Inclusions induced phase separation in mixed lipid film

The effect of rigid inclusions on the phase behavior of a film containing a mixture of lipid molecules is investigated. In the proposed model, the inclusion-induced deformation of the film, and the resulting energy cost are strongly dependent upon the spontaneous curvature of the mixed film. The spontaneous curvature is in turn strongly influenced by the composition of film. This coupling between the film composition and the energy per inclusion leads to a lateral modulation of the composition, which follows the local curvature of the membrane. In particular, it is shown that the inclusion may induce a global phase separation in a film which would otherwise be homogeneously mixed. The mixed film is then composed of patches of different average composition, separated by the inclusions. This process may be of relevance to explain some aspects of lipid-protein association in biological membranes.Comment: 19 pages, 5 figure

Long-Range Interaction between Heterogeneously Charged Membranes

Despite their neutrality, surfaces or membranes with equal amounts of positive and negative charge can exhibit long-range electrostatic interactions if the surface charge is heterogeneous; this can happen when the surface charges form finite-size domain structures. These domains can be formed in lipid membranes where the balance of the different ranges of strong but short-ranged hydrophobic interactions and longer-ranged electrostatic repulsion result in a finite, stable domain size. If the domain size is large enough, oppositely charged domains in two opposing surfaces or membranes can be strongly correlated by the elecrostatic interactions; these correlations give rise to an attractive interaction of the two membranes or surfaces over separations on the order of the domain size. We use numerical simulations to demonstrate the existence of strong attractions at separations of tens of nanometers. Large line tensions result in larger domains but also increase the charge density within the domain. This promotes correlations and, as a result, increases the intermembrane attraction. On the other hand, increasing the salt concentration increases both the domain size and degree of domain anticorrelation, but the interactions are ultimately reduced due to increased screening. The result is a decrease in the net attraction as salt concentration is increased

Surface tension in bilayer membranes with fixed projected area

We study the elastic response of bilayer membranes with fixed projected area to both stretching and shape deformations. A surface tension is associated to each of these deformations. By using model amphiphilic membranes and computer simulations, we are able to observe both the types of deformation, and thus, both the surface tensions, related to each type of deformation, are measured for the same system. These surface tensions are found to assume different values in the same bilayer membrane: in particular they vanish for different values of the projected area. We introduce a simple theory which relates the two quantities and successfully apply it to the data obtained with computer simulations

Self-limited self-assembly of chiral filaments

The assembly of filamentous bundles with controlled diameters is common in biological systems and desirable for the development of nanomaterials. We discuss dynamical simulations and free energy calculations on patchy spheres with chiral pair interactions that spontaneously assemble into filamentous bundles. The chirality frustrates long-range crystal order by introducing twist between interacting subunits. For some ranges of system parameters this constraint leads to bundles with a finite diameter as the equilibrium state, and in other cases frustration is relieved by the formation of defects. While some self-limited structures can be modeled as twisted filaments arranged with local hexagonal symmetry, other structures are surprising in their complexity.Comment: 5 pages, 5 figure

Saddle-splay modulus of a particle-laden fluid interface

The scaled-particle theory equation of state for the two-dimensional hard-disk fluid on a curved surface is proposed and used to determine the saddle-splay modulus of a particle-laden fluid interface. The resulting contribution to saddle-splay modulus, which is caused by thermal motion of the adsorbed particles, is comparable in magnitude with the saddle-splay modulus of a simple fluid interface.Comment: 10 pages, 2 figure

Swelling of particle-encapsulating random manifolds

We study the statistical mechanics of a closed random manifold of fixed area and fluctuating volume, encapsulating a fixed number of noninteracting particles. Scaling analysis yields a unified description of such swollen manifolds, according to which the mean volume gradually increases with particle number, following a single scaling law. This is markedly different from the swelling under fixed pressure difference, where certain models exhibit criticality. We thereby indicate when the swelling due to encapsulated particles is thermodynamically inequivalent to that caused by fixed pressure. The general predictions are supported by Monte Carlo simulations of two particle-encapsulating model systems -- a two-dimensional self-avoiding ring and a three-dimensional self-avoiding fluid vesicle. In the former the particle-induced swelling is thermodynamically equivalent to the pressure-induced one whereas in the latter it is not.Comment: 8 pages, 6 figure

