Dukor and Keiderling 1991; Woody 1992; Wilson et al. 1996; Park et al. 1997; Sreerama and Woody 1999; Pappu and Rose 2002; Rucker and Creamer 2002; Shi et al. 2002; Ding et al. 2003; Ferreon and Hilser 2003; Chellgren and Creamer 2004; Vila et al. 2004;). The P_II conformation is characterized by a left-handed helical turn with the amide hydrogen and the carboxyl oxygen of each peptide backbone projecting into solution, presumably making favorable interactions with the solvent (Han et al. 1998; Eker et al. 2002; 2003; Weise and Weisshaar 2003). The P_II conformation appears to also facilitate favorable intrachain n → π* interactions between the oxygen of a peptide bond and the subsequent carbonyl carbon, which should be a stabilizing factor (Hinderaker and Raines 2003). As such, the P_II structure has emerged as an important component in the ensemble of disordered states of protein and small polypeptides.

Recently, calorimetric methods were used to measure experimentally the energetics associated with Ala and Gly substitutions at a surface-exposed proline residue in a peptide ligand that binds to its protein partner in the P_II conformation (Ferreon and Hilser 2003). The complex used in those studies involved a 10-amino acid stretch of the Sos protein (Ac-VP₁P₂P₃V₄P₅P₆R₇R₈R₉Y-amide) and the C-terminal Src Homology 3 (SH3) domain of SEM-5. The high-resolution X-ray structure of the SH3:Sos complex shows that the proline residue at position 3 (P₃) of the Sos peptide resides in the P_II conformation (φ, ψ = −67, 150) when bound (Lim et al. 1994). In addition, P₃ is observed to not participate in any direct binding interaction with the SH3 domain (Lim et al. 1994). Because of the lack of a direct binding interaction of P₃ with the SH3 domain, amino acid substitutions at this position can affect the SH3:Sos binding reaction only through changes in the conformational degrees of freedom (configurational entropy) of the unbound ligand. As such, amino acid substitutions applied to P₃ were used to report on the ability of position 3 in the Sos peptide to be prefolded to the P_II conformation in the unbound state. The results of those mutational experiments demonstrated that Ala and Gly substitutions have a diminished mutational effect on the ΔG of binding, relative to the effects seen in helical proteins for instance (D'Aquino et al. 1996), and suggested a significant position-specific bias for P_II in the unbound states of Sos, even for the non-proline residues (Ferreon and Hilser 2003, 2004; Hamburger et al. 2004). It was not investigated in the previous studies, however, whether or not the conformational bias in the unbound Sos ligand can be explained in terms other than that of a P_II preference.

Here, we test computationally the notion of whether a bias in the unbound states of the Sos ligand is specific for the P_II conformation, or if a bias to any other region of (φ, ψ) space can also result in the same observed binding energetics. Computationally, a hard sphere collision (HSC) model (Richards 1977) was used to generate ensembles of the Sos ligand in unbound conformations. Each computer generated state for the ligand was then docked to the SH3 binding site using the high-resolution structure of the SH3:Sos complex (Lim et al. 1994) as a template, allowing for differentiation of the ligand states into those that were “binding competent” and those that were not. By employing a structure-based calculation with a parameterized energy function (Baldwin 1986; Murphy and Freire 1992; Murphy et al. 1992; Lee et al. 1994; Xie and Freire 1994; Gómez et al. 1995; D'Aquino et al. 1996; Hebermann and Murphy 1996; Luque et al. 1996), the ΔG associated with a redistribution of the unbound ensemble to the binding competent states was estimated. Performing this calculation on each of the P₃ → Ala and the P₃ → Gly variants relative to that determined for the wild-type Sos peptide, a ΔΔG of binding was simulated for each mutant. The simulations were then repeated with conformational biases to various regions of the backbone dihedral angle (φ, ψ) space applied to the ensembles, and at stepped rates of bias. The simulations with the HSC model demonstrated that, of the regions of (φ, ψ) modeled for bias in the unbound ensembles, only the bias to the P_II conformation, and at rates of bias similar to the experimentally observed rates, quantitatively reproduced the experimental binding energetics, supporting the hypothesis that the unbound Sos peptide is biased specifically for the P_II structure, even at non-proline positions.

Methods

We have developed a mini-protein modeling (MPMOD) program to generate conformers of small polypeptide chains by a random search of conformational space. The HSC model (Richards 1977), based upon van der Waals atomic radii, was used as the only scoring function to eliminate grossly improbable conformations. The idea for sampling peptide conformational space in this manner was based on the program RANMOD by Balaram and colleagues (Sowdhamini et al. 1993).

