Kinetics of membrane adhesion mediated by ligand-receptor interaction studied with a biomimetic system

Modeling Receptor Motility along Advecting Lipid Membranes

This work aims to overview multiphysics mechanobiological computational models for receptor dynamics along advecting cell membranes. Continuum and statistical models of receptor motility are the two main modeling methodologies identified in reviewing the state of the art. Within the former modeling class, a further subdivision based on different biological purposes and processes of proteins’ motion is recognized; cell adhesion, cell contractility, endocytosis, and receptor relocations on advecting membranes are the most relevant biological processes identified in which receptor motility is pivotal. Numerical and/or experimental methods and approaches are highlighted in the exposure of the reviewed works provided by the literature, pertinent to the topic of the present manuscript. With a main focus on the continuum models of receptor motility, we discuss appropriate multiphyisics laws to model the mass flux of receptor proteins in the reproduction of receptor relocation and recruitment along cell membranes to describe receptor–ligand chemical interactions, and the cell’s structural response. The mass flux of receptor modeling is further supported by a discussion on the methodology utilized to evaluate the protein diffusion coefficient developed over the years.

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.

Molecular Biomechanics Controls Protein Mixing and Segregation in Adherent Membranes

Cells interact with their environment by forming complex structures involving a multitude of proteins within assemblies in the plasma membrane. Despite the omnipresence of these assemblies, a number of questions about the correlations between the organisation of domains and the biomechanical properties of the involved proteins, namely their length, flexibility and affinity, as well as about the coupling to the elastic, fluctuating membrane, remain open. Here we address these issues by developing an effective Kinetic Monte Carlo simulation to model membrane adhesion. We apply this model to a typical experiment in which a cell binds to a functionalized solid supported bilayer and use two ligand-receptor pairs to study these couplings. We find that differences in affinity and length of proteins forming adhesive contacts result in several characteristic features in the calculated phase diagrams. One such feature is mixed states occurring even with proteins with length differences of 10 nm. Another feature are stable nanodomains with segregated proteins appearing on time scales of cell experiments, and for biologically relevant parameters. Furthermore, we show that macroscopic ring-like patterns can spontaneously form as a consequence of emergent protein fluxes. The capacity to form domains is captured by an order parameter that is founded on the virial coefficients for the membrane mediated interactions between bonds, which allow us to collapse all the data. These findings show that taking into account the role of the membrane allows us to recover a number of experimentally observed patterns. This is an important perspective in the context of explicit biological systems, which can now be studied in significant detail.

The GDP-Bound State of Mitochondrial Mfn1 Induces Membrane Adhesion of Apposing Lipid Vesicles through a Cooperative Binding Mechanism

Mitochondria are double-membrane organelles that continuously undergo fission and fusion. Outer mitochondrial membrane fusion is mediated by the membrane proteins mitofusin 1 (Mfn1) and mitofusin 2 (Mfn2), carrying a GTP hydrolyzing domain (GTPase) and two coiled-coil repeats. The detailed mechanism on how the GTP hydrolysis allows Mfns to approach adjacent membranes into proximity and promote their fusion is currently under debate. Using model membranes built up as giant unilamellar vesicles (GUVs), we show here that Mfn1 promotes membrane adhesion of apposing lipid vesicles. The adhesion forces were sustained by the GDP-bound state of Mfn1 after GTP hydrolysis. In contrast, the incubation with the GDP:AlF4−, which mimics the GTP transition state, did not induce membrane adhesion. Due to the flexible nature of lipid membranes, the adhesion strength depended on the surface concentration of Mfn1 through a cooperative binding mechanism. We discuss a possible scenario for the outer mitochondrial membrane fusion based on the modulated action of Mfn1.

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.

