Multi-component membranes such as ternary mixtures of lipids and cholesterol can exhibit coexistence regions between two liquid phases. When such membranes adhere to a corrugated substrate, the phase separation process strongly depends on the interplay between substrate topography, bending rigidities, and line tension of the membrane domains as we show theoretically via energy minimization and Monte Carlo simulations. For sufficiently large bending rigidity contrast between the two membrane phases, the corrugated substrate truncates the phase separation process and leads to a stable pattern of membrane domains. Our theory is consistent with recent experimental observations and provides a possible control mechanism for domain patterns in biological membranes.
We have employed our recently developed Green's function formalism to study the dielectric behavior of a model membrane, formed by two periodic interfaces separating two media of different dielectric constants. The Maxwell's equations are converted into a surface integral equation; thus it greatly simplifies the solutions and yields accurate results for membranes of arbitrary shape. The integral equation is solved and dielectric dispersion spectrum is obtained for a model corrugated membrane. We report a giant dielectric dispersion as the amplitude of corrugation becomes large.
We investigate liquid layers adsorbed at spherical and corrugated cylindrical substrates. The effective Hamiltonians for the liquid-gas interfaces fluctuating in the presence of such curved substrates are derived via the mean-field density functional theory. Their structure is compared with the Helfrich Hamiltonian which is parametrized by the bending and Gaussian rigidity coefficients. For long-ranged interparticle interactions of van der Waals type these coefficients turn out to be non-universal functions of interfacial curvatures; their form varies from one interface to another. We discuss …
We investigate - with Monte Carlo computer simulations - the phase behaviour of dimeric colloidal molecules on periodic substrates with square symmetry. The molecules are formed in a two-dimensional suspension of like charged colloids subject to periodic external confinement, which can be experimentally realized by optical methods. We study the evolution of positional and orientational order by varying the temperature across the melting transition. We propose and evaluate appropriate order parameters as well as the specific heat capacity and show that the decay of positional correlations belon…
The thermal fluctuation spectrum of a fluid membrane coupled harmonically to a solid support by an array of tethers is calculated. For strong tethers, this spectrum exhibits non-monotonic, anisotropic behavior with a relative maximum at a wavelength about twice the tether distance. The root mean square displacement is evaluated to estimate typical membrane displacements. Possible applications cover pillar-supported or polymer-tethered membranes.
The molecular structure of a multilayer of 1,2-distearoyl-sn-glycero-3-phosphocholine (DSPC) adsorbed on the surface of the hydrosol of silica nanoparticles has been studied by the synchrotron radiation scattering method. According to the reflectometry data, the multilayer is formed by planar phospholipid bilayers with a thickness of 69 +/- 1 Angstrom and its total thickness is about 400 Angstrom. Grazing-incidence diffraction indicates that the bilayers are in the crystal state with an area of 41.6 +/- 0.7 Angstrom^2 per molecule.
We present numerical calculations of lamellar phases of di-block copolymers (BCP) confined between two surfaces, where the top surface is flat and the bottom one is corrugated. The corrugated substrate is assumed to have a single $q$-mode of lateral undulations with a wavenumber q_s and amplitude R. We focus on the effects of substrate roughness, parameterized by the dimensionless quantity, q_sR, on the relative stability between parallel and perpendicular orientations of the lamellar phase. The competition between film confinement, energy cost of elastic deformation and gain in surface energy…
The organization of lipids in biological membranes is essential for cellular functions such as signal transduction and membrane trafficking. A major challenge is how to control lateral lipid composition in supported membranes which are crucial for the design of biosensors and investigation of cellular processes. Here, we undertake the first theoretical study of lateral organization of mixed lipids in bilayers induced by a geometrically patterned substrate, and examine the physical mechanism of patterned substrate-induced structural formation in the supported lipid bilayers. A rich variety of c…
Fluctuation spectra of fluid compound membrane systems are calculated. The systems addressed contain two (or more) almost parallel membranes that are connected by harmonic tethers or by a continuous, harmonic confining potential. Additionally, such a compound system can be attached to a supporting substrate. We compare quasi-analytical results for tethers with analytical results for corresponding continuous models and investigate under what circumstances the discrete nature of the tethers actually influences the fluctuations. A tethered, supported membrane pair with similar bending rigidities …
