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F. Fülöp, Institute of Pharmaceutical Chemistry, University of Szeged, Eotvos u. 6. Szeged, Hungary. Fax: + 36 62 545705, Tel.: + 36 62 545564, E-mail: firstname.lastname@example.org
As one of the most important families of non-natural polymers with the propensity to form well-defined secondary structures, the β-peptides are attracting increasing attention. The compounds incorporating β-amino acid residues have found various applications in medicinal chemistry and biochemistry. The conformational pool of β-peptides comprises several periodic folded conformations, which can be classified as helices, and nonpolar and polar strands. The latter two are prone to form pleated sheets. The numerous studies that have been performed on the side-chain dependence of the stability of the folded structures allow certain conclusions concerning the principles of design of the β-peptide foldamers. The folding propensity is influenced by local torsional, side-chain to backbone and long-range side-chain interactions. Although β-peptide foldamers are sensitive to solvent, the systematic choice of the side-chain pattern and spatiality allows the design of the desired specific secondary structure. The application of β-peptide foldamers may open up new directions in the synthesis of highly organized artificial tertiary structures with biochemical functions.
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The macromolecules and ligands responsible for the functioning of living organisms are basically built up from a very restricted number of building blocks (e.g. α-amino acids and nucleic acids). Proteins with a propensity to fold into well-determined hierarchical 3D structures, such as enzymes and receptors, have developed in nature in an evolutionary time scale. However, thanks to the tremendous efforts that have been devoted to the field, scientists now have a clearer picture of the background to these developments [1,2]. The principles of protein design are not restricted to the realm of the heteropolymers of α-amino acids, but can be generalized and extended to any polymer with a tendency to fold into the periodic and/or specific compact structures referred to as foldamers [3,4]. Such foldamers include synthetic oligomers constructed from β-amino acids as monomers, designated β-peptides, which are among the most thoroughly studied and important models in foldamer chemistry.
For the biopolymer community, there are a number of reasons for the synthesis of β-amino acid-containing compounds and analysis of their structures. As concerns the aspects of foldamer design, β-peptides are very close relatives of α-peptides, their structures containing amide bonds that allow the formation of stabilizing H-bonds. Further, the β-amino acids are homologues of the α-amino acids, the amide groups in the β-peptide backbone being separated by two carbon atoms. This provides new options regarding the substituent pattern and the spatiality on C2 and C3 with a view to control the secondary structure. The field of drug design can also benefit from the structural properties of β-amino acids. The incorporation of β-amino acids is a successful approach to the creation of peptidomimetics with potent biological activity that are resistant to proteolysis [5–11].
It is interesting that the first β-amino acids were not produced in scientific laboratories. The conditions on primitive Earth were such as to lead to the formation of β-alanine  and β-amino acids originating presumably from comets or asteroids have also been found . Natural sources too produce β-amino acids [14–17], but reliable and efficient synthetic routes are indispensable; the relevant methods have recently been extensively reviewed [18–29].
Despite the availability of reviews on β-peptide foldamers [30–32], there is increasing interest in the new results and conclusions, which justifies the present survey on the design principles.
The conformational pool of β-peptides
It is clear from the general constitution of the β-amino acids (Fig. 1) that the conformational space can be described in a very similar way as for the α-residues. According to the convention of Banerjee and Balaram, the soft torsional degrees of freedom are defined as CO-N-C3-C2, C3-C2-CO-N and N-C3-C2-CO designated φ, ψ and θ, respectively . It may be concluded from the presence of the additional torsion that the increased conformational space relative to the α-peptides significantly decreases the folding propensity of the β-peptides, in consequence of the higher entropy loss . The initial efforts in the laboratories of Seebach [35–38] and Gellman [39–41] and the increasing body of high-resolution structural data clearly demonstrated that β-peptides have an intrinsic propensity to fold into well-defined periodic structures. Soon after the first experimental observations, theoretical methods were deployed to explain the formation of such highly ordered structures [42–46]. The main conclusion from the ab initio quantum chemical calculations carried out on blocked monomers and short oligomers is that the propensity to form periodic structures with helical symmetry is inherently encoded in the β-amino acid monomers. Obviously, these minimal models did not allow an exact quantitative estimation of the relative stabilities of the possible secondary structures as a function of the substituent pattern, but the results did facilitate an enumeration and classification of the periodic conformations in terms of the φ,ψ,θ map (Fig. 2). The folded β-peptide structures can be classified on the basis of the grouping of the α-peptide secondary structures . The periodic conformations include various types of helices and strand-like structures (Fig. 3). The sheet nucleating turn segments are discussed later. Different designations are available in the literature for these ordered conformations. In the present review, we follow the nomenclature introduced by Gellman . In order to avoid ambiguity, it must be stated that all the periodic structures possess helical symmetry, but strands will be distinguished from helices on the basis of the angle of the backbone H-bonds. The structures stabilized by H-bonds with an angle < 120° are classified as nonpolar strands, as these conformations may expose the amide bonds to participation in long-range interactions, with the formation of pleated sheets.
