Helices and other secondary structures of [beta]- …as few as four residues (NMR analysis in MeOH,...

Helices and Other SecondaryStructures of b- and c-Peptides

Dieter Seebach1

David F. Hook1

Alice Glattli21 Laboratorium fur OrganischeChemie der Eidgenossischen

Technischen HochschuleZurich, Wolfgang-Pauli-Strasse

10, CH-8093 Zurich,Switzerland

2 Laboratorium furPhysikalische Chemie der

Eidgenossischen TechnischenHochschule Zurich,

Wolfgang-Pauli-Strasse 10,CH-8093 Zurich,

Switzerland

Received 1 September 2005;revised 4 October 2005;

accepted 10 October 2005Published online 18 October 2005 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/bip.20391

Abstract: The principal secondary structural motifs adopted by peptides assembled from b-aminoacid units are discussed: the 14-, 12-, 10-, 12/10-, and 8-helices, as well as the hairpin turn,extended structures, stacks, and sheets. Features that promote a particular folding propensity areoutlined and illustrated by structures determined in solution (NMR) and in the solid-state (x-ray).The N–Cb–Ca–CO dihedral angles from molecular dynamics simulations, which are indicative of aparticular secondary structure, are presented. A brief description of a helix and a turn of g-peptidesis also given. # 2005 Wiley Periodicals, Inc. Biopolymers (Pept Sci) 84: 23–37, 2006

This article was originally published online as an accepted preprint. The ‘‘Published Online’’ datecorresponds to the preprint version. You can request a copy of the preprint by emailing theBiopolymers editorial office at [email protected]

Keywords: b-amino acid; conformational analysis; GROMOS simulation package; hairpin turn;helix; molecular dynamics simulation; NMR; b-peptide; g-peptide; secondary structure; torsion angle

INTRODUCTION

In 1995, our group embarked on a research project

defined by the question: what happens when each

amino acid residue in a peptide, with the natural protei-

nogenic side chains, is homologated by insertion of

one or two CH2 groups? The most important answers,

as far as structural changes are concerned, are summar-

ized in Figure 1.

(i) The oligomers of the homologated L-amino

acids fold to helices in solution, with chain length of

as few as four residues (NMR analysis in MeOH,

Current address for D. F. Hook: Novartis Pharma AG, Basel,Switzerland.

Current address for A. Glattli: BASF Aktiengesellschaft, Lud-wigshafen, Germany.

Correspondence to: D. Seebach; e-mail: [email protected]

Biopolymers (Peptide Science), Vol. 84, 23–37 (2006)

# 2005 Wiley Periodicals, Inc.

23

MeOH/H2O or pyridine). (ii) On progressing from a-to b- to g-peptides, the stability of the helices in-

creases, although the number of hydrogen bond

donors and acceptors per chain atom decreases (one

of each in 3, 4, and 5 chain atoms, respectively). (iii)

The helicity reverses upon each homologation step:

(P) or right-handed for the 3.613- and 310-a-, (M) or

left-handed for the 314-b-, and (P) again for the 2.614-

g-helical peptides. (iv) The direction of the helix mac-

rodipole also reverses with homologation: it points

from N- to C- in a-, from C- to N- in b-, and again

from the N- to C-terminus in g-peptidic helices. (v)

From a- to b- to g-peptides, there is an alternating

switch of helix stabilities of terminally protected

(RO2C-N, C-OR) versus unprotected derivatives: the

degree of helicity decreases upon deprotection of a-and g-peptides1,2 and increases when b-peptides are

deprotected.3,4 This effect can be correlated with

pole–charge interactions, a kind of intrinsic ‘‘cap-

ping’’ effect5 in the b-peptidic helix. (vi) The helicesof b3- and b2-peptides have opposite chirality, (M)

versus (P), and the helix consisting of b2-amino acids

is less stable. (vii) In the NMR-solution structures of

b-peptide helices, the C-terminus is less structurally

ordered and unwinding occurs.

