Nanoscale mechanical properties of lipid bilayers and their relevance in biomembrane organization and function

The mechanical properties of biological systems are emerging as fundamental in determining their functional activity. For example, cells continuously probe their environment by applying forces and, at the same time, are exposed to forces produced by the same environment. Also in biological membranes, the activity of membrane related proteins are affected by the overall mechanical properties of the hosting environment. Traditionally, the mesoscopic mechanical properties of lipid bilayers have been studied by micropipette aspiration techniques. In recent years, the possibility of probing mechanical properties of lipid bilayers at the nanoscale has been promoted by the force spectroscopy potentiality of Atomic Force Microscopes (AFM). By acquiring force-curves on supported lipid bilayers (SLBs) it is possible to probe the mechanical properties on a scale relevant to the interaction between membrane proteins and lipid bilayers and to monitor changes of these properties as a result of a changing environment. Here, we review a series of force spectroscopy experiments performed on SLBs with an emphasis on the functional consequences the measured mechanical properties can have on membrane proteins. We also discuss the force spectroscopy experiments on SLBs in the context of theories developed for dynamic force spectroscopy experiments with the aim to extract the kinetic and energetic description of the process of membrane rupture

Demonstration of an electrostatic-shielded cantilever

The fabrication and performances of cantilevered probes with reduced parasitic capacitance starting from a commercial Si3N4 cantilever chip is presented. Nanomachining and metal deposition induced by focused ion beam techniques were employed in order to modify the original insulating pyramidal tip and insert a conducting metallic tip. Two parallel metallic electrodes deposited on the original cantilever arms are employed for tip biasing and as ground plane in order to minimize the electrostatic force due to the capacitive interaction between cantilever and sample surface. Excitation spectra and force-to-distance characterization are shown with different electrode configurations. Applications of this scheme in electrostatic force microscopy, Kelvin probe microscopy and local anodic oxidation is discussed.Comment: 4 pages and 3 figures. Submitted to Applied Physics Letter

Focusing on the Fixed Point of 4D Simplicial Gravity

Our earlier renormalization group analysis of simplicial gravity is extended. A high statistics study of the volume and coupling constant dependence of the cumulants of the node distribution is carried out. It appears that the phase transition of the theory is of first order, contrary to what is generally believed.Comment: Latex, 20 pages, 6 postscript figures, published versio

Operator Formulation of q-Deformed Dual String Model

We present an operator formulation of the q-deformed dual string model amplitude using an infinite set of q-harmonic oscillators. The formalism attains the crossing symmetry and factorization and allows to express the general n-point function as a factorized product of vertices and propagators.Comment: 6pages, Late

Diffeomorphic approximation of Sobolev homeomorphisms

Every homeomorphism h : X -> Y between planar open sets that belongs to the Sobolev class W^{1,p}(X,Y), 1<p<\infty, can be approximated in the Sobolev norm by diffeomorphisms.Comment: 21 pages, 5 figure

Adhesion mechanisms of the contact interface of TiO2 nanoparticles in films and aggregates

Fundamental knowledge about the mechanisms of adhesion between oxide particles with diameters of few nanometers is impeded by the difficulties associated with direct measurements of contact forces at such a small size scale. Here we develop a strategy based on AFM force spectroscopy combined with all-atom molecular dynamics simulations to quantify and explain the nature of the contact forces between 10 nm small TiO2 nanoparticles. The method is based on the statistical analysis of the force peaks measured in repeated approaching/retracting loops of an AFM cantilever into a film of nanoparticle agglomerates and relies on the in-situ imaging of the film stretching behavior in an AFM/TEM setup. Sliding and rolling events first lead to local rearrangements in the film structure when subjected to tensile load, prior to its final rupture caused by the reversible detaching of individual nanoparticles. The associated contact force of about 2.5 nN is in quantitative agreement with the results of molecular dynamics simulations of the particle–particle detachment. We reveal that the contact forces are dominated by the structure of water layers adsorbed on the particles’ surfaces at ambient conditions. This leads to nonmonotonous force–displacement curves that can be explained only in part by classical capillary effects and highlights the importance of considering explicitly the molecular nature of the adsorbates

