Relation between Chandrasekhar's X-function and the eigenvalues of integral operators with difference kernels

Abstract is not available.

Coarse-Grained Molecular Dynamics Simulation of the Aggregation Properties of Multiheaded Cationic Surfactants in Water

The aggregation property of multiheaded surfactants has been investigated by constant pressure molecular dynamics (MD) simulation in aqueous medium. The model multiheaded surfactants contain more than one headgroup (x = 2, 3, and 4) for a single tail group. This increases the hydrophilic charge progressively over the hydrophobic tail which has dramatic consequences in the aggregation behavior. In particular, we have looked at the change in the aggregation property such as critical micellar concentration (cmc), aggregation number, and size of the micelles for the multiheaded surfactants in water. We find with increasing number of headgroups of the Multiheaded surfactants that the cmc values increase and the aggregation numbers as well as the size of the micelles decrease. These trends are in agreement with the experimental findings as reported earlier with x = 1, 2, and 3. We also predict the aggregation properties of multiheaded surfactant With four headgroups (x = 4) for which no experimental studies exist yet.

X-ray studies on crystalline complexes involving amino acids and peptides. XXIII. Variability in ionization state, conformation and molecular aggregation in the complexes of succinic acid with DL- and L-lysine

Crystalline complexes of succinic acid with DL- and L-lysine have been prepared and analysed by X-ray diffraction. DL-Lysine complex: C6HIsN202 + 1 2- 1 ~C4H404 .~C4H604, Mr -- 264"2, PI, a = 5"506 (4), =8.070(2), c=14.089(2) A,, a=92.02(1), /3= 100"69 (3), y = 95"85 (3) ~>, Z = 2, Dx = 1"44 g cm -3, R = 0.059 for 2546 observed reflections. Form I of the e-lysine complex: C6HIsN20-, ~ .C4H504, Mr = 264.2, P1, a = 5" 125 (2), b = 8"087 (1), c = 8"689 (1) A,, a = 112.06 (1), /3 = 99.08 (2), y = 93"77(2) °, Z--l, D,,,=1"34(3), Dx=l"34gcm 3 R = 0.033 for 1475 observed reflections. Form II of + I 2- the e-lysine complex: C6H15N202 .,iC4H404 .- 1 I ") 4C4H604.4(C4HsO4""H'"CaH404)" , Mr = 264"2, P1, a = 10.143 (4), b = 10.256 (2), c = 12"916 (3) A,, a = 105.00 (2),/3 = 99-09 (3), y = 92"78 (3)::, Z = 4, Dm= 1"37(4), D,.= 1.38gcm 3, R=0.067 for 2809 observed reflections. The succinic acid molecules in the structures exhibit a variety of ionization states. Two of the lysine conformations found in the complexes have been observed for the first time in crystals containing lysine. Form II of the L-lysine complex is highly pseudosymmetric. In all the complexes, unlike molecules aggregate into separate alternating layers. The basic element of aggregation in the lysine layer in the complexes is an S2-type head-to-tail sequence. This element combines in different ways in the three structures. The basic element of aggre gation in the succinic acid layer in the complexes is a hydrogen-bonded ribbon. The ribbons are interconnected indirectly through amino groups in the lysine layer.

Preservation of native conformation during aluminium-induced aggregation of tau protein

