Super-resolution imaging of highly curved membrane structures in giant vesicles encapsulating molecular condensates

Molecular crowding is an inherent feature of the cell interior. Synthetic cells as provided by giant unilamellar vesicles (GUVs) encapsulating macromolecules (polyethylene-glycol and dextran) represent an excellent mimetic system to study membrane transformations associated with molecular crowding and protein condensation. Similarly to cells, such GUVs loaded with macromolecules exhibit highly curved structures such as internal nanotubes. In addition, upon liquid-liquid phase separation as inside living cells, the membrane of GUVs encapsulating an aqueous two-phase system deforms to form apparent kinks at the contact line of the interface between the two aqueous phases. These structures, nanotubes and kinks, have dimensions below optical resolution and if resolved, can provide information about material properties such as membrane spontaneous curvature and intrinsic contact angle describing the wettability contrast of the encapsulated phases to the membrane. Previous experimental studies were based on conventional optical microscopy which cannot resolve these membrane and wetting properties. Here, we studied these structures with super-resolution microscopy, namely stimulated emission depletion (STED) microscopy, together with microfluidic manipulation. We demonstrate the cylindrical nature of the nanotubes with unprecedented detail based on the superior resolution of STED and automated data analysis. The spontaneous curvature deduced from the nanotube diameters is in excellent agreement with theoretical predictions. Furthermore, we were able to resolve the membrane “kink” structure as a smoothly curved membrane demonstrating the existence of the intrinsic contact angle. We find very good agreement between the directly measured values and the theoretically predicted ones based on the apparent contact angles on the micrometer scale. During different stages of cellular events, biomembranes undergo a variety of shape transformations such as the formation of buds and nanotubes regulated by membrane necks. We demonstrate that these highly curved membrane structures are amenable to STED imaging and show that such studies provide important insights in the membrane properties and interactions underlying cellular activities

Critical phenomena of thick branes in warped spacetimes

We have investigated the effects of a generic bulk first-order phase transition on thick Minkowski branes in warped geometries. As occurs in Euclidean space, when the system is brought near the phase transition an interface separating two ordered phases splits into two interfaces with a disordered phase in between. A remarkable and distinctive feature is that the critical temperature of the phase transition is lowered due to pure geometrical effects. We have studied a variety of critical exponents and the evolution of the transverse-traceless sector of the metric fluctuations.Comment: revtex4, 4 pages, 4 figures, some comments added, typos corrected, published in PR

Conformally invariant bending energy for hypersurfaces

The most general conformally invariant bending energy of a closed four-dimensional surface, polynomial in the extrinsic curvature and its derivatives, is constructed. This invariance manifests itself as a set of constraints on the corresponding stress tensor. If the topology is fixed, there are three independent polynomial invariants: two of these are the straighforward quartic analogues of the quadratic Willmore energy for a two-dimensional surface; one is intrinsic (the Weyl invariant), the other extrinsic; the third invariant involves a sum of a quadratic in gradients of the extrinsic curvature -- which is not itself invariant -- and a quartic in the curvature. The four-dimensional energy quadratic in extrinsic curvature plays a central role in this construction.Comment: 16 page

Second variation of the Helfrich-Canham Hamiltonian and reparametrization invariance

A covariant approach towards a theory of deformations is developed to examine both the first and second variation of the Helfrich-Canham Hamiltonian -- quadratic in the extrinsic curvature -- which describes fluid vesicles at mesoscopic scales. Deformations are decomposed into tangential and normal components; At first order, tangential deformations may always be identified with a reparametrization; at second order, they differ. The relationship between tangential deformations and reparametrizations, as well as the coupling between tangential and normal deformations, is examined at this order for both the metric and the extrinsic curvature tensors. Expressions for the expansion to second order in deformations of geometrical invariants constructed with these tensors are obtained; in particular, the expansion of the Hamiltonian to this order about an equilibrium is considered. Our approach applies as well to any geometrical model for membranes.Comment: 20 page