Construction of a polypeptide chain

The procedure to generate an atom from a unit peptide has been given by many authors (Nemethy and Scheraga 1965; Ramachandran and Sasisekharan 1968; Go and Scheraga 1970; Bruccoleri and Karplus 1987). Starting from a unit peptide, all other atoms of a polypeptide chain can be determined by the well-known rotational matrix (Jeffreys and Jeffreys 1950). The backbone atoms (N, Cα, C, O, HN, and HCα) were generated making use of the dihedral angles φ, ψ, and ω and the standard bond angles and bond lengths (Momany et al. 1975). Cβ and the backbone atom HCα were treated specially because of tetrahedral geometry with the N and C atoms, and do not depend on the dihedral angles (φ, ψ, ω). Of the two possible positions of the Cβ atom, the one corresponding to the L-amino acid residues was used throughout the studies.

The side-chain atoms of a polypeptide were built in the same manner as the backbone atoms. The bond lengths and bond angles were also taken from the published values (Momany et al. 1975). There are maximally four types of side-chain dihedral angles (χ₁, χ₂, χ₃, and χ₄) for the 20 amino acids. In our study, we used the rotamer library of Lovell and coworkers (Lovell et al. 2000) for sampling side-chain dihedral angles. To reduce bias in sampling rotamers, we first kept all of the rotamers that did not collide with the backbone atoms for each residue. Next, we picked one set of rotamers randomly for all of the residues in a chain. To increase the probability of rotamer pairs without van der Waals contact violations, five-time random tries were performed. If none of the five tries satisfied the van der Waals check, the backbone was rejected and a new peptide chain was generated.

Determination of the dihedral angles (φ, ψ, ω)

A random number generator based on Knuth's subtractive method was used to generate numbers randomly which distribute uniformly in the range of 0.0–1.0 (Knuth 1981). These random values had no sensible sequential correlation, and the period was practically infinite. The random numbers were used to sample (φ, ψ) values restricted to the allowed regions of the Ramachandran plots, in order to sample the conformational space efficiently (Mandel et al. 1977). The 20 amino acid types were divided into four categories, depending on the regions of conformational space that are accessible to the backbone dihedrals: one category for glycine, one for proline, one for the Cβ-branched amino acids (valine, isoleucine, and threonine), and one for all other amino acids (referred to as Alanine-like in Fig. 1). The regions of (φ, ψ) conformational space accessible to each of the four categories are shown in Figure 1.

Figure 1.

Accessible (φ, ψ) space in a polypeptide chain for amino acid types. Conformational states of small polypeptide chains were generated by a random search of backbone dihedral angles in which the (φ, ψ) values were limited to the allowed Ramachandran regions. Each of the 20 amino acid types were placed in one of four categories dependent upon which regions of (φ, ψ) were accessible to the backbone dihedrals: one category for glycine, one for proline, one for the Cβ-branched amino acids (valine, isoleucine, and threonine), and one for all other amino acids (alanine-like). Shown are the distributions of paired (φ, ψ) values that were sampled in the random generation of states using the HSC model.

For modeling conformational bias to specific regions of (φ, ψ), the randomly selected φ and ψ values were weighted accordingly. As an example, for a bias of 30% to the (φ, ψ) region of (−75 ± 10, 145 ± 10; i.e., the P_II structure), 30% of the paired (φ, ψ) values for any of the residues in the polypeptide chain, averaged over the entire ensemble, were distributed randomly in the region of (−75 ± 10, 145 ± 10) prior to the van der Waals check. The remaining 70% of the paired (φ, ψ) values were thus distributed randomly in the allowed Ramachandran areas outside of (−75 ± 10, 145 ± 10), also prior to the van der Waals check.

The trans and cis forms of the peptides have the dihedral angles (ω) of 180° and 0°, respectively. The non-proline amino acids favor the trans form by a ratio of ∼1000:1, but for proline the trans form is favored only by ∼4:1. In our simulations with the HSC model, the non-proline amino acids were given 100% trans form and the proline sampled the cis form at a rate of 10% if the preceding amino acid was non-proline, and at a rate of 6% if the preceding amino acid was proline (MacArthur and Thornton 1991). The dihedral angle ω was also given a Gaussian fluctuation of ±5° around the value of 180° or 0°.

The van der Waals’ steric contacts

The HSC model was used as the scoring function to eliminate grossly improbable conformers. Ramachandran and his colleagues worked out a list of contact distances for each kind of atom pair that occurred in protein, based on the X-ray data available at that time (Ramachandran et al. 1963). The atom pair distances were classified into two limits, “normal” and “extreme,” as shown in Table 1. Those distances were ∼0.3 Å–0.5 Å smaller than the summation of the van der Waals radii of two atoms (Gavezzotti 1983). They concluded that the structure was less stable for the distance of “extreme” limit than for the distance of “normal” limit. The existence of hydrogen bonds or other attractive effects, however, cause the contact distances to be in the “extreme” limit. Iijima et al. (1987) calibrated the van der Waals radii of atoms making use of inverse Ramachandran plots. The calibrations were based on the comparison of the Ramachandran plots obtained from high-resolution X-ray data of proteins and peptides with the allowed conformational space for the di-peptide molecular models built from the published standard angles and bond lengths. The “calibrated” contact distances for each atom pair are ∼0.1 Å–0.2 Å shorter than the “extreme” limit (Table 1).

