Small-amplitude protein conformational dynamics: Second-order analytic relation between cartesian coordinates and dihedral angles

An analytic expression for protein atomic displacements in Cartesian coordinate space (CCS) against small changes in dihedral angles is derived. To study time-dependent dynamics of a native protein molecule in CCS from dynamics in the internal coordinate space (ICS), it is necessary to convert small changes of internal coordinate variables to Cartesian coordinate variables. When we are interested in molecular motion, six degrees of freedom for translational and rotational motion of the molecule must be eliminated in this conversion, and this conversion is achieved by requiring the Eckart condition to hold. In this article, only dihedral angles are treated as independent internal variables (i.e., bond angles and bond lengths are fixed), and Cartesian coordinates of atoms are given analytically by a second-order Taylor expansion in terms of small deviations of variable dihedral angles. Coefficients of the first-order terms are collected in the K matrix obtained previously by Noguti and Go (1983) (see ref. 2). Coefficients of the second-order terms, which are for the first time derived here, are associated with the (newly termed) L matrix. The effect of including the resulting quadratic terms is compared against the precise numerical treatment using the Eckart condition. A normal mode analysis (NMA) in the dihedral angle space (DAS) of the protein bovine pancreatic trypsin inhibitor (BPTI) has been performed to calculate shift of mean atomic positions and mean square fluctuations around the mean positions. The analysis shows that the second-order terms involving the L matrix have significant contributions to atomic fluctuations at room temperature. This indicates that NMA in CCS involves significant errors when applied for such large molecules as proteins. These errors can be avoided by carrying out NMA in DAS and by considering terms up to second order in the conversion of atomic motion from DAS to CCS. © 1995 by John Wiley & Sons, Inc.     

Second-order spectrum of water in the K4Fe(CN)6.3H2O crystal

Second-order infrared spectra of the crystal K₄Fe(CN)₆.3H₂O are obtained in the region of 3700–7200 cm^?1 at 90 K. The bands corresponding to overtones and combinations of the stretching and bending modes of the different water molecules are discussed and interpreted. The anharmonicity constants are estimated using the observed frequencies.     

IR spectra of long-chain α,ω-alkanediols: 1,22-docosanediol and 1,44-tetratetracontanediol

The IR absorption spectra of α,ω-alkanediols with different chain lengths, HO(CH₂)₂₂OH and HO(CH₂)₄₄OH, in the spectral range of 400–5000 cm^?1 are analyzed. The assignment of numerous absorption bands to vibration modes in short methylene sequences and terminal hydroxyl groups is suggested. The splitting of IR absorption bands into doublets at 720–730 cm^?1 (rocking vibrations of CH₂ groups) and 1463–1473 cm^?1 (bending vibrations of CH₂ groups) testifies that the crystal unit subcells in the lamellae of alkanediols are orthorhombic with parameters typical of normal hydrocarbons. The specific features of absorption bands due to O-H stretching and C-O-H bending vibrations have been analyzed. These bands appear during formation of lengthy associates from hydrogen bonds formed by hydroxyl groups on the surface of elementary lamellae. A sharp increase in the intensity of the absorption bands in progression of C-C stretching and CH₂ wagging vibrations due to the anharmonic Fermi resonance with the stretching vibrations of C-O groups in the terminal hydroxyl groups has been detected.     

