Adhesive switching of membranes: experiment and theory

Demixing of homogeneous binary lipid membranes induced by protein inclusions

We study a model of a lipid bilayer membrane described by two order parameters: the chemical composition described using the Gaussian model and the spatial configuration described with the elastic deformation model of a membrane with a finite thickness or, equivalently, for an adherent membrane. We assume and explain on physical grounds the linear coupling between the two order parameters. Using the exact solution, we calculate the correlation functions and order parameter profiles. We also study the domains that form around inclusions on the membrane. We propose and compare six distinct ways to quantify the size of such domains. Despite its simplicity, the model has many interesting features like the Fisher-Widom line and two distinct critical regions.

In Situ Hydrogelation of Cellular Monolayers Enables Conformal Biomembrane Functionalization for Xeno-Free Feeder Substrate Engineering

The intricate functionalities of cellular membranes have inspired strategies for deriving and anchoring cell-surface components onto solid substrates for biological studies, biosensor applications, and tissue engineering. However, introducing conformal and right-side-out cell membrane coverage onto planar substrates requires cumbersome protocols susceptible to significant device-to-device variability. Here, a facile approach for biomembrane functionalization of planar substrates is demonstrated by subjecting confluent cellular monolayer to intracellular hydrogel polymerization. The resulting cell-gel hybrid, herein termed GELL (gelated cell), exhibits extraordinary stability and retains the structural integrity, membrane fluidity, membrane protein mobility, and topology of living cells. In assessing the utility of GELL layers as a tissue engineering feeder substrate for stem cell maintenance, GELL feeder prepared from primary mouse embryonic fibroblasts not only preserves the stemness of murine stem cells but also exhibits advantages over live feeder cells owing to the GELL's inanimate, non-metabolizing nature. The preparation of a xeno-free feeder substrate devoid of non-human components is further shown with HeLa cells, and the resulting  HeLa GELL feeder effectively sustains the growth and stemness of both murine and human induced pluripotent stem cells. The study highlights a novel bio-functionalization strategy that introduces new opportunities for tissue engineering and other biomedical applications.

Shear dynamics of confined membranes

We model the nonlinear response of a lubricated contact composed of a two-dimensional lipid membrane immersed in a simple fluid between two parallel flat and porous walls under shear. The nonlinear dynamics of the membrane gives rise to a rich dynamical behavior depending on the shear velocity. In quiescent conditions (i.e., absence of shear), the membrane freezes into a disordered labyrinthine wrinkle pattern. We determine the wavelength of this pattern as a function of the excess area of the membrane for a fairly general form of the confinement potential using a sine-profile ansatz for the wrinkles. In the presence of shear, we find four different regimes depending on the shear rate. Regime I. For small shear, the labyrinthine pattern is still frozen, but exhibits a small drift which is mainly along the shear direction. In this regime, the tangential forces on the walls due to the presence of the membrane increase linearly with the shear rate. Regime II. When the shear rate is increased above a critical value, the membrane rearranges, and wrinkles start to align along the shear direction. This regime is accompanied by a sharp drop of the tangential forces on the wall. The membrane usually reaches a steady-state configuration drifting with a small constant velocity at long times. However, we also rarely observe oscillatory dynamics in this regime. Regime III. For larger shear rates, the wrinkles align strongly along the shear direction, with a set of dislocation defects which assemble in pairs. The tangential forces are then controlled by the number of dislocations, and by the number of wrinkles between the two dislocations within each dislocation pairs. In this dislocation-dominated regime, the tangential forces in the transverse direction most often exceed those in the shear direction. Regime IV. For even larger shear, the membrane organizes into a perfect array of parallel stripes with no defects. The wavelength of the wrinkles is still identical to the wavelength in the absence of shear. In this final regime, the tangential forces due to the membrane vanish. These behaviors give rise to a non-linear rheological behavior of lubricated contacts containing membranes.

On the control of dispersion interactions between biological membranes and protein coated biointerfaces

HYPOTHESIS

Interaction of cellular membranes with biointerfaces is of vital importance for a number of medical devices and implants. Adhesiveness of these surfaces and cells is often regulated by depositing a layer of bovine serum albumin (BSA) or other protein coatings. However, anomalously large separations between phospholipid membranes and the biointerfaces in various conditions and buffers have been observed, which could not be understood using available theoretical arguments.

METHODS

Using the Lifshitz theory, we here evaluate the distance-dependent Hamaker coefficient describing the dispersion interaction between a biointerface and a membrane to understand the relative positioning of two surfaces. Our theoretical modeling is supported by experiments where the biointerface is represented by a glass substrate with deposited BSA and protein layers. These biointerfaces are allowed to interact with giant unilamellar vesicles decorated with polyethylene glycol (PEG) using PEG lipids to mimic cellular membranes and their pericellular coat.

RESULTS

We demonstrate that careful treatment of the van der Waals interactions is critical for explaining the lack of adhesiveness of the membranes with protein-decorated biointerfaces. We show that BSA alone indeed passivates the glass, but depositing an additional protein layer on the surface BSA, or producing multiple layers of proteins and BSA results in repulsive dispersion forces responsible for 100 nm large equilibrium separations between the two surfaces.

Critical role of lipid membranes in polarization and migration of cells: a biophysical view

Cell migration plays vital roles in many biologically relevant processes such as tissue morphogenesis and cancer metastasis, and it has fascinated biophysicists over the past several decades. However, despite an increasing number of studies highlighting the orchestration of proteins involved in different signaling pathways, the functional roles of lipid membranes have been essentially overlooked. Lipid membranes are generally considered to be a functionless two-dimensional matrix of proteins, although many proteins regulating cell migration gain functions only after they are recruited to the membrane surface and self-organize their functional domains. In this review, we summarize how the logistical recruitment and release of proteins to and from lipid membranes coordinates complex spatiotemporal molecular processes. As predicted from the classical framework of the Smoluchowski equation of diffusion, lipid/protein membranes serve as a 2D reaction hub that contributes to the effective and robust regulation of polarization and migration of cells involving several competing pathways.

