Dynamics of specific vesicle-substrate adhesion: from local events to global dynamics

Supported Lipid Bilayers and the Study of Two-Dimensional Binding Kinetics

Binding between protein molecules on contacting cells is essential in initiating and regulating several key biological processes. In contrast to interactions between molecules in solution, these events are restricted to the two-dimensional (2D) plane of the meeting cell surfaces. However, converting between the more commonly available binding kinetics measured in solution and the so-called 2D binding kinetics has proven a complicated task since for the latter several factors other than the protein-protein interaction per se have an impact. A few important examples of these are: protein density, membrane fluctuations, force on the bond and the use of auxiliary binding molecules. The development of model membranes, and in particular supported lipid bilayers (SLBs), has made it possible to simplify the studied contact to analyze these effects and to measure 2D binding kinetics of individual protein-protein interactions. We will in this review give an overview of, and discuss, how different SLB systems have been used for this and compare different methods to measure binding kinetics in cell-SLB contacts. Typically, the SLB is functionalized with fluorescently labelled ligands whose interaction with the corresponding receptor on a binding cell can be detected. This interaction can either be studied 1) by an accumulation of ligands in the cell-SLB contact, whose magnitude depends on the density of the proteins and binding affinity of the interaction, or 2) by tracking single ligands in the SLB, which upon interaction with a receptor result in a change of motion of the diffusing ligand. The advantages and disadvantages of other methods measuring 2D binding kinetics will also be discussed and compared to the fluorescence-based methods. Although binding kinetic measurements in cell-SLB contacts have provided novel information on how ligands interact with receptors in vivo the number of these measurements is still limited. This is influenced by the complexity of the system as well as the required experimental time. Moreover, the outcome can vary significantly between studies, highlighting the necessity for continued development of methods to study 2D binding kinetics with higher precision and ease.

Integrin-Functionalised Giant Unilamellar Vesicles via Gel-Assisted Formation: Good Practices and Pitfalls

Giant unilamellar vesicles (GUV) are powerful tools to explore physics and biochemistry of the cell membrane in controlled conditions. For example, GUVs were extensively used to probe cell adhesion, but often using non-physiological linkers, due to the difficulty of incorporating transmembrane adhesion proteins into model membranes. Here we describe a new protocol for making GUVs incorporating the transmembrane protein integrin using gel-assisted swelling. We report an optimised protocol, enumerating the pitfalls encountered and precautions to be taken to maintain the robustness of the protocol. We characterise intermediate steps of small proteoliposome formation and the final formed GUVs. We show that the integrin molecules are successfully incorporated and are functional.

Dynamics of particle uptake at cell membranes

Receptor-mediated endocytosis requires that the energy of adhesion overcomes the deformation energy of the plasma membrane. The resulting driving force is balanced by dissipative forces, leading to deterministic dynamical equations. While the shape of the free membrane does not play an important role for tensed and loose membranes, in the intermediate regime it leads to an important energy barrier. Here we show that this barrier is similar to but different from an effective line tension and suggest a simple analytical approximation for it. We then explore the rich dynamics of uptake for particles of different shapes and present the corresponding dynamical state diagrams. We also extend our model to include stochastic fluctuations, which facilitate uptake and lead to corresponding changes in the phase diagrams.

Surface Tension Controls the Hydraulic Fracture of Adhesive Interfaces Bridged by Molecular Bonds

Biological function requires cell-cell adhesions to tune their cohesiveness; for instance, during the opening of new fluid-filled cavities under hydraulic pressure. To understand the physical mechanisms supporting this adaptability, we develop a stochastic model for the hydraulic fracture of adhesive interfaces bridged by molecular bonds. We find that surface tension strongly enhances the stability of these interfaces by controlling flaw sensitivity, lifetime, and optimal architecture in terms of bond clustering. We also show that bond mobility embrittles adhesions and changes the mechanism of decohesion. Our study provides a mechanistic background to understand the biological regulation of cell-cell cohesion and fracture.

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.