Infrared and raman spectroscopy of stressed polyethylene

Polyethylene films were stressed in uniaxial tension at room temperature while the infrared (FTIR) or Raman spectra were simultaneously measured. The purpose of these experiments was to gain an understanding of the molecular origins of the stress-induced vibrational frequency shifts Δν and determine the mechanisms of molecular deformation and fracture of PE molecules with stress σ. The PE samples consisted of ultradrawn, high-density, ultrahigh-molecular-weight, solid-state-extruded films and the stress was applied parallel to the nearly perfectly oriented orthorhombic crystal c-axis direction. The experimental frequency shifting coefficients α = (?ν/?σ)_σ→0 were compared with calculated α values determined from a vibrational analysis of an isolated PE chain using conformational energy minimization methods in which both harmonic and anharmonic (Morse) potential energy functions were used for the C? C stretching modes in the valence force field. The following α values were obtained and are compared with theory (anharmonic case in parentheses, in cm^?1/GPa): C? C symmetric stretch, α(1127) = ?5.9 (?5.3); CC asymmetric stretch, α(1059) = ?11.2 to ?5.7 (?5.8); CH₂ rock, α(730/720) = ?2.0 to ?3.0 (?2.2); CH₂ scissors, α(1472/1462) = ?1.0 to ?1.2 (?1.1); CH₂ twist, α(1295) ? 0(0.8); CH₂ wag, α(1370) undetermined owing to weak bands (?4.6); CH₂ stretch α(3000) ≈ 0. The largest negative frequency shifts were observed for the C? C stretching modes, in agreement with the calculations using the Morse potential. The harmonic potential for C? C stretching resulted in small positive α values for both the CC stretching and CH₂ wagging modes, while the other modes were unaffected by this choice of potential. The relative contribution of C? C bond stretching and C?C valence angle bending to the c-axis strain was about 1:1, in agreement with experiment. The Young's tensile modulus of a PE chain was calculated as E_c = 267 GPa.     

On vibrational bonding of IHI

The vibrational bond of IHI is described in analogy to the covalent bond of H₂⁺ by a Born—Oppenheimer-type separation of light (“hydrogenic” ≡ “electronic”) and heavy (“iodines” ≡ “protons”) particle degrees of freedom. Competing potential energy decreases and hydrogen zero-point energy increases (for the IHI antisymmetric stretching and bending modes) yield a minimum in the iodine symmetric stretching mode's potential energy which supports one bound vibrational IHI state.     

Far infrared spectra between 4 and 200 cm−1 of poly-l-alanine

The far infrared absorption spectrum of α-helical poly-L-alanine is measured between 4 and 200 cm^?1. Two predicted infrared active longitudinal acoustic modes of the α-helix are not observed, and this result is explained in terms of intermolecular interactions.     

Structure and molecular conformation of tussah silk fibroin films: Effect of methanol

Structural changes of tussah (Antheraea pernyi) silk fibroin films treated with different water-methanol solutions at 20°C were studied as a function of methanol concentration and immersion time. X-ray diffraction measurements showed that the α-helix structure, typical of untreated tussah films, did not change for short immersion times (2 min), regardless of methanol concentration. However, crystallization to β-sheet structure was observed following immersion of tussah films for 30 min in methanol solutions ranging from 20 to 60% (v/v). IR spectra of tussah films untreated and methanol treated for 2 min exhibited strong absorption bands at 1265, 892, and 622 cm^?1, typical of the α-helix conformation. The intensity of the bands assigned to the β-sheet conformation (1245, 965, and 698 cm^?1) increased for the sample treated with 40% methanol for 30 min. Raman spectra of tussah films with α-helix molecular conformation exhibited strong bands at 1657 (amide I), 1263 (amide III), 1106, 908, 530, and 376 cm^?1. Following α → β conformational transition, amide I and III bands shifted to 1668, and to 1241, 1230 cm^?1, respectively. The band at 1106 cm^?1 disappeared and new bands appeared at 1095 and 1073 cm^?1, whereas the intensity of the bands at 530 and 376 cm^?1 decreased significantly. ©1995 John Wiley & Sons, Inc.     