Recent Advances and Prospects in the Research of Nascent Adhesions

Nascent adhesions are submicron transient structures promoting the early adhesion of cells to the extracellular matrix. Nascent adhesions typically consist of several tens of integrins, and serve as platforms for the recruitment and activation of proteins to build mature focal adhesions. They are also associated with early stage signaling and the mechanoresponse. Despite their crucial role in sampling the local extracellular matrix, very little is known about the mechanism of their formation. Consequently, there is a strong scientific activity focused on elucidating the physical and biochemical foundation of their development and function. Precisely the results of this effort will be summarized in this article.

Mechanobiology in cortical waves and oscillations

Cortical actin waves have emerged as a widely prevalent phenomena and brought pattern formation to many fields of cell biology. Cortical excitabilities, reminiscent of the electric excitability in neurons, are likely fundamental property of the cell cortex. Although they have been mostly considered to be biochemical in nature, accumulating evidence support the role of mechanics in the pattern formation process. Both pattern formation and mechanobiology approach biological phenomena at the collective level, either by looking at the mesoscale dynamical behavior of molecular networks or by using collective physical properties to characterize biological systems. As such they are very different from the traditional reductionist, bottom-up view of biology, which brings new challenges and potential opportunities. In this essay, we aim to provide our perspectives on what the proposed mechanochemical feedbacks are and open questions regarding their role in cortical excitable and oscillatory dynamics.

Detachment of giant liposomes - coupling of receptor mobility and membrane shape

Cellular adhesion is an intricate physical process controlled by ligand-receptor affinity, density, mobility, and external forces transmitted through the elastic properties of the cell. As a model for cellular adhesion we study the detachment of cell-sized liposomes and membrane-coated silica beads from supported bilayers using atomic force microscopy. Adhesion between the two surfaces is mediated by the interaction between the adhesive lipid anchored saccharides lactosylceramide and the ganglioside G_M3. We found that force-distance curves of liposome detachment have a very peculiar, partially concave shape, reminiscent of the nonlinear extension of polymers. By contrast, detachment of membrane coated beads led to force-distance curves similar to the detachment of living cells. Theoretical modelling of the enforced detachment suggests that the non-convex force curve shape arises from the mobility of ligands provoking a switch of shapes from spherical to unduloidal during detachment.

Forces during cellular uptake of viruses and nanoparticles at the ventral side

Many intracellular pathogens, such as mammalian reovirus, mimic extracellular matrix motifs to specifically interact with the host membrane. Whether and how cell-matrix interactions influence virus particle uptake is unknown, as it is usually studied from the dorsal side. Here we show that the forces exerted at the ventral side of adherent cells during reovirus uptake exceed the binding strength of biotin-neutravidin anchoring viruses to a biofunctionalized substrate. Analysis of virus dissociation kinetics using the Bell model revealed mean forces higher than 30 pN per virus, preferentially applied in the cell periphery where close matrix contacts form. Utilizing 100 nm-sized nanoparticles decorated with integrin adhesion motifs, we demonstrate that the uptake forces scale with the adhesion energy, while actin/myosin inhibitions strongly reduce the uptake frequency, but not uptake kinetics. We hypothesize that particle adhesion and the push by the substrate provide the main driving forces for uptake.

Many intracellular pathogens mimic extracellular matrix motifs to specifically interact with the host membrane which may influences virus particle uptake. Here authors use single molecule tension sensors to reveal the minimal forces exerted on single virus particles and demonstrate that the uptake forces scale with the adhesion energy.

Statistical Mechanics of an Elastically Pinned Membrane: Equilibrium Dynamics and Power Spectrum

In biological settings, membranes typically interact locally with other membranes: the extracellular matrix in the exterior or internal cellular structures such as the cytoskeleton, locally pinning the membrane. Characterizing the dynamical properties of such interactions presents a difficult task. Significant progress has been achieved through simulations and experiments, yet analytical progress in modeling pinned membranes has been impeded by the complexity of governing equations. Here, we circumvent these difficulties by calculating analytically the time-dependent Green's function of the operator governing the dynamics of an elastically pinned membrane in a hydrodynamic surrounding and subject to external forces. This enables us to calculate the equilibrium power spectral density for an overdamped membrane pinned by an elastic, permanently attached spring subject to thermal excitations. By considering the effects of the finite experimental resolution on the measured spectra, we show that the elasticity of the pinning can be extracted from the experimentally measured spectrum. Membrane fluctuations can thus be used as a tool to probe mechanical properties of the underlying structures. Such a tool may be particularly relevant in the context of cell mechanics, in which the elasticity of the membrane's attachment to the cytoskeleton could be measured.

Hydrodynamics of transient cell-cell contact: The role of membrane permeability and active protrusion length

In many biological settings, two or more cells come into physical contact to form a cell-cell interface. In some cases, the cell-cell contact must be transient, forming on timescales of seconds. One example is offered by the T cell, an immune cell which must attach to the surface of other cells in order to decipher information about disease. The aspect ratio of these interfaces (tens of nanometers thick and tens of micrometers in diameter) puts them into the thin-layer limit, or "lubrication limit", of fluid dynamics. A key question is how the receptors and ligands on opposing cells come into contact. What are the relative roles of thermal undulations of the plasma membrane and deterministic forces from active filopodia? We use a computational fluid dynamics algorithm capable of simulating 10-nanometer-scale fluid-structure interactions with thermal fluctuations up to seconds- and microns-scales. We use this to simulate two opposing membranes, variously including thermal fluctuations, active forces, and membrane permeability. In some regimes dominated by thermal fluctuations, proximity is a rare event, which we capture by computing mean first-passage times using a Weighted Ensemble rare-event computational method. Our results demonstrate a parameter regime in which the time it takes for an active force to drive local contact actually increases if the cells are being held closer together (e.g., by nonspecific adhesion), a phenomenon we attribute to the thin-layer effect. This leads to an optimal initial cell-cell separation for fastest receptor-ligand binding, which could have relevance for the role of cellular protrusions like microvilli. We reproduce a previous experimental observation that fluctuation spatial scales are largely unaffected, but timescales are dramatically slowed, by the thin-layer effect. We also find that membrane permeability would need to be above physiological levels to abrogate the thin-layer effect.