Table 1.

The short contact distances between each kind of atom pair, given in angstroms (Å)

Of the three types of the short contact distances, the extreme and the calibrated distance limits were used for the van der Waals check. The extreme distances were used only for the backbone atom pairs checked. The calibrated distances were used for the side chain to side chain or side chain to backbone atom pair check. The reasons for using the two contact distances were the following: (1) to provide flexibility for the backbone and slightly more flexibility for the side chains, (2) to compensate the inaccuracy that is caused by the fixed geometrical parameters used to build the polypeptides, (3) to include the possibility of hydrogen bonds or some attractive features in the conformer, and (4) to save computing time by using slightly less restrictive limits. Also, for each atom, all of the possible nonbonded atom pairs were checked for van der Waals distance violations, whereas atom pairs in the same residue were not checked.

Aligning the conformers to the SH3:Sos binding site

After ensembles of ligand conformers were generated, a “binding” test was performed. The first step was to align the conformer to the template, which was the Sos ligand in the co-crystal structure complex (Lim et al. 1994). The second step was to screen the docked ligand conformer with the protein substrate using the HSC model. For the Sos ligand (Ac-VP₁P₂P₃V₄P₅P₆R₇R₈R₉Y-amide), the stretch of residues containing the prolines P₂ through P₆ was used for the alignment procedure. Alignment involved a simple rotation and translation of the computer generated conformer so as to minimize the root-mean-square deviations (RMSD) in the positions of the backbone heavy atoms of N, Cα, and C, paired by residue, between the crystallographic structure and the computer generated structure. Ligand conformers that passed the following three tests were considered binding competent: (1) The docked ligand did not violate steric contact limits with the protein substrate given by the calibrated pair distances (Table 1), (2) the averaged RMSD between the conformer and template among the backbone heavy atoms N, Cα, and C for residues P₂ through P₆ was no greater than 0.5 Å, and (3) the averaged deviation in backbone dihedral angles (φ, ψ) between the conformer and template for residues P₂ through P₆ was no greater than 50°. As discussed in the Results section, the RMSD and (φ, ψ) difference limits were determined by comparison of the simulated ΔΔG_bind values, calculated by the HSC model, with the expected effect of amino acid-dependent changes in available (φ, ψ) space on ΔG (D'Aquino et al. 1996). In defining binding competent states, selecting more restrictive limits to the RMSD and averaged (φ, ψ) differences between the computer generated ligands and the template did not increase the accuracy in the simulated ΔΔG_bind values. Excessively permissive limits, however, had the effect of compressing the ΔΔG_bind values because overly permissive limits preferentially favor binding for the P₃ → Ala and P₃ → Gly Sos variants, which are less constrained conformationally, relative to the wild type (see Fig. 4).

Figure 4.

Defining the binding competent states of the unbound Sos ensemble in terms of the RMSD and the averaged position-specific deviation in dihedral angle (φ, ψ) relative to the template ligand of the co-crystal structure. In the top two panels, the range in the RMSD (for the backbone heavy atoms) and the deviation in (φ, ψ) values, relative to the template and averaged over residues P₂ through P₆, are shown for the ensembles of the wild-type (circles), the P₃ → Ala (squares), and the P₃ → Gly (triangles) Sos peptides. In the bottom panels, shown are the effects on the simulated ΔΔG_bind values of imposing different limits of RMSD and averaged (φ, ψ) deviations in defining which states of the Sos ensembles were binding competent. The ΔΔG_bind for the P₃ → Ala (squares) and P₃ → Gly (triangles) Sos variants were compared to the expected values of 1200 cal·mol⁻¹, and 1900 cal·mol⁻¹ (gray dashed lines), respectively. From this comparative analysis, states of the unbound Sos ensembles that were within 0.5 Å RMSD, and the averaged (φ, ψ) deviation was less the 50°, relative to the template, were considered binding competent, provided the docked ligand did not violate steric contact limits with the SH3 substrate. For the series of binding simulations in which the RMSD limit was varied (bottom left panel), an averaged (φ, ψ) deviation limit of 50° was used; when the averaged (φ, ψ) deviation limit was tested (bottom right panel), an RMSD limit of 0.5 Å was used.

