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Polyproline II Helix Conformation in a Proline-Rich Environment: A Theoretical Study

Jorge A. Vila ^* , Héctor A. Baldoni , Daniel R. Ripoll , Avijit Ghosh  ^¶ and Harold A. Scheraga 

^* Universidad Nacional de San Luis, Facultad de Ciencias Físico Matemáticas y Naturales, Instituto de Matemática Aplicada San Luis, Consejo Nacional de Investigaciones Científicas y Técnicas, Ejército de Los Andes, San Luis, Argentina; Universidad Nacional de San Luis, Departamento de Química, Chacabuco, San Luis, Argentina; and The Baker Laboratory of Chemistry and Chemical Biology, The Computational Biology Service Unit, Cornell Theory Center, and ^¶ The Department of Computer Science, Cornell University, Ithaca, New York

Correspondence: Address reprint requests to Harold A. Scheraga, Baker Laboratory of Chemistry and Chemical Biology, Cornell University, Ithaca, NY 14853-1301. Tel.: 607-255-4034; E-mail: has5{at}cornell.edu.

	ABSTRACT

TOP ABSTRACT INTRODUCTION METHODS RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Interest centers here on whether a polyproline II helix can propagate through adjacent non-proline residues, and on shedding light on recent experimental observations suggesting the presence of significant PP_II structure in a short alanine-based peptide with no proline in the sequence. For this purpose, we explored the formation of polyproline II helices in proline-rich peptides with the sequences Ac-(Pro)₃-X-(Pro)₃-Gly-Tyr-NH₂, with X = Pro (PPP), Ala (PAP), Gln (PQP), Gly (PGP), and Val (PVP), and Ac-(Pro)₃-Ala-Ala-(Pro)₃-Gly-Tyr-NH₂ (PAAP), by using a theoretical approach that includes a solvent effect as well as cis trans isomerization of the peptide groups and puckering conformations of the pyrrolidine ring of the proline residues. Since ¹³C chemical shifts have proven to be useful for identifying secondary-structure preferences in proteins and peptides, and because values of the dihedral angles (,) are the main determinants of their magnitudes, we have, therefore, computed the Boltzmann-averaged ¹³C chemical shifts for the guest residues in the PXP peptide (X = Pro, Ala, Gln, Gly, and Val) with a combination of approaches, involving molecular mechanics, statistical mechanics, and quantum mechanics. In addition, an improved procedure was used to carry out the conformational searches and to compute the solvent polarization effects faster and more accurately than in previous work. The current theoretical work and additional experimental evidence show that, in short proline-rich peptides, alanine decreases the polyproline II helix content. In particular, the theoretical evidence accumulated in this work calls into question the proposal that alanine has a strong preference to adopt conformations in the polyproline II region of the Ramachandran map.

	INTRODUCTION

TOP ABSTRACT INTRODUCTION METHODS RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
A nonstructured conformation of a polypeptide, the so-called statistical-coil state, corresponds to an energy-weighted ensemble of conformations in which a single residue can occupy any of the regions of the Ramachandran map (Ramachandran et al., 1963) with a certain probability specified by the Boltzmann distribution (Vila et al., 2002). This definition at the residue level is no longer valid for oligopeptides or polypeptides in which interresidue interactions introduce additional energetic contributions. Long-range and sequence-dependent interactions render the statistical-coil definition inapplicable for a polypeptide, i.e., a nonstructured state of an oligopeptide or polypeptide is then a collective property, and corresponds to an energy-weighted ensemble of conformations in which the sequence can occupy any accessible region in the conformational space.

Whether or not the most populated region occupied by oligopeptides or polypeptides in a nonstructured state is the left-handed polyproline II (PP_II) conformation has been the object of much discussion, as in an early review by Woody (1992), and in numerous recent articles and reviews (Creamer, 1998; Sreerama and Woody, 1999; Stapley and Creamer, 1999; Kelly et al., 2001; Rucker and Creamer, 2002; Shi et al., 2002a,b; Pappu and Rose, 2002). Among the experimental studies, Kelly et al. (2001) examined the conformational preferences of some naturally occurring amino acids and used circular dichroism (CD) to study the left-handed PP_II-helix. In particular, Kelly and co-workers used a host-guest technique based on the sequences Ac-(Pro)₃-X-(Pro)₃-Gly-Tyr-NH₂, with X = Pro (PPP), Ala (PAP), Gln (PQP), Gly (PGP), Leu (PLP), Met (PMP), Ile (PIP), Val (PVP), Asn (PNP), and Ac-(Pro)₃-Ala-Ala-(Pro)₃-Gly-Tyr-NH₂ (PAAP) to derive an intrinsic propensity scale for the PP_II-helical conformation, and to examine whether the helix is propagated through two adjacent alanines. Their experiments showed that the decrease of the PP_II helix content in going from PPP to PAP to PAAP is nonlinear with respect to the number of alanines, i.e., the difference between PAP and PAAP (9%) was greater than that between PPP and PAP (3%). Despite this nonlinearity, Kelly and co-workers suggested possible reasons that could influence the conformational preferences of alanine residues when they are flanked by prolines; based on these possible reasons, they suggest that 1), PAAP still possesses significant PP_II character; 2), alanine has a relatively high intrinsic propensity to adopt this structure; and 3), the PP_II helix can propagate through two adjacent non-proline residues.