Glycan-decorated protocells: novel features for rebuilding cellular processes

In synthetic biology approaches, lipid vesicles are widely used as protocell models. While many compounds have been encapsulated in vesicles (e.g. DNA, cytoskeleton and enzymes), the incorporation of glycocalyx components in the lipid bilayer has attracted much less attention so far. In recent years, glycoconjugates have been integrated in the membrane of giant unilamellar vesicles (GUVs). These minimal membrane systems have largely contributed to shed light on the molecular mechanisms of cellular processes. In this review, we first introduce several preparation and biophysical characterization methods of GUVs. Then, we highlight specific applications of protocells investigating glycolipid-mediated endocytosis of toxins, viruses and bacteria. In addition, we delineate how prototissues have been assembled from glycan-decorated protocells by using lectin-mediated cross-linking of opposed glycoreceptors (e.g. glycolipids and glycopeptides). In future applications, glycan-decorated protocells might be useful for investigating cell-cell interactions (e.g. adhesion and communication). We also speculate about the implication of lectin-glycoreceptor interactions in membrane fusion processes.

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.

Binding kinetics of membrane-anchored receptors and ligands: Molecular dynamics simulations and theory

The adhesion of biological membranes is mediated by the binding of membrane-anchored receptor and ligand proteins. Central questions are how the binding kinetics of these proteins is affected by the membranes and by the membrane anchoring of the proteins. In this article, we (i) present detailed data for the binding of membrane-anchored proteins from coarse-grained molecular dynamics simulations and (ii) provide a theory that describes how the binding kinetics depends on the average separation and thermal roughness of the adhering membranes and on the anchoring, lengths, and length variations of the proteins. An important element of our theory is the tilt of bound receptor-ligand complexes and transition-state complexes relative to the membrane normals. This tilt results from an interplay of the anchoring energy and rotational entropy of the complexes and facilitates the formation of receptor-ligand bonds at membrane separations smaller than the preferred separation for binding. In our simulations, we have considered both lipid-anchored and transmembrane receptor and ligand proteins. We find that the binding equilibrium constant and binding on-rate constant of lipid-anchored proteins are considerably smaller than the binding constant and on-rate constant of rigid transmembrane proteins with identical binding domains.

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).

The glycocalyx promotes cooperative binding and clustering of adhesion receptors

Cell adhesion plays a pivotal role in various biological processes, e.g., immune responses, cancer metastasis, and stem cell differentiation. The adhesion behaviors depend subtly on the binding kinetics of receptors and ligands restricted at the cell-substrate interfaces. Although much effort has been directed toward investigating the kinetics of adhesion molecules, the role of the glycocalyx, anchored on cell surfaces as an exterior layer, is still unclear. In this paper, we propose a theoretical approach to study the collective binding kinetics of a few and a large number of binders in the presence of the glycocalyx, representing the cases of initial and mature adhesions of cells, respectively. The analytical results are validated by finding good agreement with our Monte Carlo simulations. In the force loading case, the on-rate and affinity increase as more bonds form, whereas this cooperative effect is not observed in the displacement loading case. The increased thickness and stiffness of the glycocalyx tend to decrease the affinity for a few bonds, while they have less influence on the affinity for a large number of bonds. Moreover, for a flexible membrane with thermally-excited shape fluctuations, the glycocalyx is exhibited to promote the formation of bond clusters, mainly due to the cooperative binding of binders. This study helps to understand the cooperative kinetics of adhesion receptors under physiologically relevant loading conditions and sheds light on the novel role of the glycocalyx in cell adhesion.

Weak reversible cross links may decrease the strength of aligned fiber bundles

Reversible cross-linking is an effective strategy to specifically tailor the mechanical properties of polymeric materials that can be found in a variety of biological as well as man-made materials. Using a simple model in this paper the influence of weak, reversible cross-links on the mechanical properties of aligned fiber bundles is investigated. Special emphasis in this analysis is put on the strength of the investigated structures. Using Monte Carlo methods two topologies of cross-links exceeding the strength of the covalent backbone are studied. Most surprisingly only two cross-links are sufficient to break the backbone of a multi chain system, resulting in a reduced strength of the material. The found effect crucially depends on the ratio of inter- to intra-chain cross-links and, thus, on the grafting density that determines this ratio.

