Nucleation of ligand-receptor domains in membrane adhesion

Cell adhesion and spreading on fluid membranes through microtubules-dependent mechanotransduction

Integrin clusters facilitate mechanical force transmission (mechanotransduction) and regulate biochemical signaling during cell adhesion. However, most studies have focused on rigid substrates. On fluid substrates like supported lipid bilayers (SLBs), integrin ligands are mobile, and adhesive complexes are traditionally thought unable to anchor for cell spreading. Here, we demonstrate that cells spread on SLBs coated with Invasin, a high-affinity integrin ligand. Unlike SLBs functionalized with RGD peptides, integrin clusters on Invasin-SLBs grow in size and complexity comparable to those on glass. While actomyosin contraction dominates adhesion maturation on stiff substrates, we find that on fluid SLBs, integrin mechanotransduction and cell spreading rely on dynein pulling forces along microtubules perpendicular to the membranes and microtubules pushing on adhesive complexes, respectively. These forces, potentially present on non-deformable surfaces, are revealed in fluid substrate systems. Supported by a theoretical model, our findings demonstrate a mechanical role for microtubules in integrin clustering.

The method for assessing the specificity of developing CAR therapies

The effectiveness of antitumor chimeric antigen receptor (CAR) therapy mainly dealt with an elevated sensitivity of CAR cells to target cells. However, CAR therapies are associated with nonspecific side effects: on-target off-tumor toxicity. Sensitivity and specificity of CAR cells are the most important properties of the recognition process of target cells among other cells. Current developments are mainly concentrated on exploring molecular biology methods for designing CAR cells with the highest sensitivity, while the problem of the CAR cell specificity is rarely considered. For the assessment of CAR cell specificity, we suggest that, in addition to an elevated level of CAR-antigen affinity, the ability of CARs for clustering should be taken into account. We assume that the CAR cell cytotoxicity is determined by CAR clustering. The latter is treated within the framework of nucleation theory. The master equation for the probability of CAR cell cytotoxicity is derived. The size of a critical CAR cluster is found to be one of two most essential parameters. The conditions for necessary sensitivity and sufficient specificity are explored. Relevant parametric diagrams are derived. Possible applications of the method for assessing the specificity of developing CAR therapies are discussed.

Membrane Fluctuation Model for Understanding the Effect of Receptor Nanoclustering on the Activation of Natural Killer Cells through Biomechanical Feedback

We investigated the role of ligand clustering and density in the activation of natural killer (NK) cells. To that end, we designed reductionist arrays of nanopatterned ligands arranged with different cluster geometries and densities and probed their effects on NK cell activation. We used these arrays as an artificial microenvironment for the stimulation of NK cells and studied the effect of the array geometry on the NK cell immune response. We found that ligand density significantly regulated NK cell activation while ligand clustering had an impact only at a specific density threshold. We also rationalized these findings by introducing a theoretical membrane fluctuation model that considers biomechanical feedback between ligand-receptor bonds and the cell membrane. These findings provide important insight into NK cell mechanobiology, which is fundamentally important and essential for designing immunotherapeutic strategies targeting cancer.

Membrane Tilt Drives Phase Separation of Adhesion Receptors

Cell adhesion receptors are transmembrane proteins that bind cells to their environment. These proteins typically cluster into disk-shaped or linear structures. Here, we show that such clustering patterns spontaneously emerge when the receptor senses the membrane deformation gradient, for example, by reaching a lower-energy conformation when the membrane is tilted relative to the underlying binding substrate. Increasing the strength of the membrane gradient-sensing mechanism first yields isolated disk-shaped clusters and then long linear structures. Our theory is coherent with experimental estimates of the parameters, suggesting that a tilt-induced clustering mechanism is relevant in the context of cell adhesion.

Curvature-induced clustering of cell adhesion proteins

Cell adhesion proteins typically form stable clusters that anchor the cell membrane to its environment. Several works have suggested that cell membrane protein clusters can emerge from a local feedback between the membrane curvature and the density of proteins. Here, we investigate the effect of such a curvature-sensing mechanism in the context of cell adhesion proteins. We show how clustering emerges in an intermediate range of adhesion and curvature-sensing strengths. We identify key differences with the tilt-induced gradient sensing mechanism we previously proposed (Lin et al., arXiv:2307.03670).

