Searching for Periodic Structures in β-Peptides - American Chemical

J. Phys. Chem. B 2001, 105, 5559-5567

5559

Searching for Periodic Structures in β-Peptides Robert Gu1 nther and Hans-Jo1 rg Hofmann*,† Institut fu¨ r Biochemie, Fakulta¨ t fu¨ r Biowissenschaften, Pharmazie und Psychologie, UniVersita¨ t Leipzig, Talstr. 33, D-04103 Leipzig, Germany

Krzysztof Kuczera*,‡ Department of Chemistry and Department of Molecular Biosciences, UniVersity of Kansas, 2010 Mallot Hall, Lawrence, Kansas 66045, U.S.A. ReceiVed: January 4, 2001; In Final Form: March 21, 2001

Hexamers of β-amino acids with different substituent patterns at the CR- and Cβ-backbone atoms (none, β2, β3, β2,2, β3,3, (R,S)β2,3, (S,S)β2,3) were the subject of molecular dynamics simulations on the basis of the CHARMm23.1 force field to generate conformational free energy surfaces for concerted changes in (φ,ψ) dihedrals employing a multidimensional conformational integration approach. Application of this technique provides insight into the intrinsic folding propensities of these homooligomers including cooperativity effects. The free energy surfaces give a complete overview of all possible periodic secondary structures. Most striking are the various helix types characterized by hydrogen-bonded pseudocycles of different size and direction of hydrogen bond formation, e.g. H14, H12, and H10. There are also β-strand like periodic structures of considerable stability. It is shown that the formation of various helix types and sheetlike structures strongly depends on the substituent pattern. On the basis of this information, it might be possible to design definite secondary structures in β-peptides to mimic native peptide structures.

Introduction Peptides and proteins play an important role in numerous biological processes. Their correct function depends on a welldefined three-dimensional structure, which is characterized by various secondary structure elements like helices, sheets, and reverse turns. One goal of peptide research is to obtain biologically active compounds with improved properties by structure modification of native peptides.1-4 Of course, such peptidomimetics must reflect those structural properties of their native counterparts that are necessary for a biological effect. In this context, oligomers of β-amino acids, called β-peptides, have attracted much attention in the past few years as an interesting extension of the ever-growing class of peptidomimetics.3,5-11 In comparison to R-amino acids, β-amino acids have an extra methylene group in their backbone. Surprisingly, rather than causing higher conformational flexibility, the incorporation of the additional Cβ-atoms leads to considerable stabilization of characteristic secondary structures already in short oligomers with only 4 to 6 residues.5,6,12-15 Most striking are the various typesofhelicesdifferingintheirhydrogenbondingpatterns.12,14,16-20 First hints of helix formation in β-peptides stem from X-ray studies on poly(R-isobutyl-L-aspartate) in the early 80s.21,22 Since the mid-90s, several NMR and X-ray studies have indicated the H14-helix as a particularly preferred helical conformation for β-amino acid oligomers.8,12,13,15,19,21 This helical structure is a 31-helix characterized by 14-membered hydrogen-bonded pseudocycles formed between the NH-group of residue i and the CO-group of residue (i + 3). The forward direction of hydrogen bonding along the sequence is opposite * To whom correspondence should be addressed. † E-mail: [email protected]. ‡ E-mail: [email protected].

to helices of R-peptides, where the hydrogen bonds are always formed in the backward direction. However, helices with the backward formation of hydrogen bonds could also be found in β-peptides, as for instance in oligomers of the conformationally constrained trans-2-aminocyclopentanecarboxylic acid.17,18 In the resulting 2.51-helix, hydrogen bonds are formed between the NH-group of residue i and the CO-group of the preceding residue (i - 3) leading to 12-membered hydrogen-bonded pseudocycles (H12-helix). The “mixed“ helices are very interesting; they combine hydrogen-bonded cycles of different size and direction, e.g., 10- and 12-membered pseudocycles, in alternating order.16,23 Recently, we have predicted a novel periodic 31-helix with 10-membered hydrogen-bonded cycles (H10-helix) in a completely different conformation subspace of β-peptides.24 Apart from the various helices, it has been shown that β-peptides are also able to form sheetlike structures and reverse turns.5-7,12,25-30 It could be very useful for peptide chemistry to get a systematic overview of all possibilities of secondary structure formation in β-peptides, in particular of the formation of periodic structures, where all amino acid constituents have the same torsion angle values. One approach is to derive periodic structures by oligomerization of conformers of monomer units obtained in systematic conformational searches. This was successfully done for various substituted β-amino acid monomers.20,24,31,32 However, such a procedure does not take into account cooperativity effects. Thus, it cannot be excluded that further possibilities become only visible in longer sequences. To search for periodic structures of longer β-peptides as completely as possible and to examine systematically the influence of substituents, we have employed conformational free energy simulations.33,34 Such a procedure is expected to be superior to a simple adiabatic mapping for several reasons. By averaging over a range of thermally available molecular

10.1021/jp010021v CCC: $20.00 © 2001 American Chemical Society Published on Web 05/17/2001

5560 J. Phys. Chem. B, Vol. 105, No. 23, 2001

Gu¨nther et al.

