Differential stability of the triple helix of (Pro-Pro-Gly)10 in H2O and D2O: thermodynamic and structural explanations

(Pro-Pro-Gly)10 [(PPG10)], a collagen-like polypeptide, forms a triple-helical, polyproline-II structure in aqueous solution at temperatures somewhat lower than physiological, with a melting temperature of 24.5 degrees C. In this article, we present circular dichroism spectra that demonstrate an increase of the melting temperature with the addition of increasing amounts of D2O to an H2O solution of (PPG)10, with the melting temperature reaching 40 degrees C in pure D2O. A thermodynamic analysis of the data demonstrates that this result is due to an increasing enthalpy of unfolding in D2O vs. H2O. To provide a theoretical explanation for this result, we have used a model for hydration of (PPG)10 that we developed previously, in which inter-chain water bridges are formed between sterically crowded waters and peptide bond carbonyls. Energy minimizations were performed upon this model using hydrogen bond parameters for water, and altered hydrogen bond parameters that reproduced the differences in carbonyl oxygen-water oxygen distances found in small-molecule crystal structures containing oxygen-oxygen hydrogen bonds between organic molecules and H2O or D2O. It was found that using hydrogen bond parameters that reproduced the distance typical of hydrogen bonds to D2O resulted in a significant lowering of the potential energy of hydrated (PPG)10. This lowering of the energy involved energetic terms that were only indirectly related to the altered hydrogen bond parameters, and were therefore not artifactual; the intra-(PPG10) energy, plus the water-(PPG10) van der Waals energy (not including hydrogen bond interactions), were lowered enough to qualitatively account for the lower enthalpy of the triple-helical conformation, relative to the unfolded state, in D2O vs. H2O. This result indicates that the geometry of the carbonyl-D2O hydrogen bonds allows formation of good hydrogen bonds without making as much of an energetic sacrifice from other factors as in the case of hydration by H2O.     

Modular design of synthetic protein mimics. Characterization of the helical conformation of a 13-residue peptide in crystals

The incorporation of alpha-aminoisobutyryl (Aib) residues into peptide sequences facilitates helical folding. Aib-containing sequences have been chosen for the design of rigid helical segments in a modular approach to the construction of a synthetic protein mimic. The helical conformation of the synthetic peptide Boc-Aib-(Val-Ala-Leu-Aib)3-OMe in crystals is established by X-ray diffraction. The 13-residue apolar peptide adopts a helical form in the crystal with seven alpha-type hydrogen bonds in the middle and 3(10)-type hydrogen bonds at either end. The helices stack in columns, zigzag rather than linear, by means of direct NH...OC head to tail hydrogen bonds. Leucyl side chains are extended on one side of the helix and valyl side chains on the other side. Water molecules form hydrogen bonds with several backbone carbonyl oxygens that also participate in alpha-helix hydrogen bonds. There is no apparent distortion of the helix caused by hydration. The space group is P2(1)2(1)2(1), with a = 9.964 (3) A, b = 20.117 (3) A, c = 39.311 (6) A, Z = 4, and dx = 1.127 g/cm3 for C64H106N13O16.1.33H2O. The final agreement factor R was 0.089 for 3667 data observed greater than 3 sigma(F) with a resolution of 0.9 A.     

Hydratation of the rubredoxin polypeptide chain from data on the spatial structure

The hydration water distribution around the main chain protein rubredoxin has been analysed using the crystal data at high resolution obtained earlier. The analysis was based on the consideration of all nearest neighbour atoms around the N and O atoms of peptide groups. The atoms which can form hydrogen binds were the subject of final analysis. The nitrogen atom of a peptide NH group has only one vacancy for neighbours. The oxygen atom of a peptide CO group has one, two or more neighbours, some of them are oxygen-water atoms. About 27% of NH and 53% of CO peptide groups are hydrated, that corresponds to 0.12 H2O per gram of protein. A detailed analysis shows that NH and CO groups of the main chain are hydrated according to the principle of maximum possible in situ saturation of hydrogen bonds. Thus the peptide groups incorporated in the peptide hydrogen bond network were not hydrated as a rule. Consequently, for rubredoxin a pleated sheet region, some regions for the large and small main chain loops, and Fe-containing pocket are not hydrated. A method for evaluation of the main chain hydration is proposed when the coordinates of protein atoms are available.     