The β-peptide foldamers have a number of interesting structural features. The H-bonds stabilizing the periodic conformations can attain parallel or antiparallel orientations with respect to the directionality of the β-peptide chain. The orientation of the H-bonds is closely connected to the number of atoms comprising the H-bonded ring formed between the donor and acceptor atoms. For the structures with 6-, 10- and 14-membered rings, the donor to acceptor orientation is parallel to the chain directionality on going from the N-terminal to the C-terminal, while in the 8- and 12-helices and in the 8-strand the orientation is antiparallel. Besides the novel H-bonding patterns, the sense of the helix twist can also vary, leading to right-handed or left-handed helices. Figures 2 and 3 depict only the periodic conformations with left-handed helicity, but the right-handed ones can easily be obtained via a mirror operation that results in φ, ψ- and θ-values of opposite sign and inverted configuration in the event of chiral substitution at C2 and C3. Apart from the handedness, the size of the H-bonded ring does not uniquely describe the theoretically possible periodic structures within the conformational families of 6-strands and 8-helices. For the left-handed 6-strands, there are three obvious combinations of backbone dihedral angles, which can produce periodic structures designated 6I, 6II and 6III following the classification of Hofmann . The left-handed 8-helices can also be clustered into two subfamilies: 8I and 8II. It must be emphasized that the conformational pool of β-peptide helical structures is not complete without the experimentally observed and theoretically studied alternating 10/12 helix (Fig. 3) [36,37,48]. This conformation has two sets of φ,ψ angles: φ1 ≈ −90°, ψ1 ≈ 100°, φ2 ≈ 100°, ψ2 ≈ −90°, and a uniform θ ≈ −60°. These torsions result in an alternating orientation of the amide groups and thereby a reduced dipole moment.
Not only the helical conformations are encoded in the β-amino acid monomers. It has been shown that the torsion θ can occupy an antiperiplanar local conformation that leads to a strand structure with a tendency to form parallel and antiparallel pleated sheets . As the amide carbonyls in this strand point in the same direction, the structure has a net dipole moment that is fundamentally different from the situation for the β-sheets formed by the α-peptides, where the amide bonds point in alternating directions, so that there is no net dipole.
Following this survey of the conformational pool of β-peptides, it should be noted that the torsion θ cannot be considered a very flexible conformational degree of freedom. With a few exceptions, its angle is in most cases restricted to synclinal (θ≈ ± 60°) or antiperiplanar (θ≈ 180°). Accordingly, steps have been taken towards handling the conformational pool of β-peptides in terms of the reduced φ,ψ space which is achievable in special cases [47,49]. However, the reduced representation does not in general allow a unique description of the various periodic conformations. For example, the 6II-strand and 14-helix heavily overlap in the φ, ψ map and θ is necessary to distinguish the conformations unambiguously. When the folded structures with different modes of handedness and various nonfolded structures are considered , the problems with the reduced representation become even more severe.
Substituent effects on local geometry
The two carbon atoms in the β-peptide backbone provide and efficient means with which to influence the intrinsic secondary structural propensity of β-amino acid residues. It has been demonstrated persuasively that the secondary structure motif can be efficiently controlled by altering the substituent pattern [51,52]. In the approach of Wu and Wang, the effects exerted by the substituents can be separated into two groups of components . One involves the impact on the local conformational stability at the residue level, referred to as the torsional effect. The other group comprises the medium- and long-range effects due to steric and electrostatic interresidue interactions.
