Self‐Assembly of the Cyclic Lipopeptide Daptomycin: Spherical Micelle Formation Does Not Depend on the Presence of Calcium Chloride

The cyclic lipopeptide Daptomycin, used as a treatment for infections where antimicrobial resistance is observed, is shown to self‐assemble into spherical micelles above a critical aggregation concentration. Micelles are observed either in the absence or presence of CaCl₂, in contrast to claims in the literature that CaCl₂ is required for micellization.     

Excitation decay pathways of Lhca proteins: a time-resolved fluorescence study

Light-harvesting complex I (LHCI), which serves as a peripheral antenna for photosystem I (PSI) in green plants, consists mainly of four polypeptides, Lhca1-4. We report room temperature emission properties of individual reconstituted monomeric Lhca proteins (Lhca1, -2, -3, and -4) and dimeric Lhca1/4, performed by steady-state and time-resolved fluorescence techniques. The emission quantum yields of the samples are approximately 0.12, 0.085, 0.081, 0.041, and 0.063 for Lhca1, -2, -3, -4, and the -1/4 dimer, respectively, which is considerably lower than the value of 0.22 found for light-harvesting complex II (LHCII), the main peripheral antenna complex of photosystem II in green plants. The decay components of LHCI proteins can be divided in two categories: Lhca1 and Lhca3 have decay times of 1.1-1.6 ns and 3.3-3.6 ns, and Lhca2 and Lhca4 have decay times of 0.7-0.9 ns and 3.1-3.2 ns. These categories seem to correlate with the pigment composition of the samples. All decay times are faster than that observed previously for LHCII. When the absolute emission yields and the lifetimes of the Lhca samples are combined, the overall emission properties of the individual Lhca proteins are expressed in terms of their emitting dipole moment strength. In the samples without extreme red states, that is, Lhca1 and Lhca2, the emitting dipole moment has a value close to unity (relative to monomeric chlorophyll in acetone), which is similar to that for LHCII, whereas, in the samples with the red-most state (F-730), that is, Lhca3, -4, and the -1/4 dimer, the emitting dipole moment has a value less than unity (0.6-0.8), which can be explained by mixing the red-most (exciton) state with a dark charge-transfer state, as suggested in previous PSI red pigment studies. In addition, we find a lifetime component of approximately 50-150 ps in all red-pigment-containing samples, which cannot be due to "slow" energy transfer, but is instead assigned to an unrelaxed state of the pigment-protein, which, on this time-scale, is converted into the final emitting state.     

Cellulose nanocrystal submonolayers by spin coating

Dilute concentrations of cellulose nanocrystal solutions were spin coated onto different substrates to investigate the effect of the substrate on the nanocrystal submonolayers. Three substrates were probed: silica, titania, and amorphous cellulose. According to atomic force microscopy (AFM) images, anionic cellulose nanocrystals formed small aggregates on the anionic silica substrate, whereas a uniform two-dimensional distribution of nanocrystals was achieved on the cationic titania substrate. The uniform distribution of cellulose nanocrystal submonolayers on titania is an important factor when dimensional analysis of the nanocrystals is desired. Furthermore, the amount of nanocrystals deposited on titania was multifold in comparison to the amounts on silica, as revealed by AFM image analysis and X-ray photoelectron spectroscopy. Amorphous cellulose, the third substrate, resulted in a somewhat homogeneous distribution of the nanocrystal submonolayers, but the amounts were as low as those on the silica substrate. These differences in the cellulose nanocrystal deposition were attributed to electrostatic effects: anionic cellulose nanocrystals are adsorbed on cationic titania in addition to the normal spin coating deposition. The anionic silica surface, on the other hand, causes aggregation of the weakly anionic cellulose nanocrystals which are forced on the repulsive substrate by spin coating. The electrostatically driven adsorption also influences the film thickness of continuous ultrathin films of cellulose nanocrystals. The thicker films of charged nanocrystals on a substrate of opposite charge means that the film thickness is not independent of the substrate when spin coating cellulose nanocrystals in the ultrathin regime (<100 nm).     