Another fundamental difference between a- and b-peptidic helices was uncovered when the NMR-solu-

tion structure in methanol was determined in an eico-

sapeptide carrying the 20 proteinogenic side chains

(Figure 2). Despite the large resulting macrodipole

this peptide folds to the 14-helix over the full

length—this would not have been observed for a cor-

responding a-peptide (cf. the single-domain proteins

studied by Baldwin et al.5). Thus, b-peptides not onlyfold to 314-helices with as few as six, but also with as

many as 20 residues! For detailed discussions with

ample citation we refer to an extensive review article6

and a recent full paper7 by Seebach et al.

THE HELICES OF b-PEPTIDES

Five distinct helices have so far been identified in the

field of b-peptides: the 14-,3,4,7–21 a 12-,22–29 a 10-,30,31

the 12/10-,3,32–35 and an 8-helix,36,37 which are defined

by the sizes of 8-, 10-, 12-, and 14-membered hydro-

FIGURE 1 A comparison of the most common helices formed by peptides consisting of a-, b-,and g-amino acids. The a-, b3-, and g4-amino acids shown here have L-configuration except for

b2hSer, -Thr, and -Cys. The b2-amino acid shown has (R)-configuration.6

24 Seebach, Hook, and Glattli

Biopolymers (Peptide Science) DOI 10.1002/bip

gen-bonded rings. Extended arrangements, namely

parallel and antiparallel pleated sheets (the latter being

inherently part of a hairpin turn),38–45 a non-aggregat-

ing linear structure,46 and stacks47–49 have also been

identified. NMR spectroscopy has emerged as the most

useful tool in determining the secondary structures of

b-peptides. Samples suitable for single-crystal or pow-

der x-ray diffraction structure determination have, so

far, only been obtained from b-peptides consisting of

the conformationally restricted trans-2-aminocyclo-

pentanecarboxylic acid (ACPC)29 and trans-2-amino-

cyclohexanecarboxylic acid (ACHC)18,50 units and

from sheet- and stack-forming b-peptides.41,45,47,49

The 14-Helix. This secondary structure has emerged

as the best documented of the folding structures of b-peptides.6 There are 14-membered hydrogen-bonded

rings between N��H (i) and C¼¼O (i þ 2) in a three-

residue repeating arrangement. As can be seen from

the structure of the eicosamer (Figure 2),7 there is a

deviation from an idealized (M)-14-helix; substituents

in the (i)- and (i þ 3) positions are not exactly posi-

tioned on top of each other, but offset by ca. 158 in a

right-handed direction (a ‘‘3.2-helix’’). For steric rea-

sons only H, OH, or F are allowed8 in the axial posi-

tions (Figure 3), a methyl group is not. Thus, homo-

logs of Aib (b2- and b3hAib, homoaminoisobutyric

acid) are helix-breaking in the ‘‘b-regime,’’4 while

Aib itself is strongly 310-helix–inducing in the

‘‘a-world.’’51 b2,3-Amino acid residues of (S,S)- or

l-configuration52 strongly favor the synclinal53 con-

formation and stabilize the 14-helix,3 and (S,S)-trans-2-ACHC moieties lock it.17,18,50,54,55

The 12/10-Helix. Since an L-b3- and an (S)-b2 amino

acid fit in the left-handed 14-helix (the side chains of

both are in allowed lateral positions, green in Figure 3),

peptides containing alternatively b3- and b2-residuesof these configurations were expected to fold to the

314-helix, as do all-L-b3- and all-(S)-b2-pepti-des.3,7,13,56,57 In contrast, they were found to form a

peculiar, right-handed 2.712,10-helix (Figure 4) con-

FIGURE 2 The NMR-solution structure of a b3-eicosapeptide consisting of the 20 homologated

proteinogenic amino acids. The sequence has been designed such that there would be two salt-

bridges (Lys Asp and Arg Glu), but no N- and C-terminus ‘‘capping,’’ which would counteract the

macrodipole.

b- and g-Peptide Secondary Structures 25


sisting of alternating 12- and 10-membered hydro-

gen-bonded rings (Figure 4B).3,7,34,35,58

The dimer segment containing an amide bond with

no adjacent substituents (NH-CHR��CH2��CO��NH��CH2��CHR��CO) is part of the 12-membered

ring, the one with substituents (NH��CH2��CHR��CO��NH��CHR��CH2��CO) being part of the 10-

membered ring.