Vibrational analysis of l-alanine and deuterated analogs

Raman spectra of the polycrystalline l-alanine analogs CH₃CH(NH⁺₃)COO^?, CH₃CH(ND⁺₃)-COO^?, CD₃CD(NH⁺₃)COO^?, and CD₃CD(ND⁺₃)COO^? have been obtained. A normal coordinate analysis is carried out based on the experimental frequencies of the four isotopic analogs and a 34 parameter valence-type force field defined in terms of local symmetry coordinates. The final refinement, in which five stretching force constants are constrained to fixed values obtained from bond length data, results in an average error of 7 cm^?1 (0.9%) for the observed frequencies of the four isotopically substituted molecules. Band assignments are given in terms of the potential energy distribution for local symmetry coordinates. For non-deuterated l-alanine, the vibrations above 1420 cm^?1 and below 950 cm^?1 may be described as localized group vibrations. By contrast, the eight modes in the middle frequency range, viz. the three skeletal stretching, the COO^? symmetric stretching, one NH⁺₃ rocking, the symmetric CH₃ deformation, and the two methyne CH deformation vibrations, are very strongly coupled to one another. Some decoupling appears to take place in the perdeutero molecule, and all but five modes can be described as localized group vibrations.     

CN stretching and NO2 deformation vibrations and normal coordinate analysis of m-dinitrobenzene and m-dinitrobenzene-d4

Two bands appear for each CN stretching and nitro deformation vibration in the infrared and Raman spectra of m-dinitrobenzene and m-dinitrobenzene-d₄. The 907 cm^?1 bending mode in the vibrational spectra of m-dinitrobenzene undergo 30 cm^?1 upward shift upon d₄ substitution. A normal coordinate analysis pointed out that the 937 cm^?1 bending and 727 cm^?1 CN stretching vibrations as well as 18b CD in-plane deformation are mixed to a great extent. The other nitro bending mode undergo also an inverse isotopic effect (2 cm^?1 upward shift) due to coupling with the 18a CD in-plane deformation vibration.     

Internal rotation and framework relaxation in ethene thiol

New and existing data on the ground and excited CS torsional states of the stable rotamers of ethene thiol have been analysed to give a potential function for internal rotation around the CS bond. The barrier between the syn and anti rotamers is found to be 800 cm^?1 and that at the planar anti conformation itself to be 12 cm^?1. the syn conformation is 50 cm^?2 more stable than the ‘quasi-planar’ anti conformation Satisfactory reproduction of the observed trends in rotational constants with torsional excitations has been achieved by introducing extensive relaxation of the CCS angle and the CS bond length during internal rotation. The CCS angle reduces by up to 5° v'hilst the CS bond length increases by up to 0.02 A during rotation from the syn to anti conformation. The use of ab initio M.O. calculations to provide an indication of the most significant aspects of structure relaxation is described.     

The vibrational spectra and stability of dipyrrolylmethene hydrobromides and their oxa and thia derivatives

This paper presents the IR spectra of solid alkyl substituted α,α-, α,β-, and β,β-dipyrrolylmethene hydrobromides and their oxa and thia derivatives recorded in KBr pellets over the frequency range 400–4000 cm^?1. The conclusion was drawn that the NH bonds in the pyrrole fragments of α,α-dipyrrolylmethene were identical, as distinct from the α,β and β,β isomers. The influence of functional substitution in the dipyrrolylmethene molecule on the frequencies of NH stretching vibrations was discussed. A satisfactory correlation between NH bond vibrational frequencies and the enthalpies of vaporization of gaseous hydrogen bromide from crystalline samples under heating was observed. This allows the IR data to be used as a criterion of the stability of dipyrrolylmethene salts and their oxa and thia derivatives.     

Infrared and Raman spectroscopic characterization of the phosphate mineral kosnarite KZr2(PO4)3 in comparison with other pegmatitic phosphates