Experiments on supported lipid bilayers featuring liquid ordered/disordered domains have shown that the spatial arrangement of the lipid domains and their chemical composition are strongly affected by the curvature of the substrate. Furthermore, theoretical predictions suggest that both these effects are intimately related with the closed topology of the bilayer. In this work, we test this hypothesis by fabricating supported membranes consisting of colloidal particles of various shapes lying on a flat substrate. A single lipid bilayer coats both colloids and substrate, allowing local lipid exc…
We investigate interactions between an elastic membrane and a substrate characterized by quenched positional disorder in the height function. We show that the positional disorder transforms the standard secondary DLVO minimum into two separate states: the hovering state characterized by a planar membrane at a finite separation from the interface and a pinned state where the membrane follows closely the asperities of the substrate and is as a consequence quite corrugated. The transition between the two states is continuous and depends on the parameters of the underlying DLVO potential as well a…
The detachment dynamics of a fluid membrane with an isotropic spontaneous curvature from a flat substrate are studied by using meshless membrane simulations. The membrane is detached from an open edge leading to vesicle formation. With strong adhesion, the competition between the bending and adhesion energies determines the minimum value of the spontaneous curvature for the detachment. In contrast, with weak adhesion, a detachment occurs at smaller spontaneous curvatures due to the membrane thermal undulation. When parts of the membrane are pinned on the substrate, the detachment becomes slowe…
Membrane phase behavior induced by the binding of curvature-inducing proteins is studied by a combination of analytical and numerical approaches. In thermal equilibrium under the detailed balance between binding and unbinding, the membrane exhibits three phases: an unbound uniform flat phase (U), a bound uniform flat phase (B), and a separated/corrugated phase (SC). In the SC phase, the bound proteins form hexagonally-ordered bowl-shaped domains. The transitions between the U and SC phases and between the B and SC phases are second order and first order, respectively. At a small spontaneous cu…
We study protein diffusion in multicomponent lipid membranes close to a rigid substrate separated by a layer of viscous fluid. The large-distance, long-time asymptotics for Brownian motion are calculated using a nonlinear stochastic Navier-Stokes equation including the effect of friction with the substrate. The advective nonlinearity, neglected in previous treatments, gives only a small correction to the renormalized viscosity and diffusion coefficient at room temperature. We find, however, that in realistic multicomponent lipid mixtures, close to a critical point for phase separation, protein…
We consider a membrane both weakly and strongly adhering to a geometrically structured substrate. The interaction potential is assumed to be local, via the Deryagin approximation, and harmonic. Consequently, we can analytically describe a variety of different geometries: as well as randomly rough self-affine surfaces, smooth substrates interrupted by an isolated cylindrical pit, a single elongated trench or a periodic array of trenches are investigated. We present more general expressions for the adhesion energy and membrane configuration in Fourier space and find that, compared to planar surf…
The Gaussian (saddle splay) rigidity of fluid membranes controls their equilibrium topology but is notoriously difficult to measure. In lipid mixtures, typical of living cells, linear interfaces separate liquid ordered (LO) from liquid disordered (LD) bilayer phases at subcritical temperatures. Here we consider such membranes supported by curved supports that thereby control the membrane curvatures. We show how spectral analysis of the fluctuations of the LO-LD interface provides a novel way of measuring the difference in Gaussian rigidity between the two phases. We provide a number of conditi…
Nanocomposite membranes are an emerging filtration material in the production of clean water. Recently, the fabrication of porous nanocomposite membranes via solvent transfer induced phase separation (STrIPS) was introduced. During STrIPS, the phase separation of two immiscible liquids is arrested by the attachment of nanoparticles at the liquid-liquid interface, generating a porous particle-stabilized membrane template. STrIPS nanocomposite membranes, however, have so far only been produced as hollow fibers. To overcome this, we designed a roll-to-roll (R2R)-process for the continuous fabrica…