As in the 14-helices, the conformation around the

C(2)–C(3) ethane bonds is (þ)-synclinal in the b2- andin the b3-amino acid residues. The distribution of the

substituents on the surface of the helix is ‘‘irregular’’

(Figure 4C).34 Most notably, the 12/10-helix has no

resulting macrodipole; the C¼¼O (and the N��H)

bonds have an alternating up/down direction with

respect to the helix axis (Figure 4A). For the delicate

balance between 14- and 12/10-helices,3,35 see discus-

sions in the literature6,7,34 and under Modeling Studies,

below.

The 12-Helix. When the substituents in the 2- and 3-

positions of the b-amino acid become part of a five-

membered ring (cyclopentane, pyrrolidine), the ac-

cessible dihedral angle range in the trans-substitutedring is restricted to values above ca. 858. The oligom-

ers of such non-protein–derived amino acids have

been found to fold to 2.612-helices in the crystalline

state, as well as in solution (Figure 5).22–29

With b-peptides consisting of homologated protei-

nogenic amino acid residues, the 12-helix has not

been detected experimentally, although molecular

dynamics (MD) simulations and ab initio calculations

suggest its existence (vide infra). The oligopeptides

from cis-2-ACPC adopt a sheet-like structure.59

The 10-Helix. This b-peptidic folding pattern has

been recently reported for the terminally unprotected

tetramer of trans-ACHC in solution.30 Interestingly,

the corresponding pentamer and hexamer were found

to form the 14-helix,30 just like the terminally pro-

tected oligomers made of four, five, and six ACHC

residues, under the same conditions.18,50,54,55 In

oligomers of another, rather odd b-amino acid—cis-3-aminooxetane-2-carboxylic acid—a 10-helical ar-

rangement has also been reported.31

For other b-peptidic 10-membered hydrogen-

bonded ring systems, we refer to the section on turn

structures below.

An 8-Helix? Like the 10-helix, the 8-helix has not

been observed in any type of oligomer composed of

homologated proteinogenic amino acids (see section

8 in Seebach et al.6). Two remarkable examples are,

however, shown in Figure 6. Structural parameters

from x-ray diffraction of crystalline b-di-, b-tri-, andb-tetrapeptides consisting of achiral 1-aminomethyl-

cyclopropane carboxylic acid residues were used to

model a longer oligomer (Figure 6A), which has a

stair-like arrangement where each step consists of a

folded eight-membered hydrogen-bonded ring;60 as ex-

pected, the C¼¼O bond bisects the three-membered

ring, having a rigidifying effect on the backbone.

A twisted form of the stair of A, i.e., a (P)-28-helixB was derived from an NMR analysis in methanol

solution of an oligomer composed of (2R,3S)-2-

FIGURE 3 The ideal (M)-314-helix (pitch ca. 5 A) with lateral substituents in the (i) and (i þ 3)

positions (allowed for nonhydrogen atoms) and axial positions (only hydrogen, hydroxy, or fluorine

permitted). Newman projection along the Cb–Ca bond of b-amino acid residues in the (M)-14-helix.



hydroxy-3-aminocarboxylic acid moieties with Val,

Ala, and Leu side chains.37 MD simulations, how-

ever, suggested a preference for this b-peptide to

form 12-membered H-bonded rings: it was pointed

out61 that the measured NMR data are equally com-

patible with a (P)-2.512-helix structure (Figure 6C).