ALUMINIUM exposure has been shown to result in aggregation of microtubule-associated protein tau in vitro. In the light of recent observations that the native random structure of tau protein is maintained in its monomeric and dimeric states as well as in the paired helical filaments characteristic of Alzheimer's disease, it is likely that factors playing a causative role in neurofibrillary pathology would not drastically alter the native conformation of tau protein. We have studied the interaction of tau protein with aluminium using circular dichroism (CD) and 27(Al) NMR spectroscopy. The CD studies revealed a five-fold increase in the observed ellipticity of the tau-aluminium assembly. The increase in elipticity was not associated with a change in the general conformation of the protein and was most likely due to an aggregation of the tau protein induced by aluminium. Al-27 NMR spectroscopy confirmed the binding of aluminium to tau protein. Hyperphosphorylation of tau in Alzheimer's disease is known to be associated with defective microtubule assembly in this condition. Abnormally phosphorylated tau exists in a polymerized form in the paired helical filaments (PHF) which constitute the neurofibrillary tangles found in Alzheimer's disease. While it is hypothesized that its altered biophysical characteristics render abnormally phosphorylated tau resistant to proteolysis, causing the formation of stable deposits,the sequence of events resulting in the polymerization of tau are little understood, as are the additional factors or modifications required for tills process. Based on the results of our spectroscopic studies, a model for the sequence of events occurring in neurofibrillary pathology is proposed.

The curvature invariant for a class of homogeneous operators

For an operator T in the class B-n(), introduced by Cowen and Douglas, the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle E-T determine the unitary equivalence class of the operator T. In a subsequent paper, the authors ask if the simultaneous unitary equivalence class of the curvature and these covariant derivatives are necessary to determine the unitary equivalence class of the operator T is an element of B-n(). Here we show that some of the covariant derivatives are necessary. Our examples consist of homogeneous operators in B-n(). For homogeneous operators, the simultaneous unitary equivalence class of the curvature and all its covariant derivatives at any point w in the unit disc are determined from the simultaneous unitary equivalence class at 0. This shows that it is enough to calculate all the invariants and compare them at just one point, say 0. These calculations are then carried out in number of examples. One of our main results is that the curvature along with its covariant derivative of order (0, 1) at 0 determines the equivalence class of generic homogeneous Hermitian holomorphic vector bundles over the unit disc.

Aggregation of apolar peptides in organic solvents. Concentration dependence of 1H-nmr parameters for peptide NH groups in 310 helical decapeptide fragment of suzukacillin

Peptide NH chemical shifts and their temperature dependences have been monitored as a function of concentration for the decapeptide, Boc-Aib-Pro-Val-Aib-Val-Ala-Aib-Ala-Aib-Aib-OMe in CDCl3 (0.001-0.06M) and (CD3)2SO (0.001-0.03M). The chemical shifts and temperature coefficients for all nine NH groups show no significant concentration dependence in (CD3)2SO. Seven NH groups yield low values of temperature coefficients over the entire range, while one yields an intermediate value. In CDCl3, the Aib(1) NH group shows a large concentration dependence of both chemical shift and temperature coefficient, in contrast to the other eight NH groups. The data suggest that in (CD3)2SO, the peptide adopts a 310 helical conformation and is monomeric over the entire concentration range. In CDCl3, the 310 helical peptide associates at a concentration of 0.01M, with the Aib(1) NH involved in an intermolecular hydrogen bond. Association does not disrupt the intramolecular hydrogen-bonding pattern in the decapeptide.

Wigner distributions for finite-state systems without redundant phase-point operators

We set up Wigner distributions for N-state quantum systems following a Dirac-inspired approach. In contrast to much of the work in this study, requiring a 2N x 2N phase space, particularly when N is even, our approach is uniformly based on an N x N phase-space grid and thereby avoids the necessity of having to invoke a `quadrupled' phase space and hence the attendant redundance. Both N odd and even cases are analysed in detail and it is found that there are striking differences between the two. While the N odd case permits full implementation of the marginal property, the even case does so only in a restricted sense. This has the consequence that in the even case one is led to several equally good definitions of the Wigner distributions as opposed to the odd case where the choice turns out to be unique.

