Raman spectroscopic elucidation of DNA backbone conformations for poly(dG-dT).poly(dA-dC) and poly(dA-dT).poly(dA-dT) in CsF solution

Raman spectra have been recorded for poly(dG-dT) · poly(dA-dC) and poly(dA-dT) · poly(dA-dT) in low salt and at high concentrations of CsF. Poly(dG-dT) · poly(dA-dC) shows no change in the 682-cm^?1 guanine mode, demonstrating the absence of the Z-structure at high salt. The 790-cm^?1 phosphodiester symmetric stretch, however, shifts up 5 cm^?1 in 4.3M CsF, suggesting a slight conformational change, associated with ion binding or hydration changes. Poly(dA-dT) · poly(dA-dT) shows an additional broad band at 816 cm^?1, attributed to the phosphodiester modes associated with the C3′-endo deoxyribose units in the alternating B-structure. In this case, both the 841- and the 816-cm^?1 asymmetric phosphodiester stretches, associated with the C2′- and C3′-endo units, shift down on addition of CsF in a sequential manner. Correlation of this sequence with that previously observed for the two ³¹P-nmr resonances, establishes that the phosphodiester stretching frequencies depend on the conformation of the 5′-sugar, and not on the 3′-sugar.     

Intensity Changes of Base and Backbone Raman Modes in the B to Z Transition of poly(dG-dm5C)

Abstract

Raman spectroscopy was employed to investigate the temperature-induced B to Z transition of poly(dG-dm-⁵C). The transition midpoint was about 37°C for a solvent containing 20 mM Mg²⁺. A 10-fold change in Mg²⁺ concentration altered the transition midpoint by at least 60°C. Raman spectra of the B and Z forms of poly(dG-dm⁵C) exhibited characteristics similar to those observed with poly(dG-dC). The 682 cm^?1 guanine mode and 835 cm^?1 backbone mode were present in the B conformation. In the Z form the intensities of these two bands decrease substantially and new peaks were observed at 621 cm^?1, 805 and 819 cm¹. Several bands unique to poly(dG-dm⁵C) were also observed. Transition profiles of band intensity vs. temperature were determined for fourteen Raman bands. The curves of all of the base vibrations and one backbone mode had the same slope and midpoint. This indicates that conformational changes in the guanine and methycytosine bases occur concurrently.     

A vitrational study of poly (L-proline) I and II in the far infrared.

The far infrared spectra of poly(L -proline) I (190–35 cm^?1) and II (400–35 cm^?1) were obtained in the solid state at both 300° and 110°K. A significant difference in the region below 100 cm^?1 was observed. A very intense band located at 60 cm^?1 in the infrared spectrum of form II has no counterpart in form I. This indicates the sensitivity of low-frequency vibrations to the difference in conformation assumed by both forms in the solid state. Additional bands observed in this study are correlated with ir and Raman data previously reported and tentative assignments are made using the results of normal mode calculations (in the single-chain approximation) which have been reported.     

FT-IR and 1H NMR spectroscopic evidence of sugar ring conformational change in NH4GpG on complexation to form cis-[Pt(NH3)2(GpG)]+

The conformational change of the ribose ring in NH₄GpG and cis-[Pt(NH₃)₂(GpG)]⁺ was confirmed by FT-IR spectroscopic evidence as being C2′-endo, C3′-endo, anti, gg sugar ring pucker in the solid state. These results were compared with ¹H NMR spectral data in aqueous solution. The FT-IR spectrum of NH₄GpG shows marker bands at 802 cm^?1 and 797 cm^?1 which are assigned to the C3′-endo, anti, gg sugar-phosphate vibrations of ribose (?pG) and ribose (Gp?), respectively. The FT-IR spectrum of cis-[Pt(NH₃)₂(GpG)]⁺ (with N7N7 chelation in the GpG sequence) shows a marker band at 800 cm^?1 which is assigned to the C3′-endo, and a new shoulder band at 820 cm^?1 related to a C2′-endo ring pucker. The ribose conformation of (?pG) moiety in NH₄-GpG, C3′-endo, anti, gg changes into C2′-endo, anti, gg when a platinum atom is chelated to N7N7 in the GpG sequence.     