We study the behavior of fluids, confined by geometrically structured substrates, upon approaching a critical point at T = Tc in their bulk phase diagram. As generic substrate structures periodic arrays of wedges and ridges are considered. Based on general renormalization group arguments we calculate, within mean field approximation, the universal scaling functions for order parameter profiles of a fluid close to a single structured substrate and discuss the decay of its spatial variation into the bulk. We compare the excess adsorption at corrugated substrates with the one at planar walls. The…
Membranes derived from ultrathin polymeric films are promising to meet fast separations, but currently available approaches to produce polymer films with greatly reduced thicknesses on porous supports still faces challenges. Here, defect-free ultrathin polymer covering films (UPCFs) are realized by a facile general approach of rapid solvent evaporation. By fast evaporating dilute polymer solutions, we realize ultrathin coating (~30 nm) of porous substrates exclusively on the top surface, forming UPCFs with a block copolymer of polystyrene-block-poly(2-vinyl pyridine) at room temperature or a h…
We grafted polyacrylic acid brushes containing cysteine side chains at a defined surface density on planar lipid membranes. Specular X-ray reflectivity data indicated that the addition of Cd2+ ions induces the compaction of the polymer brush layer and modulates the adhesion of lipid vesicles. The critical threshold level inducing the switch from non-wetting to partial wetting state, [Cd2+] = 0.25 mM, was determined by microinterferometry. The interactions between vesicles and brushes were evaluated by height fluctuations of the membrane in contact with brushes and the shape of vesicles near th…
We have used an original analysis of reflection interference contrast microscopy (RICM) to detect an ultra-weak specific interaction between a glycolipid vesicle and a lectin-coated substrate. The membrane height fluctuations in the contact zone are observed with a high illumination aperture; the membrane profile and the membrane-substrate distance are quantitatively determined using the new analysis, which accounts for multiple interfaces and multiple incidence rays. We showed that this refined version of RICM theory is necessary, specifically in the case of intermediate membranesubstrate dis…
The dependence of the structure of a phospholipid layer (DSPC and SOPC) adsorbed on a hydrosol substrate on the concentration of NaOH in a solution of 5-nm silica particles has been studied by X-ray reflectrometry with the use of synchrotron radiation. Profiles of the electron density (polarizability) have been reconstructed from the experimental data within a model-independent approach. According to these profiles, the thickness of the lipid film can vary from a monolayer (~ 35 Angstrom) to several bilayers (~ 450 Angstrom). At the volume concentration of NaOH of ~ 0.5 mol/L, the film on the …
We numerically examine the two-dimensional ordering of a stripe forming system of particles with competing long-range repulsion and short-range attraction in the presence of a quasi-one-dimensional corrugated substrate. As a function of increasing substrate strength or the ratio of the number of particles to the number of substrate minima we show that a remarkable variety of distinct orderings can be realized, including modulated stripes, prolate clump phases, two dimensional ordered kink structures, crystalline void phases, and smectic phases. Additionally in some cases the stripes align perp…
Internalization of particles by cells plays a crucial role for adsorbing nutrients and fighting infection. Endocytosis is one of the most important mechanisms of the particles uptake which encompass multiple pathways. Although endocytosis is a complex mechanism involving biochemical signaling and active force generation, the energetic cost associated to the large deformations of the cell membrane wrapping around the foreign particle is an important factor controlling this process, which can be studied using quantitative physical models. Of particular interest is the competition between membran…
We explore the relative stability of three possible orientations of cylinder-forming di-block copolymer on a sinusoidally corrugated substrate. The cylinders can be aligned either parallel to the substrate, with their long axis being oriented along or orthogonal to the corrugation trenches, or perpendicular to the substrate. Using self-consistent field theory, we investigate the influence of substrate roughness and surface preference on the phase transition between the three orientations. When the substrate preference, $u$, towards one of components is small, increasing the substrate roughness…
Two-dimensionally nanoconfined water between ideal planar walls has been the subject of ample study, aiming at understanding the intrinsic response of water to confinement, avoiding the consideration of the chemistry of actual confining materials. In this work, we study the response of such nanoconfined water under a periodic confining potential by means of computer simulations, both using empirical potentials and from first-principles. We propose a periodic confining potential emulating the atomistic oscillation of the confining walls, which allows varying the lattice parameter and amplitude …
