Decrumpling membranes by quantum effects

The phase diagram of an incompressible fluid membrane subject to quantum and thermal fluctuations is calculated exactly in a large number of dimensions of configuration space. At zero temperature, a crumpling transition is found at a critical bending rigidity $1/\alpha_{\rm c}$. For membranes of fixed lateral size, a crumpling transition occurs at nonzero temperatures in an auxiliary mean field approximation. As the lateral size L of the membrane becomes large, the flat regime shrinks with $1/\ln L$.Comment: 9 pages, 4 figure

Global Energy Matching Method for Atomistic-to-Continuum Modeling of Self-Assembling Biopolymer Aggregates

This paper studies mathematical models of biopolymer supramolecular aggregates that are formed by the self-assembly of single monomers. We develop a new multiscale numerical approach to model the structural properties of such aggregates. This theoretical approach establishes micro-macro relations between the geometrical and mechanical properties of the monomers and supramolecular aggregates. Most atomistic-to-continuum methods are constrained by a crystalline order or a periodic setting and therefore cannot be directly applied to modeling of soft matter. By contrast, the energy matching method developed in this paper does not require crystalline order and, therefore, can be applied to general microstructures with strongly variable spatial correlations. In this paper we use this method to compute the shape and the bending stiffness of their supramolecular aggregates from known chiral and amphiphilic properties of the short chain peptide monomers. Numerical implementation of our approach demonstrates consistency with results obtained by molecular dynamics simulations

On Shape Transformations and Shape Fluctuations of Cellular Compartments and Vesicles

We discuss the shape formation and shape transitions of simple bilayer vesicles in context with their role in biology. In the first part several classes of shape changes of vesicles of one lipid component are described and it is shown that these can be explained in terms of the bending energy concept in particular augmented by the bilayer coupling hypothesis. In the second part shape changes and vesicle fission of vesicles composed of membranes of lipid mixtures are reported. These are explained in terms of coupling between local curvature and phase separation

Bilayer Membrane in Confined Geometry: Interlayer Slide and Steric Repulsion

We derived free energy functional of a bilayer lipid membrane from the first principles of elasticity theory. The model explicitly includes position-dependent mutual slide of monolayers and bending deformation. Our free energy functional of liquid-crystalline membrane allows for incompressibility of the membrane and vanishing of the in-plane shear modulus and obeys reflectional and rotational symmetries of the flat bilayer. Interlayer slide at the mid-plane of the membrane results in local difference of surface densities of the monolayers. The slide amplitude directly enters free energy via the strain tensor. For small bending deformations the ratio between bending modulus and area compression coefficient, Kb/KA, is proportional to the square of monolayer thickness, h. Using the functional we performed self-consistent calculation of steric potential acting on bilayer between parallel confining walls separated by distance 2d. We found that temperature-dependent curvature at the minimum of confining potential is enhanced four times for a bilayer with slide as compared with a unit bilayer. We also calculate viscous modes of bilayer membrane between confining walls. Pure bending of the membrane is investigated, which is decoupled from area dilation at small amplitudes. Three sources of viscous dissipation are considered: water and membrane viscosities and interlayer drag. Dispersion has two branches. Confinement between the walls modifies the bending mode with respect to membrane in bulk solution. Simultaneously, inter-layer slipping mode, damped by viscous drag, remains unchanged by confinement.Comment: 23 pages,3 figures, pd

Propagation of a finite-amplitude potential vorticity front along the wall of a stratified fluid