TABLE 1: Substituent Patterns in the Investigated β-Peptide Hexamer Model Compounds

TABLE 2: Comparison of Torsion Angles of Minimum Energy Conformations of the Blocked β-Amino Acid Monomer Ba Obtained by ab Initio MO Theory at the HF/6-31G* Level and CHARMm23.1 Molecular Mechanicsb HF/6-31G*c confc‘

hexamer

R1

R2

R3

R4

symbol

Ac-[β-hAla]6-NHMe Ac-[β2-hAla]6-NHMe Ac-[β3-hAla]6-NHMe Ac-[β2,2-hAla]6-NHMe Ac-[β3,3-hAla]6-NHMe Ac-[(R,S)β2,3-hAla]6-NHMe Ac-[(S,S)β2,3-hAla]6-NHMe

-H -CH3 -H -CH3 -H -H -CH3

-H -H -H -CH3 -H -CH3 -H

-H -H -CH3 -H -CH3 -CH3 -CH3

-H -H -H -H -CH3 -H -H

U6 A6 B6 (A2)6 (B2)6 (RS)6 (SS)6

structures consistent with a given set of constraints, we obtain a smooth free energy surface with well-defined free energy minima, whereas adiabatic mapping often runs into difficulties due to multiple local minima of the potential energy. The free energy differences between the identified stable states are closer related to the observable conformer population ratios than are energy differences. Additionally, the free energy differences in a vacuum may be used as starting point for computing stability differences in solution by addition of corrections for electrostatic and cavitation energy terms describing solvation.35 To investigate the substituent influence on the formation of periodic secondary structures the β-peptide hexamer models given in Table 1 have been selected. The basic simulation method is the multidimensional conformational free energy thermodynamic integration (CFTI) approach. This method enables the calculation of the conformational free energy gradient with respect to several coordinates from a single molecular dynamics (MD) simulation with appropriate constraints. It has been successfully applied to the analysis of the conformational free energy surface of several peptides both in a vacuum and in solution.35-38 We have applied CFTI to generate free energy gradient maps covering whole quadrants of (φ,ψ)-space for the selected β-peptide hexamer models in vacuo. These gradient maps allow us to locate those free energy minima that correspond to stable periodic structures. The positions of the minima were further refined by a free energy minimization procedure, and the relative free energies of different stable states were evaluated by thermodynamic integration. Methodology Molecular Mechanics. The formalism used in this study is based on molecular mechanics employing the CHARMm23.1 all-atom force field39,40 as it is incorporated in Quanta97 (Molecular Simulations Inc., San Diego). Gasteiger charges were assigned to the β-amino acid residues. To make sure that the CHARMm23.1 force field reproduces the conformational properties of the β-amino acid residues, several conformational search strategies were applied to the blocked monomers B, U, A, A2, B2, RS, and SS (Table 1), and results were compared with those obtained from ab initio MO calculations.24,31,32 At first, conformational grid searches were performed in intervals of 30° for the torsion angles φ, θ, and ψ (cf. Table 1). Additionally, a simulated annealing protocol was used to complement the molecular mechanics study. In this case, an 1 ns high-temperature trajectory was generated at 1000 K saving

B1 B2 B2′ B3 B3′ B4 B5 B6 B7 B8 B9 B9′ B10 B11 B12

φ

θ

CHARMm23.1 ι

φ

θ

ι

-143.7 -63.8 -144.6 -155.9 -60.8 -98.5 -71.9 144.4 -80.9 -75.3 174.3 -78.6 60.4 -124.1 86.7 61.7 169.8 102.4 -63.7 -45.0 111.2 -69.1 -58.7 93.3 55.3 51.1 -116.0 58.3 56.3 -99.9 63.5 59.3 -159.0 f B3′ -160.6 56.0 102.6 -159.7 59.3 76.9 -111.9 60.2 25.6 -104.2 59.2 65.4 -75.6 168.6 178.6 -73.9 176.2 155.3 61.7 163.5 150.2 f B2′ -91.4 49.8 90.4 f B6 78.8 -47.0 -95.3 85.4 -60.9 -82.3 -155.0 63.4 -129.3 -160.2 62.6 -101.0 -109.4 74.1 -90.8 -100.6 69.5 -89.9 -159.9 -68.0 29.5 -150.4 -61.3 95.1

typed C6 C8 C8 C8 C8 C6 C6 C8

H14 H12

a Cf. Table 1. b Angles in degrees. c Data taken from Ref 24. d C : x hydrogen-bonded cycle with x atoms; Hx: monomer of a helix with x-membered hydrogen-bonded turns.