Clutch model for focal adhesions predicts reduced self-stabilization under oblique pulling

Cell-matrix adhesions connect the cytoskeleton to the extracellular environment and are essential for maintaining the integrity of tissue and whole organisms. Remarkably, cell adhesions can adapt their size and composition to an applied force such that their size and strength increases proportionally to the load. Mathematical models for the clutch-like force transmission at adhesions are frequently based on the assumption that mechanical load is applied tangentially to the adhesion plane. Recently, we suggested a molecular mechanism that can explain adhesion growth under load for planar cell adhesions. The mechanism is based on conformation changes of adhesion molecules that are dynamically exchanged with a reservoir. Tangential loading drives the occupation of some states out of equilibrium, which for thermodynamic reasons, leads to the association of further molecules with the cluster, which we refer to as self-stabilization. Here, we generalize this model to forces that pull at an oblique angle to the plane supporting the cell, and examine if this idealized model also predicts self-stabilization. We also allow for a variable distance between the parallel planes representing cytoskeletal F-actin and transmembrane integrins. Simulation results demonstrate that the binding mechanism and the geometry of the cluster have a strong influence on the response of adhesion clusters to force. For oblique angles smaller than about 40∘, we observe a growth of the adhesion site under force. However this self-stabilization is reduced as the angle between the force and substrate plane increases, with vanishing self-stabilization for normal pulling. Overall, these results highlight the fundamental difference between the assumption of pulling and shearing forces in commonly used models of cell adhesion.

Generic self-stabilization mechanism for biomolecular adhesions under load

Mechanical loading generally weakens adhesive structures and eventually leads to their rupture. However, biological systems can adapt to loads by strengthening adhesions, which is essential for maintaining the integrity of tissue and whole organisms. Inspired by cellular focal adhesions, we suggest here a generic, molecular mechanism that allows adhesion systems to harness applied loads for self-stabilization through adhesion growth. The mechanism is based on conformation changes of adhesion molecules that are dynamically exchanged with a reservoir. Tangential loading drives the occupation of some states out of equilibrium, which, for thermodynamic reasons, leads to association of further molecules with the cluster. Self-stabilization robustly increases adhesion lifetimes in broad parameter ranges. Unlike for catch-bonds, bond rupture rates can increase monotonically with force. The self-stabilization principle can be realized in many ways in complex adhesion-state networks; we show how it naturally occurs in cellular adhesions involving the adaptor proteins talin and vinculin.

Cellular adhesions have the remarkable property that they adapt their stability to the applied mechanical load. Here, authors describe a generic physical mechanism that explains self-stabilization of idealized adhesion systems under shear.

Calcium regulates the interplay between the tight junction and epithelial adherens junction at the plasma membrane

The apical junctional complex (AJC) is a membrane protein ultrastructure that regulates cell adhesion and homeostasis. The tight junction (TJ) and the adherens junction (AJ) are substructures of the AJC. The interplay between TJ and AJ membrane proteins to assemble the AJC remains unclear. We employed synthetic biology strategies to express the basic membrane elements of a simple AJC-the adhesive extracellular domains of junctional adhesion molecule A (JAM-A), epithelial cadherin, claudin 1, and occludin-to study their interactions. Our results suggest that calcium concentration fluctuations and JAM-A, acting as an interface molecule between the TJ and AJ, orchestrate their interplay. Calcium affects the secondary structure, oligomerization, and binding affinity of homotypic and heterotypic interactions of TJ and AJ components, thus acting as a molecular switch influencing AJC dynamics.

Biomechanics as driver of aggregation of tethers in adherent membranes

Cell adhesion is an important cellular process and is mediated by adhesion proteins residing on the cell membrane. Sometimes, two types of linker proteins are involved in adhesion, and they can segregate to form domains through a poorly understood size-exclusion process. We present an experimental and theoretical study of adhesion via linkers of two different sizes, realised in a mimetic model-system, based on giant unilamellar vesicles interacting with supported lipid bilayers. Here, adhesion is mediated by DNA linkers with two different lengths, but with the same binding enthalpy. We study the organisation of these linkers into domains as a function of relative fraction of long and short DNA constructs. Experimentally, we find that, irrespective of the composition, the adhesion domains are uniform with coexisting DNA bridge types, despite their relative difference in length of 9 nm. However, simulations suggest formation of nanodomains of the minority fraction at short length scales, which is below the optical resolution of the microscope. The nano-aggregation is more significant for long bridges, which are also more stable.