The Structure of Triple Helical Poly(U)·Poly(A)·Poly(U) Studied by Raman Spectroscopy

Abstract

Using Raman spectroscopy, we examined the ribose-phosphate backbone conformation, the hydrogen bonding interactions, and the stacking of the bases of the poly(U)·poly(A) ·poly(U) triple helix. We compared the Raman spectra of poly(U)·poly(A)·poly(U) in H₂O and D₂O with those obtained for single-stranded poly(A) and poly(U) and for double-stranded poly(A)·poly(U). The presence of a Raman band at 863 cm^?1 indicated that the backbone conformations of the two poly(U) chains are different in the triple helix. The sugar conformation of the poly(U) chain held to the poly(A) by Watson-Crick base pairing is C3′ endo; that of the second poly(U) chain may be C2′ endo. Raman hypochromism of the bands associated with base vibrations demonstrated that uracil residues stack to the same extent in double helical poly(A)·poly(U) and in the triple-stranded structure. An increase in the Raman hypochromism of the bands associated with adenine bases indicated that the stacking of adenine residues is greater in the triple helix than in the double helical form. Our data further suggest that the environment of the carbonyls of the uracil residues is different for the different strands.     

A UV resonance Raman investigation of poly(rI): Evidence for cation-dependent structural perturbations

Poly(rI) stabilized by either Na⁺ or K⁺ was investigated using uv resonance Raman (UVRR) spectroscopy. Raman excitation profiles of inosine 5′-monophosphate demonstrated the 250 nm excitation selectively enhances base stacking interactions, while ribose and carbonyl stretching vibrations are preferentially enhanced with 210 nm excitation. These wavelengths were used to examine the structure of poly(rI) in the presence of either K⁺ or Na⁺ as a function of temperature. UVRR studies revealed that the K⁺ stabilized form is more thermally stable, yielding a T_m of ∼ 47°C compared to a T_m of ∼ 30°C for the Na⁺ stabilized form. We observed that both the ribosyl conformation and the coordination of the carbonyl groups depend on the nature of the cation. The C₆O stretching frequency indicates that Na⁺ coordinates much more strongly to the carbonyl groups than K⁺ (1672 cm⁻¹ Na⁺ vs 1684 cm⁻¹ K⁺ at 4°C). Conformationally sensitive modes of the phosphate backbone and the ribosyl ring indicate that Na⁺ stabilized poly(rI) predominantly exists in a C_3′-endo ribose conformation, whereas K⁺ stabilized poly(rI) adopts a C_2′-endo conformation possibly as a consequence of the larger ionic radius of the K⁺ ion. © 1998 John Wiley & Sons, Inc. Biopoly 46: 475–487, 1998     

Spectroscopic studies on the structure of poly(8-bromoadenylic acid): Effect of glycosidic torsion angle on the conformation and flexibility in polyribonucleotides

The helix–coil transition and conformational structure of poly(8-bromoadenylic acid) [poly(8BrA)] have been investigated using ¹H- and ¹³C-nmr, CD, and ir spectroscopy. The results have been compared with the structure of the related 5′-mono- and polynucleotides. The chemical shifts of H(2′), H(3′), C(2′), and C(3′) nmr signals show an interesting correlation with both the puckering of ribose ring and glycosidic bond torsion angle. Poly(8BrA) shows an upfield shift of the C(3′) signal and a downfield shift of the H(3′) signal compared to the chemical shifts in poly(A). These shifts are consistent with a C(3′) endo-syn conformation for poly(8BrA). A similar effect has been reported previously and is also observed here on the C(2′) and H(2′) signals when the preferred conformation is C(2′)endo-syn (e.g., in 5′-8BrAMP). The chemical-shift parameters thus act as a probe for studying syn ? anti and N ? S equilibria in solutions. The three-bond ¹H-′¹³C coupling constants between H(1′) and C(8) and C(4) have been measured in poly(8BrA) and 5′-8BrAMP and their structural implications have been discussed. The observed preference of a C(3′)endo-syn conformation for poly(8BrA), coupled with other evidence, throws doubt on the validity of a correlation previously reported whereby a syn conformation is associated with a C(2′)endo ribose pucker. The backbone conformation of randomly coiled poly(8BrA) is very similar to the structures found in polyribonucleotides: poly(A) and poly(U). All three polymers show strong preferences for the backbone angles found in RNA helices. The CD spectrum of poly(8BrA) has a striking relationship to that of poly(A). The signs of all extrema are inverted, and the magnitudes are related by a constant factor. We suggest that these differences result from a change in the angle between coupled transition moment vectors in the two polymers. Infrared spectra of poly(8BrA) in H₂O and D₂O solution are reported for the frequency range below 1400 cm^?1. The antisymmetric >PO stretching vibration is observed at an unusually low frequency in the helix (1214 cm^?1). The symmetric >PO stretch occurs at ～1095 cm^?1 but is not resolved from a ring vibration near this frequency. A conformationally sensitive band, characteristic of helical RNA structures, is observed at 817 cm^?1 and disappears when the helix is melted. This observation confirms the conclusion that ordered poly(8BrA) has a regular helical structure with an RNA backbone conformation. A stereochemical explanation is provided for the failure of poly(8BrA) (or other syn polymers) to form double helices with anti-polyribonucleotides.     