Probing the Interface Structure of Adhering Cells by Contrast Variation Neutron Reflectometry

Cellular adhesion is a central element in tissue mechanics, biological cell-cell signaling, and cell motility. In this context, the cell-substrate distance has been investigated in the past by studying natural cells and biomimetic cell models adhering on solid substrates. The amount of water in the membrane substrate gap, however, is difficult to determine. Here, we present a neutron reflectivity (NR) structural study of confluent epithelial cell monolayers on silicon substrates. In order to ensure valid in vitro conditions, we developed a cell culture sample chamber allowing us to grow and cultivate cells under proper cell culture conditions while performing in vitro neutron reflectivity measurements. The cell chamber also enabled perfusion with cell medium and hence allowed for contrast variation in situ by sterile exchange of buffer with different H₂O-to-D₂O ratio. Contrast variation reduces the ambiguity of data modeling for determining the thickness and degree of hydration of the interfacial cleft between the adherent cells and the substrate. Our data suggest a three-layer interfacial organization. The first layer bound to the silicon surface interface is in agreement with a very dense protein film with a thickness of 9 ± 2 nm, followed by a highly hydrated 24 ± 4 nm thick layer, and a several tens of nanometers thick layer attributed to the composite membrane. Hence, the results provide clear evidence of a highly hydrated intermediate region between the composite cell membrane and the substrate, reminiscent of the basal lamina.

Adhesion of Active Cytoskeletal Vesicles

Regulation of adhesion is a ubiquitous feature of living cells, observed during processes such as motility, antigen recognition, or rigidity sensing. At the molecular scale, a myriad of mechanisms are necessary to recruit and activate the essential proteins, whereas at the cellular scale, efficient regulation of adhesion relies on the cell's ability to adapt its global shape. To understand the role of shape remodeling during adhesion, we use a synthetic biology approach to design a minimal experimental model, starting with a limited number of building blocks. We assemble cytoskeletal vesicles whose size, reduced volume, and cytoskeletal contractility can be independently tuned. We show that these cytoskeletal vesicles can sustain strong adhesion to solid substrates only if the actin cortex is actively remodeled significantly. When the cytoskeletal vesicles are deformed under hypertonic osmotic pressure, they develop a crumpled geometry with deformations. In the presence of molecular motors, these deformations are dynamic in nature, and the excess membrane area generated thereby can be used to gain adhesion energy. The cytoskeletal vesicles are able to attach to the rigid glass surfaces even under strong adhesive forces just like the cortex-free vesicles. The balance of deformability and adhesion strength is identified to be key to enable cytoskeletal vesicles to adhere to solid substrates.

Statistical Mechanics of an Elastically Pinned Membrane: Static Profile and Correlations

The relation between thermal fluctuations and the mechanical response of a free membrane has been explored in great detail, both theoretically and experimentally. However, understanding this relationship for membranes locally pinned by proteins is significantly more challenging. Given that the coupling of the membrane to the cell cytoskeleton, to the extracellular matrix, and to other internal structures is crucial for the regulation of a number of cellular processes, understanding the role of the pinning is of great interest. In this manuscript, we consider a single protein (elastic spring of a finite rest length) pinning a membrane modeled in the Monge gauge. First, we determine the Green's function for the system and complement this approach by the calculation of the mode-coupling coefficients for the plane wave expansion and the orthonormal fluctuation modes, in turn building a set of tools for numerical and analytic studies of a pinned membrane. Furthermore, we explore static correlations of the free and the pinned membrane, as well as the membrane shape, showing that all three are mutually interdependent and have an identical long-range behavior characterized by the correlation length. Interestingly, the latter displays a nonmonotonic behavior as a function of membrane tension. Importantly, exploiting these relations allows for the experimental determination of the elastic parameters of the pinning. Last but not least, we calculate the interaction potential between two pinning sites and show that even in the absence of the membrane deformation, the pinnings will be subject to an attractive force because of changes in membrane fluctuations.

Adhesion dynamics of confined membranes

We report on the modeling of the dynamics of confined lipid membranes. We derive a thin film model in the lubrication limit which describes an inextensible liquid membrane with bending rigidity confined between two adhesive walls. The resulting equations share similarities with the Swift-Hohenberg model. However, inextensibility is enforced by a time-dependent nonlocal tension. Depending on the excess membrane area available in the system, three different dynamical regimes, denoted as A, B and C, are found from the numerical solution of the model. In regime A, membranes with small excess area form flat adhesion domains and freeze. Such freezing is interpreted by means of an effective model for curvature-driven domain wall motion. The nonlocal membrane tension tends to a negative value corresponding to the linear stability threshold of flat domain walls in the Swift-Hohenberg equation. In regime B, membranes with intermediate excess areas exhibit endless coarsening with coexistence of flat adhesion domains and wrinkle domains. The tension tends to the nonlinear stability threshold of flat domain walls in the Swift-Hohenberg equation. The fraction of the system covered by the wrinkle phase increases linearly with the excess area in regime B. In regime C, membranes with large excess area are completely covered by a frozen labyrinthine pattern of wrinkles. As the excess area is increased, the tension increases and the wavelength of the wrinkles decreases. For large membrane area, there is a crossover to a regime where the extrema of the wrinkles are in contact with the walls. In all regimes after an initial transient, robust localised structures form, leading to an exact conservation of the number of adhesion domains.