3-Aza-62,63 and 3-oxa-b-amino-acid64,65 oligomers

have also been found to fold to 8-helices.63,64

(b3hPro)n: A helix without intramolecular hydrogenbonds? Polyproline [Poly(Pro)n] and polyhydroxypro-

line [Poly(Hyp)n], where Hyp is 4-hydroxyproline]

play an important role in nature. They fold to helices

and triple helices (collagen) without backbone stabili-

zation by intramolecular hydrogen bonding. Oligomers

of homologated proline (b3hPro or (S)-pyrrolidin-2-ylacetic acid and b2hPro or (R)-piperidin-3-carboxylic

FIGURE 4 The (P)-2.712/10-helix of b3/b2-mixed peptides. (A) NMR structure in MeOH solu-

tion of the b-nona-peptide Boc-b3hVal-b2hAla-b3hLeu-b2hVal-b3hAla-b2hLeu-b3hVal-b2hAla-b3hLeu-OBn. (B) Schematic presentation of the 12- and 10-membered hydrogen-bonded rings. (C)

View along the axis of the R-b2hVal-b3hAla-b2hLeu-b3hVal-b2hAla-b3hLeu-OR0 helix (NMR

structure in MeOH). (D) Newman projection along the Cb–Ca bond. For nomenclature see also

Figure 3 and Seebach et al.6



acid) have also been prepared.66,67 From crystal struc-

ture data of (b3hPro)2,3 derivatives a higher oligomer

was modeled,66 which is, indeed, a helix (Figure 7).

OTHER SECONDARY STRUCTURESOF b-PEPTIDES

Besides helical arrangements, b-peptides, like the

a-peptidic prototypes, can attain non-aggregating ex-

tended-chain structures, can assemble to pleated sheets,

fold to hairpin turns, and stack in crystals. Keeping in

mind certain simple rules, which we have learned in

10 years of b-peptide research6 and/or which are knownfrom the age-old world of a-peptides, we can now con-

struct most of these arrangements by design.

Thus, a b-peptide made of u-2-methyl-3-aminocar-

boxylic acids units ((2R,3S)- or (2S,3R)-configura-

tion) cannot possibly fold to a 14-helix (rule: no alkylsubstituent in an axial position!). Such a b2,3-peptideis therefore forced to stay in an extended form, with

an antiperiplanar (ap) conformation of the amino

acid residues, with all C¼¼O bonds pointing in one

direction and all N��H bonds in the opposite direction

and with the side chains approximately perpendicular

to the amide planes—an ideal structure for assembly of

parallel (Figure 8A)41,46,56,68,69 or antiparallel (cf. also

Figure 10 below)40,41,69,70 pleated sheets.

Sheet formation can be prevented by remembering

another rule: ‘‘no substituent other than hydrogenmay be pointing inwards of the ring held together bytwo hydrogen bonds in a pleated sheet.’’ A b-peptideconsisting of 2,2-dimethyl-3-aminocarboxylic acid

(b2,2hAib)68 is thus ‘‘condemned’’ to stay in an

extended arrangement and not assemble to a pleated

sheet (Figure 8B).46

FIGURE 5 The x-ray crystal structure of the (M)-2.612-helix consisting of 8 (R,R)-2-aminocyc-

lopentanecarboxylic-acid (ACPC) residues (left). The termini are protected (N-Boc, C-OBn). Con-formational space of the highly flexible trans-substituted cyclopentane ring (right).



A hairpin turn can be constructed by incorporating

turn-inducing (cf. the 12/10 helix, above) or turn-enforc-

ing structural elements, and, attaching to them sheet-

favoring appendices (Figures 9 and 10).38,40–44,69–72

The amide group in the 10-membered hydrogen-

bonded ring of the b2/b3 section ((S)-b2hXaa-(L-b3hXaa-)) and the adjacent side chains actually

have the same geometry found in an a-peptidic bII0-turn, built from an (S)- and an (R)-Xaa amino acid;

this allowed mimicking of the somatostatin peptide

receptor interaction with a – metabolically sta-

ble73,74 – b-peptide.75,76 Turns are structurally in-

herent to cyclic peptides. Cyclo-b-tri, -tetra-, and-hexapeptides have been prepared.6 The simple tri-

FIGURE 6 Stairs and helices of b-amino acids not derived from proteinogenic a-amino acids.

(A and B) Stairs and twisted stairs (a 28-helix) built from folded 8-membered hydrogen-bonded

rings. (C) An alternative structure for the hydroxylated b-hexapeptide (a 2.512-helix!).