snapshots every picosecond. The resulting 1000 conformations were the starting points for further molecular dynamics simulations of 10 ps evolution time. Within this period, the temperature was linearly scaled down to 300 K. Subsequent energy minimization provided the conformers which were compared with the quantum chemical data. The minimum conformations obtained in this way for the blocked monomer B by molecular mechanics are compared with the data of ab initio MO theory in Table 2. Apart from the conformer B4, which changed into B3′, when starting from the ab initio structure, all other conformers with hydrogen bonds are well reproduced. Moreover, the basic units of the β-peptide helices H12 (B11) and H14 (B10) were also found as minimum energy conformations, although the 12- and 14-membered hydrogen-bonded pseudocycles cannot be formed at the monomer level. According to our molecular mechanics calculations, the ab initio monomers B8 and B9, which do not form periodic structures when oligomerized, change into the conformers B2′ and B6, respectively. Conformational searches on the monomers U, A, A2, B2, RS, and SS (Table 1) also produced good agreement with the results of ab initio MO theory. As is usually the case, our molecular mechanics calculations yielded more minima than found by ab initio MO theory. However, these minima are of higher energy and need not be considered. For a further test of the reliability of the CHARMm23.1 force field, the blocked tetramer of B was optimized starting from various minimum conformations predicted by ab initio MO theory.24 All conformers (H6, H8, H10, H12 and H14, respectively) were reproduced by the CHARMm23.1 force field with an rmsd for the C atoms less than 1 Å in each case. The energy differences of these structures were in a range of 6 kcal/mol with H14 as the most stable one, followed by H10, H8I, H12 , and H6, which is in good agreement with the data obtained by ab initio MO theory. Obviously, the conformational properties of β-amino acid monomers and oligomers are well described by the CHARMm23.1 force field. Molecular Dynamics. The molecular dynamics simulations for the determination of the free energy gradient maps were performed on the blocked hexamers of the model compounds B6, U6, A6, (A2)6, (B2)6, (RS)6, and (SS)6, respectively (Table 1). For the Van der Waals interactions a cutoff of 12 Å was applied employing a switch function between 10 and 12 Å.33 The electrostatic interactions were truncated by shifting at 12

Periodic Structures in β-Peptides Å.33 Free energy gradient maps were determined for regular structures with the same values of (φ,ψ) at each residue between -180° and 180° for B6 and between -180° and 0° for the other model compounds in grid intervals of 6°. For each point on the φ/ψ-maps the molecules were simulated in vacuo, with the φ and ψ values in all residues kept fixed. Experimental12,13,19,41-43 and theoretical data20,24,31,32,41,44 indicated a preference for gauche conformations in CR-Cβ-rotations especially for β-amino acids with an (S)-Cβ-substitution. Accordingly, central torsional angles θ of all residues were initially set to 60° but were not constrained during the simulations. Thus, the β-peptide could relax into an energetically preferred conformation for the fixed values of φ and ψ by adjusting the central torsion angles θ. The conformations studied here correspond, therefore, to regular structures in φ/ψ-space which may be identified by the triple set (φ,θ,ψ), where θ reflects the average value of all central CR-Cβ torsions of each residue in the periodic structure at a given (φ,ψ) pair (vide infra). Using this strategy, β-peptide secondary structures showing an alternating periodicity, i.e., repeating units of two different β-amino acid conformers, as for instance found in the H10/12- or H12/10-helices (12/10/12/10/ ...) cannot be obtained. At each simulation point the initial structure was constructed from model parameters, briefly energy minimized and subjected to 20 ps equilibration and 40 ps trajectory generation. Throughout, the φ and ψ dihedrals were kept at their target values using the holonomic constraint method of Tobias and Brooks.36,45,46 Molecular dynamics simulations were performed using the Verlet algorithm with 2 fs time steps and SHAKE constraints applied to all bonds involving hydrogens. During the equilibration phase, the system was brought to 300 K by multiple velocity rescaling. In the trajectory generation phase, the MD simulations were performed at constant energy at a temperature of 300 K. The forces acting on the constrained coordinates were averaged over the trajectory to yield the corresponding free energy derivatives, as described in previous CFTI applications.36,37 Because most of the soft degrees of freedom of the simulated systems were fixed, 40 ps trajectories were sufficient to generate reliable free energy derivatives, which can be seen from the smooth nature of the calculated gradient maps. Using the CFTI protocol, derivatives of the free energy with respect to all the fixed coordinates, (∂A/∂ξk), were calculated, where ξk are the φ and ψ dihedrals of the individual residues. The simulations of the blocked hexapeptides involved 12 dihedral constraints, two per residue. The six components of the free energy gradient with respect to the individual φ and ψ dihedrals, respectively, were added up leading to an effective two-dimensional (2D) free energy gradient (∂A/∂φ, ∂A/∂ψ), which describes concerted transitions between regular structures in (φ,ψ) space. Reducing the dimension of the free energy surface from 12 to 2 allows a more facile analysis of the results. Following only concerted changes in φ and ψ, we obtained a partial description of the complete 12-dimensional conformational space. However, the 12-dimensional gradient was available at each grid point on the free energy gradient map.36,37 Besides, fixing only φ and ψ and not applying any constraints to θ, we obtained a preferred conformation of the molecule under a given set of φ and ψ for each point on the free energy gradient φ/ψ map. Consequently, the method contained a bias toward more realistic structures by avoiding strange and high energetic conformers. Because no constraints were applied to the θ dihedrals, this torsion angle could also realize different values in each residue resulting in nonperiodic structures, even though the φ and ψ of each β-amino acid unit had identical

