Ground-state energy of a classical artificial molecule

We study the ground-state energy of a classical artificial molecule formed by two-dimensional clusters (artificial atoms) of N/2 charged particles separated by a distance d. For the small molecules of N = 2 and 4, we obtain analytical expressions for this energy. For the larger ones, we calculate the ground-state energy using molecular dynamics simulation for N up to 128. From our numerical results, we are able to find out a function to approximate the ground-state energy of the molecules covering the range from atoms to molecules for any inter-atom distance d and for particle number from N = 8 to 128 within a difference less than one percent from the MD data.

Influence of fixed electric charges on potential profile across the squid axon membrane

The potential profile for a model of squid axon membrane has been determined for two physiological states: resting and action states. The non-linear Poisson-Boltzmann equation has been solved by considering the volumetric charge densities due to charges dissolved in an electrolytic solution and fixed on both glycocalyx and cytoplasmatic proteins. Results showing the features of the potential profile along the outer electrolytic region are similar for both resting and action states. However, the potential fall along glycocalyx at action state is lower than at resting. A small variation in the Na+ concentration drastically affects the surface membrane potentials and vice versa. We conclude that effects on the potential profile due to surface lipidic bilayer charge and contiguous electric double layers are more relevant than those provoked by fixed charges distributed along the cell cytoplasm. (c) 2007 Elsevier B.V. All rights reserved.

Tightened Lieb-Oxford Bound for Systems of Fixed Particle Number

The Lieb-Oxford bound is a constraint upon approximate exchange-correlation functionals. We explore a nonempirical tightening of that bound in both universal and electron number-dependent form. The test functional is PBE. Regarding both atomization energies (slightly worsened) and bond lengths (slightly improved), we find the PBE functional to be remarkably insensitive to the value of the Lieb-Oxford bound. This both rationalizes the use of the original Lieb-Oxford constant in PBE and suggests that enhancement factors more sensitive to sharpened constraints await discovery.

The Mobility of Chondroitin Sulfate in Articular and Artificial Cartilage Characterized by (13)C Magic-Angle Spinning NMR Spectroscopy

We have studied the molecular dynamics of one of the major macromolecules in articular cartilage, chondroitin sulfate. Applying (13)C high-resolution magic-angle spinning NMR techniques, the NMR signals of all rigid macromolecules in cartilage can be suppressed, allowing the exclusive detection of the highly mobile chondroitin sulfate. The technique is also used to detect the chondroitin sulfate in artificial tissue-engineered cartilage. The tissue-engineered material that is based on matrix producing chondrocytes cultured in a collagen gel should provide properties as close as possible to those of the natural cartilage. Nuclear relaxation times of the chondroitin sulfate were determined for both tissues. Although T(1) relaxation times are rather similar, the T(2) relaxation in tissue-engineered cartilage is significantly shorter. This suggests that the motions of chondroitin sulfate in data:rat and artificial cartilage different. The nuclear relaxation times of chondroitin sulfate in natural and tissue-engineered cartilage were modeled using a broad distribution function for the motional correlation times. Although the description of the microscopic molecular dynamics of the chondroitin sulfate in natural and artificial cartilage required the identical broad distribution functions for the correlation times of motion, significant differences in the correlation times of motion that are extracted from the model indicate that the artificial tissue does not fully meet the standards of the natural ideal. This could also be confirmed by macroscopic biomechanical elasticity measurements. Nevertheless, these results suggest that NMR is a useful tool for the investigation of the quality of artificially engineered tissue. (C) 2010 Wiley Periodicals, Inc. Biopolymers 93: 520-532, 2010.

ABELIANIZED OBSTRUCTION FOR FIXED POINTS OF FIBER-PRESERVING MAPS OF SURFACE BUNDLES

Let f: M -> M be a fiber-preserving map where S -> M -> B is a bundle and S is a closed surface. We study the abelianized obstruction, which is a cohomology class in dimension 2, to deform f to a fixed point free map by a fiber-preserving homotopy. The vanishing of this obstruction is only a necessary condition in order to have such deformation, but in some cases it is sufficient. We describe this obstruction and we prove that the vanishing of this class is equivalent to the existence of solution of a system of equations over a certain group ring with coefficients given by Fox derivatives.

NIELSEN COINCIDENCE THEORY OF FIBRE-PRESERVING MAPS AND DOLD`S FIXED POINT INDEX

Let M -> B, N -> B be fibrations and f(1), f(2): M -> N be a pair of fibre-preserving maps. Using normal bordism techniques we define an invariant which is an obstruction to deforming the pair f(1), f(2) over B to a coincidence free pair of maps. In the special case where the two fibrations axe the same and one of the maps is the identity, a weak version of our omega-invariant turns out to equal Dold`s fixed point index of fibre-preserving maps. The concepts of Reidemeister classes and Nielsen coincidence classes over B are developed. As an illustration we compute e.g. the minimal number of coincidence components for all homotopy classes of maps between S(1)-bundles over S(1) as well as their Nielsen and Reidemeister numbers.

Fixed points on Klein bottle fiber bundles over the circle

The main purpose of this work is to study fixed points of fiber-preserving maps over the circle S(1) for spaces which are fiber bundles over S(1) and the fiber is the Klein bottle K. We classify all such maps which can be deformed fiberwise to a fixed point free map. The similar problem for torus fiber bundles over S(1) has been solved recently.

Coincidence Wecken homotopies versus Wecken homotopies relative to a fixed homotopy in one of the maps

We study the 1-parameter Wecken problem versus the restricted Wecken problem, for coincidence free pairs of maps between surfaces. For this we use properties of the function space between two surfaces and of the pure braid group on two strings of a surface. When the target surface is either the 2-sphere or the torus it is known that the two problems are the same. We classify most pairs of homotopy classes of maps according to the answer of the two problems are either the same or different when the target is either projective space or the Klein bottle. Some partial results are given for surfaces of negative Euler characteristic. (C) 2010 Elsevier B.V. All rights reserved.

Artificial Neural Networks and the Study of the Psychoactivity of Cannabinoid Compounds

Cannabinoid compounds have widely been employed because of its medicinal and psychotropic properties. These compounds are isolated from Cannabis sativa (or marijuana) and are used in several medical treatments, such as glaucoma, nausea associated to chemotherapy, pain and many other situations. More recently, its use as appetite stimulant has been indicated in patients with cachexia or AIDS. In this work, the influence of several molecular descriptors on the psychoactivity of 50 cannabinoid compounds is analyzed aiming one obtain a model able to predict the psychoactivity of new cannabinoids. For this purpose, initially, the selection of descriptors was carried out using the Fisher`s weight, the correlation matrix among the calculated variables and principal component analysis. From these analyses, the following descriptors have been considered more relevant: E(LUMO) (energy of the lowest unoccupied molecular orbital), Log P (logarithm of the partition coefficient), VC4 (volume of the substituent at the C4 position) and LP1 (Lovasz-Pelikan index, a molecular branching index). To follow, two neural network models were used to construct a more adequate model for classifying new cannabinoid compounds. The first model employed was multi-layer perceptrons, with algorithm back-propagation, and the second model used was the Kohonen network. The results obtained from both networks were compared and showed that both techniques presented a high percentage of correctness to discriminate psychoactive and psychoinactive compounds. However, the Kohonen network was superior to multi-layer perceptrons.