Integrin clustering in two and three dimensions

Integrins are transmembrane proteins that allow cells to bind to their external environment. They are the primary regulators of cell-matrix interactions, with direct roles in cell motility and signaling, which in turn regulate numerous physiological processes. Under common experimental conditions, integrins tend to cluster for sturdy and effective binding to extracellular matrix molecules. These clusters often evolve into focal adhesions, which regulate downstream signaling. However, integrin clusters are more pronounced and have longer lifetimes in two-dimensional assays than in more realistic three-dimensional environments. While a number of models and theoretical approaches have focused on integrin binding and diffusion, the reasons for the differences between two- and three-dimensional clustering have remained elusive. In this study, we model an individual cluster attached to a two-dimensional collagen film and attached to collagen fibers of various sizes in three-dimensional matrices. We then discuss how our results explain differences in size and lifetime, and how they hint at reasons for other differences between the two environments. Further, we make predictions regarding the stability of clusters based on different overall intracellular conditions. Our results show good agreement with experiments and provide a quantitative basis for understanding how matrix dimensionality and structure regulate integrin behavior in environments that mimic in vivo conditions.     

Coulomb potentials in two and three dimensions under periodic boundary conditions

A method to sum over logarithmic potential in two-dimensions (2D) and Coulomb potential in three dimensions (3D) with periodic boundary conditions in all directions is given. We consider the most general form of unit cells, the rhombic cell in 2D and the triclinic cell in 3D. For the 3D case, this paper presents a generalization of Sperb's work [R. Sperb, Mol. Simulation 22, 199 (1999)]. The expressions derived in this work converge extremely fast in all region of the simulation cell. We also obtain results for slab geometry. Furthermore, self-energies for both 2D as well as 3D cases are derived. Our general formulas can be employed to obtain Madelung constants for periodic structures.     

Similarity analysis in two and three dimensions using lattice animals and polycubes

The quantification and analysis of molecular similarity are fundamental problems of both theoretical and applied chemistry. The continuum similarity problem of planar domains with Jordan curve boundaries can be discretized and quantified using interior filling animals (square cell configurations). A similar approach is applicable to the continuum similarity problem of formal molecular bodies enclosed by contour surfaces, where interior filling polycubes provide a method for discretization and quantification of molecular similarity in three dimensions. This technique leads to resolution based similarity measures (RBSMs), suitable for automatic, non-visual evaluation of the degree of similarity between shapes of general objects, in particular, of molecular charge distributions, or fused sphere Van der Waals surfaces. Using the framework of the RBSM method, the polycube method of chirality quantification is extended to the quantification of approximate symmetry of molecular electron distributions.     

Multiple morphologies of amphiphilic diblock copolymer micelles in two and three dimensions

We show that in aqueous solution, diblock copolymers, where one block is hydrophobic and the other hydrophilic can undergo self-assembly in three dimensions in a manner similar to small molecule amphiphiles. In addition, two dimensional self-assembly has been studied at the air-water interface. We describe the various morphologies which have been observed in these systems and the parameters which we can use to tailor them.     

Electrostatic potentials in systems periodic in one, two, and three dimensions

We consider the electrostatic potential in a unit cell containing N point charges Q(j) with positions r(j) inside the cell. The cell is replicated periodically in one, two, and three dimensions. The purpose is to give representations for the potential which contain only lattice sums which are absolutely convergent and uniformly convergent in the sampling position r. These representations are derived using variants of the Ewald method and are primarily intended for use in evaluating the accuracy of any algorithm to evaluate electrostatic energies and forces in simulations of dense matter, rather than necessarily for use of themselves in simulations. In reduced dimensionality the Ewald representations can be numerically inefficient and other representations are also provided with careful specification which allows two forms to be used for the potential functions in order to improve numerical performance. These mixed representations may be satisfactory in simulations.     

Particle Monte Carlo simulation of string-like colloidal assembly in two and three dimensions

We simulate structural phase behavior of polymer-grafted colloidal particles by molecular Monte Carlo technique. The interparticle potential, which has a finite repulsive square-step outside a rigid core of the colloid, was previously confirmed via numerical self-consistent field calculation. This model potential is purely repulsive. We simulate these model colloids in the canonical ensemble in two and three dimensions and find that these particles containing no interparticle attraction self-assemble and align in a string-like assembly, at low temperature and high density. This string-like colloidal assembly is related to percolation phenomena. Analyzing the cluster size distribution and the average string length, we build phase diagrams and discover that the average string length diverges around the region where the melting transition line and the percolation transition line cross. This result is similar to Ising spin systems, in which the percolation transition line and the order-disorder line meet at a critical point.     