A possible molecular mechanism for mechanotransduction at cellular focal adhesion complexes

Mechanotransduction at focal adhesion complexes is key for various cellular events. Theoretical analyses were performed to predict a potential role of lipid membranes in modulating mechanotransduction at focal adhesions. Calculations suggested that the size of nanostructural constraints and mechanical pulling applied on lipid membranes affect the generation of cellular traction forces and signaling transduction at focal adhesions. This work provides predictions on how lipid membranes contribute to mechanotransduction at cellular focal adhesions.

Molecular-scale spatio-chemical control of the activating-inhibitory signal integration in NK cells

The role of juxtaposition of activating and inhibitory receptors in signal inhibition of cytotoxic lymphocytes remains strongly debated. The challenge lies in the lack of tools that allow simultaneous spatial manipulation of signaling molecules. To circumvent this, we produced a nanoengineered multifunctional platform with molecular-scale spatial control of ligands, which was applied to elucidate KIR2DL1-mediated inhibition of NKG2D signaling-receptors of natural killer cells. This platform was conceived by bimetallic nanodot patterning with molecular-scale registry, followed by a ternary functionalization with distinct moieties. We found that a 40-nm gap between activating and inhibitory ligands provided optimal inhibitory conditions. Supported by theoretical modeling, we interpret these findings as a consequence of the size mismatch and conformational flexibility of ligands in their spatial interaction. This highly versatile approach provides an important insight into the spatial mechanism of inhibitory immune checkpoints, which is essential for the rational design of future immunotherapies.

More than just a barrier: using physical models to couple membrane shape to cell function

The correct execution of many cellular processes, such as division and motility, requires the cell to adopt a specific shape. Physically, these shapes are determined by the interplay of the plasma membrane and internal cellular driving factors. While the plasma membrane defines the boundary of the cell, processes inside the cell can result in the generation of forces that deform the membrane. These processes include protein binding, the assembly of protein superstructures, and the growth and contraction of cytoskeletal networks. Due to the complexity of the cell, relating observed membrane deformations back to internal processes is a challenging problem. Here, we review cell shape changes in endocytosis, cell adhesion, cell migration and cell division and discuss how by modeling membrane deformations we can investigate the inner working principles of the cell.

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.

Recent Advances and Prospects in the Research of Nascent Adhesions

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

Programmable interactions with biomimetic DNA linkers at fluid membranes and interfaces

At the heart of the structured architecture and complex dynamics of biological systems are specific and timely interactions operated by biomolecules. In many instances, biomolecular agents are spatially confined to flexible lipid membranes where, among other functions, they control cell adhesion, motility and tissue formation. Besides being central to several biological processes, multivalent interactions mediated by reactive linkers confined to deformable substrates underpin the design of synthetic-biological platforms and advanced biomimetic materials. Here we review recent advances on the experimental study and theoretical modelling of a heterogeneous class of biomimetic systems in which synthetic linkers mediate multivalent interactions between fluid and deformable colloidal units, including lipid vesicles and emulsion droplets. Linkers are often prepared from synthetic DNA nanostructures, enabling full programmability of the thermodynamic and kinetic properties of their mutual interactions. The coupling of the statistical effects of multivalent interactions with substrate fluidity and deformability gives rise to a rich emerging phenomenology that, in the context of self-assembled soft materials, has been shown to produce exotic phase behaviour, stimuli-responsiveness, and kinetic programmability of the self-assembly process. Applications to (synthetic) biology will also be reviewed.

A Theoretical Analysis of Receptor-Mediated Endocytosis of Nanoparticles in Wall Shear Flow

This study theoretically investigates receptor–ligand-mediated endocytosis of nanoparticles (NPs) in wall shear flow. The endocytosis is modeled as a birth–death process and relationships between coefficients in the model and the wall shear rate have been derived to deal with the effects of the shear flow. Model predictions show that flow-induced alteration in bond formation rates does not affect the endocytosis significantly, and the suppression of hydrodynamic load on endocytosis is eminent only when diameters of NPs are large (around 700[Formula: see text]nm) and the shear rate is sufficiently high. In the latter case, it is shown that the hydrodynamic load suppresses the initial attachment of NPs to cells more than the following internalization. The model also predicts that shear-promoted expression of certain ligands can lead to observable increase in the number of endocytozed NPs in typical flow-chamber experiments, and the promotion can also cause selective endocytosis of NPs by cells at high shear rate regions if the ligand surface density on NPs or the original expression of receptors on cells in the absence of flow is low.