Calculation of the Gibbs free energy (ΔG) of each conformer in the unbound ensemble and its relationship to the ΔΔG of binding for each Sos variant

The Gibbs free energy (ΔG) for each conformer generated was estimated by using a structure-based calculation, which has an energy function that has been parameterized to solvent-accessible surface areas, and that has been calibrated previously and tested extensively (Baldwin 1986; Murphy and Freire 1992; Murphy et al. 1992; Lee et al. 1994; Xie and Freire 1994; Gómez et al. 1995; D'Aquino et al. 1996; Hebermann and Murphy 1996; Luque et al. 1996). The ΔG value was calculated for each ligand conformer in the unbound state (i.e., in the absence of its SH3 substrate) and does not include any terms relating to intermolecular interactions that may exist in the bound complex. From the ΔG value, the probability of each conformer can be described by the Boltzmann relationship,

where the statistical weight of each conformer (K_i) is determined by the relative Gibbs free energy of that conformer (K_i = exp[−ΔG_i/RT]), where R is the gas constant and T is the absolute temperature), and the summation is over all conformers in the ensemble. The state probabilities calculated with Equation 3 were used to estimate the ΔG of binding (ΔG_bind) of each Sos variant (i.e., P₃ → Ala, P₃ → Gly, and the wild type) as determined from the natural log of the ratio of the summed probability of all states in an ensemble that were classified as binding competent, P _bind, to the summed probability of all other ensemble states,

The ΔΔG of binding (ΔΔG_bind) was thus determined as the difference in ΔG_bind values between the mutant and wild type,

Results

Proline residues, when preceded in a polypeptide chain by another proline residue, are often found in the P_II conformation (Cowan and McGavin 1955; Okabayashi et al. 1968; Deber et al. 1970; Helbecque and Loucheux-Lefebvre 1982; Dukor and Keiderling 1991; Dukor et al. 1991). Steric collisions between the atoms of the peptide chain, however, cannot account fully for the restriction of its structure to P_II. This can be seen in Figure 2, which shows the allowed backbone dihedral angles (φ, ψ) for an internal proline of a polyproline peptide. The distribution of allowed backbone dihedral angles was determined from states generated randomly by the HSC model for a polypeptide chain consisting of three proline residues, P₁P₂P₃. The polyproline chain was allowed to sample freely φ and ψ values ranging from −180° to +180° and, for this simulation, the backbone dihedrals were not limited to the allowed Ramachandran regions (see Fig. 1). Despite the ability of the peptide chain to sample conformational space outside of the Ramachandran regions, because of steric collisions between the atoms of an individual chain, the backbone dihedrals remained restricted primarily to the allowed Ramachandran areas. Overlaid on the plot are the values of (φ, ψ) that define the P_II structure (−75 ± 10, 145 ± 10) (Cowan and McGavin 1955; Okabayashi et al. 1968; Deber et al. 1970; Helbecque and Loucheux-Lefebvre 1982; Dukor and Keiderling 1991; Dukor et al. 1991). The results presented in Figure 2 suggest that a bias favoring the P_II structure needs to be added artificially to the HSC model when generating conformational states of polyproline, if the peptide chain is to prefer the P_II conformation over other states that are sterically possible. In other words, the HSC model has no inherent bias for the P_II structure, even for polyproline. Because the HSC model lacks a P_II preference, we have used this model to simulate the conformational states of the polyproline Sos peptide in an attempt to reproduce computationally the binding energetics that were measured experimentally for the binding of Sos to the C-terminal SH3 domain of SEM-5 (Ferreon and Hilser 2003), the results of which were interpreted as indicating a significant P_II bias for the Sos peptide, even for the unbound ligand and for the non-proline residue positions (Ferreon and Hilser 2003, 2004; Hamburger et al. 2004). By varying the rate of P_II bias added to the (φ, ψ) sampling in the HSC simulation of the Sos conformational ensemble, as well as varying the regions of (φ, ψ) that were favored, we were able to test computationally the hypothesis of a structural bias for P_II in the unstructured and unbound states of the Sos peptide.

Figure 2.

The P_II bias in polyproline peptides is not entirely steric in origin. Shown are the regions of (φ, ψ) accessible to the internal proline (P₂) of a polypeptide chain consisting of three proline residues, P₁P₂P₃, which demonstrates that the HSC model cannot account for the restriction of polyproline to the P_II structure. For the simulation presented in this figure, all residues of the polyproline chain were free to sample φ and ψ values from −180° to 180°, and were not limited to the allowed Ramachandran regions. Five thousand states that did not contain van der Waals distance violations between the atoms of the tri-peptide chain were generated randomly. The distribution of paired (φ, ψ) values for the internal proline (P₂) within the 5000 random states is color coded according to the counts in which any particular (φ, ψ) pair was observed, as indicated. Overlaid on this plot are the values of (φ, ψ) that typically define the P_II structure (−75 ± 10, 145 ± 10) (Cowan and McGavin 1955; Okabayashi et al. 1968; Deber et al. 1970; Helbecque and Loucheux-Lefebvre 1982; Dukor and Keiderling 1991^; Dukor et al. 1991).