Evaluation of the electron momentum density of crystalline systems from ab initio linear combination of atomic orbitals calculations

Alternative techniques are presented for the evaluation of the electron momentum density (EMD) of crystalline systems from ab initio linear combination of atomic‐orbitals calculations performed in the frame of one‐electron self‐consistent‐field Hamiltonians. Their respective merits and drawbacks are analyzed with reference to two periodic systems with very different electronic features: the fully covalent crystalline silicon and the ionic lithium fluoride. Beyond one‐electron Hamiltonians, a post‐Hartree–Fock correction to the EMD of crystalline materials is also illustrated in the case of lithium fluoride. © 2012 Wiley Periodicals, Inc.     

Ammonium violurate: a compact structure with extensive hydrogen bonding in three dimensions

The title compound [systematic name: ammonium pyrimidine‐2,4‐5,6(1H,3H)‐tetrone 5‐oximate], NH₄⁺·C₄H₂N₃O₄⁻, crystallizes from water in the triclinic space group P and is ismorphous with a known rubidium complex [Gillier (1965). Bull. Soc. Chim. Fr. pp. 2373–2384]. The principal feature of the structure is hydrogen bonding; each ammonium H atom acts as a bifurcated donor and three of the four violurate O atoms are bifurcated acceptors, with the fourth acting as a trifurcated acceptor. The pattern of hydrogen bonding around the cation is very similar to the rubidium coordination environment in the related structure. The violurate anions pack as hydrogen‐bonded crinkled tapes, which are linked and separated by the ammonium cations to give a compact three‐dimensional structure.     

Determination of hexavalent chromium in exhaled breath condensate and environmental air among chrome plating workers

Chromium speciation has attracted attention because of the different toxicity of Cr(III), which is considered relatively non-toxic, and Cr(VI), which can cross cell membranes mainly as a chromate anion and has been classified as a class I human carcinogen. The aims of the present study were to measure soluble Cr(VI) levels in environmental samples, to develop a simple method of quantifying Cr(VI) in exhaled breath condensate (EBC), and to follow the kinetics of EBC Cr(VI) in chrome plating workers.Personal air samples were collected from 10 chrome platers; EBC was collected from the same workers immediately after the work shift on Tuesday and before the work shift on the following Wednesday. Environmental and EBC Cr(VI) levels were determined by means of colorimetry and electrothermal absorption atomic spectrometry, respectively.The method of detecting Cr(VI) in environmental air was based on the extraction of the Cr(VI)-diphenylcarbazide (Cr(VI)-DPC) complex in 1-butanol, whereas EBC Cr(VI) was determined using a solvent extraction of Cr(VI) as an ion pair with tetrabutylammonium ion, and subsequent direct determination of the complex (Cr(VI)-DPC) in EBC.Kinetic data showed that airborne Cr(VI) was reduced by 50% in airway lining fluid sampled at the end of exposure and that there was a further 50% reduction after about 15 h. The persistence of Cr(VI) in EBC supports the use of EBC in assessing target tissue levels of Cr(VI).     

Computer simulation of a binary polymer mixture in three dimensions

The behavior of a binary polymer mixture was simulated on a cubic lattice over both the miscibility and immiscibility regions. The number and distribution of interactions in the mixture were found to be different from the mean-field picture; however, the observed phase behavior agrees with that predicted by the mean-field theory and is not affected by the observed concentration fluctuations. The relationship between the phenomenological χ parameter and the heterosegmental interaction energy was investigated. Polymer chains show nearly ideal behavior, even for strongly interacting mixtures; this simplifies the theoretical treatment of polymer mixtures analogous to homopolymer melts.     

Determination of phenytoin in exhaled breath condensate using electromembrane extraction followed by capillary electrophoresis

Application of hollow fiber-based electromembrane extraction was studied for extraction and quantification of phenytoin from exhaled breath condensate (EBC). Phenytoin is extracted from EBC through a supported liquid membrane consisting of 1-octanol impregnated in the walls of a hollow fiber, and into an alkaline aqueous acceptor solution inside the lumen of the fiber. Under the obtained conditions of electromembrane extraction, that is, the extraction time of 15 min, stirring speed of 750 rpm, donor phase pH at 11.0, acceptor pH at 13.0, and an applied voltage of 15 V across the supported liquid membrane, an enrichment factor of 102-fold correspond to extraction percent of 25.5% was achieved. Good linearity was obtained over the concentration range of 0.001–0.10 µg/mL (r² = 0.9992). Limits of detection and quantitation were 0.001 and 0.003 µg/mL, respectively. The proposed method was successfully applied to determine phenytoin from EBC samples of patients receiving the drug. No interfering peaks were detected that indicating excellent selectivity of the method. The intra- and interday precisions (RSDs) were less than 14%.     