Minimal Bending Energies of Bilayer Polyhedra

Motivated by recent experiments on bilayer polyhedra composed of amphiphilic molecules, we study the elastic bending energies of bilayer vesicles forming polyhedral shapes. Allowing for segregation of excess amphiphiles along the ridges of polyhedra, we find that bilayer polyhedra can indeed have lower bending energies than spherical bilayer vesicles. However, our analysis also implies that, contrary to what has been suggested on the basis of experiments, the snub dodecahedron, rather than the icosahedron, generally represents the energetically favorable shape of bilayer polyhedra

Solvent-free coarse-grained lipid model for large-scale simulations

A coarse-grained molecular model, which consists of a spherical particle and an orientation vector, is proposed to simulate lipid membrane on a large length scale. The solvent is implicitly represented by an effective attractive interaction between particles. A bilayer structure is formed by orientation-dependent (tilt and bending) potentials. In this model, the membrane properties (bending rigidity, line tension of membrane edge, area compression modulus, lateral diffusion coefficient, and flip-flop rate) can be varied over broad ranges. The stability of the bilayer membrane is investigated via droplet-vesicle transition. The rupture of the bilayer and worm-like micelle formation can be induced by an increase in the spontaneous curvature of the monolayer membrane.Comment: 13 pages, 19 figure

Intraocular Lens Tilt Due to Optic-Haptic Junction Distortion Following Intrascleral Haptic Fixation With the Yamane Technique

Purpose: To report two patients with a complication of Yamane intrascleral haptic fixation surgery (ISHF) with the Zeiss CT Lucia 602 lens: severely tilted intraocular lens (IOL) leading to significantly decreased vision in the early post-operative period. Observations: We report two patients presenting with severely tilted IOL implants one day and one month following Yamane ISHF. The first patient is a monocular 81-year-old woman referred for treatment of cornea edema. Initial surgery involved replacement of an anterior chamber lens with a CT Lucia 602 posterior chamber lens using Yamane technique and Descemet\u27s stripping endothelial keratoplasty. The patient returned at one month follow-up with poor vision and IOL tilt observable at the slit lamp through a peripheral iridectomy site. Explanation of the Zeiss lens revealed haptic distortion at the optic-haptic insertion point such that each haptic was about 45° off axis to the plane of the optic in approximately equal and opposite directions. The second patient, a 75-year-old woman, was referred with a completely dislocated lens-bag complex in the right eye. The initial operative treatment for this patient included pars plana vitrectomy, retrieval and removal of the dislocated lens-bag complex, and placement of a Zeiss 602 lens via Yamane ISHF technique. On the first postoperative day, the patient was count fingers in the right eye with an intraocular pressure of 5 mm Hg and obvious IOL tilt on slit lamp examination. Explanation of the lens revealed severely distorted haptics relative to the optic by more than a 60-degree angle on both sides. In both cases, initial surgery was performed with an IOL inspected prior to implantation and found to have normal appearing haptics. At the end of each case, there was adequate centration and no tilt of the IOL. Management in both patients included removal of the defective lens and placement of a new, same power CT Lucia 602 lens via the Yamane technique. Visual acuity improved from CF to 20/30 best corrected after reoperation in both cases. Conclusions and importance: In summary, we describe a complication of Yamane ISHF with the CT Lucia 602 lens in which there is lens tilting associated with distortion at the optic-haptic fastening zone in the early postoperative period. In the event of a titled lens following Yamane ISHF, awareness of this complication may help surgeons consider lens replacement, as the haptics may be permanently distorted or damaged

Irreversibility in response to forces acting on graphene sheets

The amount of rippling in graphene sheets is related to the interactions with the substrate or with the suspending structure. Here, we report on an irreversibility in the response to forces that act on suspended graphene sheets. This may explain why one always observes a ripple structure on suspended graphene. We show that a compression-relaxation mechanism produces static ripples on graphene sheets and determine a peculiar temperature $T_c$, such that for $T<T_c$ the free-energy of the rippled graphene is smaller than that of roughened graphene. We also show that $T_c$ depends on the structural parameters and increases with increasing sample size.Comment: 4 pages, 4 Figure