For equilibrium processes where a protein interacts with its peptide ligand, such as the association of SH3 with Sos, the peptide is believed to be unstructured in the unbound state and the binding reaction is coupled to the folding of the peptide (Fig. 3). Thus, in the unbound ensemble, the Sos peptide samples freely many conformational states, some of which are competent to bind SH3, and some of which are not. Upon binding to the SH3 substrate, the Sos ensemble is redistributed to the binding competent forms, which carries with it a cost to the free energy of the reaction. The Gibbs free energy of the SH3:Sos binding reaction (ΔG_bind) can be represented as,

Figure 3.

Binding equilibrium involving a conformational ensemble of the Sos peptide. The association process consists of the redistribution of the Sos peptide conformational ensemble from the binding incompetent states to the binding competent P_II species. The linkage relationship describing the binding reaction is provided in the lower half of the figure. The position of P₃ in the bound Sos ligand demonstrates that this proline does not interact directly with the SH3 substrate (Lim et al. 1994), and thus substitutions at this site affect ΔG_int minimally (Ferreon and Hilser 2003). The simulations with the HSC model presented in this manuscript computed ΔΔG_bind values based on the effect on ΔG_conf (i.e., on K_conf) resulting from Ala and Gly substitutions of P₃.

where ΔG_int is the free energy of the interaction between binding competent forms of SH3 and Sos, and ΔG_conf,_SH3 and ΔG_{conf, Sos} are the free energy of folding SH3 and Sos, respectively, to the binding competent forms.

In the co-crystal structure complex, the solvent-exposed third proline (P₃) of the Sos peptide does not participate in any direct binding interaction with the SH3 substrate (Lim et al. 1994). In addition, comparison of the ¹H-¹⁵N HSQC spectra of the C-terminal SH3 domain of SEM-5 when complexed with Sos and when complexed with P₃ → Ala and P₃ → Gly Sos variants, demonstrated that Ala and Gly substitutions of P₃ do not affect the structure of the binding interface (Ferreon and Hilser 2003). Because Ala and Gly substitutions of P₃ do not seem to disrupt the binding interaction relative to the wild-type ligand, the interaction term (ΔG_int) of Equation 6 should cancel when taking the difference in the ΔG_bind values between the wild-type and the Sos variants, as should the free energy of folding the SH3 protein substrate (ΔG_conf,_SH3). As such, the difference in the binding free energy of the wild-type Sos ligand relative to the P₃ → Ala and P₃ → Gly mutants should be simply the difference in the free energy of folding Sos to the binding competent forms,

where X is the non-proline amino acid (e.g., Ala or Gly). Equation 7 simplifies greatly the physical interpretation of the ΔΔG_bind values for P₃ → Ala and P₃ → Gly Sos variants. If Sos is prefolded to the binding competent P_II structure when unbound, the binding difference will be zero (ΔΔG_bind, P₃ → X ∼ 0). If, on the other hand, the unbound Sos peptide populates a disordered or random coil state, the difference in binding free energy will not be zero (ΔΔG_bind, P₃ → X ≠ 0) as substitutions of Pro to Ala and Gly will increase the conformational degrees of freedom of Sos in the unbound ensemble, increasing the free energy of folding Sos to the binding competent forms.

Computationally, the HSC model was used to generate states of the Sos ligand in the absence of its SH3 substrate. In order to simulate binding energetics associated with formation of the SH3:Sos complex, a structural definition of which states of the unbound Sos ensemble were “binding competent” was required. Then, with an adequate energy function to calculate the relative probability of each ligand state, the ΔG _bind for each Sos variant can be estimated from the ratio of the summed probability of all states in the unbound Sos ensemble that are binding competent, to the summed probability of all other states (see Equation 4 in Methods).