Raman spectroscopic study of poly (β-benzyl-L-aspartate) and sequential polypeptides

Poly-β-benzyl-L -aspartate (poly[Asp(OBzl)]) forms either a lefthanded α-helix, β-sheet, ω-helix, or random coil under appropriate conditions. In this paper the Raman spectra of the above poly[Asp(OBzl)] conformations are compared. The Raman active amide I line shifts from 1663 cm^?1 to 1679 cm^?1 upon thermal conversion of poly[Asp(OBzl)] from the α-helical to β-sheet conformation while an intense line appearing at 890 cm^?1 in the spectrum of the α-helix decreases in intensity. The 890 cm^?1 line also displays weak intensity when the polymer is dissolved in chloroform–dichloroacetic acid solution and therefore is converted to the random coil. This line probably arises from a skeletal vibration and is expected to be conformationally sensitive. Similar behavior in the intensity of skeletal vibrations is discussed for other polypeptides undergoing conformational transitions. The Raman spectra of two cross-β-sheet copolypeptides, poly(Ala-Gly) and poly(Ser-Gly), are examined. These sequential polypeptides are model compounds for the crystalline regions of Bombyx mori silk fibroin which forms an extensive β-sheet structure. The amide I, III, and skeletal vibrations appeared in the Raman spectra of these polypeptides at the frequencies and intensities associated with β-sheet homopolypeptides. Since the sequential copolypeptides are intermediate in complexity between the homopolypeptides and the proteins, these results indicate that Raman structure–frequency correlations obtained from homopolypeptide studies can now be applied to protein spectra with greater confidence. The perturbation scheme developed by Krimm and Abe for explaining the frequency splitting of the amide I vibrations in β-sheet polyglycine is applied to poly(L -valine), poly-(Ala-Gly), poly(Ser-Gly), and poly[Asp(OBzl)]. The value of the “unperturbed” frequency, V₀, for poly[Asp(OBzl)] was significantly greater than the corresponding values for the other polypeptides. A structural origin for this difference may be displacement of adjacent hydrogen-bonded chains relative to the standard β-sheet conformation.     

DNA binding of a spermine derivative: Spectroscopic study of anthracene-9-carbonyl-n1-spermine with poly[d(G-C)·(d(G-C))] and poly[d(A-T) · d(A-T)]

The binding of polyamines, including spermidine ( 1 ) and spermine ( 2 ), to poly[d(G-C) · d(G-C) ] was probed using spectroscopic studies of anthracene-9-carbonyl-N¹-spermine ( 3 ); data from normal absorption, linear dichroism (LD), and circular dichroism (CD) are reported. Ligand LD and CD for transitions located in the DNA region of the spectrum were used. The data show that 3 binds to DNA in a manner characteristic of both its amine and polycyclic aromatic parts. With poly [(dG-dC) · (dG-dC)], binding modes are occupied sequentially and different modes correspond to different structural perturbations of the DNA. The most stable binding mode for 3 with poly[d(G-C) · d(G-C)] has a site size of 6 ± 1 bases, and an equilibrium binding constant of (2.2 ± 1.1) × 10⁷ M^?1 with the anthracene moiety intercalated. It dominates the spectra from mixing ratios of approximately 133:1 until 6:1 DNA phosphate: 3 is reached. The analogous data for poly [d(A-T) · d(A-T)] between mixing ratios 36:1 and 7:1 indicates a site size of 8.3 ± 1.1 bases and an equilibrium binding constant of (6.6 ± 3.3) × 10⁵ M^?1. Thus, 3 binds preferentially to poly [d(G-C) · d(G-C)] at these concentrations. © 1994 John Wiley & Sons, Inc.     