Mechanics of post-fusion exocytotic vesicle

Exocytosis is an important cellular process controlled by metabolic signaling. It involves vesicle fusion to the plasma membrane, followed by the opening of a fusion pore, and the subsequent release of the vesicular lumen content into the extracellular space. While most modeling efforts focus on the events leading to membrane fusion, how the vesicular membrane remodels after fusing to plasma membrane remains unclear. This latter event dictates the nature and the efficiency of exocytotic vesicular secretions, and is thus critical for exocytotic function. We provide a generic membrane mechanical model to systematically study the fate of post-fusion vesicles. We show that while membrane stiffness favors full-collapse vesicle fusion into the plasma membrane, the intravesicular pressure swells the vesicle and causes the fusion pore to shrink. Dimensions of the vesicle and its associated fusion pore further modulate this mechanical antagonism. We systematically define the mechanical conditions that account for the full spectrum of the observed vesicular secretion modes. Our model therefore can serve as a unified theoretical framework that sheds light on the elaborate control mechanism of exocytosis.

Measuring thin films using quantitative frustrated total internal reflection (FTIR)

In the study of interactions between liquids and solids, an accurate measurement of the film thickness between the two media is essential to study the dynamics. As interferometry is restricted by the wavelength of the light source used, recent studies of thinner films have prompted the use of frustrated total internal reflection (FTIR). In many studies the assumption of a simple exponential decay of the intensity with film thickness was used. In the present study we highlight that this model does not satisfy the Fresnel equations and thus gives an underestimation of the films. We show that the multiple reflections and transmissions at both the upper and the lower interfaces of the film must be taken into account to accurately describe the measured intensity. In order to quantitatively validate the FTIR technique, we measured the film thickness of the air gap between a convex lens of known geometry and a flat surface and obtain excellent agreement. Furthermore, we also found that we can accurately measure the elastic deformations of the lens under loads by comparing them with the results of the Herzian theory.

Thixotropy and shear thinning of lubricated contacts with confined membranes

We have modeled the nonlinear dynamics and the rheological behavior of a system under shear containing a membrane confined between two attractive walls. The presence of the membrane induces additional tangential forces on the walls that always increase the global friction. At low shear rates, the membrane exhibits chaotic dynamics with slow coarsening leading to thixotropy, i.e. to a slow decrease of the membrane-induced tangential forces on the walls. At intermediate shear rates, the membrane profile presents stationary periodic patterns. At higher shear rates, membrane dynamics are governed by a nonlinear evolution equation which is similar to the Kuramoto-Sivashinski equation, but with a sixth-order stabilizing term. The membrane experiences chaotic dynamics without coarsening. As a consequence of the nonlinear dynamics of the membrane at intermediate and large shear rates, the system exhibits shear thinning.

Binding constants of membrane-anchored receptors and ligands: A general theory corroborated by Monte Carlo simulations

Adhesion processes of biological membranes that enclose cells and cellular organelles are essential for immune responses, tissue formation, and signaling. These processes depend sensitively on the binding constant K2D of the membrane-anchored receptor and ligand proteins that mediate adhesion, which is difficult to measure in the "two-dimensional" (2D) membrane environment of the proteins. An important problem therefore is to relate K2D to the binding constant K3D of soluble variants of the receptors and ligands that lack the membrane anchors and are free to diffuse in three dimensions (3D). In this article, we present a general theory for the binding constants K2D and K3D of rather stiff proteins whose main degrees of freedom are translation and rotation, along membranes and around anchor points "in 2D," or unconstrained "in 3D." The theory generalizes previous results by describing how K2D depends both on the average separation and thermal nanoscale roughness of the apposing membranes, and on the length and anchoring flexibility of the receptors and ligands. Our theoretical results for the ratio K2D/K3D of the binding constants agree with detailed results from Monte Carlo simulations without any data fitting, which indicates that the theory captures the essential features of the "dimensionality reduction" due to membrane anchoring. In our Monte Carlo simulations, we consider a novel coarse-grained model of biomembrane adhesion in which the membranes are represented as discretized elastic surfaces, and the receptors and ligands as anchored molecules that diffuse continuously along the membranes and rotate at their anchor points.

Binding equilibrium and kinetics of membrane-anchored receptors and ligands in cell adhesion: Insights from computational model systems and theory

The adhesion of cell membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. In this article, we review recent results from simulations and theory that lead to novel insights on how the binding equilibrium and kinetics of these proteins is affected by the membranes and by the membrane anchoring and molecular properties of the proteins. Simulations and theory both indicate that the binding equilibrium constant [Formula: see text] and the on- and off-rate constants of anchored receptors and ligands in their 2-dimensional (2D) membrane environment strongly depend on the membrane roughness from thermally excited shape fluctuations on nanoscales. Recent theory corroborated by simulations provides a general relation between [Formula: see text] and the binding constant [Formula: see text] of soluble variants of the receptors and ligands that lack the membrane anchors and are free to diffuse in 3 dimensions (3D).

Nanometric thermal fluctuations of weakly confined biomembranes measured with microsecond time-resolution

We probe the bending fluctuations of bio-membranes using highly deflated giant unilamellar vesicles (GUVs) bound to a substrate by a weak potential arising from generic interactions. The substrate is either homogeneous, with GUVs bound only by the weak potential, or is chemically functionalized with a micro-pattern of very strong specific binders. In both cases, the weakly adhered membrane is seen to be confined at a well-defined distance above the surface while it continues to fluctuate strongly. We quantify the fluctuations of the weakly confined membrane at the substrate proximal surface as well as of the free membrane at the distal surface of the same GUV. This strategy enables us to probe in detail the damping of fluctuations in the presence of the substrate, and to independently measure the membrane tension and the strength of the generic interaction potential. Measurements were done using two complementary techniques - dynamic optical displacement spectroscopy (DODS, resolution: 20 nm, 10 μs), and dual wavelength reflection interference contrast microscopy (DW-RICM, resolution: 4 nm, 50 ms). After accounting for the spatio-temporal resolution of the techniques, an excellent agreement between the two measurements was obtained. For both weakly confined systems we explore in detail the link between fluctuations on the one hand and membrane tension and the interaction potential on the other hand.