Biomaterials functionalized with nanoclusters of integrin- and syndecan-binding ligands improve cell adhesion and mechanosensing under shear flow conditions

We have engineered biomaterials that display nanoclusters of ligands that bind both integrin and syndecan-4 cell receptors. These surfaces regulate cell behaviors under static conditions including adhesion, spreading, actin stress fiber formation, and migration. The syndecan-4 receptors are also critical mediators of cellular mechanotransduction. In this contribution we assess whether this novel class of materials can regulate the response of cells to applied mechanical stimulation, using the shear stress imparted by laminar fluid flow as a model stimulus. Specifically, we assess endothelial cell detachment due to flow, cell alignment due to flow, and cell adhesion from the flowing fluid. A high degree of cell retention was observed on surfaces containing integrin-binding ligands or a mixed population of integrin- and syndecan-binding ligands. However, the presence of both ligand types was necessary for the cells to align in the direction of flow. These results imply that integrin engagement is necessary for adhesion strength, but engagement of both receptor types aids in appropriate mechanotransduction. Additionally, it was found that surfaces functionalized with both ligand types were able to scavenge a larger number of cells from flow, and to do so at a faster rate, compared to surfaces functionalized with only integrin- or syndecan-binding ligands. These results show that interfaces functionalized with both integrin- and syndecan-binding ligands regulate a significant range of biophysical cell behaviors in response to shear stress.

Mechanisms of Motor-Independent Membrane Remodeling Driven by Dynamic Microtubules

Microtubule-dependent organization of membranous organelles occurs through motor-based pulling and by coupling microtubule dynamics to membrane remodeling. For example, tubules of endoplasmic reticulum (ER) can be extended by kinesin- and dynein-mediated transport and through the association with the tips of dynamic microtubules. The binding between ER and growing microtubule plus ends requires End Binding (EB) proteins and the transmembrane protein STIM1, which form a tip-attachment complex (TAC), but it is unknown whether these proteins are sufficient for membrane remodeling. Furthermore, EBs and their partners undergo rapid turnover at microtubule ends, and it is unclear how highly transient protein-protein interactions can induce load-bearing processive motion. Here, we reconstituted membrane tubulation in a minimal system with giant unilamellar vesicles, dynamic microtubules, an EB protein, and a membrane-bound protein that can interact with EBs and microtubules. We showed that these components are sufficient to drive membrane remodeling by three mechanisms: membrane tubulation induced by growing microtubule ends, motor-independent membrane sliding along microtubule shafts, and membrane pulling by shrinking microtubules. Experiments and modeling demonstrated that the first two mechanisms can be explained by adhesion-driven biased membrane spreading on microtubules. Optical trapping revealed that growing and shrinking microtubule ends can exert forces of ∼0.5 and ∼5 pN, respectively, through attached proteins. Rapidly exchanging molecules that connect membranes to dynamic microtubules can thus bear a sufficient load to induce membrane deformation and motility. Furthermore, combining TAC components and a membrane-attached kinesin in the same in vitro assays demonstrated that they can cooperate in promoting membrane tubule extension.

Fundamental Characteristics of Neuron Adhesion Revealed by Forced Peeling and Time-Dependent Healing

A current bottleneck in the advance of neurophysics is the lack of reliable methods to quantitatively measure the interactions between neural cells and their microenvironment. Here, we present an experimental technique to probe the fundamental characteristics of neuron adhesion through repeated peeling of well-developed neurite branches on a substrate with an atomic force microscopy cantilever. At the same time, a total internal reflection fluorescence microscope is also used to monitor the activities of neural cell adhesion molecules (NCAMs) during detaching. It was found that NCAMs aggregate into clusters at the neurite-substrate interface, resulting in strong local attachment with an adhesion energy of ∼0.1 mJ/m² and sudden force jumps in the recorded force-displacement curve. Furthermore, by introducing a healing period between two forced peelings, we showed that stable neurite-substrate attachment can be re-established in 2-5 min. These findings are rationalized by a stochastic model, accounting for the breakage and rebinding of NCAM-based molecular bonds along the interface, and provide new insights into the mechanics of neuron adhesion as well as many related biological processes including axon outgrowth and nerve regeneration.

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.