Detection by high pressure infrared spectrometry of hydrogen-bonding between water and triacetyl glycerol

The barotropic behavior of neat and aqueous 1,2,3-triacetyl glycerol was investigated by FT-IR spectroscopy over the pressure range 0.001 to 35 kbar. The infrared spectrum in the presence of water shows bands characteristic of hydrogen bonded carbonyl groups. An increase in hydrostatic pressure leads to a strengthening of the intermolecular hydrogen bond between water and the lipid ester C = O groups. The pressure-induced formation of ice VI at 9 kbar does not affect this hydrogen bond, however, the formation, at 20 kbar, of ice VII in which the water/water hydrogen bonds are stronger than the lipid C = O/water hydrogen bonds, frees the lipid carbonyl groups from the hydrogen-bonding to water.     

Hydrogen bonding monitored by deuterium isotope effects on carbonyl 13C chemical shift in BPTI: intra-residue hydrogen bonds in antiparallel beta-sheet.

Deuterium isotope effects on carbonyl 13C magnetic shielding were measured for the backbone carbonyl groups in BPTI (basic pancreatic trypsin inhibitor), and interpreted as a measure of hydrogen bond energies. The effects originate from peptide amide proton deuterium substitution and were observed on carbonyl carbons separated by two or three covalent bonds from the amide H/D. Two-bond isotope effects depend on the energy of the hydrogen bond donated by NH/D. Calibration of the effect with model compound data leads to hydrogen bond enthalpies less than 4.7 kcal/mol. Isotope effects over three bonds from the amide H/D to the carbonyl carbon of the same amino acid residue are observed for seven carbonyl resonances in BPTI. The three-bond isotope effects are highly related to the various backbone conformations. The largest effects are observed for residues with an approximate syn- periplanar conformation of the H-N-C alpha-C = O atoms, as realized for many residues in the BPTI antiparallel beta-sheet. The residues that show measurable three-bond effects have unusually short distances between H and O. The size of this effect decreases rapidly with increased O..H distance in the open five-membered ring. This observation suggests appreciable interactions in these rings.     

Helix-forming tendencies of amino acids depend on the restrictions of side-chain rotamer conformations: crystal structure of the tripeptide GAI in two crystalline forms.

In our attempts to design crystalline alpha-helical peptides, we synthesized and crystallized GAI (C11H21N3O4) in two crystal forms, GAI1 and GAI2. Form 1 (GAI1) Gly-L-Ala-L-Ile (C11H21N3O4.3H2O) crystals are monoclinic, space group P2(1) with a = 8.171(2), b = 6.072(4), c = 16.443(4) A, beta = 101.24(2) degrees, V = 800 A3, Dc = 1.300 g cm-3 and Z = 2, R = 0.081 for 482 reflections. Form 2 (GAI2) Gly-L-Ala-L-Ile (C11H21N3O4.1/2H2O) is triclinic, space group P1 with a = 5.830(1), b = 8.832(2), c = 15.008(2) A, alpha = 102.88(1), beta = 101.16(2), gamma = 70.72(2) degrees, V = 705 A3, Z = 2, Dc = 1.264 g cm-3, R = 0.04 for 2582 reflections. GAI1 is isomorphous with GAV and forms a helix, whereas GAI2 does not. In GAI1, the tripeptide molecule is held in a near helical conformation by a water molecule that bridges the NH3+ and COO- groups, and acts as the fourth residue needed to complete the turn by forming two hydrogen bonds. Two other water molecules form intermolecular hydrogen bonds in stabilizing the helical structure so that the end result is a column of molecules that looks like an incipient alpha-helix. GAI2 imitates a cyclic peptide and traps a water molecule. The conformation angles chi 11 and chi 12 for the side chain are (-63.7 degrees, 171.1 degrees) for the helical GAI1, and (-65.1 degrees, 58.6 degrees) and (-65.0 degrees, 58.9 degrees) for the two independent nonhelical molecules in GAI2; in GAI1, both the C gamma atoms point away from the helix, whereas in GAI2 the C gamma atom with the g+ conformation points inward to the helix and causes sterical interaction with atoms in the adjacent peptide plane. From these results, it is clear that the helix-forming tendencies of amino acids correlate with the restrictions of side-chain rotamer conformations. Both the peptide units in GAI1 are trans and show significant deviation from planarity [omega 1 = -168(1) degrees; omega 2 = -171(1) degrees] whereas both the peptide units in both the molecules A and B in GAI2 do not show significant deviation from planarity [omega 1 = 179.3(3) degrees; omega 2 = -179.3(3) degrees for molecule A and omega 1 = 179.5(3) degrees; omega 2 = -179.4(3) degrees for molecule B], indicating that the peptide planes in these incipient alpha-helical peptides are considerably bent.     

