A posteriori estimates for the Stokes eigenvalue problem

We consider the Stokes eigenvalue problem. For the eigenvalues we derive both upper and lower a‐posteriori error bounds. The estimates are verified by numerical computations. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Influence of ethanol on lipid membranes: from lateral pressure profiles to dynamics and partitioning

We have combined experiments with atomic-scale molecular dynamics simulations to consider the influence of ethanol on a variety of lipid membrane properties. We first employed isothermal titration calorimetry together with the solvent-null method to study the partitioning of ethanol molecules into saturated and unsaturated membrane systems. The results show that ethanol partitioning is considerably more favorable in unsaturated bilayers, which are characterized by their more disordered nature compared to their saturated counterparts. Simulation studies at varying ethanol concentrations propose that the partitioning of ethanol depends on its concentration, implying that the partitioning is a nonideal process. To gain further insight into the permeation of alcohols and their influence on lipid dynamics, we also employed molecular dynamics simulations to quantify kinetic events associated with the permeation of alcohols across a membrane, and to characterize the rotational and lateral diffusion of lipids and alcohols in these systems. The simulation results are in agreement with available experimental data and further show that alcohols have a small but non-vanishing effect on the dynamics of lipids in a membrane. The influence of ethanol on the lateral pressure profile of a lipid bilayer is found to be prominent: ethanol reduces the tension at the membrane-water interface and reduces the peaks in the lateral pressure profile close to the membrane-water interface. The changes in the lateral pressure profile are several hundred atmospheres. This supports the hypothesis that anesthetics may act by changing the lateral pressure profile exerted on proteins embedded in membranes.     

Quasistatic Dynamics with Intermittency

We study an intermittent quasistatic dynamical system composed of nonuniformly hyperbolic Pomeau–Manneville maps with time-dependent parameters. We prove an ergodic theorem which shows almost sure convergence of time averages in a certain parameter range, and identify the unique physical family of measures. The theorem also shows convergence in probability in a larger parameter range. In the process, we establish other results that will be useful for further analysis of the statistical properties of the model.     

Control of calcium oxalate crystal growth by face-specific adsorption of an osteopontin phosphopeptide

Mineral-associated proteins have been proposed to regulate many aspects of biomineralization, including the location, type, orientation, shape, and texture of crystals. To understand how proteins achieve this exquisite level of control, we are studying the interaction between the phosphoprotein osteopontin (OPN) and the biomineral calcium oxalate monohydrate (COM). In the present study, we have synthesized peptides corresponding to amino acids 220-235 of rat bone OPN (pSHEpSTEQSDAIDpSAEK), one of several highly phosphorylated, aspartic-, and glutamic acid-rich sequences found in the protein. To investigate the role of phosphorylation in interaction with crystals, peptides containing no (P0), one (P1), or all three (P3) phosphates were prepared. Using a novel combination of confocal microscopy and scanning electron microscopy, we show that these peptides adsorb preferentially to {100} faces of COM and inhibit growth of these faces in a phosphorylation-dependent manner. To characterize the mechanism of adsorption of OPN peptides to COM, we have performed the first atomic-scale molecular-dynamics simulation of a protein-crystal interaction. P3 adsorbs to the {100} face much more rapidly than P1, which in turn adsorbs more rapidly than P0. In all cases, aspartic and glutamic acid, not phosphoserine, are the amino acids in closest contact with the crystal surface. These studies have identified a COM face-specific adsorption motif in OPN and delineated separate roles for carboxylate and phosphate groups in inhibition of crystal growth by mineral-associated phosphoproteins. We propose that the formation of close-range, stable, and face-specific interactions is a key factor in the ability of phosphoproteins to regulate biomineralization processes.     

Are Methylaluminoxane Activators Sheets?

Density functional theory calculations on neutral sheet models for methylaluminoxane (MAO) indicate that these structures, containing 5-coordinate and 4-coordinate Al, are likely precursors to ion-pairs seen during the hydrolysis of trimethylaluminum (Me₃Al) in the presence of donors such as octamethyltrisiloxane (OMTS). Ionization by both methide ([Me]⁻) and [Me₂Al]⁺ abstraction, involving this donor, were studied by polarizable continuum model calculations in fluorobenzene (PhF) and o-difluorobenzene (DFB) media. These studies suggest that low MW, 5-coordinate sheets ionize by [Me₂Al]⁺ abstraction, while [Me]⁻ abstraction from Me₃Al-OMTS is the likely process for higher MW 4-coordinate sheets. Further, comparison of anion stabilities per mole of aluminoxane repeat unit (MeAlO)_n, suggest that anions such as [(MeAlO)₇(Me₃Al)₄Me]⁻=[ 7,4 ]⁻ are especially stable compared to higher homologues, even though their neutral precursors are unstable.     