Theoretical studies of proline-rich peptides were carried out recently by Creamer (1998), who simulated a series of peptides with the sequences Ac-Ala-(Pro)₃-X-(Pro)₃-Ala-NMe (with X = Ala, Val, Leu, Phe, and Gly). These simulations employed the following approximations: 1), a hard sphere potential with a united-atom approximation, i.e., the hydrogens attached to carbon atoms were not treated explicitly; 2), excluded-volume effects with no attractive components, i.e., a hard-sphere potential with only two possible energy states—zero when there are no atomic overlaps, or infinite energy when atoms overlap; 3), no solvent was included in the calculations; 4), only the trans-conformation of proline was considered, i.e., neither proline cis trans isomerization nor ring puckering were considered. The amino acid sequence used by Creamer (1998) was similar, but not identical, to the one studied by Kelly et al (2001). Of all the approximations used by Creamer (1998), the neglect of both solvent effects and cis trans isomerization should be emphasized, since it is well known that 1), solvent effects play an important role in conformational transitions in polypeptides and proteins, in particular in polyprolines; i.e., there is both theoretical (Tanaka and Scheraga, 1975a,b) and experimental (Steinberg, et al., 1960; Gornick et al., 1964; Mandelkern 1967; Strassmair et al., 1969) evidence that solvent effects plays a dominant role influencing the form I form II transition in poly(L-proline) and 2), that the cis trans isomerization around the X-Pro peptide groups plays a key role in the rate-determining steps of protein folding (Brandts et al., 1975). The cis and trans forms of proline peptide groups are almost isoenergetic, with the trans form being slightly more favorable, and small peptides exhibit a mixture of cis and trans forms (Wüthrich, et al., 1974; Zimmerman and Scheraga, 1976); hence, consideration of the cis-trans conversion cannot be neglected in any theoretical analysis of proline-rich peptides. Moreover, these properties of the peptide group are important not only in oligopeptides and globular proteins but also in homopolymers of proline, i.e., polyproline I is all cis in a right-handed helical conformation whereas PP_II is all trans in a left-handed helical conformation, depending on the solvent (Steinberg, et al., 1960).

The all-trans conformation lies near = -78°, = 146° (Cowan and McGavin, 1955), which falls in the F region defined by Zimmerman et al. (1977) as -110° -40° and 130° 180° in the map of Ramachandran et al. (1963). The nearby E region encompasses the ß-pleated-sheet structure (Arnott et al., 1967). We assign a PP_II conformation to any residue in the F region. The CD spectrum of the PPP peptide exhibits a maximum at 228 nm and a minimum at 205 nm (Kelly et al., 2001), characteristic of a PP_II helix formed by a polyproline peptide in aqueous solution (Woody, 1992). Significantly smaller molar ellipticity may indicate shorter helices and/or larger deviations from the long PP_II helix conformation (Ma et al., 2001). The corresponding CD spectrum of a ß-sheet structure typically has positive and negative bands at 195 and 218 nm, respectively (Sreerama and Woody, 2003).

In this article, we have carried out a detailed theoretical study of the oligopeptides studied by Kelly et al. (2001) to 1), understand whether a polyproline II helix can propagate through adjacent non-proline residues and 2), shed light on the recent experimental observations by Shi et al. (2002a,b), showing the presence of significant PP_II structure in a short alanine-based peptide in a non-prolyl environment.