To determine which ligand states in the unbound ensemble were binding competent, first, each computer generated state was docked to the protein substrate using as a template the co-crystal structure complex (Lim et al. 1994). Barring steric collisions of the docked Sos ligand with SH3, the RMSD among backbone heavy atoms and the averaged deviation in backbone dihedral angles (φ, ψ) relative to the template ligand were used to define a state as binding competent. Shown in Figure 4 is the range of RMSD and averaged (φ, ψ) difference values observed for the unbound Sos ensembles of the wild-type and the P₃ → Ala and P₃ → Gly variants. As can be seen, the RMSD values range from ∼0.25 Å to 2.5 Å, relative to the template ligand, while the averaged (φ, ψ) difference values range from ∼10° to 100°. Comparison of the simulated ΔΔG _bind values to the effect on ΔG expected for Pro to Ala (∼1200 cal·mol⁻¹) and for Pro to Gly (∼1900 cal·mol⁻¹) substitutions at surface exposed sites (D'Aquino et al. 1996), which is based on the change in available (φ, ψ) space due to the side chain differences (i.e., ΔΔG_bind ≈ ΔΔG_conf), was used to determine the RMSD and averaged (φ, ψ) difference limits that defined a state in the unbound Sos ensemble as “binding competent.” This is shown also in Figure 4. It was observed that limiting the binding competent states to those Sos states, which were within ∼0.5 Å RMSD from the template, gave ΔΔG_bind values in the HSC simulations of ∼1200 cal·mol⁻¹ for the P₃ → Ala Sos variant, and ∼1900 cal·mol⁻¹ for the P₃ → Gly variant. Relaxing the RMSD limit, however, had the effect of decreasing the relative ΔΔG_bind values, as permissive limits favored preferentially those Sos peptides that were less constrained conformationally (i.e., the P₃ → Ala and P₃ → Gly variants). In contrast, the simulated ΔΔG_bind values were somewhat independent of the averaged (φ, ψ) difference limits imposed. Based on this comparative analysis, all states in the unbound Sos ensemble that were within 0.5 Å RMSD from the template, and the averaged position-specific difference in (φ, ψ) was less than 50°, also relative to the template ligand, were defined as binding competent in our simulations, provided that the ligand did not violate steric contact limits with the SH3 substrate upon docking.

Experimentally, the previous binding studies indicated that the unbound Sos ensemble does not populate a true random coil distribution of states at position 3 of the ligand, but rather its ensemble is biased toward the binding competent P_II structure (Ferreon and Hilser 2003, 2004; Hamburger et al. 2004). This is summarized in Figure 5. The value of ΔΔG_bind for the P₃ → Ala substitution measured by experiment (552 cal·mol⁻¹) (Ferreon and Hilser 2003) was significantly less than the ∼1200 cal·mol⁻¹ that was expected based upon a 7.87-fold increase in the available conformational space (φ, ψ) associated with the substitution (D'Aquino et al. 1996). Similar results were obtained with the P₃ → Gly variant of Sos; an experimental ΔΔG_bind value was observed (1173 cal·mol⁻¹) (Ferreon and Hilser 2003) that was significantly less than the ∼1900 cal·mol⁻¹ expected, assuming unbound Sos behaves as a random coil at the third position (D'Aquino et al. 1996). The lower than expected values of ΔΔG_bind measured for the Ala and Gly substitutions of P₃ were interpreted as a position-specific preference for binding competent structures (i.e., P_II) in the unbound states of the Sos peptide (Ferreon and Hilser 2003, 2004; Hamburger et al. 2004).

Figure 5.

The effect of the P₃ → Ala and P₃ → Gly substitutions on ΔΔG_bind. Shown are the values of ΔΔG_bind, in cal·mol⁻¹, determined from experimental calorimetric measurements (open columns) and from computer simulations using the HSC model (filled, black columns).

The unique properties of the P₃ position in the Sos peptide, i.e., it is solvent-exposed and adopts P_II in the bound complex (Lim et al. 1994), and Ala and Gly substitutions at this site do not affect the binding interface (Ferreon and Hilser 2003), provide a mechanism to estimate the P_II bias for Ala and Gly in the unbound states of Sos from the ΔΔG _bind values measured experimentally for the Sos variants. Because substitutions at surface-exposed sites affect ΔG based upon differences in the conformational degeneracy (Ω) of the substituted residues (D'Aquino et al. 1996), Equation 7 can be written as,

where , and (1 + K_conf) is the conformational partition function for the unbound Sos peptide (see Fig. 3; K_conf is the conformational equilibrium constant between the binding competent P_II conformers of the Sos peptide, and the states that are unstructured at the third position). The importance of the linkage relationship of Equation 8 is that experimental measurement of ΔΔG_bind offers a method to determine the magnitude of K_conf, and as an extension, the P_II bias that is equal to 1/(1 + K_conf). By this method, calorimetric measurements of the SH3:Sos binding thermodynamics demonstrated that the P₃ → Ala and P₃ → Gly variants are biased at position 3 for the P_II structure in the unbound states by ∼30% and 10%, respectively (Ferreon and Hilser 2003, 2004; Hamburger et al. 2004). For comparison, shown in Figure 6 are the results of simulations with the HSC model of the SH3:Sos binding reaction when stepped rates of P_II bias were applied to the (φ, ψ) sampling in the generation of the unbound Sos ensembles. As shown in the figure, the simulations of the ΔΔG_bind values with the HSC model are consistent with the experimentally measured values only when a P_II bias is applied. It was observed also that increasing the area of (φ, ψ), that defines the P_II conformation from (−75 ± 10, 145 ± 10) to (−75 ± 25, 145 ± 25), did not affect quantitatively the results of the binding simulations.

Figure 6.