FIGURE 7 Model of poly-(S)-b3-homoproline, created with data acquired from the solid-state

(x-ray) structures of di- and tripeptide building blocks [H-(bhPro)3-OBn and Boc-(bhPro)2,3-OBn].Since this b-peptide lacks N��H protons, no stabilization of the secondary structure can be afforded

through intramolecular hydrogen bond interactions. The helix is right-handed and can be specified as a

103-helix (crystallographic nomenclature: three turns required to place residue (iþ 10) above residue i).



FIGURE 8 (A) Parallel pleated sheet of a b-tripeptide from u-2-methyl-3-amino acids. Com-

pounds of this type are extremely insoluble; in contrast to an a-peptidic sheet all C¼¼O bonds point

in the same direction, as do the N��H bonds, rendering the b-peptidic sheet polar.41,68 (B) In a

similar backbone conformation as in A, geminal dimethyl-substitution prevents the N��H group

from engaging in hydrogen bond donation (a kind of A1,3 effect). Compounds of this type have good

solubility in organic media; the structure shown in B has been derived from solid-phase NMR experi-

ments (REDOR technique) with a magnetically labeled derivative.46 For a sheet structure with sc-conformation of bhGly residues see Chung et al.69

FIGURE 9 Simple b-peptidic turn structures. (A) Preferred conformation of the b-dipeptidederivative (S,S)-N-acetyl-b2hVal-b3hPhe-NHCH3 (NMR in MeOH, and MD simulation).71 (B) A

geminally disubstituted b2,2-amino acid as a turn stabilizer? (crystal structure).43 (C) b2hPro as

turn-inducing residues (crystal structure).69



FIGURE 10 A b-hexa- and b-octapeptide folded to hairpin turns. (A) Combination of a turn-induc-

ing b2/b3-segment with two linearly enforced b2,3-dimer segments (NMR-structure in MeOH).41 (B)

Zn2þ-enforced turn structure (NMR-structure in H2O) of an otherwise 14-helical-b-peptide.70

FIGURE 11 (A) Solid-state structure (powder x-ray diffraction) of cyclo(b3hAla)4. The molecules

stack through four intermolecular C¼¼O� � �H��N hydrogen bonds, to form columns, which are

arranged in an antiparallel manner;47,49 the compound is extremely insoluble. (B) A cyclo-b-peptideconsisting of two b2- and two b3-amino acids (NMR-solution structure in MeOH); there is a transan-

nular hydrogen bond creating a bicyclic system, which contains a 10- and a 12-membered hydrogen-

bonded ring;78,80 cf. the turn structures (Figure 9) and the 10-, 12-, and 12/10-helices, above.



and tetrapeptides stack to highly insoluble solids

(Figure 11A),47–49 although soluble derivatives can

be obtained by introducing functionalized side

chains.21,77–80 In the solution structures of the

cyclo-b-tetrapeptides there is a transannular hydro-

gen bond; the structures may therefore be consid-

ered as a pair of fused 10- and 12-membered turns

(Figure 11B).78,80

HELIX AND TURN OF c-PEPTIDES

Double homologation of proteinogenic amino acids

in peptides leads to g2-, g3-, and g4-peptides.6 Of these

most simple derivatives an NMR-solution structure

has only been found for a g4-hexapeptide, which was

shown to be a 2.614-helix (cf. Figure 1).81,82 More

heavily side-chain–substituted derivatives, such as

g2,4- and g2,3,4-peptides1,83 can also fold to a 2.614-

helix (Figure 12A). The conformation around both

C��C ethane bonds (N��Cg��Cb��Ca and Cg��Cb��Ca��CO) is sc in these helices.

Depending upon the relative configuration of the

g2,4-residues, turn motifs can also be construc-

ted1,84,85 (Figure 12B). For both secondary structures

to be observed in solution, the required chain length

can be even shorter than in the case of b-peptides:four residues for the helix and two for the turn.