In this research, we have used vibrational spectroscopy to study the phosphate mineral kosnarite KZr₂(PO₄)₃. Interest in this mineral rests with the ability of zirconium phosphates (ZP) to lock in radioactive elements. ZP have the capacity to concentrate and immobilize the actinide fraction of radioactive phases in homogeneous zirconium phosphate phases. The Raman spectrum of kosnarite is characterized by a very intense band at 1,026?cm^?1 assigned to the symmetric stretching vibration of the PO₄ ^3? ??₁ symmetric stretching vibration. The series of bands at 561, 595 and 638?cm^?1 are assigned to the ??₄ out-of-plane bending modes of the PO₄ ^3? units. The intense band at 437?cm^?1 with other bands of lower wavenumber at 387, 405 and 421?cm^?1 is assigned to the ??₂ in-plane bending modes of the PO₄ ^3? units. The number of bands in the antisymmetric stretching region supports the concept that the symmetry of the phosphate anion in the kosnarite structure is preserved. The width of the infrared spectral profile and its complexity in contrast to the well-resolved Raman spectrum show that the pegmatitic phosphates are better studied with Raman spectroscopy.     

Mechanisms of frequency shifting in the infrared spectrum of stressed polymer

In the vibrational spectrum of a polymer obtained under tensile stress loading conditions, several modes of molecular deformation can lead to different mechanisms of frequency shifting and asymmetric band deformation. Theoretically and experimentally it has been observed that quasielastic deformations (reduction of force constants due to bond weakening under stress), pure elastic bond stretching and angle bending, conformational variations, and several types of chain defects can cause linear shifts in frequency and infrared band distortion. A detailed study of the deformation spectra of isotactic polypropylene and polyphenyl-p-sulfide indicated that quasielastic and elastic mechanisms are the major contributors to frequency shifting, principally affecting stretching and bending vibrational modes. Conformational mechanisms can affect torsional modes whereas the defect mechanism, when present, can cause random distortion of an infrared band. The latter mechanism is difficult to quantize. The extent to which each mechanism contributes to the total spectral deformation can be a function of morphology, macroscopic loading conditions, thermal and strain histories.     

Vibrational properties of the gallium monohydrides SrGaGeH, BaGaSiH, BaGaGeH, and BaGaSnH

Vibrational properties of the gallium monohydrides SrGaGeH, BaGaSiH, BaGaGeH, and BaGaSnH (AeGaTtH) have been investigated by means of inelastic neutron scattering (INS) and first principles calculations. The compounds contain separated Ga–H units being part of a two dimensional polyanionic layer, [TtGaH]²⁻ (Tt=Si, Ge, Sn). The INS spectra show internal Ga–H bending and stretching modes at frequencies around 900 and 1200 cm⁻¹, respectively. While the stretching mode is virtually invariant with respect to the variable chemical environment of the Ga–H unit, the bending mode frequency varies and is highest for BaGaSiH and lowest for BaGaSnH. The stretching mode is a direct measure of the Ga–H bond strength, whereas the bending mode reflects indirectly the strength of alkaline earth metal–hydrogen interaction. Accordingly, the terminal Ga–H bond in solid state AeGaTtH is distinct, but—compared to molecular gallium hydrides—very weak.     

Vibrational studies,barrier height and thermodynamic functions for biomolecules: 5-Trifluoromethyl uracil

Laser Raman (50–4000 cm⁻¹) and IR (200–4000 cm⁻¹) spectra of 5-trifluoromethyl uracil have been recorded and analysed. It has been possible to assign all the 39 (26a′+13a″) normal modes of vibration. Consistent assignments have been made for the internal modes of the CF₃ group, especially for the antisymmetric CF₃ stretching and bending modes. Using thus assigned vibrational frequencies and assumed structural parameters, thermodynamic functions, in the temperature range 100–1000 K, have been computed and the barrier to the internal rotation for the CF₃ top has been determined.     