J. Phys. Chem. B, Vol. 105, No. 23, 2001 5561 values. To identify such conformations and separate them from the periodic ones, the averages and fluctuations for the dihedrals θ of the residues 2 to 5 were calculated along the trajectory. If the average values of the individual CR-Cβ torsions agreed within (20° and the fluctuations of all dihedrals θ were less than 40°, the particular conformation was considered to be periodic and marked as a gray area on the φ/ψ-map. The reduced free energy surfaces were obtained by integration of the twodimensional gradients starting from the grid point next to the lowest-lying free energy minimum as previously described.36,37 Free energy minimum grid points found on the reduced free energy gradient maps were starting points for free energy optimizations using the steepest descent method in analogy to a procedure already described by one of us.37 A typical optimization in the two-dimensional (φ,ψ) space took about 10 to 15 steps when starting from a low free energy gradient grid point identified on the free energy maps. Free energy differences between the optimized structures were evaluated by numerical integration of the free energy gradient along a straight line connecting the corresponding points in (φ,ψ) space. The gradients were calculated in additional simulations for points equally spaced along the straight line using a procedure analogous to that one used in free energy gradient map evaluation. The number of points was chosen such that their spacing was about 2°, allowing for improved estimation of the free energy differences between the minima. It should be stressed that the free energy differences between the locally stable states may be evaluated correctly in this approach because these quantities are independent of path. However, the barriers between the stable states are almost certainly exaggerated, because a concerted transition pathway is considered here, whereas most evidence points to a sequential mechanism for peptide conformational transitions. Computation of one point on the free energy gradient map took about 30 min of CPU time on an IBM RS/6000-550 machine. It should be remembered, that each residue in the β-peptide hexamer contains three backbone torsion angles (φ,θ,ψ). Thus, there are 18 backbone torsions corresponding to a number of degrees of freedom similar to that in a blocked alanine nonapeptide. Therefore, the complete φ/ψ map with 3600 grid points was investigated only for the hexamer B6 because most experimental work was carried out on oligomers consisting of β3-substituted β-amino acids.8,12,15,21,42,47,48 For the other model compounds, the calculations were performed in the range of -180° and 0 ° for φ and ψ in 6° steps resulting in 900 grid points. This corresponds to the third quadrant of the Ramachandran plot, which contains the most important periodic secondary structures in β-peptides (vide infra). Results and Discussion Free Energy Gradient Map of B6. Secondary structure formation in β-peptides was first reported for oligomers of R-isobutyl-aspartate, a Cβ-substituted β-amino acid.21 Because β-amino acids substituted at Cβ are easily accessible from R-amino acids by the Arndt-Eistert-reaction,12 β-peptides composed of β3-substituted β-amino acids have frequently been subjects of experimental studies. Therefore, we have chosen the model compound B6 as a prototype of a β-peptide to explore the whole conformational space for all values of φ and ψ between -180° and 180°. The free energy gradient map and the free energy surface obtained from its integration are presented in Figures 1 and 2. Eight local minima corresponding to stable periodic structures of the hexamer were found on the free energy surface (cf. Table 3). These structures are denoted by H14, H12,

5562 J. Phys. Chem. B, Vol. 105, No. 23, 2001

Figure 1. Reduced two-dimensional free energy gradient map of the blocked β-peptide hexamer B6 corresponding to periodic structures in the (φ,ψ)-space. Arrows indicate the direction of increasing conformational free energy.

H10, H8I, H8II, H8III, and H6II, where the subscripts give the number of atoms involved in hydrogen-bonded pseudocycles, and HE, which has no hydrogen bonds. Other regions on the map with low free energy gradients correspond to saddle points or maxima. There are areas characterized by gradients at neighboring grid points having markedly different directions, which reflect conformations with a nonperiodic structure located along possible transition paths, where the hexamer has to unfold in order to change into another minimum conformation. Figure 2 shows that the lowest free energy region is located in the third quadrant of the Ramachandran plot. In this part of the (φ,ψ)-space, the reduced free energy landscape is rather flat and the point of lowest free energy is an H14-helix (31-helix) with φ ) -156°, θ ) 58°, and ψ ) -119° after free energy minimization (Table 3). This structure can be derived from the monomer B10 in Table 2. It is in good agreement with data obtained by experiments8,12-15,17,19,49 and quantum chemical studies.20,24,31,32,50 Next to this minimum, on the slope to a rather wide valley, the free energy minimum structure of H12 could be located, which can be derived from the monomer B11 in Table 2. It is 4.9 kcal/mol less stable than H14 after free energy minimization. The estimated values of φ ) -144°, θ ) 87°, ψ ) -66° for the dihedrals of residues 2 to 5 of the optimized H12 minimum structure (2.51-helix) are in good agreement with those obtained in X-ray studies of oligomers of the above-mentioned trans-2-aminocyclopentanecarboxylic acid.17,18,51 However, this H12-helix exhibits relatively high fluctuations of the termini in the dynamics, indicating its tendency to change into the slightly more stable H8I minimum structure. It is noteworthy that this helix type was only observed in oligomers of conformationally restricted β-amino acids, where the central dihedral θ is locked by the cyclopentane ring at about -90°, whereas in our simulations this torsional angle was allowed to rotate freely. The H14-helix has an average dipole moment of 13.6 D, slightly larger than the 13.2 D dipole of H12. Because H14 also has a smaller accessible surface than H12, we would expect H14 to be stabilized relative to H12 in a polar environment both by electrostatic interactions and by cavitation energy. A concerted transition between a H12 and H14 involving solely periodic