Tunable cell-surface mimetics as engineered cell substrates

Most recent breakthroughs in understanding cell adhesion, cell migration, and cellular mechanosensitivity have been made possible by the development of engineered cell substrates of well-defined surface properties. Traditionally, these substrates mimic the extracellular matrix (ECM) environment by the use of ligand-functionalized polymeric gels of adjustable stiffness. However, such ECM mimetics are limited in their ability to replicate the rich dynamics found at cell-cell contacts. This review focuses on the application of cell surface mimetics, which are better suited for the analysis of cell adhesion, cell migration, and cellular mechanosensitivity across cell-cell interfaces. Functionalized supported lipid bilayer systems were first introduced as biomembrane-mimicking substrates to study processes of adhesion maturation during adhesion of functionalized vesicles (cell-free assay) and plated cells. However, while able to capture adhesion processes, the fluid lipid bilayer of such a relatively simple planar model membrane prevents adhering cells from transducing contractile forces to the underlying solid, making studies of cell migration and cellular mechanosensitivity largely impractical. Therefore, the main focus of this review is on polymer-tethered lipid bilayer architectures as biomembrane-mimicking cell substrate. Unlike supported lipid bilayers, these polymer-lipid composite materials enable the free assembly of linkers into linker clusters at cellular contacts without hindering cell spreading and migration and allow the controlled regulation of mechanical properties, enabling studies of cellular mechanosensitivity. The various polymer-tethered lipid bilayer architectures and their complementary properties as cell substrates are discussed.

Force-driven growth of intercellular junctions

Mechanical force regulates the formation and growth of cell-cell junctions. Cadherin is a prominent homotypic cell adhesion molecule that plays a crucial role in establishment of intercellular adhesion. It is known that the transmitted force through the cadherin-mediated junctions directly correlates with the growth and enlargement of the junctions. In this paper, we propose a physical model for the structural evolution of cell-cell junctions subjected to pulling tractions, using the Bell-Dembo-Bongard thermodynamic model. Cadherins have multiple adhesive states and may establish slip or catch bonds depending on the Ca²⁺ concentration. We conducted a comparative study between the force-dependent behavior of clusters of slip and catch bonds. The results show that the clusters of catch bonds feature some hallmarks of cell mechanotransduction in response to the pulling traction. This is a passive thermodynamic response and is entirely controlled by the effect of mechanical work of the pulling force on the free energy landscape of the junction.

Cell adhesion manipulation through single cell assembly for characterization of initial cell-to-cell interaction

BACKGROUND

Cell-to-cell interactions are complex processes that involve physical interactions, chemical binding, and biological signaling pathways. Identification of the functions of special signaling pathway in cell-to-cell interaction from the very first contact will help characterize the mechanism underlying the interaction and advance new drug discovery.

METHODS

This paper reported a case study of characterizing initial interaction between leukemia cancer cells and bone marrow stromal cells, through the use of an optical tweezers-based cell manipulation tool. Optical traps were used to assemble leukemia cells at different positions of the stromal cell layer and enable their interactions by applying a small trapping force to maintain the cell contact for a few minutes. Specific drug was used to inhibit the binding of molecules during receptor-ligand-mediated adhesion.

RESULTS AND CONCLUSIONS

Our results showed that the amount of adhesion molecule could affect cell adhesion during the first few minutes contact. We also found that leukemia cancer cells could migrate on the stromal cell layer, which was dependent on the adhesion state and activation triggered by specific chemokine. The reported approaches provided a new opportunity to investigate cell-to-cell interaction through single cell adhesion manipulation.

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.

Crowding of receptors induces ring-like adhesions in model membranes

The dynamics of formation of macromolecular structures in adherent membranes is a key to a number of cellular processes. However, the interplay between protein reaction kinetics, diffusion and the morphology of the growing domains, governed by membrane mediated interactions, is still poorly understood. Here we show, experimentally and in simulations, that a rich phase diagram emerges from the competition between binding, cooperativity, molecular crowding and membrane spreading. In the cellular context, the spontaneously-occurring organization of adhesion domains in ring-like morphologies is particularly interesting. These are stabilized by the crowding of bulky proteins, and the membrane-transmitted correlations between bonds. Depending on the density of the receptors, this phase may be circumvented, and instead, the adhesions may grow homogeneously in the contact zone between two membranes. If the development of adhesion occurs simultaneously with membrane spreading, much higher accumulation of binders can be achieved depending on the velocity of spreading. The mechanisms identified here, in the context of our mimetic model, may shed light on the structuring of adhesions in the contact zones between two living cells. 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.

