Tolerance graphs,and orders

We show that, if a tolerance graph is the complement of a comparability graph, it is a trapezoid graph, i.e., the complement of an order of interval dimension at most 2. As consequences we are able to give obstructions for the class of bounded tolerance graphs and to give an example of a graph that is alternatingly orientable but not a tolerance graph. We also characterize the tolerance graphs among complements of trees. © 1998 John Wiley & Sons, Inc. J. Graph Theory 28: 129–140, 1998     

Development and Validation of Analytical Methods for the Detection and Quantification of a Novel Dimeric Ceramide in Stratum Corneum and Other Layers of the Skin

Ceramides (CERs) are integral parts of the intercellular lipid lamellae of the stratum corneum (SC), which is responsible for the barrier function of the skin. Many skin diseases such as atopic dermatitis and psoriasis are associated with depletion or disturbance of the level of CERs in the SC. Administration of an exogenous novel dimeric ceramide (dCER) deep into the SC may help to stabilize the SC barrier substantially and to treat some skin disease conditions and with the help of the existing technology it might be possible to formulate various pharmaceutical dosage forms that can facilitate penetration of dCER into the SC. However, assessment of the rate and extent of permeability of the exogenous dCER involves appropriate analytical techniques which can discriminately quantify the exogenous dCER in the SC and in the other skin layers. Therefore, an attempt was made to develop an AMD-HPTLC and an HPLC/APCI-MS method for the detection and quantification of exogenous dCER in the SC as well as other skin layers. The method involved synthesis of the dCER and development of appropriate HPTLC and LC/ESI-MS methods for the separation and quantification of the dCER in the SC and deeper layers of the skin. The methods developed were optimized for quantification of a novel dCER. In comparison to the AMD-HPTLC method, the HPLC/MS method offers a higher sensitivity. Both methods could be used for the quantification of dCER in presence of a complex matrix (e.g., skin extract). The developed methods are complementary and could be used for the quantification of dCER in any further stage of substance research and industrial application. The methods developed are robust, linear and sensitive with a low limit of detection (LOD) and low limit of quantification (LOQ).

     

Chirality and Symmetry Breaking in a Discrete Internal Space

In previous papers the permutation group S ₄ has been suggested as an ordering scheme for quarks and leptons, and the appearance of this finite symmetry group was taken as indication for the existence of a discrete inner symmetry space underlying elementary particle interactions. Here it is pointed out that a more suitable choice than the tetrahedral group S ₄ is the pyritohedral group A ₄×Z ₂ because its vibrational spectrum exhibits exactly the mass multiplet structure of the 3 fermion generations. Furthermore it is noted that the same structure can also be obtained from a primordial symmetry breaking S ₄→A ₄. Since A ₄ is a chiral group, while S ₄ is achiral, an argument can be given why the chirality of the inner pyritohedral symmetry leads to parity violation of the weak interactions.     

General Synthesis and Physicochemical Characterisation of a Series of Peptide‐Mimic Lysine‐Based Amino‐Functionalised Lipids

A series of novel malonic acid diamides (second generation) with two long hydrophobic alkyl chains and an alkaline polar head group was synthesised and characterised as a new class of amino‐functionalised lipids. These peptide‐mimic lipids are suitable for polynucleotide transfer. The lipids bear a novel backbone consisting of a lysine unit and a malonic acid unit. Six different head‐group structures, which vary in size and number of amino groups that can be protonated, were attached to the backbone structure. Furthermore, different alkyl chains were used to build the lipophilic part (namely tetradecyl, hexadecyl, and oleyl). Phase transitions of the new compounds in aqueous dispersions at pH 10 were analysed and discussed in terms of head group and alkyl chain variations. The shape and size of the formed aggregates of selected lipid dispersions were investigated by dynamic light scattering and transmission electron microscopy.     

Monolayers of mono- and bipolar palmitic acid derivatives

Monopolar and bipolar derivatives of hexadecanoic acid (HA), 16-hydroxyhexadecanoic acid (HHA), methyl hexadecanoate (MH) and methyl 16-hydroxyhexadecanoate (MHH) have been investigated on pure water and NaCl solutions with different ion concentrations (1, 2 and 3 mol l⁻¹). Surface pressure area isotherms show that HA forms a fully condensed monolayer on pure water at 20 °C [E. Teer, C.M. Knobler, S. Siegel, D. Vollhardt, G. Brezesinski, J. Phys. Chem., B104, 43, 2000, pp. 10053–10058] whereas in the case of the corresponding bipolar HHA the hydroxy group as a second polar moiety leads to a destabilization of the monolayer. The presence of two relatively strong hydrophilic polar groups at opposite ends of the chain prevents the formation of condensed films. The esterification of the carboxyl group (MH) changes the phase sequence from L₂–Ov–LS for HA to L₂–LS. Inserting a hydroxy group at the end of the chain (MHH) shifts the liquid expanded/liquid condensed (LE/LC) phase transition to higher surface pressures but does not change the phase sequence, however it increases the chain tilt. The pressure of the first-order phase transition LE/LC is strongly temperature dependent for MH, while the transition pressure of MHH is almost temperature independent. The phase behavior of MHH and MH on pure water was further studied by surface potential, Brewster angle microscopy (BAM), fluorescence microscopy and grazing incidence X-ray diffraction (GIXD) measurements. The LC domains of MHH on pure water are so small that no inner texture can be observed by BAM in contrast to the LC domains of MH. 3M NaCl in the subphase does not change the MH textures, while it increases the size of the LC domains of MHH. The influence of the hydroxy group on the monolayer behavior is discussed in terms of the formation of hydrogen bonds. The presence of NaCl in the subphase expands the monolayers. The results obtained are explained by changes in monolayer–monolayer and monolayer–subphase interactions.     

Enzyme Aided Analysis of the Substituent Distribution along the Chain of Cellulose Acetates Regioselectively Modified by the Action of an Aspergillus niger Acetylesterase

Two cellulose acetates (CA) were regioselectively deacetylated by action of a pure Aspergillus niger acetylesterase from the carbohydrate esterase family 1. The action of acetyl esterase along the polymeric chain was monitored by a new enzyme-aided method. CA with and without esterase modification was hydrolysed with a pure endoglucanase. The fragments were deutero-acetylated and separated by preparative SEC in CHCl₃. The partial degree of substitution of the individual fragments was determined by ¹H-NMR spectroscopy. The investigation confirmed the uniform regioselective and regular deacetylation along the polysaccharide chain. The partial substitution in C₂ seemed to be of major importance for the enzyme's mode of action.     

Cooperative effects in restricted rotations of aryl groups in 2,4,6,8-tetraary-3,7-diazabicyclo[3.3.1]nonanes and related systems

The free energies, enthalpies and entropies of activation for the rotation of the aryl groups in the N,N′-dimethyl and N,N′-dichloro derivatives of rel-(2R,4S,6S,8R)-2,4,6,8-tetrakisaryl-3,7-diazabicyclo[3.3.1]nonanes have been determined and compared with related tricyclic systems which cannot undergo chair-to-boat conformational changes. It is concluded on the basis of the large, negative value of ΔS³ for rotation of the 2(4) aryl group that this rotational process is correlated with rotation of the 8(6) aryl group. The 8(6) aryl group can however rotate independently of the 2(4)-aryl group. The usefulness of the entropies of activation as a criterion for cooperative rotation of groups is briefly discussed.