Bovine serum albumin observed by infrared spectrometry. II. Hydration mechanisms and interaction configurations of embedded H(2)O molecules

The hydration mechanism of bovine serum albumin (BSA) is studied, and we analyze (de)hydration spectra displayed previously. We first determine the three elementary (de)hydration spectra on which all these (de)hydration spectra can be decomposed. They correspond to three different hydration mechanisms for the protein, which we define after a quantitative analysis performed in a second step. The first mechanism, which involves ionization of carboxylic COOH groups, occurs at low hydration levels and rapidly reaches a plateau when the hygroscopy is increased. It is a mechanism that involves a single H(2)O molecule and consequently requires somewhat severe steric conditions. The second mechanism occurs at all hydration levels and, because it involves more H(2)O molecules, requires less severe steric conditions. It consists of the simultaneous hydration of one amide N--H group and one carbonyl-amide C=O group by four H(2)O molecules and one carboxyl COO(-) group by eight H(2)O molecules. The third mechanism is simpler and consists of the introduction of H(2)O molecules into the hydrogen-bond network of the hydrated protein. It becomes important at a high hydration level, when the presence of an appreciable number of H(2)O molecules makes this hydrogen-bond network well developed. This analysis also shows that 80 H(2)O molecules remain embedded in one dried protein made of 604 peptide units. They are held by hydrogen bonds established by N--H groups and at the same time they establish two hydrogen bonds on two carbonyl-amide C=O groups. The proportion of free N--H groups can be determined together with that of carbonyl-amide C=O groups accepting no hydrogen bonds and that of carbonyl-amide C=O groups accepting two hydrogen bonds. The proportion of N--H groups establishing one hydrogen bond directly on a carbonyl-amide C=O group is 65%, which is the proportion of peptide units found in alpha helices in BSA.     

Vibrational frequency shifts as a probe of hydrogen bonds: thermal expansion and glass transition of myoglobin in mixed solvents

The contribution of hydrogen bonds to protein-solvent interactions and their impact on structural flexibility and dynamics of myoglobin are discussed. The shift of vibrational peak frequencies with the temperature of myoglobin in sucrose/water and glycerol/water solutions is used to probe the expansion of the hydrogen bond network. We observe a characteristic change in the temperature slope of the O–H stretching frequency at the glass transition which correlates with the discontinuity of the thermal expansion coefficient. The temperature-difference spectra of the amide bands show the same tendency, indicating that stronger hydrogen bonding in the bulk affects the main-chain solvent interactions in parallel. However, the hydrogen bond strength decreases relative to the bulk solvent with increasing cosolvent concentration near the protein surface, which suggests preferential hydration. Weaker and/or fewer hydrogen bonds are observed at low degrees of hydration. The central O–H stretching frequency of protein hydration water is red-shifted by 40 cm^–1 relative to the bulk. The shift increases towards lower temperatures, consistent with contraction and increasing strength of the protein-water bonds. The temperature slope shows a discontinuity near 180 K. The contraction of the network has reached a critical limit which leads to frozen-in structures. This effect may represent the molecular mechanism underlying the dynamic transition observed for the mean square displacements of the protein atoms and the heme iron of myoglobin. Received: 10 July 1996 / Accepted: 10 April 1997     

Synthetic peptide helices in crystals: structure and antiparallel and skewed packing motifs for alpha-helices in two isomeric decapeptides

The isomeric decapeptides Boc-Aib-Ala-Leu-Ala-Aib-Aib-Leu-Ala-Leu-Aib-OMe (II) and Boc-Aib-Ala-Aib-Ala-Leu-Ala-Leu-Aib-Leu-Aib-OMe (III), are predominantly alpha-helical with little effect on the conformation with interchange of Aib/Ala residues or Aib/Leu residues. The packing motif of helices in crystal II is antiparallel, whereas the helices pack in a skewed fashion in crystal III, with a 40 degrees angle between neighboring helix axes. Crystal III contains a water molecule in a hydrophobic hole that forms hydrogen bonds with two carbonyl oxygens that also participate in 5----1 type hydrogen bonds. Values for helical torsional angles phi and psi assume a much wider range than anticipated. Crystal II: C49H88N10O13, space group P2(1), with a = 16.625 (2) A, b = 9.811 (5) A, c = 18.412 (3) A, beta = 99.79 (1) degrees, Z = 2, R = 5.7% for 4338 data with magnitude of F0' greater than 3 sigma(F). Crystal III: C49H88N10O13 x 1/2H2O, space group P2(1) with a = 11.072 (2) A, b = 34.663 (5) A, c = 16.446 (3) A, beta = 107.85 (1) degrees, Z = 4, R = 8.3% for 6087 data with [F0[ greater than 3 sigma(F).     