Specific adhesion of membranes simultaneously supports dual heterogeneities in lipids and proteins

Membrane adhesion mediated by one protein species simultaneously stabilizes both ordered-phase and disordered-phase heterogeneities, distinct from the non-adhered membrane.

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.

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.

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.

Mapping single-cell-substrate interactions by surface plasmon resonance microscopy

We report the imaging of the cell-substrate adhesion of a single cell with subcellular spatial resolution. Osmotic pressure was introduced to provide a controllable mechanical stimulation to the cell attached to a substrate, and high-resolution surface plasmon resonance microscopy was used to map the response of the cell, from which local cell-substrate adhesion was determined. In addition to high spatial resolution, the approach is noninvasive and fast and allows for the continuous mapping of cell-substrate interactions and single-cell movements.

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.

'Run-and-tumble' or 'look-and-run'? A mechanical model to explore the behavior of a migrating amoeboid cell

Single cell migration constitutes a fundamental phenomenon involved in many biological events. Amoeboid cells are single cell organisms that migrate in a cyclic manner like worms. In this paper, we propose a 3D finite element model of an amoeboid cell migrating over a 2D surface. In particular, we focus on the mechanical aspect of the problem. The cell is able to generate cyclic active deformations, such as protrusion and contraction, in any direction. The progression of the cell is governed by a tight synchronization between the adhesion forces, which are alternatively applied at the front and at the rear edges of the cell, and the protrusion-contraction phases of the cell body. Finally, two important aspects have been taken into account: (1) the external stimuli in response to which the cell migrates (e.g. need to feed, morphogenetic events, normal or abnormal environment cues), (2) the heterogeneity of the 2D substrate (e.g. obstacles, rugosity, slippy regions) for which two distinct approaches have been evaluated: the 'run-and-tumble' strategy and the 'look-and-run' strategy. Overall, the results show a good agreement with respect to the experimental observations and the data from the literature (e.g. velocity and strains). Therefore, the present model helps, on one hand, to better understand the intimate relationship between the deformation modes of a cell and the adhesion strength that is required by the cell to crawl over a substrate, and, on the other hand, to put in evidence the crucial role played by mechanics during the migration process.

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.

Model system for cell adhesion mediated by weak carbohydrate-carbohydrate interactions

The multivalent carbohydrate-carbohydrate interaction between membrane-anchored epitopes derived from the marine sponge Microciona prolifera has been explored by colloidal probe microscopy. An in situ coupling of sulfated and non-sulfated disaccharides to membrane-coated surfaces was employed to mimic native cell-cell contacts.The dynamic strength of the homomeric self-association was measured as a function of calcium ions and loading rate. A deterministic model was used to estimate the basic energy landscape and number of participating bonds in the contact zone.

Spatial variation of permittivity of an electrolyte solution in contact with a charged metal surface: a mini review

Contact between a charged metal surface and an electrolyte implies a particular ion distribution near the charged surface, i.e. the electrical double layer. In this mini review, different mean-field models of relative (effective) permittivity are described within a simple lattice model, where the orientational ordering of water dipoles in the saturation regime is taken into account. The Langevin-Poisson-Boltzmann (LPB) model of spatial variation of the relative permittivity for point-like ions is described and compared to a more general Langevin-Bikerman (LB) model of spatial variation of permittivity for finite-sized ions. The Bikerman model and the Poisson-Boltzmann model are derived as limiting cases. It is shown that near the charged surface, the relative permittivity decreases due to depletion of water molecules (volume-excluded effect) and orientational ordering of water dipoles (saturation effect). At the end, the LPB and LB models are generalised by also taking into account the cavity field.