We revisit the indentation of a thin solid sheet of size $R_{sheet}$ suspended on a circular hole of radius $R \ll R_{sheet}$ in a smooth rigid substrate, addressing the effects of boundary conditions at the hole's edge. Introducing a basic theoretical model for the Van-der-Waals (VdW) sheet-substrate attraction, we demonstrate the dramatic effect of replacing the clamping condition (Schwerin model) with a sliding condition, whereby the supported part of the sheet is allowed to slide towards the indenter and relax the induced hoop compression through angstrom-scale deflections from the thermod…
Motivated by recent experimental work on multicomponent lipid membranes supported by colloidal scaffolds, we report an exhaustive theoretical investigation of the equilibrium configurations of binary mixtures on curved substrates. Starting from the Jülicher-Lipowsky generalization of the Canham-Helfrich free energy to multicomponent membranes, we derive a number of exact relations governing the structure of an interface separating two lipid phases on arbitrarily shaped substrates and its stability. We then restrict our analysis to four classes of surfaces of both applied and conceptual interes…
We theoretically consider specific adhesion of a fluctuating membrane to a hard substrate via the formation of bonds between receptors attached to the substrate and ligands in the membrane. By integrating out the degrees of freedom of the membrane shape, we show that in the biologically relevant limit specific adhesion is well described by a lattice gas model, where lattice sites correspond to bond sites. We derive an explicit expression for the effective bond interactions induced by the thermal undulations of the membrane. Furthermore, we compare kinetic Monte Carlo simulations for our lattic…
The van der Waals interaction between a lipid membrane and a substrate covered by a graphene sheet is investigated using the Lifshitz theory. The reflection coefficients are obtained for a layered planar system submerged in water. The dielectric response properties of the involved materials are also specified and discussed. Our calculations show that a graphene covered substrate can repel the biological membrane in water. This is attributed to the significant changes in the response properties of the system due to the monolayer graphene. It is also found that the van der Waals interaction is m…
We present a general linear response description of membrane adhesion at rough or chemically structured surfaces. Our method accounts for non-local Van der Waals effects and contains the more approximate (and local) Deryagin approach in a simple limit. Specializing to supported membranes we consider the effects of substrate structure on the membrane adhesion energy and configuration. Adhesion is usually less favorable for rough substrates and the membrane shape tends to follow that of the surface contours. Chemical patterning, however, favors adhesion with the membrane configuration being out …
The hydrodynamic theory of heterogeneous fluid membranes is extended to the case of a membrane adjacent to a solid substrate. We derive the coupling diffusion coefficients of pairs of membrane inclusions in the limit of large separation compared to the inclusion size. Two-dimensional compressive stresses in the membrane make the coupling coefficients decay asymptotically as $1/r^2$ with interparticle distance $r$. For the common case, where the distance to the substrate is of sub-micron scale, we present expressions for the coupling between distant disklike inclusions, which are valid for arbi…
We investigate with Monte Carlo computer simulations the capillary phase behaviour of model colloid-polymer mixtures confined between a flat wall and a corrugated wall. The corrugation is modelled via a sine wave as a function of one of the in-plane coordinates leading to a depletion attraction between colloids and the corrugated wall that is curvature dependent. We find that for increased amplitude of corrugation the region of the phase diagram where capillary condensation occurs becomes larger. We derive a Kelvin equation for this system and compare its predictions to the simulation results.…
The statistical physics and dynamics of double supported bilayers are studied theoretically. The main goal in designing double supported lipid bilayers is to obtain model systems of biomembranes: the upper bilayer is meant to be almost freely floating, the substrate being screened by the lower bilayer. The fluctuation-induced repulsion between membranes and between the lower membrane and the wall are explicitly taken into account using a Gaussian variational approach. It is shown that the variational parameters, the "effective" adsorption strength and the average distance to the substrate, dep…