Gu¨nther et al. structures is impossible, as indicated by the white and gray areas in the contour plot in Figure 2. This reflects the fact that the molecule has to unfold completely when changing into the alternative helix differing in handedness and dipole direction (cf. Figure 2). This results in nonperiodic structures on the transition path. Preliminary results of long-time molecular dynamics in solution confirm this observation. The H8I conformer is located in the center of the free energy valley in the third quadrant, 3.7 kcal/mol above the global minimum H14. H8I was already predicted for a tetramer by quantum chemical studies24,31 and can be derived from the monomer B2 in Table 2. This structure with φ ) -72°, θ ) 165° and ψ ) -87° is ladderlike, which qualifies it to mimic a β-strand. In accord with the conformational properties of the monomer (cf. Table 2), the central dihedral θ is more extended than predicted in the quantum chemical studies. Consequently, the distance between the NH of residue i and the O of residue (i-2) is about 3 Å, too long to be considered a hydrogen bond. However, there are still electrostatic interactions between the peptide groups resulting in a periodic structure with very low fluctuation in the dynamics. Considering the low energy barrier, the low fluctuations of the central dihedrals θ, and the same handedness for the same configuration, it is obvious, that this conformer may easily convert to H12 and Vice Versa. This becomes even more evident, when comparing the sequence of the dihedral values: (H8I: -72°, 165°, -87°), f (H12: -144°, 87°, -66°). The conformational relationships between these structures might formally be compared with those of the 310and the R-helices in regular R-peptides but the alteration of the shape of the β-peptide oligomers is more pronounced. Here, such a change means a transformation of a sheet- or ribbonlike structure into a helical conformation. Because the dipole moment of the H12-helix (13.2 D) is significantly different from that of the H8 structure (9.2 D), it should be possible to vary the relative stability of the two conformers by changing the polarity of the solvent. An alternative H8 structure is realized in the H8II conformer with φ ) -123°, θ ) 56° and ψ ) 21° located 13.5 kcal/mol above the global minimum in the second quadrant. It can be derived from the monomer B6 in Table 2 and was confirmed by several experiments in β-peptides and β-peptide analogues, as for instance in 1-(aminomethyl)-cyclopropanecarboxylic acid derivatives,26 in oligomers of aminoxy acids with an oxygen atom in place of the Cβ-backbone atom52 and even in hydrazino peptides (Ac-[NβH-NRH-CH2-CO]n-NHNHMe).53,54 This sheet- or ribbonlike structure, which is sometimes described as a helical one,52 seems to be a preferred conformation in oligomers consisting of β-amino acid-like building blocks. The peptide bonds are approximately perpendicular to the molecular axis exhibiting a hydrogen-bonding pattern with six- and eight-membered pseudocycles, but the hydrogen bond angles NH(i)‚‚‚OC(i) (6-ring) and NH(i)‚‚‚OC(i-2) (8-ring) deviate from ideal values. This results in a smaller dipole moment (7.8 D) compared to the helical structure alternatives. Consequently, β-peptides of this substitution type should fold into helical conformations with a higher dipole moment in a polar environment. Although separated from the lower free energy region in the third quadrant, a transition into either H12 or H8I might be possible for the H8II structure. A comparable transition would be much more difficult for the third possible form with eight-membered hydrogen-bonded rings, the H8III conformer with φ ) 62°, θ ) 61°, ψ ) -87°, which is located in the fourth quadrant of the Ramachandran plot, only 1.5 kcal/mol above the global minimum H14. This conformer was found in crystals of β3-hPro derivatives as part of a turn

Periodic Structures in β-Peptides

J. Phys. Chem. B, Vol. 105, No. 23, 2001 5563

Figure 2. Reduced two-dimensional free energy surface of the blocked β-peptide hexamer B6 in kcal/mol and periodic secondary structures corresponding to the free energy minima. Gray areas on the contour plot indicate periodic conformers.

TABLE 3: Backbone Torsion Angles and Free Energy Differences of Periodic Free Energy Minimum Conformations of the β-Peptide B6a typeb

φ

θ

ψ

∆Ac

H14 H12 H10 H8I H8II H8III H6II HEd

-156 -144 64 -72 -123 62 -159 -74

58 87 59 165 56 61 60 160

-119 -66 75 -87 21 -87 75 161

0.0 (13.5) 4.9 (13.2) 15.4 (8.9) 3.7 (9.2) 13.5 (7.8) 1.5 (6.6) 11.7 (0.4) 24.0 (8.6)

a Angles in degrees. b H : helix with x-membered hydrogen-bonded x turns. c In kcal/mol; Dipole moments in Debye in parentheses. d Extended Structure with no hydrogen bonds.