The conformation of polycytidylic acid, polyguanylic acid, polyinosinic acid, and their helical complexes in aqueous solution from laser Raman scattering

The Raman spectra of the double helical complexes of poly C–poly G and poly I–poly C at neutral p^H are presented and compared with the spectra of the constituent homopolymers. When a completely double-helical structure is formed in solution a strong sharp band at 810–814 cm^?1 appears which has previously been shown to be due to the A-type conformation of the sugar–phosphate backbone chain. By taking the ratio of the intensity of the 810–814 cm^?1 band to the intensity of the 1090–1100 cm^?1 phosphate vibration, one can obtain an estimate of the fraction of the backbone chain in the A-type conformation for both double-stranded helices and self-stacked single chains. This type of information can apparently only be obtained by Raman spectroscopy. In addition, other significant changes in Raman intensities and frequencies have been observed and tabulated: (1) the Raman intensity of certain of the ring vibrations of guanine and hypoxanthine bases decrease as these bases become increasingly stacked (Raman hypochromism), (2) the Raman band at 1464 cm^?1 in poly I is asigned to the amide II band of the cis-amide group of the hypoxanthine base. It shifts in frequency upon base pairing to 1484 cm^?1, thus permitting the determination of the fraction of I–C pairs formed.     

Structural investigation of poly d(BrU-A) by ultraviolet resonance raman spectroscopy

The resonance Raman spectra of a DNA containing bromodeoxy-uridine (BrdUrd), the poly d(BrU-A), are reported, using U.V. laser as a source of excitation. The conformational change from the ordered, base paired form of poly d(BrU-A) (at 25°C) to the melted form at high temperature (63°C) is reflected in a pronounced hyperchromism of Raman bands at 1627 cm^?1, 1352 cm^?1 and 1230 cm^?1. Particularly the band at 1627 cm^?1 assigned to the vibrations of C4 carbonyl which is hydrogen bonded to adenine increases strongly its intensity upon melting. This represents a new approach for a detection of base unpairing and of modifications in geometry of selective molecules (BrdUrd) in a DNA chain in dilute solutions (10^?4 M).     

Raman studies of nucleic acids. VII. Poly A-poly U and poly G-poly C

Laser-excited Raman spectra of the double-helical complexes poly A·poly U and poly G·poly C are reported for ²H₂O and H₂O solutions. The spectra are discussed in relation to their use as quantitative reference spectra for determining the dependence of the Raman scattering of RNA on secondary structure. The Raman line at 815 cm^?1, due to the phosphodiester group, exhibits the same intrinsic intensity in spectra of poly A·poly U and poly G·poly C and is thus dependent only upon the amount of ordering of the helix and not on the kinds of nucleotides involved. The hypochromic Raman lines in spectra of poly A·poly U are identified and their intensity changes are determined quantitatively over the temperature range 32–85°C. Comparison of the spectra in the 1500–1750 cm^?1 region reveals that the Raman lines from carbonyl group vibrations of uracil are about sevenfold more intense than those of guanine and cytosine for both paired and unpaired states and will thus dominate the spectra of RNA. The Raman frequencies in this region are also compared with previously reported infrared frequencies and give evidence of being strongly perturbed by base-stacking interactions in the helices.     

The vibrational spectra and structure of poly(rA-rU)-poly(rA-rU)

Infrared and Raman spectra of aqueous poly(rA-rU)·poly(rA-rU), the double-helical complex containing strands of alternating riboadenylate and ribouridylate residues, display significant differences from one another and from corresponding spectra of poly(rA)·poly(rU), the double-helical complex of riboadenylate and ribouridylate homopolymers. Parallel studies on the copolymer and homopolymer complexes by cesium sulfate density gradient centrifugation, ultraviolet absorption spectroscopy, hydrogenion titration, 1-N oxidation of adenine residues by monoperphthalic acid and X-ray diffraction reveal, however, that the geometry of base pairing between adenine and uracil is closely similar in each complex and apparently of the Watson-Crick type. Therefore the differences observed between vibrational spectra of poly (rA-rU)·poly (rA-rU) and poly(rA)·poly(rU) are not due to different base-pairing schemes but may be attributed to differences in vibrational coupling between vertically stacked bases. Vibrational coupling may also account for the differences between infrared and Raman spectra of the same complex. Thus, the present results indicate that infrared and Raman frequencies of RNA in the region 1750–1550 cm^?1 should be dependent on the base sequence.     

Calculated Frequency Spectrum of Z-form poly(dG-dC)·poly(dG-dC)

Abstract

The calculated phonon spectrum of Z-form poly(dG-dC)·poly(dG-dC) between 400 and 1600 cm^?1 is reported. Comparison with the available data shows the very good agreement between theory and experiment. The eigenvector displacement is used to assign the characteristics of some of the important modes.     