Hydrogen bonding: VII. Low temperature infrared spectral studies of potassium dihydrogen trifluoride,trihydrogen tetrafluoride,and tetrahydrogen pentafluoride; structure of the H3F−4 ION

We have recorded the infrared spectra of crystalline K⁺H₂F₃^?, K⁺H₃F₄^?, and K⁺H₄F₅^? at room temperature and 12–18 K. The broad (4̃00 cm^?1) anion F-H stretching bands for these three salts are not resolved at low temperature; however, in each case the F-H-F bending region is resolved into the maximum number of bands predicted by theory. The complexity of the F-H-F bending mode region shows the H₄F₅^? ion to be of lower symmetry than predicted by X-ray studies. The H₃F₄^? ion has three hydrogen fluorides hydrogen bonded to a central fluoride ion, rather than a chain type structure. The F-H stretching bands for the three ions have very similar frequencies (1750–1800 cm^?1), which shows the hydrogen bonds in the three ions to be of about the same strength, and to be significantly weaker than the hydrogen bond in the HF₂^? ion.     

Energy and angular differential cross sections for K + NO2 charge transfer reactions

Doubly differential cross sections, in energy and angle, are reported for the electron transfer reaction between potassium and nitrogen dioxide in a crossed beam apparatus at relative collision energies between 2.7 and 30.8 eV. The formation of NO^?₂ in its ground ¹A₁ and excited ³B₁ state has been observed. Theoretical consideration of these processes indicates that bond bending during the collision has a stronger influence on ion-pair formation than bond stretching. At the lower collision energies most of the excess energy is converted into internal energy of NO^?₂.     

The vibrational spectra of complexes of norbornadiene with some group VIII metals

The infrared and Raman spectra of norbornadiene complexes of Pd, Pt, Rh and Fe have been studied. An assignment of the normal modes is given and the ligand vibrations in the complex are compared with those for “free” norbornadiene. The ν(CC) stretching frequency of coordinated norbornadiene is from 1575 cm^?1 to over 1400 cm^?1.The strength of the metal—ligand bond increases in the series Pd < Pt < Rh and for halogen complexes in the series chloride < bromide < iodide. ESCA spectroscopy data obtained are in agreement with these conclusions.     

Studies of Low-Frequency Molecular Motions in Polymers by Neutron Inelastic Scattering

Abstract

The energy distribution of a monoenergetic incident neutron beam after a single scattering event provides information concerning the molecular motions of a polymer in the region 800 to 30 cm^?1. In polyethylene (Marlex 6050) several peaks are observed in the neutron spectrum between 200 and 600 cm^?1. The frequencies corresponding to these peaks are in good agreement with those predicted from a calculation of the dispersion relations of the skeletal modes (bending and stretching) taking into account interchain forces. In the case of an oriented sample of the polymer, a polarization effect can be obtained by placing the momentum transfer K of the neutron parallel or perpendicular to the chain direction S. This allows the identification of transverse and longitudinal modes of vibration. This effect has been studied in the case of polyethylene and polyoxymethylene. The frequency distribution of phonons, derived from the neutron data under certain approximations, were also obtained from samples of polyoxymethylene, polyacrylonitrile, and polyethylene glycol. These results are compared with the observed infrared and the calculated frequencies.     

Infrared spectroscopy of ethylene–vinyl chloride copolymers

This paper continues an investigation into the ethylene–vinyl chloride copolymers prepared by partial reduction of poly(vinyl chloride). The infrared spectra of the copolymers have been obtained and the individual resonances assigned. Each infrared band has been quantitatively analyzed in terms of peak position (cm^?1) and intensity, and correlations with the sequence microstructure (dyad, triads, etc.) have been determined. The infrared resonances have been found to be sensitive to long sequences; i.e., (V)_x or (E)_x where x ≥ 10. Sequences of up to 10–15 monomer units were seen to affect the position (cm^?1) and intensity of C? H stretching and bending frequencies. Methylene rocking bands between 850 and 700 cm^?1 were observed to be sequence dependent with ? V(E)_xV? resonanting at 860, 750, or 730 cm^?1 for x = 0, 1 and 2, or ≥3, respectively. The C? Cl stretching resonances, which are well known for their conformational complexity in pure PVC, were found to be dominated by sequence length effects reducing to two bands at 665 and 610 cm^?1 characteristic of and isolated ? CH? Cl unit in a long methylene chain.