	METHODS

TOP ABSTRACT INTRODUCTION METHODS RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
The general procedure
In this work, we generated ensembles of conformations of the oligopeptides studied by Kelly et al. (2001), and computed their Boltzmann-averaged chemical shifts to provide a test of the conformational preferences predicted in our simulations. The conformations were generated at pH 7 with the electrostatically driven Monte Carlo (EDMC) method (Ripoll and Scheraga, 1988; Ripoll et al., 1996). An all-atom representation of the chain was used with the ECEPP/3 force field (Momany et al., 1975; Némethy et al., 1983, 1992; Sippl et al., 1984) and explicit consideration of 1), cis trans isomerization of the peptide group for proline residues; 2), both up (U) and down (D) puckering conformations of the pyrrolidine ring, which pertain to the ( = -53.0° and ¹ = -28.1°) and ( = -68.8° and ¹ = 27.4°) positions, respectively, of the C atom of the proline residue; and 3), conformational entropy, by following the approach of G and Scheraga (1969) and Zimmerman et al. (1977) as implemented in EDMC.

To investigate the role of the solvent in the conformational preference for the helical PP_II conformation, alternative forms of the potential energy function were used to evaluate the total free energy. Gas-phase (GP) representations, i.e., the ECEPP/3 potential, with omission of solvent effects, were used. These gas-phase simulations provide a basis for comparison with the two solvation models used here, namely, a gas-phase potential represented by ECEPP/3 with a solvent-accessible surface area model, or GPSAS (Vila et al., 1991) to represent the interaction with the solvent; and a gas-phase potential represented by ECEPP/3 combined with a fast multigrid boundary element (MBE), i.e., GPSP, method to account for the solvation free energy and solvent polarization effects as well as the equilibrium binding of protons and its dependence on environmental conditions (Vorobjev et al., 1994, 1995; Vorobjev and Scheraga, 1997). These approaches provide a solution to the problem of ionization equilibria (Bashford and Karplus, 1990; Yang et al., 1993; Yang and Honig, 1993; Gilson, 1993; Beroza et al., 1995; Vila et al., 1998).

Evaluation of the total free energy
Three alternative forms were used to compute the total free energy as a function of the coordinates r_p; viz., a gas phase potential (GP),

(1)

where E_int(r_p) is the internal conformational energy of the molecule in the absence of solvent, assumed to correspond to the ECEPP/3 energy (Némethy et al., 1992) of the neutral molecule, and F_vib(r_p) is the conformational entropy contribution. The contribution from F_vib(r_p) to the total free energy has been treated by a harmonic vibrational approximation (G and Scheraga, 1969; Zimmerman et al., 1977) for each conformation obtained by using the ECEPP/3 potential function.

The next form is a gas phase potential plus a solvent-accessible surface area model (GPSAS),

(2)

where F_sas(r_p) represents the solvation free energy as defined by Vila et al. (1991), and the third form is a gas phase potential combined with the MBE method (GPSP),

(3)

where F_cav(r_p) is the free energy associated with the process of cavity creation when transferring the molecule from the gas phase into the aqueous solution; F_solv(r_p) is the free energy associated with the polarization of the aqueous solution; and F_inz(r_p, pH) is the free energy associated with the change in the state of ionization of the ionizable groups due to the transfer of the molecule from the gas phase to the solvent, at a fixed pH value.

F_cav(r_p) describes the free energy of creation of a cavity to accommodate a zero-charge peptide molecule, i.e., with all partial atomic charges set to zero. As shown previously (Sitkoff et al., 1994; Simonson and Brünger, 1994), F_cav(r_p) can be considered as the free energy of transfer of a nonpolar molecule from the gas phase to water. This free energy is proportional to the solvent-accessible surface area of the molecule. The term F_solv(r_p) is obtained by using the fast MBE method, and F_inz(r_p, pH) is calculated by using general multisite titration formalism (Bashford and Karplus, 1990; Yang et al., 1993; Vorobjev et al., 1994).

Conformational search
A full search for the global minimum of the function represented by Eq. 3 requires the energy minimization of thousands of conformations, which is beyond current computational capabilities. For this reason, a protocol that produces a reasonable sampling of the conformational space, defined by E(r_p, pH) without minimizing this particular function, is used (Vila et al., 2003). The protocol that we previously used (Ripoll et al., 1996; Vila et al., 2002, 2003) involved energy minimization of an approximate form of E(r_p, pH), viz., (E_approx(r_p)), given by E_int(r_p), by using the secant unconstrained minimization solver algorithm (Gay, 1983). In this work, E_approx(r_p) is represented by

(4)

where F_GB(r_p) represents the pairwise Generalized Born (GB) solvation model of Hawkins et al. (1996), from the laboratory of D. A. Case, as implemented by Ghosh et al. (2002). This implementation of the pairwise GB solvation model includes analytical derivatives with respect to atomic coordinates, keeping the effective Born radii fixed.