Cell-substrate interaction with cell-membrane-stress dependent adhesion

Cell-substrate interaction is examined in a two-dimensional mechanics model. The cell and substrate are treated as a shell and an elastic solid, respectively. Their interaction through adhesion is treated using nonlinear springs. Compared to previous cell mechanics models, the present model introduces a cohesive force law that is dependent not only on cell-substrate distance but also on internal cell-membrane stress. It is postulated that a living cell would establish focal adhesion sites with density dependent on the cell-membrane stress. The formulated mechanics problem is numerically solved using coupled finite elements and boundary elements for the cell and the substrate, respectively. The nodes in the adhesion zone from either side are linked by the cohesive springs. The specific cases of a cell adhering to a homogeneous substrate and a heterogeneous bimaterial substrate are examined. The analyses show that the substrate stiffness affects the adhesion behavior significantly and regulates the direction of cell adhesion, in good agreement with the experimental results in the literature. By introducing a reactive parameter (i.e., cell-membrane stress) linking biological responses of a living cell to a mechanical environment, the present model offers a unified mechanistic vehicle for characterization and prediction of living cell responses to various kinds of mechanical stimuli including local extracellular matrix and neighboring cells.

Cell-biomaterial mechanical interaction in the framework of tissue engineering: insights, computational modeling and perspectives

Tissue engineering is an emerging field of research which combines the use of cell-seeded biomaterials both in vitro and/or in vivo with the aim of promoting new tissue formation or regeneration. In this context, how cells colonize and interact with the biomaterial is critical in order to get a functional tissue engineering product. Cell-biomaterial interaction is referred to here as the phenomenon involved in adherent cells attachment to the biomaterial surface, and their related cell functions such as growth, differentiation, migration or apoptosis. This process is inherently complex in nature involving many physico-chemical events which take place at different scales ranging from molecular to cell body (organelle) levels. Moreover, it has been demonstrated that the mechanical environment at the cell-biomaterial location may play an important role in the subsequent cell function, which remains to be elucidated. In this paper, the state-of-the-art research in the physics and mechanics of cell-biomaterial interaction is reviewed with an emphasis on focal adhesions. The paper is focused on the different models developed at different scales available to simulate certain features of cell-biomaterial interaction. A proper understanding of cell-biomaterial interaction, as well as the development of predictive models in this sense, may add some light in tissue engineering and regenerative medicine fields.

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.

Reflectivity and topography of cells grown on glass-coverslips measured with phase-shifted laser feedback interference microscopy

In spite of the advantages associated with the molecular specificity of fluorescence imaging, there is still a significant need to augment these approaches with label-free imaging. Therefore, we have implemented a form of interference microscopy based upon phase-shifted, laser-feedback interferometry and developed an algorithm that can be used to separate the contribution of the elastically scattered light by sub-cellular structures from the reflection at the coverslip-buffer interface. The method offers an opportunity to probe protein aggregation, index of refraction variations and structure. We measure the topography and reflection from calibration spheres and from stress fibers and adhesions in both fixed and motile cells. Unlike the data acquired with reflection interference contrast microscopy, where the reflection from adhesions can appear dark, our approach demonstrates that these regions have high reflectivity. The data acquired from fixed and live cells show the presence of a dense actin layer located ≈ 100 nm above the coverslip interface. Finally, the measured dynamics of filopodia and the lamella in a live cell supports retrograde flow as the dominate mechanism responsible for filopodia retraction.

Nanoscale tissue engineering: spatial control over cell-materials interactions

Cells interact with the surrounding environment by making tens to hundreds of thousands of nanoscale interactions with extracellular signals and features. The goal of nanoscale tissue engineering is to harness these interactions through nanoscale biomaterials engineering in order to study and direct cellular behavior. Here, we review two- and three-dimensional (2- and 3D) nanoscale tissue engineering technologies, and provide a holistic overview of the field. Techniques that can control the average spacing and clustering of cell adhesion ligands are well established and have been highly successful in describing cell adhesion and migration in 2D. Extension of these engineering tools to 3D biomaterials has created many new hydrogel and nanofiber scaffold technologies that are being used to design in vitro experiments with more physiologically relevant conditions. Researchers are beginning to study complex cell functions in 3D. However, there is a need for biomaterials systems that provide fine control over the nanoscale presentation of bioactive ligands in 3D. Additionally, there is a need for 2- and 3D techniques that can control the nanoscale presentation of multiple bioactive ligands and that can control the temporal changes in the cellular microenvironment.