FIGURE 12 g-Peptidic helix and turn. The g-amino acids with three substituents in the tetrapep-

tide A, n ¼ 2, can be assigned D-configuration, and the helix is (M) or left-handed. L-g4-Residuesgive rise to a (P)-helix (Figure 1, far right). The g-dipeptide (top right) forms a nine-membered

hydrogen-bonded ring. Turns as the one shown in B can be used as scaffolds for a-peptidic turn

mimics, given the proper side chains adjacent to the peptide bond.84



The alkyl chain backbone takes control, while the

number of hydrogen bonds per chain atom decreases!

The structural diversity of g-amino acids and g-pepti-des has not been elucidated nearly as well as that of

b-peptides: it is expected to be richer.

MOLECULAR DYNAMICS SIMULATIONSOF b-PEPTIDE STRUCTURES

NMR-solution structures provide time and ensemble

averages of individual conformations: the time-scale

(‘‘exposure time’’) of NMR spectroscopy is in the

order of 10�7 s, very long in comparison with the

rate of conformational changes, which is in the range

of 10�12 s. Furthermore, the NMR analysis uses 3J-values and NOE distance bounds, and the NOE

between non-neighboring atoms is not subject to quan-

titative analysis (weak/medium/strong) and drops

with distance in the power of r–6. A structure present

in low abundance may thus ‘‘disappear,’’ while a

conformation giving rise to pronounced NOEs will be

grossly overrepresented in the NMR analysis, even in

the presence of a predominant form that gives much

weaker or, indeed, no NOEs. X-ray-crystal structures,

on the other hand, are snapshots showing a single,

solely present conformation in the solid state.

In contrast, MD simulations offer a picture at atomic

resolution and can give insight into dynamic processes,

such as those maintaining the folding/unfolding equili-

brium of a peptide. Using the GROMOS simulation

package with its thermodynamically calibrated force

field,86,87 several b-peptides have been analyzed in

methanol solution, with simulation periods of up to 250 ns

and at temperatures of 298 and 340 K. Depending on

the sampling frequency (for instance every 10 ps), a

large number of structures can be extracted from such

a long simulation. Relative populations (‘‘thermody-

namic stability’’) and average lifetimes (‘‘kinetic

stability’’) can be calculated.88,89 In a most fruitful col-

laboration between the van Gunsteren and Seebach

groups at the ETH,6,40,58,61,71,89–97 it was established

that the GROMOS force field is able to describe the

folding of all b-peptidic secondary structures that were

experimentally determined by NMR spectroscopy: the

14-helix,58,88,89,91,92,96,98,99 the 12/10-helix,58,89,91,94,98,99

and the hairpin turn40,89,94,98 (Figure 13).

At 298 K the b-heptapeptide with a central,

helix-stabilizing, l-(2Me)-b3hAla residue (Figure

13A) is found to preferentially form a 14-helix

(53% populated in the simulation starting from a

fully extended conformation). Under the same con-

ditions the 12/10-helix constitutes 52% of the con-

formations of the b3/b2-nonapeptide (Figure 13B)

and the b-hexapeptide shown in Figure 13C is

folded to a hairpin structure in 20% of the con-

formations. From simulation data, the b-heptapep-tide lacking Val and Ile side chains and having

two positively charged Lys side chains, a (P)-12-helix structure (ca. 5% of the population) could be

extracted (Figure 13D). Clearly, the 14- and the 12/

10-helices, as well as the turn-part of the hairpin,

have (þ)-sc dihedral angles close to the ideal one

of staggered ethane (608), while in the 12-helix the

values are nearer to þ908 (cf. Figure 5). Also, in

the antiparallel sheet section of the turn, angles near

the ideal 1808 are obtained. Besides folding to the

major secondary structures A–C in Figure 13, these

peptides sample overlapping conformational spaces: in

addition to the turn, there are 12/10- helical struc-

tures94 and together with the 12/10-helix there are

also 14-helical structures,97 and, of course, there are

numerous partially folded helices and structures with

single 10-, 12-, and 14-membered hydrogen-bonded

rings.58 These MD simulations are compatible with

the conclusion from temperature-dependent NMR

and CD measurements, namely that the folding/unfold-

ing process of b-peptides-and of g-peptides-is non-

cooperative.82,100

The MD simulations also confirm that the effect of

secondary alkyl side chain groups (Val and Ile) on the

14-helix’s stability14,101–104 is probably more due to a

destabilizing effect of the ap conformation of b-pepti-dic residues with such side chains46,96-after all, the

fully helical b-eicosapeptide shown in Figure 2 con-

tains only one bhVal and one bhIle. Subtle structural

differences caused by terminal protection/deprotection

of b-peptides97 and effects of charged side chains on

folding rate and helix stability of b-peptides (cf. hydro-gen-bridges between Lys-!-NH�

3-groups and backbone

carbonyl oxygens)93 were also investigated by MD

simulation, providing further insights into the folding/

unfolding equilibrium at atomistic detail.

The MD simulations of b-peptides have helped to

deepen our understanding and permit questioning of

some generally accepted ‘‘facts’’ of a-peptide chem-

istry, as is evident from publication titles such as:

‘‘Peptide Folding: When Simulation Meets Experi-

ment,’’91 ‘‘Can One Derive the Conformational Pref-

erence of a b-Peptide from its CD Spectrum?,’’90

‘‘Molecular Dynamics Simulations of Small Pepti-

des: Can One Derive Conformational Preferences

from ROESY Spectra?,’’71 ‘‘a- and b-PolypeptidesShow a Different Stability of Helical Secondary

Structures,’’95 or ‘‘The Key to Solving the Protein-

Folding Problem Lies in an Accurate Description of

the Denatured State.’’98



Besides molecular dynamics simulations, ab initio

calculations of b-, g-, and �-peptides have been con-

ducted primarily by the groups of Hofmann105–109

and Wu.110–114 It is beyond the scope of this article to

describe the results obtained: remarkably, the folded

structures of b-peptides can be derived from the

structure of their monomeric building blocks, and the

12-helix of a b-peptide is more stable than the 14-

helix, according to these calculations.

We thank Albert K. Beck, Drs. Oliver Flogel and Michael

Limbach, and Misiona Gardiner for their help in producing

the figures and preparing the manuscript of this review

article.

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2. Hanessian, S.; Luo, X.; Schaum, R. Tetrahedron Lett

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3. Hanessian, S.; Luo, X.; Schaum, R.; Michnick, S.

J Am Chem Soc 1998, 120, 8659–8570.

4. Seebach, D.; Abele, S.; Gademann, K.; Guichard, G.;

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Widmer, H. Helv Chim Acta 1996, 79, 2043–2066.

FIGURE 13 Models of secondary structures of the b-peptides A–D from MD simulations. The

numbers of structures are given, from which the indicated average values of the N–Cb–Ca–CO dihedral

angels are derived. The simulation times are between 50 and 250 ns. For details on the simulations and

original publications see: b-peptide A,93,96 b-peptide B,97 b-peptide C.40 From the resulting trajectories

at 298 and 340 K, structures were taken at 10-ps intervals for conformational analysis. Only fully

folded helices or hairpins, including terminal residues, were considered for the dihedral angle analysis,whereas for the calculation of the helix or hairpin population the terminal residues were not consid-ered, as they show increased flexibility. This means that for the dihedral angle analysis fewer confor-

mations were used than for the determination of the helical population. As an example, the 14-helical

conformation of b-peptide A is populated to the extent of 52% (10,400 structures) at 298 K and 48%

(9,600 structures) at 340 K, while only 5,798 at 298 K and 4,717 fully helical structures at 340 K (in

total 10,515 structures) were considered to calculate the average dihedral backbone angles. This more

stringent choice of conformations for the dihedral analysis ensures that also for the termini the resulting

average dihedral angle represents the average over a single dihedral-angle distribution peak. b-PeptideD shows no well-defined conformational preference in the simulations: besides the 5% 12-helix, there

are 2% 14-helix structures, with a major contribution of partially folded 14-helices; according to

NMR-coupling constants the key Cb–Ca torsion angle is (þ)-sc; for modeling and NMR measurements

of related b-peptides lacking the secondary-alkyl side chains of Val and Ile see Glattli et al.96



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Helices and other secondary structures of [beta]- …as few as four residues (NMR analysis in MeOH,...

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