The term F_GB(r_p) is a good representation of the free energy of solvation F_solv(r_p) used in Eq. 3, since this approximate solution of the Poisson-Boltzmann, as given by the GB model, has been shown to give results that are close to the exact solution (Tsui and Case, 2001; Onufriev et al., 2002). Consequently, the new protocol is expected to provide better results than the procedure used previously (Vila et al., 1998, 2001, 2002), i.e., when E_approx(r_p) = E_int(r_p).

It should be pointed out that, during the calculation with the GPSP approach, the total free energy, E(r_p, pH), of the conformations is always computed by Eq. 3, i.e., by computing the solvent polarization effects with the fast MBE method, even though the conformational search was carried out with Eq. 4, i.e., with the GB potential.

Clustering analysis
Classification of the accepted conformations listed in Table 1 was carried out with the clustering procedure used by Vila et al. (2003) to study statistical-coil peptides in solution, i.e., through a minimal tree (the minimal spanning tree method described by Ripoll et al., 1999), and then the minimal tree was partitioned in terms of a specified root mean-square deviation (RMSD) cutoff, leading to a given number of families. The families resulting from the RMSD clustering procedure were ranked in increasing order according to their total free energy, given by Eq. 1. For each family, we evaluated both the number of conformations belonging to that family and the set of dihedral angles of the lowest-energy conformation. We refer to the lowest-energy conformation of a family as the leading member. The Boltzmann averages over all the families for a given peptide were computed by using only the leading member of each family. A cutoff of 2 Å RMSD between all heavy atoms in the peptides PXP and PAAP, with no cutoff in the energy, was used during the clustering procedure. As shown previously (Vila et al., 2003), higher-number clusters, i.e., these with higher energy, will not make any significant contribution to the Boltzmann average because the leading members of such families are much higher in energy than the leading members of lower-number clustered families. For this reason, we chose a cutoff in the total number of cluster families for each amino acid X; i.e., we considered only those families that represent >95% of the total number of accepted conformations. The reduced number of ensembles of conformations that meet this criterion are listed in parentheses in the last column of Table 1.

Quantum-chemical calculations of the ¹³C chemical shift
The conformations of the PXP and PAAP molecules, employed for calculating the ¹³C shielding, corresponded to the leading members of each family. These conformations were not energy-minimized at the quantum chemical level of theory because such geometry-optimized structures lead only to very small additional effects on the computed shielding (Sun et al., 2002; Vila et al., 2002). However, these conformations represent energy-minimized structures obtained with the geometries defined by the ECCEP/3 force field.

All ¹³C shielding calculations were carried out by using a hybrid density functional level of theory (Parr and Yang, 1989) with the gauge-independent atomic orbitals procedure (Wolinski et al., 1990) as implemented in the Gaussian 98 program (Frisch et al., 1998). The selected (hybrid density functional level of theory) B3LYP methods employed two different exchange-correlation functionals—Becke's three-parameter functional (Becke, 1993) in combination with nonlocal correlation provided by the Lee-Yang-Parr expression (Lee et al., 1988), which contains both local and nonlocal terms. This functional has proven to be a very good choice to predict ¹³C magnetic shielding tensors as proposed by Cheeseman et al. (1996).

Since NMR shielding tensors are predominantly local properties, it is possible to obtain theoretical shielding values of good quality by using large basis sets located only on the atoms whose shifts are of interest, whereas the rest of the atoms in the molecule are given more modest bases (Chesnut and Moore, 1989). This is called the locally dense basis approach, and its use enables us to minimize the length of the chemical-shift calculations while maintaining the accuracy of the results. This approach has been revised by Laws et al. (1995), who concluded that the results correlate very well with calculations using a very large basis set, although the time is significantly reduced. In the present work, the X and the Ala residues in the PXP and PAAP peptides, respectively, were treated with a 6-311+G(2d,p) locally dense basis set, whereas the remaining residues in the molecule were described by a 3-21G basis set. These basis-set notations refer to those of Pople and co-workers (Hehre et al., 1986), as implemented in the Gaussian 98 program (Frisch et al., 1998). Recently, by using the locally dense approximation, Sun et al. (2002) found good agreement between theory and experiment, making its use very attractive for treating large systems such as the peptides studied in this work. The reason for such good agreement between theory and experiment, by using the locally dense approximation, resides in the physical basis of the chemical shift effect, i.e., as noted by Chesnut and Moore (1989): "the chemical shift is sensitive to the electron distribution near the resonant nucleus and therefore requires a good description of that distribution in the vicinity of the resonant nucleus and a lesser description further away...".