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.

Mechanical forces in cell monolayers

In various physiological processes, the cell collective is organized in a monolayer, such as seen in a simple epithelium. The advances in the understanding of mechanical behavior of the monolayer and its underlying cellular and molecular mechanisms will help to elucidate the properties of cell collectives. In this Review, we discuss recent in vitro studies on monolayer mechanics and their implications on collective dynamics, regulation of monolayer mechanics by physical confinement and geometrical cues and the effect of tissue mechanics on biological processes, such as cell division and extrusion. In particular, we focus on the active nematic property of cell monolayers and the emerging approach to view biological systems in the light of liquid crystal theory. We also highlight the mechanosensing and mechanotransduction mechanisms at the sub-cellular and molecular level that are mediated by the contractile actomyosin cytoskeleton and cell-cell adhesion proteins, such as E-cadherin and α-catenin. To conclude, we argue that, in order to have a holistic understanding of the cellular response to biophysical environments, interdisciplinary approaches and multiple techniques - from large-scale traction force measurements to molecular force protein sensors - must be employed.

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.

Membrane-Mediated Cooperativity of Proteins

Besides direct protein-protein interactions, indirect interactions mediated by membranes play an important role for the assembly and cooperative function of proteins in membrane shaping and adhesion. The intricate shapes of biological membranes are generated by proteins that locally induce membrane curvature. Indirect curvature-mediated interactions between these proteins arise because the proteins jointly affect the bending energy of the membranes. These curvature-mediated interactions are attractive for crescent-shaped proteins and are a driving force in the assembly of the proteins during membrane tubulation. Membrane adhesion results from the binding of receptor and ligand proteins that are anchored in the apposing membranes. The binding of these proteins strongly depends on nanoscale shape fluctuations of the membranes, leading to a fluctuation-mediated binding cooperativity. A length mismatch between receptor-ligand complexes in membrane adhesion zones causes repulsive curvature-mediated interactions that are a driving force for the length-based segregation of proteins during membrane adhesion.

Early T cell receptor signals globally modulate ligand:receptor affinities during antigen discrimination

Antigen discrimination by T cells is based on subtle differences in binding of the T cell receptor (TCR) for its peptide major histocompatibility complex (pMHC) ligand. While such binding characteristics are readily mapped with great precision in reconstituted biochemical systems, it is less clear how these interactions are affected in the live cell environment. Here we utilize single-molecule imaging to individually resolve all of the pMHC:TCR binding events in live T cells. The quantitative measurements reveal an active feedback mechanism that globally modulates the probability of pMHC:TCR binding throughout the cell–cell interface, without affecting the unbinding rate. The result is to increase the efficiency with which TCRs scan for antigen pMHC after the first few molecular encounters have occurred.

Antigen discrimination by T cells occurs at the junction between a T cell and an antigen-presenting cell. Juxtacrine binding between numerous adhesion, signaling, and costimulatory molecules defines both the topographical and lateral geometry of this cell–cell interface, within which T cell receptor (TCR) and peptide major histocompatibility complex (pMHC) interact. These physical constraints on receptor and ligand movement have significant potential to modulate their molecular binding properties. Here, we monitor individual ligand:receptor binding and unbinding events in space and time by single-molecule imaging in live primary T cells for a range of different pMHC ligands and surface densities. Direct observations of pMHC:TCR and CD80:CD28 binding events reveal that the in situ affinity of both pMHC and CD80 ligands for their respective receptors is modulated by the steady-state number of agonist pMHC:TCR interactions experienced by the cell. By resolving every single pMHC:TCR interaction it is evident that this cooperativity is accomplished by increasing the kinetic on-rate without altering the off-rate and has a component that is not spatially localized. Furthermore, positive cooperativity is observed under conditions where the T cell activation probability is low. This TCR-mediated feedback is a global effect on the intercellular junction. It is triggered by the first few individual pMHC:TCR binding events and effectively increases the efficiency of TCR scanning for antigen before the T cell is committed to activation.