structure55,56 and can be related to the monomer B3′ in Table 2. The peptide bonds are perpendicular to the molecular axis leading to a lower dipole moment (6.6 D) and enabling the formation of β-sheet structures. A rather interesting secondary structure is the H10-helix (31helix) with φ ) 64°, θ ) 59°, ψ ) 75° in the first quadrant of the Ramachandran plot, which samples another conformation subspace of β-peptides. This novel type of a helical conformer was first predicted in our preceding quantum chemical studies on β-amino acid oligomers24 and hydrazino peptides.54 Until

now, there is no experimental proof of this helix type in a β-peptide. The lower dipole moment of 8.9 D in comparison to those of the competing helical structures H12 (13.2 D) and H14 (13.6 D) and the considerably larger accessible surface area leading to a higher cavitation energy suggest that the H10-helix should be relatively destabilized in a polar environment. Quantum chemical calculations on the blocked β-amino acid B revealed, that the most stable monomer exhibits a sixmembered hydrogen-bonded pseudocycle.24,31 Oligomerization of such conformers could easily be realized. As shown in Table 2, three conformers with six-membered pseudocycles were obtained for Cβ-substituted β-amino acids. Despite this, there is just one H6 conformer on the free energy gradient map. Considering only the dihedrals φ and ψ, a periodic oligomer of the most stable monomer B1 would be located in the third quadrant of the Ramachandran plot near the region of the minimum conformations H12 and H14. Remembering that the central dihedral θ of each residue was initially set to 60°, it is obvious that conformations of the H12- or H14-helix type can be obtained more easily than H6I, which involves a change of the sign of θ during the simulation. In fact, a structure, which formally corresponds to an H6I-conformer with φ ≈ -150°, θ ≈ -60°, ψ ≈ -90° might be located on the transition path between H14 and H12, when the molecule unfolds completely. The alternative B4 would be located in the fourth quadrant of

5564 J. Phys. Chem. B, Vol. 105, No. 23, 2001 the Ramachandran plot near the H8III minimum. Comparing the dihedrals found for this conformer with those of B3′ as the monomer of H8III, it becomes clear that the molecule corresponding to this H6III oligomer tends to convert into the H8III sheetlike structure, which could be validated by free energy optimizations starting from idealized H6III conformers. Only the H6II structure, which can be derived from the third monomer with a six-membered hydrogen-bonded pseudocycle, B5 in Table 2, could be confirmed as a free energy minimum with φ ) -159°, θ ) 60°, ψ ) 75° in the second quadrant of the Ramachandran plot in the neighborhood of the H8II region. H6II and H8II are approximately equivalent in free energy with respect to the global H14 minimum. Additionally, the relatively small free energy barrier and the small dihedral angle differences between these strand-like structures indicate that both conformers should easily interconvert. Apart from the hydrogen-bonded secondary structures, an extended periodic conformer HE derived from B7 in Table 2 could also be located as a free energy minimum structure on the Ramachandran plot. Although rather stable in the dynamics, its free energy difference from the global minimum H14 is too high for consideration as a competing secondary structure element of B6. Moreover, the free energy barrier separating it from the H14 minimum is only about 4 kcal/mol, which makes a transition into H14 probable. Free Energy Gradient Maps of the Hexamers U6, A6, (A2)6, (B2)6, (RS)6, and (SS)6. Considering the larger variety of substituent patterns in β-peptides in comparison to natural R-peptides, it is interesting to study the changes of the free energy gradient map induced by substitution at the CR- and/or Cβ-backbone atoms. Because most important periodic structures of the B6 system were found in the third quadrant of the Ramachandran plot, we confined ourselves to this region investigating the blocked hexamer models U6, A6, (A2)6, (B2)6, (RS)6, and (SS)6, respectively (cf. Table 1). Figure 3 shows the reduced two-dimensional free energy surfaces obtained for the model compounds. Obviously, the number and position of the substituents have great impact on the shape of the free energy landscapes of these β-peptide hexamers. The various minimum conformations and their relative free energies relative to the global minima obtained by free energy optimization are collected in Tables 4 and 5. Because of the restriction to the third quadrant of the Ramachandran plot, the H10, H8II, H8III, H6II, and H6III structures are not available. For the unsubstituted β-peptide U6 (Figure 3a), the H12-helix disappears. Looking at the values for φ and ψ, this structure would lie on a smooth slope of the free energy surface indicating its tendency to transform into the more stable H8I structure. Obviously, a single (S)-β3-substitution is required for the formation of this helical secondary structure, which is reflected by the existence of H12 only as a local free energy minimum of the (S,S)-β2,3-disubstituted ((SS)6) model compound (Figure 3f). Although monosubstituted at Cβ, the hexamer composed of (R,S)-β2,3-disubstituted β-amino acids (RS)6 (Figure 3e) does not form this conformation due to the methyl groups at CR in the (R)-configuration pointing in the axial direction, which disturbs the formation of the helical structure. This holds also for the geminally disubstituted oligomers (A2)6 and (B2)6. These β-peptides rather fold into the H8I conformers, which was proved by free energy optimizations starting from idealized H12 conformations. As shown in Table 4, the H8I minimum structures of all investigated β-peptides are somewhat extended leading to an s-trans-conformation for the central dihedrals θ and, consequently, increasing the hydrogen bond lengths. Thus, in

