Calculation of Forces at Focal Adhesions from Elastic Substrate Data: The Effect of Localized Force and the Need for Regularization

AbstractForces exerted by stationary cells have been investigated on the level of single focal adhesions by combining elastic substrates, fluorescence labeling of focal adhesions, and the assumption of localized force when solving the inverse problem of linear elasticity theory. Data simulation confirms that the inverse problem is ill-posed in the presence of noise and shows that in general a regularization scheme is needed to arrive at a reliable force estimate. Spatial and force resolution are restricted by the smoothing action of the elastic kernel, depend on the details of the force and displacement patterns, and are estimated by data simulation. Corrections arising from the spatial distribution of force and from finite substrate size are treated in the framework of a force multipolar expansion. Our method is computationally cheap and could be used to study mechanical activity of cells in real time

Fate of Zero-Temperature Ising Ferromagnets

We investigate the relaxation of homogeneous Ising ferromagnets on finite lattices with zero-temperature spin-flip dynamics. On the square lattice, a frozen two-stripe state is apparently reached approximately 1/4 of the time, while the ground state is reached otherwise. The asymptotic relaxation is characterized by two distinct time scales, with the longer stemming from the influence of a long-lived diagonal stripe ``defect''. In greater than two dimensions, the probability to reach the ground state rapidly vanishes as the size increases and the system typically ends up wandering forever within an iso-energy set of stochastically ``blinking'' metastable states.Comment: 4 pages in column format, 6 figure

Equilibrium and nonequilibrium fluctuations at the interface between two fluid phases

We have performed small-angle light-scattering measurements of the static structure factor of a critical binary mixture undergoing diffusive partial remixing. An uncommon scattering geometry integrates the structure factor over the sample thickness, allowing different regions of the concentration profile to be probed simultaneously. Our experiment shows the existence of interface capillary waves throughout the macroscopic evolution to an equilibrium interface, and allows to derive the time evolution of surface tension. Interfacial properties are shown to attain their equilibrium values quickly compared to the system's macroscopic equilibration time.Comment: 10 pages, 5 figures, submitted to PR

Effect of Lipid Characteristics on the Structure of Transmembrane Proteins

AbstractThe activity of embedded proteins is known to vary with lipid characteristics. Indeed, it has been shown that some cell-membrane proteins cannot function unless certain non-bilayer-forming lipids (i.e., nonzero spontaneous curvature) are present. In this paper we show that membranes exert a line tension on transmembrane proteins. The line tension, on the order of 1–100kT/protein, varies with the lipid properties and the protein configuration. Thus, membranes composed of different lipids favor different protein conformations. Model predictions are in excellent agreement with the data of Keller et al. (Biophys. J. 1993, 65:23–27) regarding the conductance of alamethicin channels

Elastic interactions of active cells with soft materials

Anchorage-dependent cells collect information on the mechanical properties of the environment through their contractile machineries and use this information to position and orient themselves. Since the probing process is anisotropic, cellular force patterns during active mechanosensing can be modelled as anisotropic force contraction dipoles. Their build-up depends on the mechanical properties of the environment, including elastic rigidity and prestrain. In a finite sized sample, it also depends on sample geometry and boundary conditions through image strain fields. We discuss the interactions of active cells with an elastic environment and compare it to the case of physical force dipoles. Despite marked differences, both cases can be described in the same theoretical framework. We exactly solve the elastic equations for anisotropic force contraction dipoles in different geometries (full space, halfspace and sphere) and with different boundary conditions. These results are then used to predict optimal position and orientation of mechanosensing cells in soft material.Comment: Revtex, 38 pages, 8 Postscript files included; revised version, accepted for publication in Phys. Rev.

Domain Growth and Finite-Size-Scaling in the Kinetic Ising Model

This paper describes the application of finite-size scaling concepts to domain growth in systems with a non-conserved order parameter. A finite-size scaling ansatz for the time-dependent order parameter distribution function is proposed, and tested with extensive Monte-Carlo simulations of domain growth in the 2-D spin-flip kinetic Ising model. The scaling properties of the distribution functions serve to elucidate the configurational self-similarity that underlies the dynamic scaling picture. Moreover, it is demonstrated that the application of finite-size-scaling techniques facilitates the accurate determination of the bulk growth exponent even in the presence of strong finite-size effects, the scale and character of which are graphically exposed by the order parameter distribution function. In addition it is found that one commonly used measure of domain size--the scaled second moment of the magnetisation distribution--belies the full extent of these finite-size effects.Comment: 13 pages, Latex. Figures available on request. Rep #9401

Full Connectivity: Corners, edges and faces

We develop a cluster expansion for the probability of full connectivity of high density random networks in confined geometries. In contrast to percolation phenomena at lower densities, boundary effects, which have previously been largely neglected, are not only relevant but dominant. We derive general analytical formulas that show a persistence of universality in a different form to percolation theory, and provide numerical confirmation. We also demonstrate the simplicity of our approach in three simple but instructive examples and discuss the practical benefits of its application to different models.Comment: 28 pages, 8 figure

Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given

V. MAGNETIC EXCITATIONSRAMAN SCATTERING STUDIES OF SPIN ORDER AND FLUCTUATIONS IN THE EUROPIUM CHALCOGENIDES

Ici on examine la diffusion de lumière, à la fois inélastique et dépandente de la phase magnétique, des phonons dans les chalcogénides d'europium attirant l'attention sur l'allure des spectres près des transitions à phase magnétique. Par suite du mécanisme de diffusion Raman "un phonon-un spin" qui donne lieu à ces spectres, on observe des lignes Raman du premier ordre de type aussi large (Ɗν[MATH] 30cm-1) que fin (Ɗν ≤ 1cm-1). La dépendance de température calculée des spectres Raman à lignes larges s'est rapportée aux variations de spin et est comparée avec l'expérience. On montre que les lignes fines, observées dans les phases magnétiques ordonnées aux énergies de phonon non [MATH] = 0, sont une mesure directe du carré du paramètre d'ordre (exposant β). Les spectres Raman observés sont mis en corrélation avec les propriétés magnétiques des composés EuSe et EuTe près des transitions à phase métamagnétique (EuSe) et spin flop-paramagnétique (EuTe). La théorie aussi bien que l'expérience montrent que la dépendance de température et de champ magnétique de ces spectres Raman est une sonde sensible des variations de spin et de l'ordre de spin dans ces substances.Magnetic phase dependent, inelastic light scattering from phonons in the europium chalcogenides is reviewed with an emphasis on the behavior of the spectra near magnetic phase transitions. As a result of the one phonon-one spin Raman scattering mechanism which gives rise to these spectra, both broad (Ɗν[MATH] 30cm-1) and sharp (Ɗν ≤ 1cm-1) first-order Raman lines are observed. The calculated temperature dependence of the broadline Raman spectra is related to spin fluctuations and compared with experiment. The sharp lines, observed in the ordered magnetic phases at non [MATH] = 0 phonon energies, are shown to be a direct measure of the square of the order parameter (exponent ß). The observed Raman spectra are correlated with the magnetic properties of EuSe and EuTe near the metamagnetic (EuSe) and spin flop to paramagnetic (EuTe) phase transitions. Both theory and experiment indicate that the temperature and magnetic field dependence of these Raman spectra is a sensitive probe of spin fluctuations and spin order in these materials

Entropically driven attraction between telechelic brushes

We discuss the structure and the interaction of telechelic brushes. We show that the association of functionalized chain ends is capable of giving rise to attractive interactions between telechelic brush-covered surfaces, in contrast to conventional repulsion. Our predictions for the interaction free energy are in agreement with experimental data