Model for probing membrane-cortex adhesion by micropipette aspiration and fluctuation spectroscopy

We propose a model for membrane-cortex adhesion that couples membrane deformations, hydrodynamics, and kinetics of membrane-cortex ligands. In its simplest form, the model gives explicit predictions for the critical pressure for membrane detachment and for the value of adhesion energy. We show that these quantities exhibit a significant dependence on the active acto-myosin stresses. The model provides a simple framework to access quantitative information on cortical activity by means of micropipette experiments. We also extend the model to incorporate fluctuations and show that detailed information on the stability of membrane-cortex coupling can be obtained by a combination of micropipette aspiration and fluctuation spectroscopy measurements.

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.

Membrane adhesion and the formation of heterogeneities: biology, biophysics, and biotechnology

Membrane adhesion is essential to many vital biological processes. Sites of membrane adhesion are often associated with heterogeneities in the lipid and protein composition of the membrane. These heterogeneities are thought to play functional roles by facilitating interactions between proteins. However, the causal links between membrane adhesion and membrane heterogeneities are not known. Here we survey the state of the field and indicate what we think are understudied areas ripe for development.

Association rates of membrane-coupled cell adhesion molecules

Thus far, understanding how the confined cellular environment affects the lifetime of bonds, as well as the extraction of complexation rates, has been a major challenge in studies of cell adhesion. Based on a theoretical description of the growth curves of adhesion domains, we present a new (to our knowledge) method to measure the association rate k(on) of ligand-receptor pairs incorporated into lipid membranes. As a proof of principle, we apply this method to several systems. We find that the k(on) for the interaction of biotin with neutravidin is larger than that for integrin binding to RGD or sialyl Lewis(x) to E-selectin. Furthermore, we find k(on) to be enhanced by membrane fluctuations that increase the probability for encounters between the binders. The opposite effect on k(on) could be attributed to the presence of repulsive polymers that mimic the glycocalyx, which points to two potential mechanisms for controlling the speed of protein complexation during the cell recognition process.

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.

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.

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.

Energetics of adhesion cluster formation in the context of biological membranes

The orchestration of cellular adhesion is an intricate process that involves a multitude of specialized proteins but at the same time follows a simple physical plan. It is still not totally known why cells create clusters of bonds to adhere on a substrate. Besides experimental methods to study cellular adhesion there exist several different theoretical models to describe the stability of focal adhesion clusters. The model proposed in this work makes it possible to understand the formation of adhesion bond clusters. It explains the emergence of a long-range bond-bond attraction that originates from the finite membrane elasticity as the driving force of cluster growth. In combination with a thermally driven bond disintegration such a model will eventually be able to explain the kinetic stability of finite size bond clusters. The model extends conventional two-state models where bonds are either open or closed by introducing a rich scenario of metastable states associated with hysteretic behavior in the bond closure and rupture dynamics.

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.

Membrane dynamics correlate with formation of signaling clusters during cell spreading

The morphology and duration of contacts between cells and adhesive surfaces play a key role in several biological processes, such as cell migration, cell differentiation, and the immune response. The interaction of receptors on the cell membrane with ligands on the adhesive surface leads to triggering of signaling pathways, which allow cytoskeletal rearrangement, and large-scale deformation of the cell membrane, which allows the cell to spread over the substrate. Despite numerous studies of cell spreading, the nanometer-scale dynamics of the membrane during formation of contacts, spreading, and initiation of signaling are not well understood. Using interference reflection microscopy, we study the kinetics of cell spreading at the micron scale, as well as the topography and fluctuations of the membrane at the nanometer scale during spreading of Jurkat T cells on antibody-coated substrates. We observed two modes of spreading, which were characterized by dramatic differences in membrane dynamics and topography. Formation of signaling clusters was closely related to the movement and morphology of the membrane in contact with the activating surface. Our results suggest that cell membrane morphology may be a critical constraint on signaling at the cell-substrate interface.

Effective tension and fluctuations in active membranes

We calculate the fluctuation spectrum of the shape of a lipid vesicle or cell exposed to a nonthermal source of noise. In particular, we take constraints on the membrane area and the volume of fluid that it encapsulates into account when obtaining expressions for the dependency of the membrane tension on the noise. We then investigate three possible origins of the nonthermal noise taken from the literature: A direct force, which models an external medium pushing on the membrane, a curvature force, which models a fluctuating spontaneous curvature, and a permeation force coming from an active transport of fluid through the membrane. For the direct force and curvature force cases, we compare our results to existing experiments on active membranes.