The effect on the computed ΔΔG_bind values of varying the rate of P_II bias in the HSC modeled Sos ensembles. The rates of P_II bias for Ala and Gly positions in Sos were linked by Equation 10; likewise for the P_II bias applied to all other residue types in Sos. Results for the P₃ → Ala Sos variant are shown in the top panel, the P₃ → Gly variant results are shown in the bottom panel. The value of ΔΔG_bind measured calorimetrically by experiment (Exp.) is given for comparison and demonstrates that the HSC simulations reproduced the experimental values best when Ala was modeled to have a P_II bias of ∼30% and Gly a bias of ∼11% (highlighted in the figure). Shown by the gray columns is the effect of increasing the P_II-specific region in (φ, ψ) from (−75 ± 10, 145 ± 10) to (−75 ± 25, 145 ± 25).

It should be noted, however, that the rates of P_II bias for Ala and Gly were thought to be coupled (Ferreon and Hilser 2004; Hamburger et al. 2004). It was shown previously that the difference in P_II bias observed between the Pro → Ala and Pro → Gly substitution variants of Sos can be accounted for by the differences in the conformational degeneracy of Ala and Gly when not in the P_II conformation (Ferreon and Hilser 2004). Thus, the per-residue equilibrium constant (K_conf) between the P_II state and the ensemble of non-P_II conformations can be expressed as a product of two terms, the degeneracy (Ω) of all non-P_II conformations, which is residue-specific (D'Aquino et al. 1996), and the microscopic P_II bias, κ_mic,

Because the amino acid types appear to share a common κ_mic, the rate of P_II bias modeled in our HSC simulations for Ala determined the rate of P_II bias modeled for Gly. A common κ_mic suggests also that the P_II bias for all amino acid types can be calculated from the measured Ala value, although this has yet to be tested experimentally. The relationship between the P_II bias, Ω, and κ_mic can be represented using Equation 9 as,

In the case of Pro → Ala substitutions in unstructured peptides, Ω is known to be ∼7.87 (D'Aquino et al. 1996). For Pro → Gly substitutions, Ω is ∼26.3 (D'Aquino et al. 1996). Thus, for the HSC simulations using a P_II bias of 30% for Ala positions in Sos, this implies a P_II bias of 11% for Gly. Likewise, increasing the P_II bias for Ala to 40% specifies a bias for P_II of 17% for Gly. The effect on ΔΔG_bind of varying in this manner the amounts of P_II bias applied to the Sos residues is provided in Figure 6. In each of the simulations, all amino acid positions in a modeled Sos ligand (i.e., not just Ala and Gly at P₃) were given P_II bias rates determined by a common κ_mic calculated with Equation 10 and based on a rate of P_II bias specified for Ala. As can be seen, the simulations with the HSC model reproduced the energetics of the SH3:Sos binding reaction best when residue positions in the Sos peptide were biased for P_II at rates based on a P_II bias of ∼30% for Ala, which implies a rate of ∼11% for Gly.

Simulations with the HSC model were also performed to test the effect on ΔΔG _bind of a conformational bias to non-P_II regions of (φ, ψ). The regions of (φ, ψ) space selected for these simulations included areas accessible by (1) all amino acid types, including proline (−75 ± 10, −20 ± 10), (2) all amino acid types except proline (−137 ± 10, 10 ± 10), and (3) Gly only (75 ± 10, 145 ± 10). The locations of these non-P_II regions in (φ, ψ) are shown in Figure 7. In each of the simulations, a common κ_mic for all amino acid types was assumed, like the simulations performed with a P_II bias, and the residue-specific conformational biases were based on a rate for Ala of 30%. The effect on ΔΔG_bind of applying a bias to the non-P_II regions of (φ, ψ) in generating the unbound Sos ensembles is also presented in Figure 7. As can be seen, only the bias to the P_II region is able to reproduce the ΔΔG_bind values observed experimentally.

Figure 7.

The conformational bias in the unbound Sos ensemble is specific for the P_II structure. The HSC model was used to randomly generate unbound ensembles of the Sos ligand with a conformational bias applied separately to different regions of the (φ, ψ) space. The regions of (φ, ψ) modeled for bias in the simulations are shown in the top panel and include the P_II region (−75 ± 10, 145 ± 10), a region accessible to Pro, Ala, and Gly amino acid types (−75 ± 10, −20 ± 10), a region accessible to Ala and Gly amino acid types, but not Pro (−137 ± 10, 10 ± 10), and a region accessible to Gly only (75 ± 10, 145 ± 10). The allowed Ramachandran regions in (φ, ψ) for Gly (gray), Ala (green), the Cβ-branched amino acids (red), and Pro (blue) are colored individually for reference to Figure 1. As can be seen in the middle and bottom panels, conformational biases to the different regions of (φ, ψ) affected the simulated ΔΔG_bind values differently (given in cal·mol⁻¹). Simulations with the P₃ → Ala variant of Sos are shown in the middle panel, and the P₃ → Gly variant is presented in the bottom panel. The simulated ΔΔG_bind values were consistent with the experimental measurements only when the applied bias was to the P_II region. All simulations assumed a common κ_mic among the amino acid types, and position-specific biases were applied based on a rate for Ala of 30%, as discussed in the text.