Visualization of in situ intracellular aggregation of two cataract-associated human gamma-crystallin mutants: Lose a tail, lose transparency

PURPOSE. To understand the molecular features underlying autosomal dominant congenital cataracts caused by the deletion mutations W156X in human gamma D-crystallin and W157X in human gamma C-crystallin. METHODS. Normal and mutant cDNAs (with the enhanced green fluorescent protein [EGFP] tag in the front) were cloned into the pEGFP-C1 vector, transfected into various cell lines, and observed under a confocal microscope for EGFP fluorescence. Normal and W156X gamma D cDNAs were also cloned into the pET21a(+) vector, and the recombinant proteins were overexpressed in the BL-21(DE3) pLysS strain of Escherichia coli, purified, and isolated. The conformational features, structural stability, and solubility in aqueous solution of the mutant protein were compared with those of the wild type using spectroscopic methods. Comparative molecular modeling was performed to provide additional structural information. RESULTS. Transfection of the EGFP-tagged mutant cDNAs into several cell lines led to the visualization of aggregates, whereas that of wild-type cDNAs did not. Turning to the properties of the expressed proteins, the mutant molecules show remarkable reduction in solubility. They also seem to have a greater degree of surface hydrophobicity than the wild-type molecules, most likely accounting for self-aggregation. Molecular modeling studies support these features. CONCLUSIONS. The deletion of C-terminal 18 residues of human gamma C-and gamma D-crystallins exposes the side chains of several hydrophobic residues in the sequence to the solvent, causing the molecule to self-aggregate. This feature appears to be reflected in situ on the introduction of the mutants in human lens epithelial cells.

Small-angle x-ray scattering study of the aggregation of gold nanoparticles during formation at the toluene-water interface

We report the results of an in situ small-angle x-ray scattering (SAXS) study of the aggregation of gold nanoparticles formed by an interfacial reaction at the toluene-water interface. The SAXS data provide a direct evidence for aggregate formation of nanoparticles having 1.3 nm gold core and an organic shell that gives a core-core separation of about 2.5 nm. Furthermore, the nanoparticles do not occupy all the cites of 13-member cluster. This occupancy decreases with reaction time and indicate reorganization of the clusters that generates planner disklike structures. A gradual increase in fractal dimension from 1.82 to 2.05 also indicate compactification of cluster aggregation with reaction time, the final exponent being close to 2 expected for disklike aggregates.

Aggregation studies in crystals of apolar helical peptides: Boc-Aib-Val-Ala-Leu-Aib-Val-Ala-Leu-Aib-OMe

In the crystal, the backbone of Boc-(Aib-Val-Ala-Leu)2-Aib-OMe adopts a helical form with four alpha-type hydrogen bonds in the middle, flanked by 3(10)-type hydrogen bonds at either end. The helical molecules stack in columns with head-to-tail hydrogen bonds, either directly between NH and CO, or bridged by solvent molecules. The packing of the helices is parallel, even in space group P2(1). Cell parameters are a = 9.837(2) A, b = 15.565(3) A, c = 20.087(5) A, beta = 96.42(2) degrees, dcalc = 1.091 g/cm3 for C46H83N9O12.1.5H2O.0.67CH3OH. There appears to be some hydration of the backbone in this apolar helix.

Parallel and antiparallel aggregation of alpha-helices. Crystal structures of two apolar decapeptides X-Trp-Ile-Ala-Aib-Ile-Val-Aib-Leu-Aib-Pro-OMe (X = Boc, Ac)