Cell adhesion to borate glasses by colloidal probe microscopy

The adhesion of osteoblast-like cells to silicate and borate glasses was measured in cell growth medium using colloidal probe microscopy. The probes consisted of silicate and borate glass spheres, 25-50 μm in diameter, attached to atomic force microscope cantilevers. Variables of the study included glass composition and time of contact of the cell to the glasses. Increasing the time of contact from 15 to 900 s increased the force of adhesion. The data could be plotted linearly on a log-log plot of adhesive force versus time. Of the seven glasses tested, five had slopes close to 0.5, suggesting a square root dependence of the adhesive force on the contact time. Such behavior can be interpreted as a diffusion limited process occurring during the early stages of cell attachment. We suggest that the rate limiting step in the adhesion process is the diffusion of integrins resident in the cell membrane to the area of cell attachment. Data presented in this paper support the hypothesis of Hench et al. that strong adhesion depends on the formation of a calcium phosphate reaction layer on the surfaces of the glass. Glasses that did not form a calcium phosphate layer exhibited a weaker adhesive force relative to those glasses that did form a calcium phosphate layer.

Modeling receptor-mediated endocytosis via mechanics of cell adhesion

A mathematical model describing how a cell membrane with diffusive mobile receptors wraps around a ligand coated cylindrical or spherical particle has been recently developed to model particle size effects in receptor mediated endocytosis. The model predicted an optimal particle size for the smallest wrapping time, as well as a minimum and a maximum particle size for successful wrapping. The results showed that particles in the size range of tens to hundreds of nanometers can enter cells even in the absence of clathrin or caveolin coats. Here we report some further progresses on modeling a spontaneous membrane curvature induced by clathrin or caveolin coats at the inner membrane leaflet as well as simultaneous entry of many particles into cells. It is found that a spontaneous membrane curvature narrows the particle size range for successful wrapping and there exists an optimal particle density for maximum particle adsorptivity.

A POROELASTIC MODEL FOR CELL CRAWLING INCLUDING MECHANICAL COUPLING BETWEEN CYTOSKELETAL CONTRACTION AND ACTIN POLYMERIZATION

Much is known about the biophysical mechanisms involved in cell crawling, but how these processes are coordinated to produce directed motion is not well understood. Here, we propose a new hypothesis whereby local cytoskeletal contraction generates fluid flow through the lamellipodium, with the pressure at the front of the cell facilitating actin polymerization which pushes the leading edge forward. The contraction, in turn, is regulated by stress in the cytoskeleton. To test this hypothesis, finite element models for a crawling cell are presented. These models are based on nonlinear poroelasticity theory, modified to include the effects of active contraction and growth, which are regulated by mechanical feedback laws. Results from the models agree reasonably well with published experimental data for cell speed, actin flow, and cytoskeletal deformation in migrating fish epidermal keratocytes. The models also suggest that oscillations can occur for certain ranges of parameter values.

Particle capture via discrete binding elements: systematic variations in binding energy for randomly distributed nanoscale surface features

This work examines how the binding strength of surface-immobilized "stickers" (representative of receptors or, in nonbiological systems, chemical heterogeneities) influences the adhesion between surfaces that are otherwise repulsive. The study focuses on a series of surfaces designed with fixed average adhesive energy per unit area and demonstrates quantitatively how a redistribution of the adhesive functionality into progressively larger clusters (stronger stickers) increases the probability of adhesive events. The work employs an electrostatic model system: relatively uniform, negative 1 μm silica spheres flow gently over negative silica flats. The flats contain small amounts of randomly positioned nanoscale cationic patches. The silica-silica interaction is repulsive; however, the cationic patches (present at sufficiently low levels that the overall surface charge remains substantially negative) produce local attractions. In this study, the attractions are relatively weak so that multiple patches engage to capture flowing particles. Experiments reveal an adhesion signature characteristic of a renormalized random distribution when the sticker strength is increased at an overall fixed binding strength per unit area of surface. The form of the particle capture curves are in good quantitative agreement with a simple model that assumes only a fixed adhesion energy needed for particle capture. Aside from the quantitative details that provide a simple formalism for anticipating particle adhesion, this work demonstrates how increasing the heterogeneities in the surface functionality can cause a system to go from being nonadhesive to becoming strongly adhesive. Indeed, systems containing small amounts of discretized adhesive functionality are always more adhesive than systems in which the same functionality is distributed uniformly over the surface (the mean field scenario).