Nanoscale characterization of vesicle adhesion by normalized total internal reflection fluorescence microscopy

We recently proposed a straightforward fluorescence microscopy technique to study adhesion of Giant Unilamellar Vesicles. This technique is based on dual observations which combine epi-fluorescence microscopy and total internal reflection fluorescence (TIRF) microscopy: TIRF images are normalized by epi-fluorescence ones. By this way, it is possible to map the membrane/substrate separation distance with a nanometric resolution, typically ~20 nm, with a maximal working range of 300-400 nm. The purpose of this paper is to demonstrate that this technique is useful to quantify vesicle adhesion from ultra-weak to strong membrane-surface interactions. Thus, we have examined unspecific and specific adhesion conditions. Concerning unspecific adhesion, we have controlled the strength of electrostatic forces between negatively charged vesicles and various functionalized surfaces which exhibit a positive or a negative effective charge. Specific adhesion was highlighted with lock-and-key forces mediated by the well defined biotin/streptavidin recognition.

Transition to coarsening for confined one-dimensional interfaces with bending rigidity

We discuss the nonlinear dynamics and fluctuations of interfaces with bending rigidity under the competing attractions of two walls with arbitrary permeabilities. This system mimics the dynamics of confined membranes. We use a two-dimensional hydrodynamic model, where membranes are effectively one-dimensional objects. In a previous work [T. Le Goff et al., Phys. Rev. E 90, 032114 (2014)], we have shown that this model predicts frozen states caused by bending rigidity-induced oscillatory interactions between kinks (or domain walls). We here demonstrate that in the presence of tension, potential asymmetry, or thermal noise, there is a finite threshold above which frozen states disappear, and perpetual coarsening is restored. Depending on the driving force, the transition to coarsening exhibits different scenarios. First, for membranes under tension, small tensions can only lead to transient coarsening or partial disordering, while above a finite threshold, membrane oscillations disappear and perpetual coarsening is found. Second, potential asymmetry is relevant in the nonconserved case only, i.e., for permeable walls, where it induces a drift force on the kinks, leading to a fast coarsening process via kink-antikink annihilation. However, below some threshold, the drift force can be balanced by the oscillatory interactions between kinks, and frozen adhesion patches can still be observed. Finally, at long times, noise restores coarsening with standard exponents depending on the permeability of the walls. However, the typical time for the appearance of coarsening exhibits an Arrhenius form. As a consequence, a finite noise amplitude is needed in order to observe coarsening in observable time.

How actin/myosin crosstalks guide the adhesion, locomotion and polarization of cells

Cell-tissue-tissue interaction is determined by specific short range forces between cell adhesion molecules (CAMs) and ligands of the tissue, long range repulsion forces mediated by cell surface grafted macromolecules and adhesion-induced elastic stresses in the cell envelope. This interplay of forces triggers the rapid random clustering of tightly coupled linkers. By coupling of actin gel patches to the intracellular domains of the CAMs, these clusters can grow in a secondary process resulting in the formation of functional adhesion microdomains (ADs). The ADs can act as biochemical steering centers by recruiting and activating functional proteins, such as GTPases and associated regulating proteins, through electrostatic-hydrophobic forces with cationic lipid domains that act as attractive centers. First, I summarize physical concepts of cell adhesion revealed by studies of biomimetic systems. Then I describe the role of the adhesion domains as biochemical signaling platforms and force transmission centers promoting cellular protrusions, in terms of a shell string model of cells. Protrusion forces are generated by actin gelation triggered by molecular machines (focal adhesion kinase (FAK), Src-kinases and associated adaptors) which assemble around newly formed integrin clusters. They recruit and activate the GTPases Rac-1 and actin gelation promoters to charged membrane domains via electrostatic-hydrophobic forces. The cell front is pushed forward in a cyclic and stepwise manner and the step-width is determined by the dynamics antagonistic interplay between Rac-1 and RhoA. The global cell polarization in the direction of motion is mediated by the actin-microtubule (MT) crosstalk at adhesion domains. Supramolecular actin-MT assemblies at the front help to promote actin polymerization. At the rear they regulate the dismantling of the ADs through the Ca(++)-mediated activation of the protease calpain and trigger their disruption by RhoA mediated contraction via stress fibers. This article is part of a Special Issue entitled: Mechanobiology.

The effect of the physical properties of the substrate on the kinetics of cell adhesion and crawling studied by an axisymmetric diffusion-energy balance coupled model

In this paper an analytical approach to study the effect of the substrate physical properties on the kinetics of adhesion and motility behavior of cells is presented. Cell adhesion is mediated by the binding of cell wall receptors and substrate's complementary ligands, and tight adhesion is accomplished by the recruitment of the cell wall binders to the adhesion zone. The binders' movement is modeled as their axisymmetric diffusion in the fluid-like cell membrane. In order to preserve the thermodynamic consistency, the energy balance for the cell-substrate interaction is imposed on the diffusion equation. Solving the axisymmetric diffusion-energy balance coupled equations, it turns out that the physical properties of the substrate (substrate's ligand spacing and stiffness) have considerable effects on the cell adhesion and motility kinetics. For a rigid substrate with uniform distribution of immobile ligands, the maximum ligand spacing which does not interrupt adhesion growth is found to be about 57 nm. It is also found that as a consequence of the reduction in the energy dissipation in the isolated adhesion system, cell adhesion is facilitated by increasing substrate's stiffness. Moreover, the directional movement of cells on a substrate with gradients in mechanical compliance is explored with an extension of the adhesion formulation. It is shown that cells tend to move from soft to stiff regions of the substrate, but their movement is decelerated as the stiffness of the substrate increases. These findings based on the proposed theoretical model are in excellent agreement with the previous experimental observations.