Rolling Adhesion of Schizont Stage Malaria-Infected Red Blood Cells in Shear Flow

To avoid clearance by the spleen, red blood cells infected with the human malaria parasite Plasmodium falciparum (iRBCs) adhere to the vascular endothelium through adhesive protrusions called "knobs" that the parasite induces on the surface of the host cell. However, the detailed relation between the developing knob structure and the resulting movement in shear flow is not known. Using flow chamber experiments on endothelial monolayers and tracking of the parasite inside the infected host cell, we find that trophozoites (intermediate-stage iRBCs) tend to flip due to their biconcave shape, whereas schizonts (late-stage iRBCs) tend to roll due to their almost spherical shape. We then use adhesive dynamics simulations for spherical cells to predict the effects of knob density and receptor multiplicity per knob on rolling adhesion of schizonts. We find that rolling adhesion requires a homogeneous coverage of the cell surface by knobs and that rolling adhesion becomes more stable and slower for higher knob density. Our experimental data suggest that schizonts are at the border between transient and stable rolling adhesion. They also allow us to establish an estimate for the molecular parameters for schizont adhesion to the vascular endothelium and to predict bond dynamics in the contact region.

Random blebbing motion: A simple model linking cell structural properties to migration characteristics

If the plasma membrane of a cell is able to delaminate locally from its actin cortex, a cellular bleb can be produced. Blebs are pressure-driven protrusions, which are noteworthy for their ability to produce cellular motion. Starting from a general continuum mechanics description, we restrict ourselves to considering cell and bleb shapes that maintain approximately spherical forms. From this assumption, we obtain a tractable algebraic system for bleb formation. By including cell-substrate adhesions, we can model blebbing cell motility. Further, by considering mechanically isolated blebbing events, which are randomly distributed over the cell, we can derive equations linking the macroscopic migration characteristics to the microscopic structural parameters of the cell. This multiscale modeling framework is then used to provide parameter estimates, which are in agreement with current experimental data. In summary, the construction of the mathematical model provides testable relationships between the bleb size and cell motility.

Integration of Cadherin Adhesion and Cytoskeleton at Adherens Junctions

The cadherin-catenin adhesion complex is the key component of the intercellular adherens junction (AJ) that contributes both to tissue stability and dynamic cell movements in epithelial and nonepithelial tissues. The cadherin adhesion complex bridges neighboring cells and the actin-myosin cytoskeleton, and thereby contributes to mechanical coupling between cells which drives many morphogenetic events and tissue repair. Mechanotransduction at cadherin adhesions enables cells to sense, signal, and respond to physical changes in their environment. Central to this process is the dynamic link of the complex to actin filaments (F-actin), themselves structurally dynamic and subject to tension generated by myosin II motors. We discuss in this review recent breakthroughs in understanding molecular and cellular aspects of the organization of the core cadherin-catenin complex in adherens junctions, its association to F-actin, its mechanosensitive regulation, and dynamics.

Kinetics of receptor-mediated endocytosis of elastic nanoparticles

It is now widely recognized that mechanical properties play critical roles in the cell uptake of nanomaterials. Here we conduct a theoretical study on the kinetics of receptor-mediated endocytosis of elastic nanoparticles that is limited by receptor diffusion, specifically focusing on how the uptake rate depends on the nanoparticle stiffness and size, membrane tension and binding strength between membrane receptors and ligands grafted on the nanoparticle surface. It is shown that, while soft nanoparticles are energetically less prone to full wrapping than stiff ones, the wrapping of the former is kinetically faster than that of the latter. Spherical and cylindrical elastic nanoparticles show dramatic differences in the effect of stiffness on the uptake rate. Additional theoretical analysis is performed to investigate the role of the stochastic receptor-ligand binding in the endocytosis of elastic nanoparticles. The relation between the uptake efficiency and uptake proneness is discussed. This study provides new insight into the elasticity effects on cell uptake and may serve as a design guideline for the controlled endocytosis and diagnostics delivery.

A phenomenological model of cell-cell adhesion mediated by cadherins

We present a phenomenological model intended to describe at the protein population level the formation of cell-cell junctions by the local recruitment of homophilic cadherin adhesion receptors. This modeling may have a much wider implication in biological processes since many adhesion receptors, channel proteins and other membrane-born proteins associate in clusters or oligomers at the cell surface. Mathematically, it consists in a degenerate reaction-diffusion system of two partial differential equations modeling the time-space evolution of two cadherin populations over a surface: the first one represents the diffusing cadherins and the second one concerns the fixed ones. After discussing the stability of the solutions of the model, we perform numerical simulations and show relevant analogies with experimental results. In particular, we show patterns or aggregates formation for a certain set of parameters. Moreover, perturbing the stationary solution, both density populations converge in large times to some saturation level. Finally, an exponential rate of convergence is numerically obtained and is shown to be in agreement, for a suitable set of parameters, with the one obtained in some in vitro experiments.