Proton-NMR study of the interaction of trans-dichloro-diamine-platinum(II) with poly(I) and poly(I).poly(C)

The fixation of trans-(NH₃)₂Cl₂ Pt(II) to poly(I)·poly(C) at low r_b (< 0.05) leads to the formation of two complexed species. The major species (ca. 82% of bound platinum) involves coordination of platinum to a single hypoxanthine base, while the other species involves coordination of two hypoxanthine bases, which are either far apart on the same strand or on separate poly(I) strands, to the platinum. These same two species are found after reaction with poly(I), as are two other species throughout the entire r_b range studied (r_b = 0–0.30). The latter two species are assigned to trans-Pt bound to two bases on a poly(I) strand with (a) one or (b) two free bases between the two bound bases. These two species, (a) and (b), account for ca. 35% of the bound platinum, although the 1:1 species remains dominant (ca. 55%). These two additional species are observed at high r_b (>0.075) after reaction with poly(I)·poly(C) but as very minor species. They are formed by reaction with melted poly(I) loops. Also at high r_b, we have observed a shifted cytidine H⁵ resonance arising from interaction of trans-Pt with a melted loop of poly(C). Most probably, this arises from an intramolecular poly(I) to poly(C) crosslink. Results from the reaction of trans-Pt with poly(C) are presented for comparison.     

Conformational properties of poly[d(G-T)].poly[d(C-A)] and poly[d(A-T)] in low- and high-salt solutions: NMR and laser Raman analysis

³¹P- and ¹H-nmr and laser Raman spectra have been obtained for poly[d(G-T)]·[d(C-A)] and poly[d(A-T)] as a function of both temperature and salt. The ³¹P spectrum of poly[d(G-T)]·[d(C-A)] appears as a quadruplet whose resonances undergo separation upon addition of CsCl to 5.5M. ¹H-nmr measurements are assigned and reported as a function of temperature and CsCl concentration. One dimensional nuclear Overhauser effect (NOE) difference spectra are also reported for poly[d(G-T)]·[d(C-A)] at low salt. NOE enhancements between the H8 protons of the purines and the C5 protons of the pyrimidines, (H and CH₃) and between the base and H-2′,2″ protons indicate a right-handed B-DNA conformation for this polymer. The NOE patterns for the TH3 and GH1 protons in H₂O indicate a Watson–Crick hydrogen-bonding scheme. At high CsCl concentrations there are upfield shifts for selected sugar protons and the AH2 proton. In addition, laser Raman spectra for poly[d(A-T)] and poly[d(G-T)]·[d(C-A)] indicate B-type conformations in low and high CsCl, with predominantly C2′-endo sugar conformations for both polymers. Also, changes in base-ring vibrations indicate that Cs⁺ binds to O2 of thymine and possibly N3 of adenine in poly[d(G-T)]·[d(C-A)] but not in poly[d(A-T)]. Further, ¹H measurements are reported for poly[d(A-T)] as a function of temperature in high CsCl concentrations. On going to high CsCl there are selective upfield shifts, with the most dramatic being observed for TH1′. At high temperature some of the protons undergo severe changes in linewidths. Those protons that undergo the largest upfield shifts also undergo the most dramatic changes in linewidths. In particular TH1′, TCH₃, AH1′, AH2, and TH6 all undergo large changes in linewidths, whereas AH8 and all the H-2′,2″ protons remain essentially constant. The maximum linewidth occurs at the same temperature for all protons (65°C). This transition does not occur for d(G-T)·d(C-A) at 65°C or at any other temperature studied. These changes are cooperative in nature and can be rationalized as a temperature-induced equilibrium between bound and unbound Cs⁺, with duplex and single-stranded DNA. NOE measurements for poly[d(A-T)] indicate that at high Cs⁺ the polymer is in a right-handed B-conformation. Assignments and NOE effects for the low-salt ¹H spectra of poly[d(A-T)] agree with those of Assa-Munt and Kearns [(1984) Biochemistry 23 , 791–796] and provide a basis for analysis of the high Cs⁺ spectra. These results indicate that both polymers adopt a B-type conformation in both low and high salt. However, a significant variation is the ability of the phosphate backbone to adopt a repeat dependent upon the base sequence. This feature is common to poly[d(G-T)]·[d(C-A)], poly[d(A-T)], and some other pyr–pur polymers [J. S. Cohen, J. B. Wouten & C. L Chatterjee (1981) Biochemistry 20 , 3049–3055] but not poly[d(G-C)].     