Gu¨nther et al. the disubstituted model compound (SS)6 both methyl groups are in a lateral arrangement similar to that of the helices H12 and H14, i.e., the CR-Cβ-bonds are perpendicular to the axis. Consequently, a transition to the slightly less stable H12-helix should be possible without rearrangement of the side chains. Considering the low dipole moment of 8.3 D of the H8I sheetlike secondary structure in comparison to that of H12 (13.3 D), such a transformation could be expected in a polar environment. The data in Table 4 show that the H14-helix is only found for the β-peptide hexamers B6 and SS6. But in these cases, it is the lowest free energy structure (Table 5). Similar to the situation for the H12-helix, a single (S)-substituent on Cβ is needed to fold into the H14-helical conformer. The values obtained for the freely rotatable central dihedrals θ of each residue in these secondary structures are in good agreement with experimental data obtained for oligomers of conformationally constrained trans-2-aminocyclohexanecarboxylic acid and trans-2-aminocyclopentanecarboxylic acid residues, respectively.13,14,17,18,57 It is remarkable that no H14 structure could be located on the free energy surface for the unsubstituted and CR-monosubstituted model compounds U6 and A6 despite missing sterical hindrance (cf. Figure 2 and Refs 6,27, and 49). This is in excellent agreement with quantum chemical calculations on the blocked β-amino acid monomers revealing that a monomer unit in an H14 conformation is only to be found for model compounds B and SS.24,31,32 However, the two hexapeptides U6 and A6 show an H14-like fold, which is characterized by hydrogen bonds between the NH-group of residue i and the nitrogen of the following residue (i + 1) (forward direction) resulting in a left-handed 3.31-helix with a pitch of about 6.8 Å. This special type of secondary structure is denoted by HNI to indicate the NH‚‚‚N hydrogen bonding pattern. It is not surprising that (R)substitution at either the Cβ- or the CR-backbone atom prevents the folding into the left-handed H14-helical structure. This can easily be understood from inspection of the H14-helix formed in B6 (Figure 2). For example, the blocked hexamer (A2)6 cannot fold into an H14-helical formation due to steric hindrance of the (R)-substituted methyl group at CR, which is in an axial position. Thus, unfavorable van der Waals contacts with the CR-atom and with the (S)-Cβ-substituent of the following residue (i + 3) occur. Consequently, this molecule exhibits the alternative helical HNI conformer, which is characterized by a higher pitch (Figure 4a). Therefore, smaller substituents at CR pointing along the helix axis might only moderately influence the formation of the HNI-helix, whereas the distortion of an H14helix would be much stronger (cf. Figure 2). Because of the arrangement of the peptide bonds in such an HNI structure the dipole moment is lower and thus a destabilization of this secondary structure in a polar environment could be expected. It is obvious that larger substituents should prevent the formation of this helix. Interestingly, the vicinally disubstituted β-peptide hexamer (RS)6 shows another fold, which is comparable to an extended H14, although it is (R)-substituted at CR. A detailed inspection of the geometry of this helix reveals distances between NH(i-3)‚‚‚OC(i) of about 3 Å or more, which is too long for typical hydrogen bonds. A comparison of this conformation with the H14-helix of the disubstituted model compound (SS)6 illustrates the influence of the (R)-configuration at the CR-atoms (Figure 5). In this case, the substituents are in axial positions and interfere with the backbone atoms of the following turn. Nevertheless, an H14-like conformation is formed by the (RS)6 model compound realizing a helix with a higher pitch of about 5.9 Å without hydrogen bonding. This type of secondary

Periodic Structures in β-Peptides

J. Phys. Chem. B, Vol. 105, No. 23, 2001 5565

Figure 3. Reduced two-dimensional free energy surfaces of the blocked hexamers (a) U6, (b) A6, (c) (A2)6, (d) (B2)6, (e) (RS)6, and (f) (SS)6 in kcal/mol. Gray areas on the contour plot indicate periodic conformers.

TABLE 4: Backbone Torsion Angles (φ,θ,ψ) of Periodic Free Energy Minimum Conformations Located in the Third Quadrant of the Ramachandran Plot of Various β-Peptide Hexamersa hexamerb B6 U6 A6 (A2)6 (B2)6 (RS)6 (SS)6 a

H6I (-174, -65, -71) (-173, -62, -82) (-177, -56, -58)

H8I

H12

H14

(-72, 165, -87) (-76, 173, -79) (-79, 170, -78) (-101, 175, -65) (-62, 173, -92) (-119, 167, -70) (-81, 169, -81)

(-145, 87, -66)

(-156, 58, -119)

(-96, 87, -88)

(-160, 65, -133) (-153, 57, -121)

HNI

HNII

(-173, 65, -108) (-170, 63, -111) (-175, 60, -120) (-179, 50, -106)

(-174, 70, -8) (-177, 93, -59) (-152, 84, -64)

Angles in degrees. b Cf. Table 1.

structure could be compared with models of (S)-3-hydroxybutanoic acid oligomers,58 which are unable to form 14-membered hydrogen bonds per se. Again, bulky substituents in (R)-position at CR should hinder the formation of this helix. Examination of the free energy landscape of (RS)6 revealed another interesting periodic conformer of this β-peptide. Free energy optimization

starting from the valley on the lower edge of the investigated quadrant resulted in an extended structure located in the second quadrant of the Ramachandran plot. It is comparable with the already discussed HE conformation of B6 but favored over the above-mentioned H14-like helix by about 2 kcal/mol. Considering the position of the methyl groups at CR and Cβ, it is very

5566 J. Phys. Chem. B, Vol. 105, No. 23, 2001

Gu¨nther et al.