The torsional effect of methyl substitution on various model fragments has been analysed thoroughly by employing ab initio MO quantum chemical calculations. The local effect on φ of monomethyl substitution at C3 with the S-configuration [(S)-β3-substitution] was studied in the cases of N-isopropylformamide and N-s-butylformamide, while the influence of (S)-β2 substitution on ψ was modelled with isobutyramide  and 2-methylbutyramide (Fig. 4) . The potential energy profile of φ indicates that its allowed values are restricted to the region between 60° and 180°. There is also a narrow minimum around −60°, with a relatively high rotational barrier. The potential energy surface for ψ was found to be rather flat, with two minima, in the range 60–180° and at around −60°. The results can be transferred to (R)-β3 and (R)-β2 substitutions by changing the signs of the dihedral angles. These analyses reveal that a side-chain in the β3 position has a significant structuring effect on the local geometry exerted through the steric interactions along φ; indeed, the first stable periodic conformation, the 14-helix, was constructed by using homochiral β3-amino acids. It is interesting to note that all the H-bond-stabilized periodic structures can be found within the range φ = 60–180° or φ = −180–60° that are in fact the preference regions of the (R)-β3 or (S)-β3, substituted β-amino acid monomers.
As concerns the nature of the β3 side-chain, a further relationship was recognized recently by Raguse et al. ; the incorporation of side-chain branching adjacent to the β-carbon atom stabilizes the 14-helix [54,55]. This effect may also be explained in terms of the local torsional effects. Force field calculations suggest (Fig. 5) that, as the steric demand of the β3 substituent in the proximity of the adjacent amide group increases, the conformational space decreases for the torsion φ (T. A. Martinek and F. Fülöp, unpublished observation). The isopropyl side-chain corresponding to the (S)-β3-hVal residue significantly increases the energy minimum at −60°, possibly making this local geometry inaccessible for the backbone, and narrows the flat minimum at around 120°. For the (S)-β3-hLeu model, only the narrowing can be observed, which is in good accord with the pronounced structuring effect of the β3-hVal residues. The β2 substitution provides a less efficient tool with which to affect the local flexibility of the torsion ψ; nevertheless, it can not be completely neglected.
As was seen above, the appropriate conformation along the torsion θ may be crucial for a certain periodic structure to be obtained. X-ray and NMR spectroscopic methods have demonstrated the intrinsic feature of β-amino acids that the local geometry of θ is confined to staggered conformations (synclinal or antiperiplanar) [46,56,57]. The local, intraresidue interactions stemming from β2 or β3 substitution cannot bring about a prevailing θ in solution, but by means of β2,3 disubstitution the conformational preference along the C2-C3 bond can be modulated successfully. A thorough comparative experimental study has suggested that the (R,S)-β2,3 or (S,R)-β2,3 relative configuration (Fig. 1) stabilizes the antiperiplanar conformation for θ via intraresidue interactions , which is a prerequisite of the polar-strand conformation found in hairpins as a model of the polar pleated sheet. These findings were supported by ab initio calculations . A noteworthy example of the conformationally constrained systems is the family of cyclic β-amino acids, where control of the torsion θ is achieved by covalent linkage between C2 and C3[31,39,52]. For these β residues, the antiperiplanar arrangement (θ = 180°) is inaccessible, and the folded structures with helical symmetry are therefore promoted. The cyclic β-amino acids may be considered too constrained to exhibit a real folding reaction ; nevertheless, a great majority of the β-peptide foldamer structures and the unordered conformations are also accessible with synclinal conformation at θ, and therefore the conformational plasticity is sufficient to allow the folding process. This is supported by the fact that the cyclic β-residue 2-aminocyclopentane-carboxylic acid (ACPC) can adopt torsion angles from ± 13° up to ± 90°, which facilitates the fine tuning of the helix type adopted by β-peptide oligomers constructed from cyclic monomers. The homo-oligomer of trans-2-aminocyclohexanecarboxylic acid (trans-ACHC) forms a 14-helix, while trans-ACPC adopts a 12-helix, requiring a larger θ to accommodate the increased pitch height .
The covalent restriction of θ by employing a cyclic β-peptide residue combined with the stereochemical tuning of the preference regions of φ and ψ produces efficient control over the secondary structure formation . If cis-(1R,2S)-ACPC is used, the C2-C3 bond can be retained in a synclinal position in spite of the (R,S)-β2,3 disubstitution, which would otherwise lead to an antiperiplanar conformation promoting a polar strand. The (S)-β3 substitution forces φ into the region 60–180°, while the (R)-β2 configuration prefers ψ = − 60–180°. This set of torsions allows only an alternating orientation of the amide bonds, which is present only in the 10/12-helix and in the nonpolar strands. As the configuration is unfavourable in the 10/12-helix for steric reasons (see later), the resulting structure is a nonpolar strand stabilized by weak six-membered H-bonds.