Author Posting. © Cambridge University Press, 2002. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 468 (2002): 179-204, doi:10.1017/S0022112002001520.A similarity solution to the long-wave shallow-water equations is obtained for a density current (reduced gravity = g[prime prime or minute], Coriolis parameter = f) propagating alongshore (y = 0). The potential vorticity q = f/H1 is uniform in [minus sign][infty infinity] < x [less-than-or-eq, slant] xnose(t), 0 < y [less-than-or-eq, slant] L(x, t), and the nose of this advancing potential vorticity front displaces fluid of greater q = f/H0, which is located at L < y < [infty infinity]. If L0 = L([minus sign][infty infinity], t), the nose point with L(xnose(t), t) = 0 moves with velocity Unose = [surd radical]g[prime prime or minute]H0 [phi], where [phi] is a function of H1/H0, f2L20/g[prime prime or minute]H0. The assumptions made in the similarity theory are verified by an initial value solution of the complete reduced-gravity shallow-water equations. The latter also reveal the new effect of a Kelvin shock wave colliding with a potential vorticity front, as is confirmed by a laboratory experiment. Also confirmed is the expansion wave structure of the intrusion, but the observed values of Unose are only in qualitative agreement; the difference is attributed to the presence of small-scale (non-hydrostatic) turbulence in the laboratory experiment but not in the numerical solutions.This work is funded by National Science Foundation grants OCE-9726584 & OCE-0092504 (M. E. S.) and OCE-9810599 (K. R. H.)

Spherical Vesicles Distorted by a Grafted Latex Bead: An Exact Solution

We present an exact solution to the problem of the global shape description of a spherical vesicle distorted by a grafted latex bead. This solution is derived by treating the nonlinearity in bending elasticity through the (topological) Bogomol'nyi decomposition technique and elastic compatibility. We recover the ``hat-model'' approximation in the limit of a small latex bead and find that the region antipodal to the grafted latex bead flattens. We also derive the appropriate shape equation using the variational principle and relevant constraints.Comment: 12 pages, 2 figures, LaTeX2e+REVTeX+AmSLaTe

Interface-mediated interactions: Entropic forces of curved membranes

Particles embedded in a fluctuating interface experience forces and torques mediated by the deformations and by the thermal fluctuations of the medium. Considering a system of two cylinders bound to a fluid membrane we show that the entropic contribution enhances the curvature-mediated repulsion between the two cylinders. This is contrary to the usual attractive Casimir force in the absence of curvature-mediated interactions. For a large distance between the cylinders, we retrieve the renormalization of the surface tension of a flat membrane due to thermal fluctuations.Comment: 11 pages, 5 figures; final version, as appeared in Phys. Rev.

Random pinning limits the size of membrane adhesion domains

Theoretical models describing specific adhesion of membranes predict (for certain parameters) a macroscopic phase separation of bonds into adhesion domains. We show that this behavior is fundamentally altered if the membrane is pinned randomly due to, e.g., proteins that anchor the membrane to the cytoskeleton. Perturbations which locally restrict membrane height fluctuations induce quenched disorder of the random-field type. This rigorously prevents the formation of macroscopic adhesion domains following the Imry-Ma argument [Y. Imry and S. K. Ma, Phys. Rev. Lett. 35, 1399 (1975)]. Our prediction of random-field disorder follows from analytical calculations, and is strikingly confirmed in large-scale Monte Carlo simulations. These simulations are based on an efficient composite Monte Carlo move, whereby membrane height and bond degrees of freedom are updated simultaneously in a single move. The application of this move should prove rewarding for other systems also.Comment: revised and extended versio

Capture on High Curvature Region: Aggregation of Colloidal Particle Bound to Giant Phospholipid Vesicles

A very recent observation on the membrane mediated attraction and ordered aggregation of colloidal particles bound to giant phospholipid vesicles (I. Koltover, J. O. R\"{a}dler, C. R. Safinya, Phys. Rev. Lett. {\bf 82}, 1991(1999)) is investigated theoretically within the frame of Helfrich curvature elasticity theory of lipid bilayer fluid membrane. Since the concave or waist regions of the vesicle possess the highest local bending energy density, the aggregation of colloidal beads on these places can reduce the elastic energy in maximum. Our calculation shows that a bead in the concave region lowers its energy $\sim 20 k_B T$. For an axisymmetrical dumbbell vesicle, the local curvature energy density along the waist is equally of maximum, the beads can thus be distributed freely with varying separation distance.Comment: 12 pages, 2 figures. REVte