TABLE 5: Free Energy Differences of Periodic Free Energy Minimum Conformations Located in the Third Quadrant of the Ramachandran Plot of Various β-Peptide Hexamersa hexamerb B6 U6 A6 (A2)6 (B2)6 (RS)6 (SS)6 a

H6I 2.0 0.3 2.7

H8I

H12

H14

3.7 2.0 4.3 4.5 2.1 6.8 7.5

4.9

0.0

11.0

0.0 0.0

HNI

HNII

0.0 0.0 0.0 0.0

5.8 10.9 14.1

b

Energies in kcal/mol. Cf. Table 1.

Figure 6. Comparison of backbone conformations of a) common R-amino acids forming a β-strand with the torsions φ ) -140° and ψ ) 135° and (b) β2-substituted β-amino acids (A6) forming an H6 structure with the torsions φ ) -173°, θ ) -62°, ψ ) -82° (cf. text).

Figure 4. Stereo plots of the two types of NH‚‚‚N hydrogen-bonded helices of the CR,R-disubstituted β-peptide (A2)6: (a) left-handed HNIhelix, (b) right-handed HNII-helix.

upper left region of the calculated free energy maps (Figure 3). These minima correspond to another HNII-helix. This conformer, which is shown for (A2)6 in Figure 4b, corresponds to a 2.41helix with a pitch of about 5.4 Å and exhibits hydrogen bonds between the peptidic NH-group of residues i and (i - 1) in the backward direction. It differs from the HNI-helix described above in handedness and dipole direction and was already predicted in several quantum chemical calculations on β-amino acid monomers24,31 and hydrazino peptides,54 respectively. Considering all competing conformers in a free simulation, this special helix type probably transforms into the neighboring H8I or H12 conformers. A concerted transition into the H14 or HNI alternatives is impossible due to the different handedness, as shown by the gray areas in the corresponding plots of Figure 3. Conclusions

Figure 5. Influence of configuration in the vicinally disubstituted β-peptide hexamers (RS)6 and (SS)6 on the H14-helical conformation: (a) H14-like helix of (RS)6 with the dihedrals φ ) -160°, θ ) 65°, ψ ) -133°, (b) H14-helix of (SS)6 with the dihedrals φ ) -153°, θ ) 57°, ψ ) -121°.

likely that this extended secondary structure element should be preferred by (R,S)-β2,3-disubstituted β-peptides.7 The model compounds U6, A6, and (A2)6, adopt H6I structures, which formally correspond to the monomer B1 in Table 2. The CR-Cβ-torsion exhibits a negative value in this β-strand-like secondary structure, which indicates that setting the central dihedral θ initially to 60° need not result in structures with only positive values for θ. In all cases, the free energy differences relative to the global minimum are less than 3 kcal/mol (Table 5). These conformers with φ ≈ -175°, θ ≈ -60° and ψ ≈ -75° are similar to a β-strand in common R-peptides, as can be seen in Figure 6 for the hexamer A6 and an idealized R-amino acid β-strand. Both the β-peptide and the R-peptide conformations exhibit NH-bonds oriented in alternating directions with the side chains pointing above and below the planes defined by the peptide bonds. This becomes even more evident when the two backbone conformations are superimposed, yielding a total rmsd < 0.7 Å for all amide bonds. Interesting, but of relatively high energy, are some periodic secondary structures of (A2)6, (B2)6, and (SS)6 located in the

On the basis of free energy gradient maps, free energy surfaces for various blocked β-peptide hexamers have been generated for the first time employing a multidimensional conformational free energy thermodynamic integration approach. Thus, a complete overview of all periodic secondary structure types can be given. The predictions derived from the free energy surfaces are in quite good agreement with the known experimental data for different helical and sheetlike structures formed by β-peptides. Considering the various substituent patterns in the β-amino acid constituents, the influence of substitution and configuration at the CR- and Cβ-backbone atoms on the intrinsic properties of secondary structure formation can be explained. The free energy surfaces show the structural and energetic relationships between the various secondary structure types and their mutual transformation possibilities. They demonstrate the potential of β-peptides for protein design. Acknowledgment. This work was supported by Deutsche Forschungsgemeinschaft (Innovationskolleg “Chemisches Signal und Biologische Antwort“), the German Fonds der Chemischen Industrie and by the Petroleum Research Fund of the American Chemical Society (Grant No. 33126-AC4). R.G. thanks Prof. Kuczera, University of Kansas at Lawrence, for support and hospitality during a stay in his laboratory. References and Notes (1) Kirshenbaum, K.; Zuckermann, R. N.; Dill, K. A. Curr. Opin. Struct. Biol. 1999, 9, 530.

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