To enable us to compare calculated and experimental values of chemical shifts (), the calculated ¹³C chemical shielding isotropic tensors (_iso) were converted to a tetramethylsilane (TMS) shift scale by using the equation = 182.48 - _iso, where the 182.48 value represents the ¹³C shielding of TMS obtained by using B3LYP/6-311 + G(2d,p)//B3LYP/6 - 31G(d) geometry. The corresponding experimental value for the ¹³C shielding of TMS is _TMS,exp = 188.1 ppm (Jameson and Jameson, 1987).

To test the locally dense approach used here, we compared ¹³C chemical shifts calculated recently (Vila et al., 2002) for the unblocked tetrapeptide GGXA by using a uniform basis set, i.e., 6-311+G(2d,p) over all residues, with the ones obtained using the locally dense approximation, i.e., in which the X residue is treated with a 6-311+G(2d,p) locally dense basis set, whereas the remaining residues in the unblocked tetrapeptide were described by a 3-21G basis set. Fig. 1 shows the statistical correlation of the ¹³C chemical shifts when the guest residue X in the GGXA peptide is alanine. The nine ¹³C chemical shifts plotted in Fig. 1 for the GGAA peptide correspond to the leading members of each family obtained after clustering the statistical-coil ensemble as described by Vila et al. (2002). Fig. 1, a and b, shows good agreement between both basis sets with a correlation coefficient of R = 0.990 and 0.997 for the ¹³C and ¹³C^ß chemical shifts, respectively. These results provide strong support for the hypothesis of Chesnut and Moore (1989) that the ¹³C chemical shifts are predominantly a local property.

View larger version (13K): [in this window] [in a new window]   FIGURE 1  (a) Correlation between the 13C chemical shifts for the guest alanine residue in the GGAA peptide computed by using a uniform basis set (Vila et al., 2002) and those computed by using the locally dense basis set approach (Chesnut and Moore, 1989) as explained in Methods. R = 0.990; slope of 0.95 for the correlation line. (b) Same as a for the 13Cß chemical shifts. R = 0.997; slope of 1.09 for the correlation line.

	RESULTS AND DISCUSSION

TOP ABSTRACT INTRODUCTION METHODS RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

We are particularly interested in the residues with higher PP_II propensity and, hence, simulations were carried out for PPP, PAP, PQP, and one representative sequence of each of the remaining two groups, viz., PGP and PVP, respectively. In addition, simulations were carried out for PAAP because 1), this represents a sequence with a different alanine content from that of PAP; 2), the sequence containing two alanines will better reflect the possibility of propagation of the PP_II helix conformation through more than one alanine; and 3), there is experimental evidence (Kelly et al., 2001) showing that the decrease of helix content from PPP to PAP to PAAP is nonlinear with respect to the number of alanines.

In this study, we carried out EDMC runs for the six different polypeptides sequences shown in Table 1. In all the sequences, the end groups were acetyl (CH₃CO-) and amino (-NH₂). For each of the runs described in Table 1, >35,000 conformations were generated, following the procedure described in the Methods section. For each sequence, three different runs were carried out, viz., 1), without consideration of solvent effects by using a gas-phase potential as described by ECEPP/3; 2), with explicit consideration of solvent effects with a solvent-accessible surface area model (using the SRFOPT set of solvation parameters described by Vila et al., 1991); and 3), by explicit consideration of solvent polarization effects from a solution of the Poisson-Boltzmann equation by using the fast MBE method developed by Vorobjev and Scheraga (1997).