An apolar helical decapeptide with different end groups, Boc- or Ac-, crystallizes in a completely parallel fashion for the Boc-analog and in an antiparallel fashion for the Ac-analog. In both crystals, the packing motif consists of rows of parallel molecules. In the Boc-crystals, adjacent rows assemble with the helix axes pointed in the same direction. In the Ac-crystals, adjacent rows assemble with the helix axes pointed in opposite directions. The conformations of the molecules in both crystals are quite similar, predominantly alpha-helical, except for the tryptophanyl side chain where chi 1 congruent to 60 degrees in the Boc- analog and congruent to 180 degrees in the Ac-analog. As a result, there is one lateral hydrogen bond between helices, N(1 epsilon)...O(7), in the Ac-analog. The structures do not provide a ready rationalization of packing preference in terms of side-chain interactions and do not support a major role for helix dipole interactions in determining helix orientation in crystals. The crystal parameters are as follow. Boc-analog: C60H97N11O13.C3H7OH, space group Pl with a = 10.250(3) A, b = 12.451(4) A, c = 15.077(6) A, alpha = 96.55(3) degrees, beta = 92.31(3) degrees, gamma = 106.37(3) degrees, Z = 1, R = 5.5% for 5581 data ([F] greater than 3.0 sigma(F)), resolution 0.89 A. Ac-analog: C57H91N11O12, space group P2(1) with a = 9.965(1) A, b = 19.707(3) A, c = 16.648(3) A, beta = 94.08(1), Z = 2, R = 7.2% for 2530 data ([F] greater than 3.0 sigma(F)), resolution 1.00 A.

Aggregation and mesomorphic properties of 'double-headed' carbohydrate amphiphiles

Sugar-based amphiphiles, consisting of two sugar head groups and an alkylene chain within the molecules, are synthesized and their aggregation and mesomorphic properties are evaluated. The hydrophilic sugar head groups, constituted with beta-D-glucopyranoside units, and the lyophilic alkylene units, are coupled to a glycerol backbone to afford the 'double-headed' sugar amphiphiles. Aggregation studies in aqueous solutions provided their critical micellar concentrations and the aggregation numbers. Mesophase characterizations by polarizing optical microscopy and differential scanning calorimetry (DSC) revealed the phase-transition behaviour of these new 'double-headed' glycolipids.

Covalent tethering of the dimer interface annuls aggregation in thymidylate synthase

Thymidylate synthase (TS), a dimeric enzyme, forms large soluble aggregates at concentrations of urea (3.3-5 M), well below that required for complete denaturation, as established by fluorescence and size-exclusion chromatography. In contrast to the wild-type enzyme, an engineered mutant of TS (T155C/E188C/C244T), TSMox, in which two subunits are crosslinked by disulfide bridges between residues 155-188' and 188-155', does not show this behavior. Aggregation behavior is restored upon disulfide bond reduction in the mutant protein, indicating the involvement of interface segments in forming soluble associated species. Intermolecular disulfide crosslinking has been used as a probe to investigate the formation of larger non-native aggregates. The studies argue for the formation of large multimeric species via a sticky patch of polypeptide from the dimer interface region that becomes exposed on partial unfolding. Covalent reinforcement of relatively fragile protein-protein interfaces may be a useful strategy in minimizing aggregation of non-native structures in multimeric proteins.

Synthesis, aggregation behavior and cholesterol solubilization studies of 16-epi-pythocholic acid (3 alpha,12 alpha,16 beta-trihydroxy-5 beta-cholan-24-oic acid)

Synthesis, aggregation behavior and in vitro cholesterol solubilization studies of 16-epi-pythocholic acid (3 alpha,12 alpha,16 beta-trihydroxy-5 beta-cholan-24-oic acid, EPCA) are reported. The synthesis of this unnatural epimer of pythocholic acid (3 alpha,12 alpha,16 alpha-trihydroxy-5 beta-cholan-24-oic acid, PCA) involves a series of simple and selective chemical transformations with an overall yield of 21% starting from readily available cholic acid (CA). The critical micellar concentration (CMC) of 16-epi-pythocholate in aqueous media was determined using pyrene as a fluorescent probe. In vitro cholesterol solubilization ability was evaluated using anhydrous cholesterol and results were compared with those of other natural di-and trihydroxy bile acids. These studies showed that 16-epi-pythocholic acid (16 beta-hydroxy-deoxycholic acid) behaves similar to cholic acid (CA) and avicholic acid (3 alpha,7 alpha,16 alpha-trihydroxy-5 beta-cholan-24-oic acid, ACA) in its aggregation behavior and cholesterol dissolution properties. (C) 2010 Elsevier Inc. All rights reserved.