On Growth, Disorder, and Field Theory

This article reviews recent developments in statistical field theory far from equilibrium. It focuses on the Kardar-Parisi-Zhang equation of stochastic surface growth and its mathematical relatives, namely the stochastic Burgers equation in fluid mechanics and directed polymers in a medium with quenched disorder. At strong stochastic driving -- or at strong disorder, respectively -- these systems develop nonperturbative scale-invariance. Presumably exact values of the scaling exponents follow from a self-consistent asymptotic theory. This theory is based on the concept of an operator product expansion formed by the local scaling fields. The key difference to standard Lagrangian field theory is the appearance of a dangerous irrelevant coupling constant generating dynamical anomalies in the continuum limit.Comment: review article, 50 pages (latex), 10 figures (eps), minor modification of original versio

Interface Fluctuations on a Hierarchical Lattice

We consider interface fluctuations on a two-dimensional layered lattice where the couplings follow a hierarchical sequence. This problem is equivalent to the diffusion process of a quantum particle in the presence of a one-dimensional hierarchical potential. According to a modified Harris criterion this type of perturbation is relevant and one expects anomalous fluctuating behavior. By transfer-matrix techniques and by an exact renormalization group transformation we have obtained analytical results for the interface fluctuation exponents, which are discontinuous at the homogeneous lattice limit.Comment: 14 pages plain Tex, one Figure upon request, Phys Rev E (in print

Cylindrical equilibrium shapes of fluid membranes

Within the framework of the well-known curvature models, a fluid lipid bilayer membrane is regarded as a surface embedded in the three-dimensional Euclidean space whose equilibrium shapes are described in terms of its mean and Gaussian curvatures by the so-called membrane shape equation. In the present paper, all solutions to this equation determining cylindrical membrane shapes are found and presented, together with the expressions for the corresponding position vectors, in explicit analytic form. The necessary and sufficient conditions for such a surface to be closed are derived and several sufficient conditions for its directrix to be simple or self-intersecting are given.Comment: 17 pages, 4 figures. Published in J. Phys. A: Math. Theore

Direct Visualization of Dislocation Dynamics in Grain Boundary Scars

Mesoscale objects with unusual structural features may serve as the analogues of atoms in the design of larger-scale materials with novel optical, electronic or mechanical behaviour. In this paper we investigate the structural features and the equilibrium dynamics of micron-scale spherical crystals formed by polystyrene particles adsorbed on the surface of a spherical water droplet. The ground state of sufficiently large crystals possesses finite-length grain boundaries (scars). We determine the elastic response of the crystal by measuring single-particle diffusion and quantify the fluctuations of individual dislocations about their equilibrium positions within a scar determining the dislocation spring constants. We observe rapid dislocation glide with fluctuations over the barriers separating one local Peierls minimum from the next and rather weak binding of dislocations to their associated scars. The long-distance (renormalised) dislocation diffusion glide constant is extracted directly from the experimental data and is found to be moderately faster than single particle diffusion. We are also able to determine the parameters of the Peierls potential induced by the underlying crystalline lattice.Comment: 11 pages, 4 figures, pdf forma

Tyrosine Sulfation of Native Mouse Psgl-1 Is Required for Optimal Leukocyte Rolling on P-Selectin In Vivo

We recently demonstrated that tyrosine sulfation is an important contributor to monocyte recruitment and retention in a mouse model of atherosclerosis. P-selectin glycoprotein ligand-1 (Psgl-1) is tyrosine-sulfated in mouse monocyte/macrophages and its interaction with P-selectin is important in monocyte recruitment in atherosclerosis. However, whether tyrosine sulfation is required for the P-selectin binding function of mouse Psgl-1 is unknown. Here we test the function of native Psgl-1 expressed in leukocytes lacking endogenous tyrosylprotein sulfotransferase (TPST) activity.Psgl-1 function was assessed by examining P-selectin dependent leukocyte rolling in post-capillary venules of C57BL6 mice transplanted with hematopoietic progenitors from wild type (WT → B6) or Tpst1;Tpst2 double knockout mice (Tpst DKO → B6) which lack TPST activity. We observed that rolling flux fractions were lower and leukocyte rolling velocities were higher in Tpst DKO → B6 venules compared to WT → B6 venules. Similar results were observed on immobilized P-selectin in vitro. Finally, Tpst DKO leukocytes bound less P-selectin than wild type leukocytes despite equivalent surface expression of Psgl-1.These findings provide direct and convincing evidence that tyrosine sulfation is required for optimal function of mouse Psgl-1 in vivo and suggests that tyrosine sulfation of Psgl-1 contributes to the development of atherosclerosis