Retention of lysozyme activity by physical immobilization in nanocellulose aerogels and antibacterial effects

Aerogels prepared from aqueous dispersions of anionic and cationic cellulose nanofibrils (CNFs) were investigated as solid supports for enzymes and silver nanoparticles and to elicit a sustained antibacterial effect. The imparted stabilization in dry conditions was studied with aerogels that were cast after mixing the enzymes with CNFs followed by dehydration (freeze-drying). The activity of lysozyme immobilized in the given CNF system was analyzed upon storage in liquid and air media. In contrast with aqueous solutions of free, unbound enzyme, which lost activity after the first day, the enzyme immobilized physically in unmodified and cationic CNF presented better stability (activity for a longer time). However, the enzyme activity was reduced in the case of anionic CNF, which was prepared by TEMPO-mediated oxidation (TO-CNF). Both humidity and temperature reduced the stability of the enzyme immobilized in the respective CNF aerogel. The antibacterial activity of CNF aerogels carrying lysozyme was also tested against gram-negative and gram-positive bacteria. The results were compared with those obtained from CNF systems loaded with silver nanoparticles (AgNP) after in situ synthesis via UV reduction. Storage in cold or dry conditions preserved the activity and antibacterial performance of enzyme-loaded CNF aerogels. As expected, the lysozyme-containing aerogels showed lower inhibition than the AgNP-containing aerogel. In this latter case, the antibacterial activity depended on the concentration and size of the nanoparticles. Compared to unmodified CNF and TO-CNF, the aerogels prepared with cationic CNF, loaded with either lysozyme or AgNPs, showed remarkably better antibacterial activity. Similar experiments were conducted with horseradish peroxidase, which confirmed, to different degrees, the observations derived from the lysozyme systems. Overall, the results indicate that non-toxic and biodegradable CNF is a suitable support for bio-active materials and is effective in protecting and retaining enzymatic and antibacterial activities.     

Linear differential equations with coefficients in weighted Bergman and Hardy spaces

Complex linear differential equations of the form

with coefficients in weighted Bergman or Hardy spaces are studied. It is shown, for example, that if the coefficient of belongs to the weighted Bergman space , where , for all , then all solutions are of order of growth at most , measured according to the Nevanlinna characteristic. In the case when all solutions are shown to be not only of order of growth zero, but of bounded characteristic. Conversely, if all solutions are of order of growth at most , then the coefficient is shown to belong to for all and .

Analogous results, when the coefficients belong to certain weighted Hardy spaces, are obtained. The non-homogeneous equation associated to is also briefly discussed.

     

A fast direct solver for elliptic problems with a divergence constraint

A fast direct solution method for a discretized vector‐valued elliptic partial differential equation with a divergence constraint is considered. Such problems are typical in many disciplines such as fluid dynamics, elasticity and electromagnetics. The method requires the problem to be posed in a rectangle and boundary conditions to be either periodic boundary conditions or the so‐called slip boundary conditions in one co‐ordinate direction. The arising saddle‐point matrix has a separable form when bilinear finite elements are used in the discretization. Based on a result for so‐called p‐circulant matrices, the saddle‐point matrix can be transformed into a block‐diagonal form by fast Fourier transformations. Thus, the fast direct solver has the same structure as methods for scalar‐valued problems which are based on Fourier analysis and, therefore, it has the same computational cost ??(N log N). Numerical experiments demonstrate the good efficiency and accuracy of the proposed method. Copyright © 2002 John Wiley & Sons, Ltd.     

Classification of Graeco‐Latin Cubes

A q‐ary code of length n, size M, and minimum distance d is called an code. An code with is said to be maximum distance separable (MDS). Here one‐error‐correcting () MDS codes are classified for small alphabets. In particular, it is shown that there are unique (5, 5³, 3)₅ and (5, 7³, 3)₇ codes and equivalence classes of (5, 8³, 3)₈ codes. The codes are equivalent to certain pairs of mutually orthogonal Latin cubes of order q, called Graeco‐Latin cubes.     

Zero distribution of solutions of complex linear differential equations determines growth of coefficients

It is shown that the exponent of convergence λ(f) of any solution f of with entire coefficients A₀(z), …, A_k?2(z), satisfies λ(f) ? λ ∈ [1, ∞) if and only if the coefficients A₀(z), …, A_k?2(z) are polynomials such that for j = 0, …, k ? 2. In the unit disc analogue of this result certain intersections of weighted Bergman spaces take the role of polynomials. The key idea in the proofs is W. J. Kim’s 1969 representation of coefficients in terms of ratios of linearly independent solutions. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim     

Glass‐embedded silver nanoparticle patterns by masked ion‐exchange process for surface‐enhanced Raman scattering

Glass‐embedded silver nanoparticle patterns were fabricated by masked silver–sodium ion‐exchange process followed by etching to reveal the particles for surface‐enhanced Raman scattering (SERS). The intensity of the enhanced Raman signal is comparable to that of the fluorescence, and the detection limit of 1 nM for Rhodamine 6G has been achieved. Raman images at different etching depths and corresponding morphological images are compared to find optimal SERS signal. Our results demonstrate that silver nanoparticle patterns embedded in glass can be used as SERS‐active substrates. Nanoparticles can be formed in a glass of high optical quality and have potential to be integrated with optical waveguides for a sensor chip. Copyright © 2010 John Wiley & Sons, Ltd.