Periodic vacuum and particles in two dimensions

Different dynamical symmetry breaking patterns are explored for the two dimensional phi4 model with higher order derivative terms. The one-loop saddle point expansion predicts a rather involved phase structure and a new Gaussian critical line. This vacuum structure is corroborated by the Monte Carlo method, as well. Analogies with the structure of solids, the density wave phases and the effects of the quenched impurities are mentioned. The unitarity of the time evolution operator in real time is established by means of the reflection positivity.Comment: Final version, additional references and the proof of reflection positivity added, 41 pages, 16 figure

Relativistic three-body bound states and the reduction from four to three dimensions

Beginning with an effective field theory based upon meson exchange, the Bethe-Salpeter equation for the three-particle propagator (six-point function) is obtained. Using the one-boson-exchange form of the kernel, this equation is then analyzed using time-ordered perturbation theory, and a three-dimensional equation for the propagator is developed. The propagator consists of a pre-factor in which the relative energies are fixed by the initial state of the particles, an intermediate part in which only global propagation of the particles occurs, and a post-factor in which relative energies are fixed by the final state of the particles. The pre- and post-factors are necessary in order to account for the transition from states where particles are off their mass shell to states described by the global propagator with all of the particle energies on shell. The pole structure of the intermediate part of the propagator is used to determine the equation for the three-body bound state: a Schr{\"o}dinger-like relativistic equation with a single, global Green's function. The role of the pre- and post-factors in the relativistic dynamics is to incorporate the poles of the breakup channels in the initial and final states. The derivation of this equation by integrating over the relative times rather than via a constraint on relative momenta allows the inclusion of retardation and dynamical boost corrections without introducing unphysical singularities.Comment: REVTeX, 21 pages, 4 figures, epsf.st

The stability for the Cauchy problem for elliptic equations

We discuss the ill-posed Cauchy problem for elliptic equations, which is pervasive in inverse boundary value problems modeled by elliptic equations. We provide essentially optimal stability results, in wide generality and under substantially minimal assumptions. As a general scheme in our arguments, we show that all such stability results can be derived by the use of a single building brick, the three-spheres inequality.Comment: 57 pages, review articl

Dynamics near the critical point: the hot renormalization group in quantum field theory

The perturbative approach to the description of long wavelength excitations at high temperature breaks down near the critical point of a second order phase transition. We study the \emph{dynamics} of these excitations in a relativistic scalar field theory at and near the critical point via a renormalization group approach at high temperature and an $\epsilon$ expansion in $d=5-\epsilon$ space-time dimensions. The long wavelength physics is determined by a non-trivial fixed point of the renormalization group. At the critical point we find that the dispersion relation and width of quasiparticles of momentum $p$ is $\omega_p \sim p^{z}$ and $\Gamma_p \sim (z-1) \omega_p$ respectively, the group velocity of quasiparticles $v_g \sim p^{z-1}$ vanishes in the long wavelength limit at the critical point. Away from the critical point for $T\gtrsim T_c$ we find $\omega_p \sim \xi^{-z}[1+(p \xi)^{2z}]^{{1/2}}$ and $\Gamma_p \sim (z-1) \omega_p \frac{(p \xi)^{2z}}{1+(p \xi)^{2z}}$ with $\xi$ the finite temperature correlation length $\xi \propto |T-T_c|^{-\nu}$. The new \emph{dynamical} exponent $z$ results from anisotropic renormalization in the spatial and time directions. For a theory with O(N) symmetry we find $z=1+ \epsilon \frac{N+2}{(N+8)^2}+\mathcal{O}(\epsilon^2)$. Critical slowing down, i.e, a vanishing width in the long-wavelength limit, and the validity of the quasiparticle picture emerge naturally from this analysis.Comment: Discussion on new dynamical universality class. To appear in Phys. Rev.