Eukaryotic cells adhere to extracellular matrix during the normal development of the organism, forming static adhesion as well as during cell motility. We study this process by considering a simplified coarse-grained model of a vesicle that has uniform adhesion energy with a flat substrate, mobile curved membrane proteins and active forces. We find that a high concentration of curved proteins alone increases the spreading of the vesicle, by the self-organization of the curved proteins at the high curvature vesicle-substrate contact line, thereby reducing the bending energy penalty at the vesic…
Rigid superhydrophobic materials have the ability to repel millimetric water drops, in typically 10 ms. Yet, most natural water-repellent materials can be deformed by impacting drops. To test the effect of deformability, we perform impacts of non-wetting drops onto thin ($\sim$ 10 \micro m), circular PDMS membranes. The bouncing mechanism is markedly modified compared to that on a rigid material: the liquid leaves the substrate as it is kicked upwards by the membrane. We show that the rebound is controlled by an interplay between the dynamics of the drop and that of the soft substrate, so that…
Supported Lipid Bilayers (SLBs) are model membranes formed at solid substrate surfaces. This architecture renders the membrane experimentally accessible to surface sensitive techniques used to study their properties, including Atomic Force Microscopy (AFM), optical fluorescence microscopy, Quartz Crystal Microbalance (QCM) and X-Ray/Neutron Reflectometry, and allows integration with technology for potential biotechnological applications such as drug screening devices. The experimental technique often dictates substrate choice or treatment, and it is anecdotally recognised that certain substrat…
A phenomenological model for the unbinding transition of multi-component fluid membranes is proposed, where the unbinding transition is described using a theory analogous to Flory-Huggins theory for polymers. The coupling between the lateral phase separation of inclusion molecules and the membrane-substrate distance explains the phase coexistence between two unbound phases as observed in recent experiments by Marx et al. [Phys. Rev. Lett. 88, 138102 (2002)]. Bellow a critical end-point temperature, we find that the unbinding transition becomes first-order for multi-component membranes.
Biomimetic membranes in contact with a planar substrate or a second membrane are studied theoretically. The membranes contain specific adhesion molecules (stickers) which are attracted by the second surface. In the absence of stickers, the trans--interaction between the membrane and the second surface is assumed to be repulsive at short separations. It is shown that the interplay of specific attractive and generic repulsive interactions can lead to the formation of a potential barrier. This barrier induces a line tension between bound and unbound membrane segments which results in lateral phas…
We propose a direct self-assembly mechanism towards obtaining defect-free perpendicular lamellar phases of diblock copolymer (BCP) thin films. In our numerical study, a thin BCP film having a flat top surface is casted on a uni-directional corrugated solid substrate. The substrate is treated chemically and has a weak preference toward one of the two BCP components. Employing self-consistent field theory (SCFT), we find that there is an enhanced synergy between two substrate characteristics: its topography (geometrical roughness) combined with a weak surface preference. This synergy produces th…
We study the interaction between capillary forces and deformation in the context of a deformable capillary adhesive: a clamped, tense membrane is adhered to a rigid substrate by the surface tension of a liquid droplet. We find that the equilibrium adhesive force for this elastocapillary adhesive is significantly enhanced in comparison to the capillary adhesion between rigid plates. In particular, the equilibrium adhesion force is orders of magnitude greater when the membrane is sufficiently deformed to contact the substrate. From a dynamic perspective, however, the formation of a fluid-filled …
Adhesion between membranes is studied using a phenomenological model, where the inter-membrane distance is coupled to the concentration of sticker molecules on the membranes. The model applies to both for adhesion of two flexible membranes and to adhesion of one flexible membrane onto a second membrane supported on a solid substrate. We mainly consider the case where the sticker molecules form bridges and adhere directly to both membranes. The calculated mean-field phase diagrams show an upward shift of the transition temperature indicating that the lateral phase separation in the membrane is …
Correlated velocity patterns and associated large length-scale transmission of traction forces have been observed in collective live cell migration as a response to a "wound". We argue that a simple physical model of a force-driven heterogeneous elastic membrane sliding over a viscous substrate can qualitatively explain a few experimentally observed facts: (i) the growth of velocity ordering which spreads from the wound boundary to the interior, (ii) the exponential tails of the traction force distributions, and (iii) the swirling pattern of velocities in the interior of the tissue.