Understanding dynamic changes in live cell adhesion with neutron reflectometry

Neutron reflectometry (NR) was used to examine various live cells adhesion to quartz substrates under different environmental conditions, including flow stress. To the best of our knowledge, these measurements represent the first successful visualization and quantization of the interface between live cells and a substrate with sub-nanometer resolution. In our first experiments, we examined live mouse fibroblast cells as opposed to past experiments using supported lipids, proteins, or peptide layers with no associated cells. We continued the NR studies of cell adhesion by investigating endothelial monolayers and glioblastoma cells under dynamic flow conditions. We demonstrated that neutron reflectometry is a powerful tool to study the strength of cellular layer adhesion in living tissues, which is a key factor in understanding the physiology of cell interactions and conditions leading to abnormal or disease circumstances. Continuative measurements, such as investigating changes in tumor cell - surface contact of various glioblastomas, could impact advancements in tumor treatments. In principle, this can help us to identify changes that correlate with tumor invasiveness. Pursuit of these studies can have significant medical impact on the understanding of complex biological problems and their effective treatment, e.g. for the development of targeted anti-invasive therapies.

Frozen states and order-disorder transition in the dynamics of confined membranes

The adhesion dynamics of a membrane confined between two permeable walls is studied using a two-dimensional hydrodynamic model. The membrane morphology decomposes into adhesion patches on the upper and the lower walls and obeys a nonlinear evolution equation that resembles that of phase-separation dynamics, which is known to lead to coarsening, i.e., to the endless growth of the adhesion patches. However, due to the membrane bending rigidity, the system evolves toward a frozen state without coarsening. This frozen state exhibits an order-disorder transition when increasing the permeability of the walls.

Disjoining pressure of an electrolyte film confined between semipermeable membranes

We consider an electrolyte solution confined by infinitesimally thin semipermeable membranes in contact with a salt-free solvent. Membranes are uncharged, but since small counter-ions leak-out into infinite salt-free reservoirs, we observe a distance-dependent membrane potential, which generates a repulsive electrostatic disjoining pressure. We obtain the distribution of the potential and of ions, and derive explicit formulas for the disjoining pressure, which are validated by computer simulations. We predict a strong short-range power-law repulsion, and a weaker long-range exponential decay. Our results also demonstrate that an interaction between membranes does strongly depend on the screening lengths, valency of an electrolyte solution, and an inter-membrane film thickness. Finally, our analysis can be directly extended to the study of more complex situations and some biological problems.

Hydrodynamic enhancement of the diffusion rate in the region between two fluctuating membranes in close opposition: a theoretical and computational study

Periodic variation of the distance between two weakly adhering bodies gives rise to a huge tangential motions of the sandwiched solvent layer (squeezing flow). Oscillations either can be induced by an external applied field or can spontaneously arise from the coupling with the solvent heat bath. First we calculated by the Navier-Stokes equation the components of the fluid velocity near two oscillating juxtaposed plates. Then we evaluated the influence of plate oscillations on the transport properties of a trace diffusant dissolved at t = 0 in the outer medium for both deterministic and stochastic excitations. By employing both analytical (Fokker-Planck) and coarse-grained molecular dynamics (MD) simulations, we proved that the entry and migration rates of the diffusant sharply increases with the oscillation amplitudes. Enhancement was related to relevant parameters like oscillation frequency, fluid layer thickness, fluid viscosity, and temperature. An extension to the case of oscillating multistacked lamellae has been also made. Theoretical and MD results suggest a significant enhancement of the diffusant flux even in the worse situation of thermally excited small amplitude fluctuations. Excitation arising from other sources (e.g., microwave or ultrasound irradiation of solid-fluid layered systems) could have a dramatic effect on the transport phenomena. Possible implications to relevant biological problems have been discussed.

Physics of cell adhesion: some lessons from cell-mimetic systems

Cell adhesion is a paradigm of the ubiquitous interplay of cell signalling, modulation of material properties and biological functions of cells. It is controlled by competition of short range attractive forces, medium range repellant forces and the elastic stresses associated with local and global deformation of the composite cell envelopes. We review the basic physical rules governing the physics of cell adhesion learned by studying cell-mimetic systems and demonstrate the importance of these rules in the context of cellular systems. We review how adhesion induced micro-domains couple to the intracellular actin and microtubule networks allowing cells to generate strong forces with a minimum of attractive cell adhesion molecules (CAMs) and to manipulate other cells through filopodia over micrometer distances. The adhesion strength can be adapted to external force fluctuations within seconds by varying the density of attractive and repellant CAMs through exocytosis and endocytosis or protease-mediated dismantling of the CAM-cytoskeleton link. Adhesion domains form local end global biochemical reaction centres enabling the control of enzymes. Actin-microtubule crosstalk at adhesion foci facilitates the mechanical stabilization of polarized cell shapes. Axon growth in tissue is guided by attractive and repulsive clues controlled by antagonistic signalling pathways.

A nanometre-scale resolution interference-based probe of interfacial phenomena between microscopic objects and surfaces

Interferometric techniques have proven useful to infer proximity and local surface profiles of microscopic objects near surfaces. But a critical trade-off emerges between accuracy and mathematical complexity when these methods are applied outside the vicinity of closest approach. Here we introduce a significant advancement that enables reflection interference contrast microscopy to provide nearly instantaneous reconstruction of an arbitrary convex object’s contour next to a bounding surface with nanometre resolution, making it possible to interrogate microparticle/surface interaction phenomena at radii of curvature 1,000 times smaller than those accessible by the conventional surface force apparatus. The unique view-from-below perspective of reflection interference contrast microscopy also reveals previously unseen deformations and allows the first direct observation of femtolitre-scale capillary condensation dynamics underneath micron-sized particles. Our implementation of reflection interference contrast microscopy provides a generally applicable nanometre-scale resolution tool that can be potentially exploited to dynamically probe ensembles of objects near surfaces so that statistical/probabilistic behaviour can be realistically captured.

Interferometric techniques can provide valuable contact and profile information of microscopic objects on surfaces. This work uses reflection interference contrast microscopy to directly observe contact phenomena and presents novel analytical methods offering high-accuracy nanoscale resolution.