Depletion versus deflection: how membrane bending can influence adhesion

During depletion-driven vesicle adhesion, a stiff membrane's resistance to bending at fixed tension prevents contact angle equilibrium and vesicle spreading over an opposing vesicle, while more flexible vesicles partially engulf opposing vesicles. Estimates of the bending cost associated with the spreading contact line, relative to the adhesion energy, were consistent with the observed spreading or lack of spreading for the flexible and stiff membranes, respectively, and predicted a lag time sometimes preceding spreading.

Effect of cell and microvillus mechanics on the transmission of applied loads to single bonds in dynamic force spectroscopy

Receptor-ligand interactions that mediate cellular adhesion are often subjected to forces that regulate their detachment via modulating off-rates. Although the dynamics of detachment is primarily controlled by the physical chemistry of adhesion molecules, cellular features such as cell deformability and microvillus viscoelasticity have been shown to affect the rolling velocity of leukocytes in vitro through experiments and simulation. In this work, we demonstrate via various micromechanical models of two cells adhered by a single (intramolecular) bond that cell deformability and microvillus viscoelasticity modulate transmission of an applied external load to an intramolecular bond, and thus the dynamics of detachment. Specifically, it is demonstrated that the intermolecular bond force is not equivalent to the instantaneous applied force and that the instantaneous bond force decreases with cellular and microvillus compliance. As cellular compliance increases, not only does the time lag between the applied load and the bond force increase, an initial response time is observed during which cell deformation is observed without transfer of force to the bond. It is further demonstrated that following tether formation the instantaneous intramoleular bond force increases linearly at a rate dependent on microvillus viscosity. Monte Carlo simulations with fixed kinetic parameters predict that both cell and microvillus compliance increase the average rupture time, although the average rupture force based on bond length remains nearly unchanged.

Cooperativity between trans and cis interactions in cadherin-mediated junction formation

Intercellullar junctions formed by cadherins, including desmosomes and adherens junctions, comprise two dimensional arrays of "trans" dimers formed between monomers emanating from opposing cell surfaces. Lateral "cis" interfaces between cadherins from the same cell surface have been proposed to play a role in cadherin clustering. Although the molecular details of cis interactions remain uncertain, they must define an anisotropic arrangement where binding is favorable only in certain orientations. Here we report Monte Carlo simulations performed on a 2D lattice constructed to account for the anisotropy in cadherin cis interactions. A crucial finding is that the "phase transition" between freely diffusing cadherin monomers and dimers and a condensed ordered 2D junction formed by dimers alone is a cooperative process involving both trans and cis interactions. Moreover, cis interactions, despite being too weak to be measured in solution, are critical to the formation of an ordered junction structure. We discuss these results in light of available experimental information on cadherin binding free energies that are transformed from their bulk solution values to interaction energies on a 2D lattice.

Specific adhesion of membranes: Mapping to an effective bond lattice gas

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 lattice gas model with full dynamic simulations that take into account both the shape fluctuations of the membrane and reactions between receptors and ligands at bond sites. We demonstrate that an appropriate mapping of the height dependent binding and unbinding rates in the full scheme to rates in the lattice gas model leads to good agreement.

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.

Integrin reconstituted in GUVs: a biomimetic system to study initial steps of cell spreading

A novel in vitro membrane system mimicking the first steps of integrin-mediated cell spreading has been developed and characterized. We have reconstituted the transmembrane alpha(IIb)beta(3) integrin into giant unilamellar vesicles (GUVs). The reconstitution process has been validated by analyzing protein incorporation and biological activity by checking the specific interaction of GUVs containing integrin with quantum dots (QD) or surfaces coated with the integrin receptor tri-peptide RGD.(1) The spreading dynamics of integrin-functionalized GUVs onto fibrinogen-coated surfaces has been monitored by Reflection Interference Contrast Microscopy (RICM). Our results are quantitatively consistent with a theoretical model based on a dewetting process coupled to binder diffusion and provide a comprehensive description of the following sequence: i) nucleation and growth of adhesive patches coupled to the diffusion of the adhesive proteins to these adhesive zones ii) fusion of patches and formation of an adhesive ring iii) complete spreading of the GUV by dewetting of the central liquid film from the border to form an adhesive circular patch that is not significantly enriched in integrins, as compared to the unbound membrane. This finding is consistent with the recognized role of the actin cytoskeleton in stabilizing focal complexes and focal adhesions in a cell-extracellular matrix contact. These very large unilamellar integrin-containing vesicles provide a unique artificial system, which could be further developed towards realistic cell mimic and used to study the complexity of integrin-mediated cell spreading.

