An affine continuum mechanical model for cross-linked F-actin networks with compliant linker proteins

Cross-linked actin networks are important building blocks of the cytoskeleton. In order to gain deeper insight into the interpretation of experimental data on actin networks, adequate models are required. In this paper we introduce an affine constitutive network model for cross-linked F-actin networks based on nonlinear continuum mechanics, and specialize it in order to reproduce the experimental behavior of in vitro reconstituted model networks. The model is based on the elastic properties of single filaments embedded in an isotropic matrix such that the overall properties of the composite are described by a free-energy function. In particular, we are able to obtain the experimentally determined shear and normal stress responses of cross-linked actin networks typically observed in rheometer tests. In the present study an extensive analysis is performed by applying the proposed model network to a simple shear deformation. The single filament model is then extended by incorporating the compliance of cross-linker proteins and further extended by including viscoelasticity. All that is needed for the finite element implementation is the constitutive model for the filaments, the linkers and the matrix, and the associated elasticity tensor in either the Lagrangian or Eulerian formulation. The model facilitates parameter studies of experimental setups such as micropipette aspiration experiments and we present such studies to illustrate the efficacy of this modeling approach

A photoelectron diffraction investigation of vanadyl phthalocyanine on Au(1 1 1)

Scanned-energy mode photoelectron diffraction using the O 1s and V 2p emission perpendicular to the surface has been used to investigate the orientation and internal conformation of vanadyl phthalocyanine (VOPc) adsorbed on Au(1 1 1). The results confirm earlier indications from scanning tunnelling microscopy that the Vdouble bond; length as m-dashO vanadyl bond points out of, and not into, the surface. The Vdouble bond; length as m-dashO bondlength is 1.60 ± 0.04 Å, not significantly different from its value in bulk crystalline VOPc. However, the V atom in the adsorbed molecule is almost coplanar with the surrounding N atoms and is thus pulled down into the approximately planar region defined by the N and C atoms by 0.52 (+0.14/−0.10) Å, relative to its location in crystalline VOPc. This change must be attributed to the bonding interaction between the molecule and the underlying metal surface

Characterization of SU(1,1) coherent states in terms of affine group wavelets

The Perelomov coherent states of SU(1,1) are labeled by elements of the quotient of SU(1,1) by the compact subgroup. Taking advantage of the fact that this quotient is isomorphic to the affine group of the real line, we are able to parameterize the coherent states by elements of that group or equivalently by points in the half-plane. Such a formulation permits to find new properties of the SU(1,1) coherent states and to relate them to affine wavelets.Comment: 11 pages, latex, to be published in J. Phys. A : Math. Ge

From constructive field theory to fractional stochastic calculus. (II) Constructive proof of convergence for the L\'evy area of fractional Brownian motion with Hurst index α∈(1/8,1/4)\alpha\in(1/8,1/4)

{Let $B=(B_1(t),...,B_d(t))$ be a $d$-dimensional fractional Brownian motion with Hurst index $\alpha<1/4$, or more generally a Gaussian process whose paths have the same local regularity. Defining properly iterated integrals of $B$ is a difficult task because of the low H\"older regularity index of its paths. Yet rough path theory shows it is the key to the construction of a stochastic calculus with respect to $B$, or to solving differential equations driven by $B$. We intend to show in a series of papers how to desingularize iterated integrals by a weak, singular non-Gaussian perturbation of the Gaussian measure defined by a limit in law procedure. Convergence is proved by using "standard" tools of constructive field theory, in particular cluster expansions and renormalization. These powerful tools allow optimal estimates, and call for an extension of Gaussian tools such as for instance the Malliavin calculus. After a first introductory paper \cite{MagUnt1}, this one concentrates on the details of the constructive proof of convergence for second-order iterated integrals, also known as L\'evy area

Adsorption structure of glycine on TiO2(1 1 0): a photoelectron diffraction determination

High-resolution core-level photoemission and scanned-energy mode photoelectron diffraction (PhD) of the O 1s and N 1s states have been used to investigate the interaction of glycine with the rutile TiO2(1 1 0) surface. Whilst there is clear evidence for the presence of the zwitterion View the MathML sourceCH2COO− with multilayer deposition, at low coverage only the deprotonated glycinate species, NH2CH2COO is present. Multiple-scattering simulations of the O 1s PhD data show the glycinate is bonded to the surface through the two carboxylate O atoms which occupy near-atop sites above the five-fold-coordinated surface Ti atoms, with a Ti–O bondlength of 2.12 ± 0.06 Å. Atomic hydrogen arising from the deprotonation is coadsorbed to form hydroxyl species at the bridging oxygen sites with an associated Ti–O bondlength of 2.01 ± 0.03 Å. Absence of any significant PhD modulations of the N 1s emission is consistent with the amino N atom not being involved in the surface bonding, unlike the case of glycinate on Cu(1 1 0) and Cu(1 0 0)

Quantitative adsorbate structure determination under catalytic reaction conditions

Current methods allow quantitative local structure determination of adsorbate geometries on surfaces in ultrahigh vacuum (UHV) but are incompatible with the higher pressures required for a steady-state catalytic reactions. Here we show that photoelectron diffraction can be used to determine the structure of the methoxy and formate reaction intermediates during the steady-state oxidation of methanol over Cu(110) by taking advantage of recent instrumental developments to allow near-ambient pressure x-ray photoelectron spectroscopy. The local methoxy site differs from that under static UHV conditions, attributed to the increased surface mobility and dynamic nature of the surface under reaction conditions

Photoelectron diffraction investigation of the structure of the clean TiO2(110)(1×1) surface

The surface relaxations of the rutile TiO2(110)(1×1) clean surface have been determined by O 1 s and Ti 2p3∕2 scanned-energy mode photoelectron diffraction. The results are in excellent agreement with recent low-energy electron diffraction (LEED) and medium energy ion scattering (MEIS) results, but in conflict with the results of some earlier investigations including one by surface x-ray diffraction. In particular, the bridging O atoms at the surface are found to relax outward, rather than inward, relative to the underlying bulk. Combined with the recent LEED and MEIS results, a consistent picture of the structure of this surface is provided. While the results of the most recent theoretical total-energy calculations are qualitatively consistent with this experimental consensus, significant quantitative differences remain

The local structure of SO2 and SO3 on Ni(1 1 1): a scanned-energy mode photoelectron diffraction study

O 1s and S 2p scanned-energy mode photoelectron diffraction (PhD) data, combined with multiple-scattering simulations, have been used to determine the local adsorption geometry of the SO2 and SO3 species on a Ni(1 1 1) surface. For SO2, the application of reasonable constraints on the molecular conformation used in the simulations leads to the conclusion that the molecule is centred over hollow sites on the surface, with the molecular plane essentially parallel to the surface, and with both S and O atoms offset from atop sites by almost the same distance of 0.65 Å. For SO3, the results are consistent with earlier work which concluded that surface bonding is through the O atoms, with the S atom higher above the surface and the molecular symmetry axis almost perpendicular to the surface. Based on the O 1s PhD data alone, three local adsorption geometries are comparably acceptable, but only one of these is consistent with the results of an earlier normal-incidence X-ray standing wave (NIXSW) study. This optimised structural model differs somewhat from that originally proposed in the NIXSW investigation