Tuning endothelial monolayer adhesion: a neutron reflectivity study

Endothelial cells, master gatekeepers of the cardiovascular system, line its inner boundary from the heart to distant capillaries constantly exposed to blood flow. Interendothelial signaling and the monolayers adhesion to the underlying collagen-rich basal lamina are key in physiology and disease. Using neutron scattering, we report the first ever interfacial structure of endothelial monolayers under dynamic flow conditions mimicking the cardiovascular system. Endothelial adhesion (defined as the separation distance ℓ between the basal cell membrane and solid boundary) is explained using developed interfacial potentials and intramembrane segregation of specific adhesion proteins. Our method provides a powerful tool for the biophysical study of cellular layer adhesion strength in living tissues.

Cell differentiation of pluripotent tissue sheets immobilized on supported membranes displaying cadherin-11

Investigating cohesive tissue sheets in controlled cultures still poses a challenge since the complex intercellular interactions are difficult to mimic in in vitro models. We used supported lipid membranes functionalized by the adhesive part of the extracellular domain of the cell adhesion molecule cadherin-11 for the immobilization of pluripotent tissue sheets, the animal cap isolated from Xenopus laevis blastula stage embryos. Cadherin-11 was bound via histidine tag to lipid membranes with chelator head groups. In the first step, quantitative functionalization of the membranes with cadherin-11 was confirmed by quartz crystal microbalance and high energy specular X-ray reflectivity. In the next step, animal cap tissue sheets induced to neural crest cell fate were cultured on the membranes functionalized with cadherin-11. The adhesion of cells within the cohesive tissue was significantly dependent on changes in lateral densities of cadherin-11. The formation of filopodia and lamellipodia in the cohesive tissue verified the viability and sustainability of the culture over several hours. The expression of the transcription factor slug in externally induced tissue demonstrated the applicability of lipid membranes displaying adhesive molecules for controlled differentiation of cohesive pluripotent tissue sheets.

Domains and rafts in membranes - hidden dimensions of selforganization

Both biomembranes and biomimetic membranes such as lipid bilayers withseveral components contain intramembrane domains and rafts.Macromolecules, which are anchored to the membrane but have no tendeney tocluster, induce curved nanodomains. Clustering of membrane componentsleads to larger domains which can grow up to a certain maximal size andthen undergo a budding process. The maximal domain size depends on theinterplay of spontaneous curvature, bending rigidity, and line tension.It is argued that this interplay governs the formation of bothclathrin-coated buds and caveolae. Finally, membrane adhesion often leadsto domain formation within the contact zone.

Nucleation of ligand-receptor domains in membrane adhesion

We present a comprehensive model for the nucleation of domains in membrane adhesion. We determine the critical number of bonds in a nucleus and calculate the probability distribution of nucleation time from a discrete master equation. The latter is characterized by only four effective rates, which account for cooperative effects between bonds. We validate our model by finding excellent agreement with extensive Langevin simulations. In the range of parameters typical for cell adhesion, we find the critical number of bonds to be small. Furthermore, we find a characteristic separation between the bonds at which nucleation is particularly fast, pointing to potential regulatory mechanisms that could be used to control the cell recognition processes.

Effect of viscous drag on multiple receptor-ligand bonds rupture force

Monte Carlo simulation of the rupture of multiple receptor-ligand bonds between two PMN cells suspended in a Newtonian fluid is performed. We demonstrate via micro-mechanical model of two cells adhered by multiple receptor-ligand bonds that viscous drag caused by relative motion of cell suspended in a Newtonian fluid modulates transmission of an applied external load to bonds. Specifically, it is demonstrated that at any time the intermolecular bond force is not equivalent to the instantaneous applied force. The difference in the instantaneous applied force and the intermolecular bond force depends on the viscosity of fluid, the size of cell, the applied loading rate, and the number of bonds at any instant of time. Viscous drag acting on cell reduces average bond rupture forces.

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 [Imry and 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.

Giant vesicles as cell models

Tremendous progress has been made in recent years in understanding the working of the living cell, including its micro-anatomy, signalling networks, and regulation of genes. However, an understanding of cellular phenomena using fundamental laws starting from first principles is still very far away. Part of the reason is that a cell is an active and exquisitely complex system where every part is linked to the other. Thus, it is difficult or even impossible to design experiments that selectively and exclusively probe a chosen aspect of the cell. Various kinds of idealised systems and cell models have been used to circumvent this problem. An important example is a giant unilamellar vesicle (GUV, also called giant liposome), which provides a cell-sized confined volume to study biochemical reactions as well as self-assembly processes that occur on the membrane. The GUV membrane can be designed suitably to present selected, correctly-oriented cell-membrane proteins, whose mobility is confined to two dimensions. Here, we present recent advances in GUV design and the use of GUVs as cell models that enable quantitative testing leading to insight into the working of real cells. We briefly recapitulate important classical concepts in membrane biophysics emphasising the advantages and limitations of GUVs. We then present results obtained over the last decades using GUVs, choosing the formation of membrane domains and cell adhesion as examples for in-depth treatment. Insight into cell adhesion obtained using micro-interferometry is treated in detail. We conclude by summarising the open questions and possible future directions.

Biomimetic emulsions reveal the effect of mechanical forces on cell-cell adhesion

Cell-cell contacts in tissues are continuously subject to mechanical forces due to homeostatic pressure and active cytoskeleton dynamics. In the process of cellular adhesion, the molecular pathways are well characterized but the role of mechanics is less well understood. To isolate the role of pressure we present a dense packing of functionalized emulsion droplets in which surface interactions are tuned to mimic those of real cells. By visualizing the microstructure in 3D we find that a threshold compression force is necessary to overcome electrostatic repulsion and surface elasticity and establish protein-mediated adhesion. Varying the droplet interaction potential maps out a phase diagram for adhesion as a function of force and salt concentration. Remarkably, fitting the data with our theoretical model predicts binder concentrations in the adhesion areas that are similar to those found in real cells. Moreover, we quantify the dependence of the area of adhesion on the applied force and thus reveal adhesion strengthening with increasing external pressure even in the absence of active cellular processes. This biomimetic approach reveals a physical origin of pressure-sensitive adhesion and its strength across cell-cell junctions.