Crystal and molecular structure of cyclo(L-prolyl-glycyl)3. A cyclic hexapeptide with a cis peptide bond

The crystal structure of cyclo(L-Pro-Gly)3 was solved using X-ray crystallographic techniques. The backbone of the peptide is asymmetric and is made up of five trans peptide units and one cis peptide. There is a hydrogen bonded water bridge that links the carbonyl oxygens, O1 and O4. The molecules exist as dimers in the crystal lattice. The two molecules of the dimer are related by crystallographic twofold symmetry and are linked by two N-H ... O hydrogen bonds. The crystals are trigonal, space group P3(2)12 with a = 11.379(3), c = 32.93(1) and z = 6. The structure was solved by multisolution methods and refined by least squares technique to an R of 0.083.     

Bound water in the collagen-like triple-helical structure.

The ir amide bands of the triple-helical polytripeptides and collagens upon hydration of films are investigated. On the basis of our assignment of the amide I components, the formation of hydrogen bonds between the peptide backbone and structural water is studied. The C1O1--HOH hydrogen bonds are found more ordered than the C3O3--HOH hydrogen bonds. The specific incorporation of water in the triple helix is followed by multistep conformational changes and by increasing of the interpeptide hydrogen-bond strength. The formation of the polypeptide hydrate structure depending on the amino acid composition and the chain length is examined.     

The molecular basis of the temperature- and pH-induced conformational transitions in elastin-based peptides

Elastin undergoes an inverse temperature transition and collapses at high temperatures in both simulation and experiment. We investigated a pH-dependent modification of this transition by simulating a glutamic acid (Glu)-substituted elastin at varying pHs and temperatures. The Glu-substituted peptide collapsed at higher temperature than the unsubstituted elastin when Glu was charged. The charge effects could be reversed by neutralization of the Glu carboxyl groups at low pH, and in that case the peptide collapsed at a lower temperature. The collapse was accompanied by the formation of beta-turns and short distorted beta-sheets. Formation of contacts between hydrophobic side chains drives the collapse at high temperature, but interactions between water and polar groups (Glu and main chain) can attenuate this effect at high pH. The overall competition and balance of the polar and nonpolar groups determined the conformational states of the peptide. Water hydration contributed to the conformational transition, and the peptide and its hydration shell must be considered. Structurally, waters near polar residues mainly formed hydrogen bonds with the protein atoms, while waters around the hydrophobic side chains tended to be parallel to the peptide groups to maximize water-water interactions.     

Direct determination of the hydrogen bonding arrangement in anhydrous β-chitin by neutron fiber diffraction

The hydrogen bonding arrangement in anhydrous β-chitin, a homopolymer of N-acetylglucosamine, was directly determined by neutron fiber diffraction. Data were collected from a sample prepared from the bathophilous tubeworm Lamellibrachia satsuma in which all labile hydrogen atoms had been replaced by deuterium. Initial positions of deuterium atoms on hydroxyl and acetamide groups were directly located in Fourier maps synthesized using phases calculated from the X-ray structure and amplitudes measured from the neutron data. The hydrogen bond arrangement in the refined structure is in general agreement with predictions based on the X-ray structure: O3 donates a hydrogen bond to the O5 ring oxygen atom of a neighboring residue in the same chain; N2 and O6 donate hydrogen bonds to the same carbonyl oxygen O7 of an adjacent chain. The intramolecular O3···O5 hydrogen bond has the most energetically favorable geometry with a hydrogen to acceptor distance of 1.77 ? and a hydrogen bond angle of 171°.     