Conformational analysis of PPP
Rucker and Creamer (2002) considered that PP_II is an energetically favorable option for oligopeptides because all backbone polar groups are well-solvated in this conformation in water, thus compensating for the lack of intramolecular hydrogen bonds. The implicit assumption in this statement is that a polyproline peptide must be all trans and, of course, any non-proline residue in this conformation must be trans. Therefore, the characteristic ratio (C) should be 20 at 30°C, according to the experimentally determined value for polyproline in an organic solvent in which the polypeptide is in the all-trans conformation (Mattice and Mandelkern, 1971). However, as shown by Mattice and Mandelkern, the characteristic ratio is C 14 in an aqueous solvent at 30°C. In water, the polyproline II (all-trans) conformation is favored over the polyproline I (all-cis) conformation (Steinberg, et al., 1960). Based on these observations, and by using a statistical analysis of randomly-coiled poly(L-proline), Tanaka and Scheraga (1975c) concluded that such a significant change in the characteristic ratio is due to a mixture of trans and cis conformations in a PP_II helix. These authors found that close agreement with the experimental results of Mattice and Mandelkern (1971) is obtained when the characteristic ratio is computed by assuming that 5% of the proline peptide bonds are in the cis conformation. In other words, the introduction of a small amount of cis peptide groups into a predominantly trans chain in poly(L-proline) can influence its characteristic ratio considerably. In line with this finding, the lowest-energy conformation (-235 Kcal/mol) computed for the PPP peptide with the GPSP potential at pH 7, shown in Fig. 2, has an end-to-end distance of 8 Å, which is shorter than a conformation that is higher in energy (-226 Kcal/mol) with all its peptide bonds in the trans state and with an end-to-end distance of 24 Å, as shown in Fig. 3. Nevertheless, the computed Boltzmann-averaged PP_II helix content for the PPP peptide, by using all the accepted conformations listed in the third column of Table 1, computed with GP and GPSP (66.7%) or with the GPSAS (68.0%) potentials, respectively, are in agreement with the 66.0 ± 2% determined experimentally by Kelly et al. (2001), as shown in Table 2. To test the adequacy of our approach for computing averages, we recomputed the Boltzmann-averaged PP_II helix content in the PXP and PAAP peptide by using both: all the accepted conformations listed in the third column of Table 1 and only the leading members, weighted by the population, of the corresponding cluster listed in the fifth column of Table 1, respectively. The values obtained are included in the fifth column of Table 2, with and without brackets, respectively. Very good agreement exists between both approaches with a correlation coefficient of R = 0.96 and a slope of 1.02 for the correlation line.

View larger version (30K): [in this window] [in a new window]   FIGURE 2  Stereo view of the leading member of family 1 of the peptide PPP, after clustering the accepted conformations shown in Table 1. The conformations of the peptide bonds for the proline residues of this structure are CTCTCTT, computed with the GPSP potential, as shown in Table 2.

View larger version (22K): [in this window] [in a new window]   FIGURE 3  Stereo view of the leading member of family 2 of the peptide PPP, after clustering the accepted conformations shown in Table 1. The conformations of the peptide bonds for the proline residues of this structure are TTTTTTT, computed with the GPSP potential.

Polyproline helix content of PXP and PAAP
In Table 3, we have listed all the Boltzmann-averaged values for the ¹³C chemical shifts for residues X and Ala in the peptides PXP and PAAP, respectively. Since the main factor determining ¹³C and ¹³C^ß chemical shifts is the set of backbone dihedral angles (,), with minor influence from the side-chain dihedral angles (Spera and Bax, 1991; Iwadate et al., 1999; Wishart and Case, 2001; Vila, et al., 2003), comparison between the predicted and measured values for the ¹³C chemical shifts will provide a test of the conformational preferences predicted in our simulations.

The ¹³C chemical shifts have been used to distinguish between cis and trans X-Pro peptide bonds in small peptides (Dorman and Bovey, 1973). For this reason, we compared the Boltzmann-averaged ¹³C^ß and ¹³C chemical shifts of residue X = PRO in the PXP peptide with the maximum and minimum values, obtained from an analysis of the ¹³C^ß and ¹³C chemical shifts of 1033 proline residues from 304 proteins for the X-Pro peptide bond in the cis and trans conformations by Schubert et al. (2002). Our calculated ¹³C^ß and ¹³C Boltzmann-averaged chemical shift values (30.2 ppm and 21.3 ppm, respectively) for proline in the PPP peptide are consistent with a peptide bond in the trans conformation since 1), they are greater than the minimum observed values (26.3 ppm and 19.3 ppm, respectively) for a peptide bond in the trans conformation, but 2), they are lower than the minimum observed values (30.7 ppm and 22.1 ppm, respectively) for a peptide bond in the cis conformation (Schubert et al., 2002). From this comparison between the computed Boltzmann-averaged values for the ¹³C^ß and ¹³C chemical shifts for the PPP peptide and the maximum and minimum experimental values observed by Schubert et al. (2002), we can conclude that the guest (proline) residue is in the trans conformation in the PPP peptide. This result is consistent with the peptide-bond conformation shown in Table 2, for the simulations carried out with the GPSP potential.

As shown in Table 2 for simulations carried out in water, all guest residues in the PXP peptide, when X is not proline, do not show a conformational preference for the F region of the Zimmermann map. We can conclude that, in the presence of water, there is no propagation of the PP_II conformational preference into the preceding (guest) residue for all the PXP sequences, when X is not proline, contrary to the proposal of Kelly et al. (2001). The lack of propagation through non-proline residues, observed in our simulations, is due to the low propensity for the PP_II conformation of any of the tested residues, arising (among others) from consideration of hydration effects. In other words, the strong tendency attributed to some amino acids for the PP_II region, and the widely-held belief that such residues in proline-rich regions will adopt this structure predominantly, will have to be revised.