Ligand-mediated adhesive mechanics of two static, deformed spheres

A self-consistent model is developed to investigate attachment/detachment kinetics of two static, deformable microspheres with irregular surface and coated with flexible binding ligands. The model highlights how the microscale binding kinetics of these ligands as well as the attractive/repulsive potential of the charged surface affects the macroscale static deformed configuration of the spheres. It is shown that in the limit of smooth, neutrally charged surface (i.e., the dimensionless inverse Debye length, [Formula: see text]), interacting via elastic binders (i.e., the dimensionless stiffness coefficient, [Formula: see text]) the adhesion mechanics approaches the regime of application of the JKR theory, and in this particular limit, the contact radius, R_c, scales with the particle radius, R, according to the scaling law, [Formula: see text]. We show that static, deformed, highly charged, ligand-coated surface of micro-spheres exhibit strong adhesion. Normal stress distribution within the contact area adjusts with the binder stiffness coefficient, from a maximum at the center to a maximum at the periphery of the region. Although reported in some in vitro experiments involving particle adhesion, until now a physical interpretation for this variation of the stress distribution for deformable, charged, ligand-coated microspheres is missing. Surface roughness results in a diminished adhesion with a distinct reduction in the pull-off force, larger separation gap, weaker normal stress and limited area of adhesion. These results are in agreement with the published experimental findings.

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 formation of ordered nanoclusters controls cadherin anchoring to actin and cell-cell contact fluidity

Visualization of single cadherins within cell membrane at nanometric resolution shows that E-cadherins arrange in ordered clusters and that these clusters control the anchoring of cadherin to actin and cell–cell contact fluidity.

Oligomerization of cadherins could provide the stability to ensure tissue cohesion. Cadherins mediate cell–cell adhesion by forming trans-interactions. They form cis-interactions whose role could be essential to stabilize intercellular junctions by shifting cadherin clusters from a fluid to an ordered phase. However, no evidence has been provided so far for cadherin oligomerization in cellulo and for its impact on cell–cell contact stability. Visualizing single cadherins within cell membrane at a nanometric resolution, we show that E-cadherins arrange in ordered clusters, providing the first demonstration of the existence of oligomeric cadherins at cell–cell contacts. Studying the consequences of the disruption of the cis-interface, we show that it is not essential for adherens junction formation. Its disruption, however, increased the mobility of junctional E-cadherin. This destabilization strongly affected E-cadherin anchoring to actin and cell–cell rearrangement during collective cell migration, indicating that the formation of oligomeric clusters controls the anchoring of cadherin to actin and cell–cell contact fluidity.

Surface deformation and shear flow in ligand mediated cell adhesion

We present a unified, multiscale model to study the attachment/detachment dynamics of two deforming, charged, near spherical cells, coated with binding ligands and subject to a slow, homogeneous shear flow in a viscous, ionic fluid medium. The binding ligands on the surface of the cells experience both attractive and repulsive forces in an ionic medium and exhibit finite resistance to rotation via bond tilting. The microscale drag forces and couples describing the fluid flow inside the small separation gap between the cells, are calculated using a combination of methods in lubrication theory and previously published numerical results. For a selected range of material and fluid parameters, a hysteretic transition of the sticking probability curves (i.e., the function [Formula: see text]) between the adhesion phase (when [Formula: see text]) and the fragmentation phase (when [Formula: see text]) is attributed to a nonlinear relation between the total nanoscale binding forces and the separation gap between the cells. We show that adhesion is favoured in highly ionic fluids, increased deformability of the cells, elastic binders and a higher fluid shear rate (until a critical threshold value of shear rate is reached). Within a selected range of critical shear rates, the continuation of the limit points (i.e., the turning points where the slope of [Formula: see text] changes sign) predict a bistable region, indicating an abrupt switching between the adhesion and the fragmentation regimes. Although, bistability in the adhesion-fragmentation phase diagram of two deformable, charged cells immersed in an ionic aqueous environment has been identified by some in vitro experiments, but until now, has not been quantified theoretically.