Crystal structure of cyclic (APGVGV)2, an analog of elastin, and a suggested mechanism for elongation/contraction of the molecule

Tropoelastin is a complex polymeric protein composed primarily of repeating segments of Val-Pro-Gly-Gly, Val-Pro-Gly-Val-Gly, and Ala-Pro-Gly-Val-Gly-Val that occurs in connective tissue and arteries. It has rubber-like extensible properties. A synthetic cyclic dodecapeptide, with a double repeat of the hexapeptide sequence, has been shown to undergo a reversible inverse temperature transition; that is, crystals grow at 60 degrees C and dissolve in the mother liquor upon cooling. An x-ray crystal structure analysis established that the cyclic backbone formed an elongated loop with a Pro-Gly, type II beta turn at both ends. Six internal cross strand NH...OC hydrogen bonds form between six NH donors and four O=C acceptors where two of the carbonyl O atoms are bifurcated acceptors. As a result, the molecule is pulled up into a corrugated profile. The corrugated loops form extended beta-sheets by additional intermolecular hydrogen bonds. An analysis of the dome region in a corrugated sheet suggests a reversible mechanism for extending and contracting the length of the whole molecule, akin to the motion of opening and closing an umbrella, caused by the motion of a water molecule with its associated hydrogen bonds acting as spokes. Crystal parameters: C44H72N12O12.3H2O, sp. gr. P2(1)2(1)2(1), a = 9.212 angstroms, b = 19.055 angstroms, c = 32.247 angstroms, d = 1.157 g/cm3.     

A sequence preference for nucleation of alpha-helix--crystal structure of Gly-L-Ala-L-Val and Gly-L-Ala-L-Leu: some comments on the geometry of leucine zippers

The synthetic peptide Gly-L-Ala-L-Val (C10H19N3O4.3H2O; GAV) crystallizes in the monoclinic space group P21, with a = 8.052(2), b = 6.032(2), c = 15.779(7) A, beta = 98.520(1) degree, V = 757.8 A3, Dx = 1.312 g cm-3, and Z = 2. The peptide Gly-L-Ala-L-Leu (C11H21N3O4.3H2O; GAL) crystallizes in the orthorhombic space group P212121, with a = 6.024(1), b = 8.171(1), c = 32.791(1) A, V = 1614 A3, Dx = 1.289 g cm-3, and Z = 4. Their crystal structures were solved by direct methods using the program SHELXS-86, and refined to an R index of 0.05 for 1489 reflections for GAV and to an R index of 0.05 for 1563 reflections for GAL. The tripeptides exist as a zwitterion in the crystal and assume a near alpha-helical backbone conformation with the following torsion angles: psi 1 = -150.7 degrees; phi 2, psi 2 = -68.7 degrees, -38.1 degrees; phi 3, psi 32 = -74.8 degrees, -44.9 degrees, 135.9 degrees for GAV; psi 1 = -150.3 degrees; phi 2, psi 2 = -67.7 degrees, -38.9 degrees; phi 3, psi 31, psi 32 = -72.2 degrees, -45.3 degrees, 137.5 degrees for GAL. Both the peptide units in both of the tripeptides show significant deviation from planarity [omega 1 = -171.3(6) degrees and omega 2 = -172.0(6) degrees for GAV; omega 1 = -171.9(5) degrees and omega 2 = -173.2(6) degrees for GAL]. The side-chain conformational angles chi 21 and chi 22 are -61.7(5) degrees and 175.7(5) degrees, respectively, for valine, and the side-chain conformations chi 12 and chi 23's are -68.5(5) degrees and (-78.4(6) degrees, 159.10(5) degrees) respectively, for leucine. Each of the tripeptide molecule is held in a near helical conformation by a water molecule that bridges the NH3+ and COO- groups, and acts as the fourth residue needed to complete the turn by forming two hydrogen bonds. Two other water molecules form intermolecular hydrogen bonds in stabilizing the helical structure so that the end result is a column of molecules that looks like an alpha-helix.     

Possible formation of the left-handed alpha-helix of poly-L-serine

A conformational study of poly-L -serine has shown that it can exist in the left-handed α-helical form. A study of a pair of peptide units with the serine sidegroup attached to the α carbon atom linking the two units showed that O? H ?O hydrogen bonds between the OH group of the side chain and a carbonyl oxygen of the first peptide group in the backbone can occur in two regions of ?, namely, ? = 15°–30° for χ₁ = 300° and for ? = 225°-230° for ? = 60°. The latter is close to a possible left-handed helix of poly-L -serine, stabilized by N? H ?O hydrogen bonds. From a study of contact criteria, the best conformation for this helix is found to be ? = 227°, Ψ = 238°, χ₁ = 65° which has n = 3.65, h = 1.51 A. The N? H ?O hydrogen bond has a length of 2.90 A. (6°) and the O? H ?O hydrogen bond is of length 2.60 A. (0°). There are no other bad short contacts in the structure. The cylindrical coordinates of the atoms, as well as a perspective view of the structure arc given in this paper.     

