Vibrational spectroscopic studies of the structure of di-amino acid peptides. Part II: cyclo(L-Asp-L-Asp) in the solid state and in aqueous solution

Solid-state protonated and N,O-deuterated Fourier transform infrared (IR) and Raman scattering spectra together with the protonated and deuterated Raman spectra in aqueous solution of the cyclic di-amino acid peptide cyclo(L-Asp-L-Asp) are reported. Vibrational band assignments have been made on the basis of comparisons with previously cited literature values for diketopiperazine (DKP) derivatives and normal coordinate analyses for both the protonated and deuterated species based upon DFT calculations at the B3-LYP/cc-pVDZ level of the isolated molecule in the gas phase. The calculated minimum energy structure for cyclo(L-Asp-L-Asp), assuming C-2 symmetry, predicts a boat conformation for the DKP ring with both the two L-aspartyl side chains being folded slightly above the ring. The C=O stretching vibrations have been assigned for the side-chain carboxylic acid group (e.g. at 1693 and 1670 cm(-1) in the Raman spectrum) and the cis amide I bands (e.g. at 1660 cm(-1) in the Raman spectrum). The presence of two bands for the carboxylic acid C=O stretching modes in the solid-state Raman spectrum can be accounted for by factor group splitting of the two nonequivalent molecules in a crystallographic unit cell. The cis amide II band is observed at 1489 cm(-1) in the solid-state Raman spectrum, which is in agreement with results for cyclic di-amino acid peptide molecules examined previously in the solid state, where the DKP ring adopts a boat conformation. Additionally, it also appears that as the molecular mass of the substituent on the C-alpha atom is increased, the amide II band wavenumber decreases to below 1500 cm(-1); this may be a consequence of increased strain on the DKP ring. The cis amide II Raman band is characterized by its relatively small deuterium shift (29 cm(-1)), which indicates that this band has a smaller N-H bending contribution than the trans amide II vibrational band observed for linear peptides.

A finite volume unstructured mesh approach to dynamic fluid-structure interaction: an assessment of the challenge of flutter analysis

Computational modelling of dynamic fluid-structure interaction (DFSI) is problematical since conventionally computational fluid dynamics (CFD) is solved using finite volume (FV) methods and computational structural mechanics (CSM) is based entirely on finite element (FE) methods. Hence, progress in modelling the emerging multi-physics problem of dynamic fluid-structure interaction in a consistent manner is frustrated and significant problems in computation convergence may be encountered in transferring and filtering data from one mesh and solution procedure to another, unless the fluid-structure coupling is either one way, very weak or both. This paper sets out the solution procedure for modelling the multi-physics dynamic fluid-structure interaction problem within a single software framework PHYSICA, using finite volume, unstructured mesh (FV-UM) procedures and will focus upon some of the problems and issues that have to be resolved for time accurate closely coupled dynamic fluid-structure flutter analysis.

A generic time and space accurate numerical approach to closely coupled fluid-structure interaction problems

Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, flow in elastic pipes and blood vessels and extrusion of metals through dies. However a comprehensive computational model of these multi-physics phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply even to the extent in metal forming, for example, that the deformation of the die is totally ignored. More recently, strategies for solving the full coupling between the fluid and soild mechanics behaviour have developed. Conventionally, the computational modelling of fluid structure interaction is problematical since computational fluid dynamics (CFD) is solved using finite volume (FV) methods and computational structural mechanics (CSM) is based entirely on finite element (FE) methods. In the past the concurrent, but rather disparate, development paths for the finite element and finite volume methods have resulted in numerical software tools for CFD and CSM that are different in almost every respect. Hence, progress is frustrated in modelling the emerging multi-physics problem of fluid structure interaction in a consistent manner. Unless the fluid-structure coupling is either one way, very weak or both, transferring and filtering data from one mesh and solution procedure to another may lead to significant problems in computational convergence. Using a novel three phase technique the full interaction between the fluid and the dynamic structural response are represented. The procedure is demonstrated on some challenging applications in complex three dimensional geometries involving aircraft flutter, metal forming and blood flow in arteries.

IR/Raman spectroscopy and DFT calculations of cyclic di-amino acid peptides. Part III: comparison of solid state and solution structures of cyclo(L-Ser-L-Ser)

B3-LYP/cc-pVDZ calculations of the gas-phase structure and vibrational spectra of the isolated molecule cyclo(L-Ser-L-Ser), a cyclic di-amino acid peptide (CDAP), were carried out by assuming C-2 symmetry. It is predicted that the minimum-energy structure is a boat conformation for the diketopiperazine (DKP) ring with both L-Beryl side chains being folded slightly above the ring. An additional structure of higher energy (15.16 kJ mol(-1)) has been calculated for a DKP ring with a planar geometry, although in this case two fundamental vibrations have been calculated with imaginary wavenumbers. The reported X-ray crystallographic structure of cyclo(L-Ser-L-Ser), shows that the DKP ring displays a near-planar conformation, with both the two L-Beryl side chains being folded above the ring. It is hypothesized that the crystal packing forces constrain the DKP ring in a planar conformation and it is probable that the lower energy boat conformation may prevail in the aqueous environment. Raman scattering and Fourier-transform infrared (FT-IR) spectra of solid state and aqueous solution samples of cyclo(L-Ser-L-Ser) are reported and discussed. Vibrational band assignments have been made on the basis of comparisons with the calculated vibrational spectra and band wavenumber shifts upon deuteration of labile protons. The experimental Raman and IR results for solid-state samples show characteristic amide I vibrations which are split (Raman:1661 and 1687 cm(-1), IR:1666 and 1680 cm(-1)), possibly due to interactions between molecules in a crystallographic unit cell. The cis amide I band is differentiated by its deuterium shift of ~ 30 cm(-1), which is larger than that previously reported for trans amide I deuterium shifts. A cis amide II mode has been assigned to a Raman band located at 1520 cm(-1). The occurrence of this cis amide II mode at a wavenumber above 1500 cm(-1) concurs with results of previously examined CDAP molecules with low molecular weight substituents on the C-alpha atoms, and is also indicative of a relatively unstrained DKP ring.

Vibrational spectroscopy and crystal structure analysis of two polymorphs of the di-amino acid peptide cyclo(L-Glu-L-Glu)

Cyclo(L-Glu-L-Glu) has been crystallised in two different polymorphic forms. Both polymorphs are monoclinic, but form 1 is in space group P21 and form 2 is in space group C2. Raman scattering and FT-IR spectroscopic studies have been conducted for the N,O-protonated and deuterated derivatives. Raman spectra of orientated single crystals, solid-state and aqueous solution samples have also been recorded. The different hydrogen-bonding patterns for the two polymorphs have the greatest effect on vibrational modes with N&bond;H and C&dbond;O stretching character. DFT (B3-LYP/cc-pVDZ) calculations of the isolated cyclo(L-Glu-L-Glu) molecule predict that the minimum energy structure, assuming C2 symmetry, has a boat conformation for the diketopiperazine ring with the two L-Glu side chains being folded above the ring. The calculated geometry is in good agreement with the X-ray crystallographic structures for both polymorphs. Normal coordinate analysis has facilitated the band assignments for the experimental vibrational spectra. Copyright © 2009 John Wiley & Sons, Ltd.