Controlling the backbone to side-chain interactions
The regions of preference of the local torsion angles may be perturbed by changing the substituent pattern, but oriented synthesis of a specific secondary structure can not be achieved without considering the medium-range backbone to side-chain interactions, which can override the local effects. The impact of the side-chain pattern on the secondary structure preference of β-peptides can be addressed to a first approximation within the framework of the ‘fitting’ theory established by Seebach et al. . The principle behind this is that any substituent in an axial orientation relative to the helix axis destabilizes the helical conformation because of the steric clash between the substituent and the β-peptide backbone. Thus, the side-chains occupying axial positions in the helical conformations push the system to nonpolar strand or polar strand conformational states. For the left handed 10- and 12-helices, the substituents R1 and R4 are axial, while for the 14-helix, R2 and R3 are axial (Fig. 6); thus, any bulky side-chain in these positions disrupts the formation of the given periodic conformation. Analysis of the steric interactions, together with the local torsional effects, allows a finer-grained analysis of the effects of substituents on the folded structures. For example, the 10-helix secondary structure has not been detected for β-peptide oligomers with noncyclic side-chains, but only for β-oligopeptides with strained oxetane side-chains , that, in general, suggests a lower stability for this specific conformation. It is clear that only substituent R2 and/or R3[(S)-β3 and/or (S)-β2 substitution, respectively] is allowed sterically for the left-handed 10-helix, but at the same time the geometry of the structure requires φ to be in the range −60° to −110°, which is in the higher energy region of the local torsion energy profile calculated for (S)-β3 substitution (see above). The 10-membered, H-bonded pseudocycle, however, can be found in the 10/12 helix that is preferentially formed by oligopeptides containing an alternating sequence (S)-β2/(S)-β3. These side-chains can occupy the preferred lateral (equatorial) position in the left-handed 10- and 12-helices and in the right-handed 14-helix as well, and therefore the local torsional effect should also be considered. The unsubstituted C3 in the first residue allows φ1 to adopt a dihedral angle of −90°, while the (S)-β2 side-chain provides a slight local conformational preference for ψ1 that promotes a dihedral angle of 100°. The second residue with the (S)-β3 substituent constitutes a strongly preferential configuration for a torsion φ2 of 100°. Overall, these torsional effects and side-chain to backbone interactions may contribute to the observed stability of the 10/12-helix for (S)-β2/(S)-β3 sequences.
The role of long-range side-chain interactions
In folded α-peptide helix design, control of the interactions between the side-chains separated by a turn of the helix is a facet of major importance [60,61]. The organizing forces may comprise the van der Waals and electrostatic interactions. As the circle of synthesizable enantiomerically pure β-amino acid building blocks widens, a variety of possible side-chains are available for participation in such stabilization [18–29]. Inspection of the 14- and 12-helices (Fig. 6) reveals that the juxtapositions necessary for the design of these energy terms are present, while the 10/12-helix lacks such directly adjacent lateral side-chains (Fig. 7). For the 14-helix, all the β2 and β3 substituents with appropriate stereochemistry are proximal, at positions i and (i + 3). The adjacent side-chains in the 12-helix are (i)β3– (i + 2)β2 and (i)β2– (i + 3)β3.
When the number of possible side-chain interactions and the pitch height are considered, the conformation most sensitive to the hydrophobic van der Waals forces is the 14-helix. This suggests that the stability of the 14-helix is augmented by the solvent-driven attractive forces between the hydrophobic side-chains. On systematic increase of the number of possible juxtapositions, extra stabilization can be observed for the 14-helix at the expense of the 10/12-helix, but β2,3-peptides with all the possible juxtapositions are destabilized by steric crowding . Unfortunately, it is difficult to confirm this trend by conducting experiments in different solvents with increasing polarity, because the higher dielectric value and specific interactions scale down the stabilizing electrostatic forces of mainly H-bonding origin, which overall counteracts the hydrophobic stabilization [55,62,63]. Sensitivity to an aqueous medium is also a characteristic of the 12-helix . It might be speculated that H-bond stabilization plays a more important role in β-peptides than in α-peptides, and this might be the price for the enlarged conformational space relative to the number of possible H-bonds . As pointed out by Wu et al. the dipole–dipole interactions due to the uniform amide orientation along the backbone are not only a stabilizing factor, but additionally a source of cooperativity in the formation of the 12- and 14-helices .