A Raman scattering study of the interactions of DNA with its water of hydration

Raman spectroscopy is used to probe the nature of the hydrogen bonds which hold the water of hydration to DNA. The ～ 3450?cm^?1 molecular O–H stretching mode shows that the first six water molecules per base pair of the primary hydration shell are very strongly bound to the DNA. The observed shift in the peak position of this mode permits a determination of the length of the hydrogen bonds for these water molecules. These hydrogen bonds appear to be about 0.3?Å shorter than the hydrogen bonds in bulk water. The linewidth of this mode shows no significant changes above water contents of about 15 water molecules per base pair. This technique of using a vibrational spectroscopy to obtain structural information about the hydration shells of DNA could be used to study the hydration shells of other biomolecules.     

Structure of myohemerythrin in the azidomet state at 1.7/1.3 A resolution

The molecular model of myohemerythrin, an oxygen-carrying protein from sipunculan worms, has been refined by stereochemically restrained least-squares minimization at 1.7/1.3 A resolution to a conventional R-value of 0.158. The estimated positional standard deviation is better than 0.15 A for most of the 979 protein atoms. The average isotropic displacement parameter, B, for the protein atoms is 23.1 A2. This high average B parameter appears to be due to the overall motion of the molecule, which correlates with the observed anisotropic diffraction. The side-chains of seven residues were modeled in two conformations, i.e. the side-chains were discretely disordered, and B parameters for several lysine and glutamate side-chains indicate that they are poorly localized. Of the residues in myohemerythrin, 66% are helical, with 62% occurring in four long alpha-helices with mean values for the backbone torsion angles of phi = -65 degrees, psi = -42 degrees, and for the hydrogen bonds distances of N ... O, 3.0 A and H ... O, 2.1 A, and angles of N ... O = C, 153 degrees, N-H ... O, 157 degrees, and H ... O = C, 147 degrees. For two-thirds of the alpha-helical residues, the torsional rotation of the C alpha-C beta bond, chi 1, is approximately -60 degrees, and for one-third chi 1 is approximately 180 degrees. Although most turns in myohemerythrin are well-categorized by previous classification, two do not fit in established patterns. Also included in the refined model are three sulfate ions, all partially occupied, and 157 water molecules, 40% of which are modeled fully occupied. Only one water molecule is internal to the protein, the remainder occur on the surface and are observed principally between symmetry-related molecules contributing, along with van der Waals' contacts, most of the interactions between molecules. There are eight intermolecular protein-protein hydrogen bonds, of which only four are between well-located atoms.     

Vibrational approach to the dynamics of an α-helix

The dynamics of a finite α-helix have been studied in the harmonic approximation by a vibrational analysis of the atomic motions about their equilibrium positions. The system were represented by an empirical potential energy function, and all degrees of freedom (bond lengths, bond angles, and torsional angles) were allowed to vary. The complete results were compared with a more restrictive model in which the peptide dihedral angle was kept rigid; also, a model potential excluding hydrogen bonds was examined. Thermal fluctuations in the backbone dihedral angles ? and ψ are 12° to 15°. The fluctuations of adjacent dihedral angles are highly correlated, and the correlation pattern is affected by the flexibility of the peptide dihedral angle. Time-dependent autocorrelations in the motion of ? and ψ appear to decay due to dephasing in less than 1 psec, while the motions of the carbonyl oxygen and amide hydrogens out of the peptide plane are more harmonic. Length fluctuations have been evaluated and exhibit a strong end effect; the calculated elastic modulus is in agreement with other values. Rigid and adiabatic total energy surfaces corresponding to dihedral angle rotations in the middle of the helix have been obtained and compared with the quadratic approximation to those surfaces. The magnitudes and correlations between the fluctuations obtained by averaging over the adiabatic energy surface most closely resemble the vibrational results. Of particular interest is the fact that hydrogen bonds play a relatively small role in the local dihedral angle fluctuations, though the hydrogen bonds are important in the energy of overall length changes.