Tension-compression asymmetry in the binding affinity of membrane-anchored receptors and ligands

Cell adhesion plays a crucial role in many biological processes of cells, e.g., immune responses, tissue morphogenesis, and stem cell differentiation. An essential problem in the molecular mechanism of cell adhesion is to characterize the binding affinity of membrane-anchored receptors and ligands under different physiological conditions. In this paper, a theoretical model is presented to study the binding affinity between a large number of anchored receptors and ligands under both tensile and compressive stresses, and corroborated by demonstrating excellent agreement with Monte Carlo simulations. It is shown that the binding affinity becomes lower as the magnitude of the applied stress increases, and drops to zero at a critical tensile or compressive stress. Interestingly, the critical compressive stress is found to be substantially smaller than the critical tensile stress for relatively long and flexible receptor-ligand complexes. This counterintuitive finding is explained by using the Euler instability theory of slender columns under compression. The tension-compression asymmetry in the binding affinity of anchored receptors and ligands depends subtly on the competition between the breaking and instability of their complexes. This study helps in understanding the role of mechanical forces in cell adhesion mediated by specific binding molecules.

Bleb Nucleation through Membrane Peeling

We study the nucleation of blebs, i.e., protrusions arising from a local detachment of the membrane from the cortex of a cell. Based on a simple model of elastic linkers with force-dependent kinetics, we show that bleb nucleation is governed by membrane peeling. By this mechanism, the growth or shrinkage of a detached membrane patch is completely determined by the linker kinetics, regardless of the energetic cost of the detachment. We predict the critical nucleation radius for membrane peeling and the corresponding effective energy barrier. These may be typically smaller than those predicted by classical nucleation theory, implying a much faster nucleation. We also perform simulations of a continuum stochastic model of membrane-cortex adhesion to obtain the statistics of bleb nucleation times as a function of the stress on the membrane. The determinant role of membrane peeling changes our understanding of bleb nucleation and opens new directions in the study of blebs.

Modeling Active Mechanosensing in Cell-Matrix Interactions

Cells actively sense the mechanical properties of the extracellular matrix, such as its rigidity, morphology, and deformation. The cell-matrix interaction influences a range of cellular processes, including cell adhesion, migration, and differentiation, among others. This article aims to review some of the recent progress that has been made in modeling mechanosensing in cell-matrix interactions at different length scales. The issues discussed include specific interactions between proteins, the structure and mechanosensitivity of focal adhesions, the cluster effects of the specific binding, the structure and behavior of stress fibers, cells' sensing of substrate stiffness, and cell reorientation on cyclically stretched substrates. The review concludes by looking toward future opportunities in the field and at the challenges to understanding active cell-matrix interactions.

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.

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.

Formation of adhesion domains in stressed and confined membranes

The adhesion bonds connecting a lipid bilayer to an underlying surface may undergo a condensation transition resulting from an interplay between a short range attractive potential between them, and a long range fluctuation-induced potential of mean force. Here, we use computer simulations of a coarse-grained molecular model of supported lipid bilayers to study this transition in confined membranes, and in membranes subjected to a non-vanishing surface tension. Our results show that confinement may alter significantly the condensation transition of the adhesion bonds, whereas the application of surface tension has a very minor effect on it. We also investigate domain formation in membranes under negative tension which, in free membranes, causes the enhancement of the amplitude of membrane thermal undulations. Our results indicate that in supported membranes, this effect of a negative surface tension on the fluctuation spectrum is largely eliminated by the pressure resulting from the mixing entropy of the adhesion bonds.

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.

Sticky surface: sphere-sphere adhesion dynamics

We present a multi-scale model to study the attachment of spherical particles with a rigid core, coated with binding ligands and suspended in the surrounding, quiescent fluid medium. This class of fluid-immersed adhesion is widespread in many natural and engineering settings, particularly in microbial surface adhesion. Our theory highlights how the micro-scale binding kinetics of these ligands, as well as the attractive/repulsive surface potential in an ionic medium affects the eventual macro-scale size distribution of the particle aggregates (flocs). The bridge between the micro-macro model is made via an aggregation kernel. Results suggest that the presence of elastic ligands on the particle surface lead to the formation of larger floc aggregates via efficient inter-floc collisions (i.e. non-zero sticking probability, g). Strong electrolytic composition of the surrounding fluid favours large floc formation as well. The kernel for the Brownian diffusion for hard spheres is recovered in the limit of perfect binding effectiveness (g→1) and in a neutral solution with no dissolved salts.

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.