Conclusions

Binding of an unstructured peptide to a protein requires overcoming the conformational free energy of folding the peptide into the binding competent conformation. As such, changes to the peptide that alter the size of the conformational manifold will affect the binding affinity. Previous calorimetric studies from our lab (Ferreon and Hilser 2004; Hamburger et al. 2004) have shown that small polypeptide chains that adopt the P_II conformation in the bound state experience a decrease in the conformational entropy increment (relative to α-helices) (D'Aquino et al. 1996) associated with changes from Pro to Ala or Gly at surface-exposed sites. Those results are consistent with the notion that the peptides are biased toward the P_II conformation in the unbound state (Ferreon and Hilser 2003, 2004; Hamburger et al. 2004), even for the non-proline residue positions. Such a P_II bias causes a decrease in the conformational entropy of folding, which in turn, causes the ΔΔG of binding for the Ala and Gly variants to be compressed relative to the Pro wild-type peptide.

Here, we have tested the assumption that the observed conformational bias in small peptides is specific for the P_II structure. A hard sphere collision model (HSC) was used to generate ensembles of unbound Sos computationally, which were then docked to the SH3 binding site and allowed for a simulation of the thermodynamics of binding. Because the HSC model does not favor the P_II conformation over other sterically accessible structures, by varying the rates of P_II bias added to the HSC model, and the specific region of (φ, ψ) space in which the bias was applied, we were able to test the hypothesis that the unbound Sos peptide has a specific preference for the P_II conformation, even for residue positions containing Ala and Gly. The results of our HSC-based simulations indicate that a conformational bias specific to the P_II structure, and at the sampling rates of ∼30% for Ala and ∼11% for Gly, reproduce the experimental binding energetics. Of note, the experimental binding data indicated similar rates of P_II bias for Ala and Gly positions, ∼30% and ∼10%, respectively, in the Sos peptide (Ferreon and Hilser 2003, 2004; Hamburger et al. 2004).

Because the experimental test system involved measuring changes in binding energy associated with proline substitutions of the Sos peptide (Ferreon and Hilser 2003, 2004; Hamburger et al. 2004), the conformational bias that was measured reported on a preference for the binding competent states of Sos when unbound, and not necessarily for P_II. The fact that the bound state of Sos in the co-crystal structure occupies P_II at the P₃ position (Lim et al. 1994) does not necessarily imply that all binding competent states occupy P_II at P₃, or the converse, that all states of Sos that occupy P_II at P₃ are not necessarily binding competent. As such, the definition of P_II used in our studies, i.e., the binding competent states of Sos, may not be consistent entirely with the definition used by other researchers, and is likely a primary reason why the P_II bias observed in the SH3:Sos system is low compared to the P_II bias observed in other experimental studies (Shi et al. 2002, 2005, 2006). Considering that the co-crystal structure of the bound complex demonstrated that the Sos peptide adopts P_II at its third position (Lim et al. 1994), it is, however, reasonable to assume that the binding competent states of Sos populate predominantly the P_II structure at P₃.

It is important to note also that the results presented here are consistent with the notion that the origin of the P_II bias is not purely entropic. As Figure 2 reveals, favorable interactions between atoms of the chain (Hinderaker and Raines 2003), and/or favorable interactions between the chain and the solvent (Han et al. 1998; Eker et al. 2002, 2003; Weise and Weisshaar 2003), are required to explain the mechanism underlying the bias. These findings are consistent with the significant enthalpy (Δh = −1.0 kcal·mol⁻¹ · residue⁻¹) and entropy (TΔs = −0.2 kcal·mol⁻¹ · residue⁻¹) values determined from our previous calorimetric analysis (Ferreon and Hilser 2004; Hamburger et al. 2004).

Finally, the previous experimental investigations into the role of a P_II bias in the unbound states of Sos also tested Pro → Ala and Pro → Gly substitutions at the P₆ position of the peptide ligand (Ferreon and Hilser 2003, 2004; Hamburger et al. 2004). While the experimental results observed with the P₆ substitution variants of Sos were consistent with those of the P₃ variants, i.e., an implied conformational bias in the unbound states of Sos interpreted to be specific to the P_II structure, the high-resolution co-crystal structure of the SH3:Sos complex shows P₆ to have a (φ, ψ) value of (−43, 101) in the bound state (Lim et al. 1994), which is outside of the traditional P_II structure range. Because of this observation in the co-crystal structure, the modeling of P₆ substitution variants were excluded from our analysis of the Sos ensemble using the HSC model.