As regards the electrostatic interactions between the side-chains, a useful tool has been developed with which to increase the stability of the 14-helix even in aqueous medium. With the choice of a negatively charged and a positively charged side-chain in the relative positions i – (i + 3), a salt-bridge can be formed at an appropriate proton concentration [67,68]. The side-chains of choice are deprotonated β3-hGlu and protonated β3-hLys or protonated β3-hOrn, whereby the most effective stabilization can be tailored. A very similar stabilization strategy of a disulfide lock between the helix side-chains may be mentioned as an instrument with which to promote formation of the 14-helix . Although this establishes a covalent constraint to prevent unfolding and therefore provides strong stabilization, it could lack the controlling flexibility of the non-bonded interactions discussed above.
Certain β-residues or structural motifs have tailored local conformational characteristics that allow the overall folding propensity of a given β-peptide to be influenced. This method of control of the secondary structure formation is well known in the field of folded α-peptide design and is referred to as nucleation . An efficient way to improve the stability of a 14-helix is to incorporate the conformationally constrained trans-ACHC in the β-peptidic sequence. Even a single trans-ACHC residue in the central position of the chain can significantly increase the stability of the 14-helix [53,70]. A similar 14-helix nucleation effect can be observed for central (R,S)-β2,3 or (S,R)-β2,3 residues . A systematic study by LePlae et al. revealed that a 12-helix nucleation effect can be detected on the use of trans-ACPC and trans-APC (trans-3-aminopyrrolidine-4-carboxylic acid) as conformationally constrained residues, and other β3-acyclic side-chains . The 12-helix is still retained in a β-heptapeptide with only three cyclically restrained residues in methanol, whereas five constrained residues are necessary in water.
Interestingly, nucleation of the alternating 10/12-helix does not require constrained residues; it can be achieved by using a β2/β3 or β3/β2 dipeptidic sequence [37,48]. Besides the local torsional preferences (see above), the reason for this may be that intrinsically the most stable β-peptide helical structure is the 10/12-helix, because of the advantageous H-bonding geometry .
Although the conformational pool of β-peptides allows polar and nonpolar strand geometries, the propensity to sheet formation in solution can be studied only by the construction of simple hairpin (strand-turn-strand) models as a result of the complexity of the long-range interactions encountered in sheets. The crucial point here is the synthesis of the stable turn motif that finally nucleates the pleated sheet structure. One strategy for sheet nucleation is the application of conformationally restricted residues in the centre of the β-peptide chain. An antiparallel sheet-nucleating 10-membered ring was synthesized by employing a central l-proline-glycolic acid segment (Fig. 8A) . The incorporation of a stabilizing 12-membered ring also resulted in an antiparallel polar pleated sheet model that was achieved by using a dinipecotic acid moiety (Fig. 8B) [71,72]. Another way to nucleate a β-peptide sheet is to take advantage of the 10-membered, H-bond-stabilized turn-forming propensity of the β2/β3 or β3/β2 dipeptidic sequence known from the 10/12-helix. Seebach et al. demonstrated the feasibility of this approach by using (S)-β2/(S)-β3 residues in the centre of an (R,S)-β2,3 peptide chain, thereby creating an antiparallel polar pleated sheet model (Fig. 8C) [73,74].
Effect of protecting groups
The studies on β-peptide secondary structures mostly cover chain lengths in the oligomeric region. These relatively short sequences are rather sensitive to the presence or absence of terminating protecting groups. It might be considered an empirical rule in β-peptide foldamer design that removal of the protecting groups from the C and N termini destabilizes the 10/12-helix , while the absence of the protection acts as a stabilizing factor for the 14-helix . The best available explanation is that the protonated N-terminus is in an advantageous charge–dipole interaction with the relatively high dipole observed for the 14-helix. This reasoning is supported by experimental observations on the stabilizing effect of the helix macrodipole in water .
Conclusions and outlook
The peptide sequences constructed from β-amino acid residues have proved their ability to fold into well-defined secondary structures. These foldamers cover a wide variety of periodic conformations comprising various helices, polar and nonpolar strands and sheets. The β-peptide backbone with an additional carbon atom provides a well-equipped toolbox with which to fine-tune the folding propensities of the sequences, which includes control of the local torsional interactions, side-chain to backbone interactions, side-chain to side-chain interactions, and nucleation.
As stated in the Introduction, there are a number of reasons why β-amino acid-containing compounds can be of interest to the biochemistry community. We would emphasize the construction of amphiphilic β-peptide helices with antimicrobial activity . These foldamers, which have the propensity to form helical bundles [76,77], have opened up a new direction towards artificial tertiary structures. The incorporation of other secondary structural elements will also hopefully result in new complex structures with useful functions .
The authors' thanks are due to the Hungarian Research Foundation (OTKA F-038320, TS-04888) for financial support.