Elucidating driving forces for liposome rupture: external perturbations and chemical affinity

Atomic force microscopy (AFM) studies under aqueous buffer probed the role of chemical affinity between liposomes, consisting of large unilamellar vesicles, and substrate surfaces in driving vesicle rupture and tethered lipid bilayer membrane (tLBM) formation on Au surfaces. 1,2-Distearoyl-sn-glycero-3-phosphoethanolamine-N-poly(ethylene glycol)-2000-N-[3-(2-pyridyldithio) propionate] (DSPE-PEG-PDP) was added to 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) vesicles to promote interactions via Au-thiolate bond formation. Forces induced by an AFM tip leading to vesicle rupture on Au were quantified as a function of DSPE-PEG-PDP composition with and without osmotic pressure. The critical forces needed to initiate rupture of vesicles with 2.5, 5, and 10 mol % DSPE-PEG-PDP are approximately 1.1, 0.8, and 0.5 nN, respectively. The critical force needed for tLBM formation decreases from 1.1 nN (without osmotic pressure) to 0.6 nN (with an osmotic pressure due to 5 mM of CaCl(2)) for vesicles having 2.5 mol % DSPE-PEG-PDP. Forces as high as 5 nN did not lead to LBM formation from pure POPC vesicles on Au. DSPE-PEG-PDP appears to be important to anchor and deform vesicles on Au surfaces. This study demonstrates how functional lipids can be used to tune vesicle-surface interactions and elucidates the role of vesicle-substrate interactions in vesicle rupture.

Use of reflectance interference contrast microscopy to characterize the endothelial glycocalyx stiffness

Reflectance interference contrast microscopy (RICM) was used to study the mechanics of the endothelial glycocalyx. This technique tracks the vertical position of a glass microsphere probe that applies very light fluctuating loads to the outermost layer of the bovine lung microvascular endothelial cell (BLMVEC) glycocalyx. Fluctuations in probe vertical position are used to estimate the effective stiffness of the underlying layer. Stiffness was measured before and after removal of specific glycocalyx components. The mean stiffness of BLMVEC glycocalyx was found to be ~7.5 kT/nm(2) (or ~31 pN/nm). Enzymatic digestion of the glycocalyx with pronase or hyaluronan with hyaluronidase increased the mean effective stiffness of the glycocalyx; however, the increase of the mean stiffness on digestion of heparan sulfate with heparinase III was not significant. The results imply that hyaluronan chains act as a cushioning layer to distribute applied forces to the glycocalyx structure. Effective stiffness was also measured for the glycocalyx exposed to 0.1%, 1.0%, and 4.0% BSA; glycocalyx compliance increased at two extreme BSA concentrations. The RICM images indicated that glycocalyx thickness increases with BSA concentrations. Results demonstrate that RICM is sensitive to detect the subtle changes of glycocalyx compliance at the fluid-fiber interface.

DYNAMICS OF VESICLE ADHESION: SPREADING VERSUS DEWETTING COUPLED TO BINDER DIFFUSION

We study the kinetics of specific adhesion of giant vesicles on complemetary (bilayer-decorated) solid surfaces. Tensed vesicles exhibit a single adhesion zone that grows slowly. Floppy vesicles adhere via many small adhesion spots that grow and fuse, merging finally into a large adhesive zone. Using approaches derived from Ref. 12, we show how the progressive mobilization of adhesive molecules (diffusing toward the patch) can explain our experimental observations.

Attachment of rod-like (BAR) proteins and membrane shape

Previous studies have shown that cellular function depends on rod-like membrane proteins, among them Bin/Amphiphysin/Rvs (BAR) proteins may curve the membrane leading to physiologically important membrane invaginations and membrane protrusions. The membrane shaping induced by BAR proteins has a major role in various biological processes such as cell motility and cell growth. Different models of binding of BAR domains to the lipid bilayer are described. The binding includes hydrophobic insertion loops and electrostatic interactions between basic amino acids at the concave region of the BAR domain and negatively charged lipids. To shed light on the elusive binding dynamics, a novel experiment is proposed to expand the technique of single-molecule AFM for the traction of binding energy of a single BAR domain.

Quantitative evaluation of mechanosensing of cells on dynamically tunable hydrogels

Thin hydrogel films based on an ABA triblock copolymer gelator [where A is pH-sensitive poly(2-(diisopropylamino)ethyl methacrylate) (PDPA) and B is biocompatible poly(2-(methacryloyloxy)ethyl phosphorylcholine) (PMPC)] were used as a stimulus-responsive substrate that allows fine adjustment of the mechanical environment experienced by mouse myoblast cells. The hydrogel film elasticity could be reversibly modulated by a factor of 40 via careful pH adjustment without adversely affecting cell viability. Myoblast cells exhibited pronounced stress fiber formation and flattening on increasing the hydrogel elasticity. As a new tool to evaluate the strength of cell adhesion, we combined a picosecond laser with an inverted microscope and utilized the strong shock wave created by the laser pulse to determine the critical pressure required for cell detachment. Furthermore, we demonstrate that an abrupt jump in the hydrogel elasticity can be utilized to monitor how cells adapt their morphology to changes in their mechanical environment.

Adhesion of soft membranes controlled by tension and interfacial polymers

We examine experimental and theoretical aspects of nonspecific adhesion of giant vesicles on modified surfaces as model systems for cell spreading. Using dual-wave interference microscopy and new analysis, membrane undulations as well as large scale vesicle shape are monitored. Measurements and modelling show that the nucleation of adhesion depends critically on the interfacial polymer and membrane tension. Patch growth is governed by local membrane geometry, adhesion energy, and local viscosity. Finally, spreading stops when tension induced by adhesion unfolds excess membrane area.