As shown for the underlined and boldfaced conformations in Table 1, column 4, a proline residue of PAAP seems to have a significant influence only on the preceding member (alanine) in the sequence (in forcing such a non-proline residue to adopt the PP_II conformation) in the simulations carried out for this peptide using the GP potential energy function. However, this influence disappears when water is included in the simulation. Alanine does not seem to propagate the PP_II helix conformation when it is surrounded by a proline-rich environment, in disagreement with the suggestion of Kelly et al. (2001).

Does Ala prefer the PP_II conformation?
The PP_II helix gives rise to a CD spectrum that is remarkably similar to that of unfolded proteins. This similarity has been used to justify the hypothesis that unfolded proteins possess considerable PP_II helix, rather than ß, content. Since the original observation of Tiffany and Krimm (1968), a plethora of experiments on proline-rich sequences have been reported, attempting to validate this hypothesis. However, many of these experimental results involve contradictions that have not been properly addressed. As an example, Shi et al. (2002a) studied the oligopeptide Ac-ZZ-(Ala)₇-OO-NH₂ [ZAO] (where Z denotes diaminobutyric acid and O is ornithine), with no proline in the sequence, by using CD and NMR experiments. Based mainly on J-vicinal coupling constants (and the corresponding -values) derived from the NMR experiments, the data were interpreted as placing all seven alanine residues in the PP_II region, even at high temperature. If this were the case, the CD spectra of Shi et al. (2002a) should be similar to those obtained by Rucker and Creamer (2002) for the peptide Ac-(Pro)₇-Gly-Tyr-NH₂ (P7). However, they are not (see Fig. 5 of Shi et al., 2002a, and Fig. 1 of Rucker and Creamer, 2002). On the other hand, the CD spectrum obtained by Shi et al. (2002a) is remarkably similar to the one obtained by Rucker and Creamer (2002) for the peptide Ac-(Lys)₇-Gly-Tyr-NH₂ (K7) at pH 12, which, according to the latter authors, has lost some PP_II helix character with an increase in the population of disordered states and/or the appearance of some small amount of ß-sheet.

Since Shi et al. (2002a) did not report the vicinal coupling constants for the whole 11-residue peptide, but only for the seven alanine residues, it is not possible to make an accurate estimate of the overall PP_II helix content based on their NMR analysis; hence, we cannot compare the PP_II helix content for the whole peptide with our estimation of 35% based on their CD spectrum. It should be noted that the CD spectrum published by Shi et al. (2002b) is shifted on the y axis when compared with the one published by Shi et al. (2002a); such a shift could easily lead to a wrong (90%) estimate of the PP_II helix content. According to N. R. Kallenbach (private communication, 2002), the correct spectrum is the one published by Shi et al. (2002a), which shows no sizeable positive shoulder in the 215–230 nm, the which, if present, would have implied a high PP_II content.

Our estimated value of 35% of PP_II helix content is in disagreement with the 90% PP_II conformation reported by Shi et al. (2002b) for the Ala₇ sequence. The suggested 90% PP_II content for the Ala₇ sequence, based on their NMR analysis, means that the PP_II helix content for the whole ZAO peptide should be at least 60%, i.e., with 7 out of 11 residues in the PP_II region. This lower value for the PP_II helix content is obtained under the assumption that neither the diaminobutyric acid nor the ornithine residues occupy the PP_II conformational region. However, the ornithine and diaminobutyric acid residues could also contribute to the PP_II helix content. For example, diaminobutyric acid has one less side-chain methylene group than ornithine and two less than lysine. A comparison of -helix stabilities of poly-L-lysine, poly-L-ornithine, and poly-L-diaminobutyric acid) shows that, in water at pH < 8, they all belong to a nonstructured state, i.e., not to an -helical structure (Grourke and Gibbs, 1971). A homopolymer of poly-L-lysine at low pH, ionic strength, and temperature exhibits a CD spectrum consistent with a PP_II helix (Woody, 1992). Recently, Rucker and Creamer (2002) suggested that the CD spectra collected at pH 7 for a lysine-rich peptide (K7) indicate a high PP_II helix content. According to Rucker and Creamer (2002), this conformational preference for the PP_II helical structure appears as the result of the nature of the backbone rather than as a consequence of electrostatic interaction between side chains. Based on this hypothesis, it is conceivable that similar behavior could be displayed by residues related to lysine, such as ornithine or diaminobutyric acid, and hence, the possibility that ornithine or diaminobutyric acid populate the PP_II region at pH 7 cannot be ruled out. In other words, there is reason to believe that such discrepancy between the NMR-determined (60%) and CD-determined (35%) PP_II helix content in the experiment of Shi et al. (2002a) could be greater than these estimates.