Effect of double bond position on lipid bilayer properties: insight through atomistic simulations

Phosphatidylcholines (PCs) are among the most common phospholipids in plasma membranes. Their structural and dynamic properties are known to be strongly affected by unsaturation of lipid hydrocarbon chains, yet the role of the exact positions of the double bonds is poorly understood. In this work, we shed light on this matter through atomic-scale molecular dynamics simulations of eight different one-component lipid bilayers comprised of PCs with 18 carbons in their acyl chains. By introducing a single double bond in each acyl chain and varying its position in a systematic manner, we elucidate the effects of a double bond on various membrane properties. Studies in the fluid phase show that a number of membrane properties depend on the double bond position. In particular, when the double bond in an acyl chain is located close to the membrane-water interface, the area per lipid is considerably larger than that found for a saturated lipid. Further, when the double bond is shifted from the interfacial region toward membrane center, the area per lipid is observed to increase and have a maximum when the double bond is in the middle of the chain. Beyond this point, the surface area decreases systematically as the double bond approaches membrane center. These changes in area per lipid are accompanied by corresponding changes in membrane thickness and ordering of the chains. Further changes are observed in the tilt angles of the chains, membrane hydration together with changes in the number of gauche conformations, and direct head group interactions. All of these effects can be associated with changes in acyl chain conformations and local effects of the double bond on the packing of the surrounding atoms.     

Effect of van der Waals interactions on H<Subscript>2</Subscript> dissociation on clean and defected Ru(0001) surface

Ab initio computational methods are used to study the relevance of van der Waals interactions in the case of a hydrogen molecule adsorption on the Ru(0001) surface. In addition to the clean surface, the effects of ruthenium adatom and vacancy on the process are studied. The adsorption characteristics are analyzed in terms of two dimensional cuts of the potential energy surface (PES). Based on the earlier studies for such systems, we mostly concentrate on the trajectories where the hydrogen molecule approaches the surface in parallel orientation. The results indicate that for a clean Ru(0001) the calculations applying the non-local van der Waals potentials yield higher barriers for the dissociation of the H₂ molecule. Of the high symmetry sites on Ru(0001), the top site is found to be the most reactive one. The vacancy and ruthenium adatom sites exhibit high dissociation barriers compared with the clean surface.     

Comparison of in vitro breast cancer visibility in analyser‐based computed tomography with histopathology,mammography, computed tomography and magnetic resonance imaging

High‐resolution analyser‐based X‐ray imaging computed tomography (HR ABI‐CT) findings on in vitro human breast cancer are compared with histopathology, mammography, computed tomography (CT) and magnetic resonance imaging. The HR ABI‐CT images provided significantly better low‐contrast visibility compared with the standard radiological images. Fine cancer structures indistinguishable and superimposed in mammograms were seen, and could be matched with the histopathological results. The mean glandular dose was less than 1 mGy in mammography and 12–13 mGy in CT and ABI‐CT. The excellent visibility of in vitro breast cancer suggests that HR ABI‐CT may have a valuable role in the future as an adjunct or even alternative to current breast diagnostics, when radiation dose is further decreased, and compact synchrotron radiation sources become available.     

Imidotungsten(VI) complexes with chelating amino and imino phenolates

The reaction of WOCl(4) with 2,4-di-tert-butyl-6-((isopropylamino)methyl)phenol followed by the reaction with phenyl isocyanate leads to the formation of imidotungsten(VI) complex [W(NPh)Cl(3)(OC(6)H(3)(CH(2)NH-i-Pr)-2-t-Bu(2)-4,6)] 4 with a chelating aminophenolate ligand. When the same procedure was applied using aminophenols with bulkier substituents in the amino group, the final product was an unexpected Schiff-base complex [W(NPh)Cl(3)(OC(6)H(3)(CH=NPh)-2-t-Bu(2)-4,6)] 5, where the ligand is derived from 2,4-di-tert-butyl-6-((phenylimino)methyl)phenol. Complex 5 is also formed in the thermal degradation of 4. On the whole, 5 appears to be formed by a disproportionation of intermediate compounds, which are analogous to complex 4. The solid-state structures of 4 and 5 have been determined by X-ray crystallography whereas the solution structures were studied by (1)H and (13)C NMR.