N-2-acetylaminofluorene modification of poly(dG-m5dC)·poly(dG-m5dC) induces the Z-DNA conformation

Poly(dG-m⁵dC)·poly(dG-m⁵dC) was modified by treatment with N-acetoxy-N-2-acetylaminofluorene (N-Aco-AAF) and its conformation examined by circular dichroism (CD) and susceptibility to S₁ nuclease digestion. A sample with a modification level of 10% shows a CD spectrum characteristic of the Z form and is resistant to digestion by S₁ nuclease. The relative reactivity of several polymers with N-Aco-AAF was shown to follow the order of ease of formation of Z DNA: poly(dG-m⁵dC)·poly(dG-m⁵dC) > poly(dG-dC)·poly(dG-dC) > poly(dG)·poly(dC). This suggests that AAF reacts more readily with Z DNA than B DNA.     

Interaction of poly(I) and poly(I)·poly(C) with chlorodiethylenetriamino platinum(II) chloride

The fixation of dien-Pt on poly(I)·poly(C) leads to only minor changes in the uv and CD spectra at ambient temperature, showing that there is little perturbation of the secondary structure in the r_b range studied (up to 0.30). However, the melting profiles show two steps. The T_m for strand separation increases linearly from 61°C (r_b = 0) to 80°C (r_b = 0.18), after which it declines on further increasing the r_b. The second melting step is not complete at 100°C, and the magnitude of the absorbance change in this second step also appears to be at a maximum at r_b = 0.18. Although dien-Pt can only coordinate to one base, the nmr spectra at 80°C also show a second type of interaction with the adjacent bases, which is only destroyed in the presence of a strong denaturing agent, 5M guanidinium hydrochloride. From these results and the spectrophotometric data, we observe that dien-Pt forms a triple sandwich by hydrogen bonding of the platinum amino groups to the adjacent hypoxanthine bases (N⁷). The presence of these hydrogen bonds accounts for the increased stability (maximal at one Pt to three hypoxanthine bases) and their rupture is seen in the second melting step. No interaction has been observed with poly(C) strand. Reaction of dien-Pt with poly(I) shows the formation of the same triple sandwich structure in the nmr spectra.     

A vibrational spectroscopic study of the self-association of polyinosinic acid and polyguanylic acid in aqueous solution

We have studied by Raman and ir spectroscopy the structure of self-associated polyinosinic acid and polyguanylic acid in aqueous solution. The results are consistent with the formation of a four-stranded complex, which melts cooperatively near 60°C in the case of poly (I) in the presence of K⁺ ions. The conformation of the ribose in both systems is mixed C2′-endo/C3′-endo, giving a structure that is intermediate between the extremes proposed previously from x-ray diffraction studies. Characteristic Raman bands for the C2′-endo ribose conformation in polyribonucleotides are identified. The four-stranded structure of poly (I) appears to be very flexible, with ≈15% of the tetrameric segments being disrupted and ≈30% of the ribose units adopting a disordered conformation prior to melting. This disordering process increases to ≈75% above the melting transition, with the remaining ≈25% of the ribose units keeping an ordered C2′-endo or C3′-endo conformation. © 1994 John Wiley & Sons, Inc.     

Fluctuations and mechanical strength of α-helices of polyglycine and poly(L-alanine)

By using the static correlations of fluctuations in the dihedral angles of the α-helices of polyglycine and poly(L -alanine) calculated previously, geometrical fluctuations of a section (consisting of up to 18 peptide units) of the α-helices of infinite length are calculated. These fluctuations are found to differ in some respects (e.g., the dependence of amplitudes on the length of section) from those of a circular rod made of homogeneous continuous material. However, the moduli of the mechanical strengths (tensile Young's modulus, bending Young's modulus, and the shear modulus) of a circular rod are calculated, whose geometrical fluctuations are approximately equal to the fluctuations of a section consisting of 18 peptide units. They are of the order of 10¹¹ dyn/cm². The tensile rigidity, flexural rigidity, and torsional rigidity are calculated to be 1.20 × 10^?3 dyn, 2.46 × 10^?19 dyn·cm² and 1.79 × 10^?19 dyn·cm² for polyglycine, and 1.96 × 10^?3 dyn, 4.05 × 10^?19 dyn·cm² and 3.28 × 10^?19 dyn·cm² for poly(L -alanine), respectively.