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 spectra and crystal structure of the di-amino acid peptide cyclo(L-Met-L-Met): Comparison of experimental data and DFT calculations

Experimental Raman and FT-IR spectra of solid-state non-deuterated and N-deuterated samples of cyclo(L-Met-L-Met) are reported and discussed. The Raman and FT-IR results show characteristic amide I vibrations (Raman: 1649 cm-1, infrared: 1675 cm-1) for molecules exhibiting a cis amide conformation. A Raman band, assigned to the cis amide II vibrational mode, is observed at sim1493 cm-1 but no IR band is observed in this region. Cyclo(L-Met-L-Met) crystallises in the triclinic space group P1 with one molecule per unit cell. The overall shape of the diketopiperazine (DKP) ring displays a (slightly distorted) boat conformation. The crystal packing employs two strong hydrogen bonds, which traverse the entire crystal via translational repeats. B3-LYP/cc-pVDZ calculations of the structure of the molecule predict a boat conformation for the DKP ring, in agreement with the experimentally determined X-ray structure. Copyright © 2009 John Wiley & Sons, Ltd.

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.

On information rates of time-varying fading channels modeled as finite-state Markov channels

We study information rates of time-varying flat-fading channels (FFC) modeled as finite-state Markov channels (FSMC). FSMCs have two main applications for FFCs: modeling channel error bursts and decoding at the receiver. Our main finding in the first application is that receiver observation noise can more adversely affect higher-order FSMCs than lower-order FSMCs, resulting in lower capacities. This is despite the fact that the underlying higher-order FFC and its corresponding FSMC are more predictable. Numerical analysis shows that at low to medium SNR conditions (SNR lsim 12 dB) and at medium to fast normalized fading rates (0.01 lsim fDT lsim 0.10), FSMC information rates are non-increasing functions of memory order. We conclude that BERs obtained by low-order FSMC modeling can provide optimistic results. To explain the capacity behavior, we present a methodology that enables analytical comparison of FSMC capacities with different memory orders. We establish sufficient conditions that predict higher/lower capacity of a reduced-order FSMC, compared to its original high-order FSMC counterpart. Finally, we investigate the achievable information rates in FSMC-based receivers for FFCs. We observe that high-order FSMC modeling at the receiver side results in a negligible information rate increase for normalized fading rates fDT lsim 0.01.

Positive dilations of piecewise monotonic Markov maps

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.

Dioxygenase-catalysed mono-, di- and tri-oxygenation of dialkyl sulfides and thioacetals: chemoenzymatic synthesis of enantiopure cis-diol sulfoxides

Toluene dioxygenase (TDO)-catalysed monooxygenation of methylsulfanylmethyl phenyl sulfide 1 and methylsulfanylmethyl 2-pyridyl sulfide 4, using whole cells of Pseudomonas putida UV4, occurred exclusively at the alkyl aryl sulfur centre to yield the alkyl aryl sulfoxides 2 and 5 respectively. These sulfoxides, accompanied by the dialkyl sulfoxides 3 and 6, were also obtained from naphthalene dioxygenase (NDO)-catalysed sulfoxidation of thioacetals 1 and 4 using intact cells of P. putida NCIMB 8859. Enzymatic oxidation of methyl benzyl sulfide 7, 2-phenyl-1,3-dithiane 19, and 2-phenyl-1,3-dithiolane 23, using TDO, gave the corresponding dialkyl sulfoxides 8, 20 and 24 as minor bioproducts. TDO-catalysed dioxygenation of the alkyl benzyl sulfides 7, 15 and 17 and the thioacetals 19 and 23, with P. putida UV4, yielded the corresponding enantiopure cis-dihydrodiols 9, 16, 18, 21 and 25 as major metabolites and cis-dihydrodiol sulfoxides 14, 22 and 26 as minor metabolites, resulting from a tandem trioxygenation of substrates 7, 19 and 23 respectively. Chemical oxidation, of the enantiopure cis-dihydrodiol sulfides 9, 16, 18 and 21 with dimethyldioxirane (DMD), gave separable mixtures of the corresponding pairs of cis-dihydrodiol sulfoxide diastereoisomers 14 and 27, 28 and 29, 30 and 31, 22 and 32. While dialkyl sulfoxide bioproducts 3, 6, 20 and 24 were of variable enantiopurity (27-greater than or equal to 98% ee), alkyl aryl monosulfoxides 2 and 5, cis-dihydrodiols 9, 16, 18, 21 and 25 and cis-dihydrodiol sulfoxide bioproducts 14, 22 and 26 were all single enantiomers (greater than or equal to 98% ee). The absolute configurations of the products, obtained from enzyme-catalysed (TDO and NDO) and chemical (DMD) oxidation methods, were determined by stereochemical correlation, circular dichroism, and X-ray crystallographic methods.