Model of SNARE-mediated membrane adhesion kinetics

SNARE proteins are conserved components of the core fusion machinery driving diverse membrane adhesion and fusion processes in the cell. In many cases micron-sized membranes adhere over large areas before fusion. Reconstituted in vitro assays have helped isolate SNARE mechanisms in small membrane adhesion-fusion and are emerging as powerful tools to study large membrane systems by use of giant unilamellar vesicles (GUVs). Here we model SNARE-mediated adhesion kinetics in SNARE-reconstituted GUV-GUV or GUV-supported bilayer experiments. Adhesion involves many SNAREs whose complexation pulls apposing membranes into contact. The contact region is a tightly bound rapidly expanding patch whose growth velocity v(patch) increases with SNARE density Gamma(snare). We find three patch expansion regimes: slow, intermediate, fast. Typical experiments belong to the fast regime where v(patch) ~ (Gamma(snare)(2/3) depends on SNARE diffusivities and complexation binding constant. The model predicts growth velocities ~10 - 300 microm/s. The patch may provide a close contact region where SNAREs can trigger fusion. Extending the model to a simple description of fusion, a broad distribution of fusion times is predicted. Increasing SNARE density accelerates fusion by boosting the patch growth velocity, thereby providing more complexes to participate in fusion. This quantifies the notion of SNAREs as dual adhesion-fusion agents.

Theoretical study of the competition between cell-cell and cell-matrix adhesions

Adhesions between neighboring cells or between cells and their surrounding tissue/matrix play a crucial role in a wide range of biological processes. In order to investigate the competitive mechanisms between cell-cell and cell-matrix adhesions, we here develop a theoretical framework for multiple interacting cells lying on a planar matrix coated with distributed ligands. This model allows us to study, from the viewpoints of energy and statistics, the effects of such physical mechanisms as binding energy of bonds, nonspecific interactions, elastic deformation of cell membranes, and mixing entropy. Our calculations show that cell-matrix adhesion cannot occur when the ligand density on the matrix is lower than a threshold value, and cell-cell adhesion does not happen for a high ligand density. Glycocalyx repulsion plays a more important role in cell-matrix adhesion than in cell-cell adhesion. In addition, it is found that the cell-cell adhesion density decreases as the number of cells increases.

Computational modeling for cell spreading on a substrate mediated by specific interactions, long-range recruiting interactions, and diffusion of binders

A continuum model was proposed to study cell spreading on a flat substrate mediated by specific interaction, long-range recruiting interaction, and the diffusion of binders. Specific interactions between the mobile receptors embedded in the cell membrane and ligands coated on the substrate surface result in cell adhesion to the substrate surface. This receptor-ligand interaction was described by a chemical reaction equation. Long-range recruiting interactions between the receptors and the substrate were simplified by a traction-separation law. The governing equations and boundary conditions were formulated for the entire process of cell spreading and solved using a finite element scheme. Parametric studies were conducted to investigate the effect of system parameters on the cell spreading kinetics. It is shown that kinetic factors play an important role in cell adhesion and three regimes, that is, the binder reaction limited regime, long-range recruiting force-driven binder recruitment limited regime, and the concentration gradient-driven diffusion limited regime, were identified.

Progress in mimetic studies of cell adhesion and the mechanosensing

Vesicle-substrate adhesion has been studied for over two decades with the motivation to understand and mimic cell adhesion. In recent years, with progress in theoretical modelling, the development of experimental techniques, and improved data-analysis procedures, considerable advances have been made in the understanding of the adhesion process. It is this progress which constitutes the focus of this review.