Diatomic interactions in momentum space bond polarity

Some fundamental aspects of bond polarity embedded in diatomic molecular orbitals are studied from the viewpoint of the electron distribution in momentum space. Electron momentum density is expressible as a product of one-center and oscillation terms, and the effect of polarity appears mainly in the latter term. Since the oscillation is not spherically symmetrical, the bond polarity is then related to the anisotropy of momentum distribution. In order to investigate this relation, directional ratios of momentum moments are introduced and their behaviors are examined for a model heteronuclear diatomic system.     

Hartree–Fock wave functions with a modified GTO basis for atoms

We have solved the atomic Hartree–Fock equations by using the algebraic approach, expanding the single-particle radial wave function in terms of a modified Gaussian type orbitals (GTOs) basis. Several atomic properties such as Kato's cusp condition for the electron density or the correct asymptotic behavior of the electron momentum density distribution are accurately verified. Additionally the energy of the atomic ground state can be obtained by using a smaller number of basis functions than in standard GTO expansions. This study has been performed for several atoms of the first three rows. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 59–64, 1997     

Electron Momentum Distributions for 4a1 Orbitals of CFxCl4-x in Low Momentum Region： a Possible Evidence of Molecular Geometry Distortion

Electron momentum distributions for 4a1 orbitals of serial freon molecules CFaC1, CF2Cl2, and CFCl3 （CFxC14-x, x=1-3） have been reanalyzed due to the severe discrepancies between theory and experiment in low momentum region. The tentative calculations using equilibrium geometries of molecular ions have exhibited a great improvement in agreement with the experimental data, which suggests that the molecular geometry distortion may be responsible for the observed high intensities at p〈0.5 a.u.. Further analyses show that the severe discrepancies at low momentum region mainly arise from the influence of molecular geometry distortion on C-Cl bonding electron density distributions.     

Application of multivariate techniques for optimization of direct method for determination of lead in naphtha and petroleum condensate by electrothermal atomic absorption spectrometry

A direct method is proposed for the determination of lead in naphtha and petroleum condensate by electrothermal atomic absorption spectrometry (ET AAS) using palladium as a permanent modifier. The procedure includes the dilution of 3 mL of sample (naphtha or petroleum condensate) to a final volume of 10 mL with xylene, and direct injection of 30 μL of this solution into the graphite furnace. The optimization of the instrumental conditions was performed using multivariate techniques. Firstly, a 2³ full factorial design was performed for preliminary evaluation of the factors: pyrolysis time, pyrolysis temperature and atomization temperature. This experiment showed that in the studied levels only the factors pyrolysis time and atomization temperature were significant. Then, a 3² full factorial design was performed for the determination of the critical conditions of these variables. The method allows the determination of lead using the standard calibration technique with a calibration curve from 2.6 to 30 μg L⁻¹ (correlation coefficient higher than 0.998). A limit of detection (3σ) of 0.8 μg L⁻¹ and a characteristic mass of 35 pg were obtained in the presence of palladium as modifier. The precision expressed as relative standard deviation (RSD) was 1.5 and 0.8% for lead concentrations of 3.0 and 30 μg L⁻¹ (n = 10). Recovery studies demonstrate that lead can be determined in naphtha and petroleum condensate using calibration with organic standard solutions. This method was applied for the determination of lead in three petroleum condensate and two naphtha samples. The concentrations found for the petroleum condensate was between 2.7 and 5.7 μg L⁻¹, while the naphtha samples did not contain any detectable lead.     

Three-dimensional EPR imaging with one spectral and two spatial dimensions

Three-dimensional EPR imaging with one spectral dimension and two spatial dimensions is demonstrated. An image can be displayed as two-dimensional spatial-spatial maps of spin density or of EPR spectral intensity at a particular value of magnetic field. The spectral dimension gives the hyperfine-split EPR spectrum at each point in the spatial-spatial plane.