Compliance of bio-adhesive substrates controls the kinetics of membrane-substrate association

Mechanical stiffness of bio-adhesive substrates is one of the major regulators of the cell adhesion and migration. In this study, we propose a theoretical model for the spontaneous growth of focal adhesion (FA) sites, on compliant elastic substrates, at the early stages of cellular adhesion. Using a purely thermodynamic approach, we demonstrate that the rate of membrane-substrate association decreases with increasing the compliance of the substrate. This can be considered as a reason for smaller spread area of the FA points after the stabilization of adhesion on compliant substrates, as reported by experiments. We also show that the extent to which the compliance of the substrate modulates the growth rate of adhesion site depends on the areal density of cell-adhesive ligands on the substrate.

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.

Quantitative reflection interference contrast microscopy (RICM) in soft matter and cell adhesion

Adhesion can be quantified by measuring the distance between the interacting surfaces. Reflection interference contrast microscopy (RICM), with its ability to measure inter-surface distances under water with nanometric precision and milliseconds time resolution, is ideally suited to studying the dynamics of adhesion in soft systems. Recent technical developments, which include innovative image analysis and the use of multi-coloured illumination, have led to renewed interest in this technique. Unambiguous quantitative measurements have been achieved for colloidal beads and model membranes, thus revealing new insights and applications. Quantification of data from cells shows exciting prospects. Herein, we review the basic principles and recent developments of RICM applied to studies of dynamical adhesion processes in soft matter and cell biology and provide practical hints to potential users.

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.

Nucleation and growth of integrin adhesions

We present a model that provides a mechanistic understanding of the processes that govern the formation of the earliest integrin adhesions ex novo from an approximately planar plasma membrane. Using an analytic analysis of the free energy of a dynamically deformable membrane containing freely diffusing receptors molecules and long repeller molecules that inhibit integrins from binding with ligands on the extracellular matrix, we predict that a coalescence of polymerizing actin filaments can deform the membrane toward the extracellular matrix and facilitate integrin binding. Monte Carlo simulations of this system show that thermally induced membrane fluctuations can either zip-up and increase the radius of a nucleated adhesion or unzip and shrink an adhesion, but the fluctuations cannot bend the ventral membrane to nucleate an adhesion. To distinguish this integrin adhesion from more mature adhesions, we refer to this early adhesion as a nouveau adhesion.

Quantification of nano-scale intermembrane contact areas by using fluorescence resonance energy transfer

Nanometer-scale intermembrane contact areas (CAs) formed between single small unilamellar lipid vesicles (SUVs) and planar supported lipid bilayers are quantified by measuring fluorescence resonance energy transfer (FRET) between a homogenous layer of donor fluorophores labeling the supported bilayer and acceptor fluorophores labeling the SUVs. The smallest CAs detected in our setup between biotinylated SUVs and dense monolayers of streptavidin were approximately 20 nm in radius. Deformation of SUVs is revealed by comparing the quenching of the donors to calculations of FRET between a perfectly spherical shell and a flat surface containing complementary fluorophores. These results confirmed the theoretical prediction that the degree of deformation scales with the SUV diameter. The size of the CA can be controlled experimentally by conjugating polyethylene glycol polymers to the SUV or the surface and thereby modulating the interfacial energy of adhesion. In this manner, we could achieve secure immobilization of SUVs under conditions of minimal deformation. Finally, we demonstrate that kinetic measurements of CA, at constant adhesion, can be used to record in real-time quantitative changes in the bilayer tension of a nano-scale lipid membrane system.

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.

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

We present a synergistic combination of simulations and experimental data on the dynamics of membrane adhesion. We show that a change in either the density or the strength of the bonds results in very different dynamics. Such behavior is explained by introducing an effective binding affinity that emerges as a result of the competition between the strength of the chemical bonds and the environment defined by the fluctuating membrane.