Consider, further, the disagreement between the estimated PP_II helix content derived from CD (35%) and NMR (60%) data, respectively, by Shi et al. (2002a). The observation made by Pappu and Rose (2002) that a seven-residue alanine-based peptide can be dominated by fluctuations around the left-handed PP_II helix ( = -78°, = 146°) and a nearby conformation ( = -147°, = 81°), i.e., populating the F and D regions, respectively, of the Zimmerman et al. (1977) map, may account for the disagreement. Because of the degeneracy of the Karplus relation between coupling constant and -value, the coupling constants are similar in the F and D regions. Thus, the assumption of such fluctuations may explain the low CD signal, although still being consistent with the observed value for the NMR-determined vicinal coupling constant. In other words, residues in the F and D regions of the Zimmerman et al. (1977) map could each display a vicinal coupling (³J_NH) constant <6.0 Hz, which is consistent with the results of Shi et al. (2002a) at 2°C. From the degenerate Karplus relation, a coupling constant <6 Hz could correspond to many values of , viz., those in whole range of -180° 180°. Therefore, one cannot identify a particular value of based only on a coupling constant of <6 Hz. Table 4 shows that non-proline residues can populate A, A^*, D, D^*, C, and F regions with coupling constants <6 Hz. It is conceivable that experimental values for ³J_NH observed by Shi et al. (2002a) could represent a Boltzmann-averaged distribution of residues displaying preferences for many regions of the Ramachandran map, because residues in these regions could also display a backbone dihedral angle consistent with a coupling constant <6.0 Hz, without displaying any particular regular structure such as - or PP_II-helices.

View this table: [in this window] [in a new window]   TABLE 4  Computation of the 3JNH coupling constant

	CONCLUSIONS

TOP ABSTRACT INTRODUCTION METHODS RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
Our theoretical results and analysis for the PXP and PAAP peptides are in qualitative agreement with 1), experimental CD spectroscopic evidence for proline-containing undecamers with alanine and glycine substituted in the central position (Petrella et al., 1996), showing that the PP_II helix content is reduced compared with the all-proline peptide; 2), experimental results of Kelly et al. (2001) on PAP and PAAP peptides; and 3), recent experimental evidence using isothermal titration calorimetry (Ferreon and Hilser, 2003) showing that the probability of the PP_II conformation in the denatured states of Ala is 30%. As Ferreon and Hilser noted, their (30%) PP_II content, estimated for Ala, differs considerably from that determined by Shi et al. (2002a), viz., 90%. The prediction of Ferreon and Hilser for Ala is in agreement with the 35% PP_II helix content that we have estimated from the CD spectrum published by Shi et al. (2002a).

Our simulations show that water affects the conformational properties of polyproline but, instead of stabilizing the extended PP_II helical form, a less extended structure is found (involving some cis residues), in good agreement with experimental observations made by Mattice and Mandelkern (1971). In addition, we find that, in the presence of water, there is no propagation of the PP_II conformational preference into the guest residues for all the PXP sequences, when X is not proline.

Finally, using two approaches, namely the reduction of the total number of conformations by the clustering procedure and the quantum chemical computation of the chemical shifts of the resulting leading members of each family by using a locally dense basis set, we have been able to treat the quantum chemical computation of Boltzmann-averaged chemical shifts of ¹³C carbons in the PXP and PAAP peptides.

	ACKNOWLEDGEMENTS

TOP ABSTRACT INTRODUCTION METHODS RESULTS AND DISCUSSION CONCLUSIONS ACKNOWLEDGEMENTS REFERENCES

 
This research was supported by grants from the National Institutes of Health (GM-14312 and TW00857) and the National Science Foundation (MCB00-03722). Support was also received from the National Foundation for Cancer Research, the National Research Council of Argentina (Consejo Nacional de Investigaciones Científicas y Técnicas), and Project No P-328402 of the Universidad Nacional de San Luis, Argentina. Part of this research was conducted using the resources of the Cornell Theory Center (which receives funding from Cornell University, the State of New York, federal agencies, foundations, and corporate partners), and the National Partnership for Advanced Computational Infrastructure at the Pittsburgh Supercomputing Center (which is supported in part by the National Science Foundation, MCA99S007P).

	FOOTNOTES

 
Avijit Ghosh's present address is Drexel University, Dept. of Physics, 3141 Chestnut St., Philadelphia, PA 19104.

Submitted on May 21, 2003; accepted for publication October 10, 2003.

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