The dynamics and mechanics of endothelial cell spreading

Cell adhesion to extracellular matrix is mediated by receptor-ligand interactions. When a cell first contacts a surface, it spreads, exerting traction forces against the surface and forming new bonds as its contact area expands. Here, we examined the changes in shape, actin polymerization, focal adhesion formation, and traction stress generation that accompany spreading of endothelial cells over a period of several hours. Bovine aortic endothelial cells were plated on polyacrylamide gels derivatized with a peptide containing the integrin binding sequence RGD, and changes in shape and traction force generation were measured. Notably, both the rate and extent of spreading increase with the density of substrate ligand. There are two prominent modes of spreading: at higher surface ligand densities cells tend to spread isotropically, whereas at lower densities of ligand the cells tend to spread anisotropically, by extending pseudopodia randomly distributed along the cell membrane. The extension of pseudopodia is followed by periods of growth in the cell body to interconnect these extensions. These cycles occur at very regular intervals and, furthermore, the extent of pseudopodial extension can be diminished by increasing the ligand density. Measurement of the traction forces exerted by the cell reveals that a cell is capable of exerting significant forces before either notable focal adhesion or stress fiber formation. Moreover, the total magnitude of force exerted by the cell is linearly related to the area of the cell during spreading. This study is the first to monitor the dynamic changes in the cell shape, spreading rate, and forces exerted during the early stages (first several hours) of endothelial cell adhesion.     

Ligand-Mediated Friction Determines Morphodynamics of Spreading T?Cells

Spreading of T cells on antigen presenting cells is a crucial initial step in immune response. Spreading occurs through rapid morphological changes concomitant with the reorganization of surface receptors and of the cytoskeleton. Ligand mobility and frictional coupling of receptors to the cytoskeleton were separately recognized as important factors but a systematic study to explore their biophysical role in spreading was hitherto missing. To explore the impact of ligand mobility, we prepared chemically identical substrates on which molecules of anti-CD3 (capable of binding and activating the T cell receptor complex), were either immobilized or able to diffuse. We quantified the T cell spreading area and cell edge dynamics using quantitative reflection interference contrast microscopy, and imaged the actin distribution. On mobile ligands, as compared to fixed ligands, the cells spread much less, the actin is centrally, rather than peripherally distributed and the edge dynamics is largely altered. Blocking myosin-II or adding molecules of ICAM1 on the substrate largely abrogates these differences. We explain these observations by building a model based on the balance of forces between activation-dependent actin polymerization and actomyosin-generated tension on one hand, and on the frictional coupling of the ligand-receptor complexes with the actin cytoskeleton, the membrane and the substrate, on the other hand. Introducing the measured edge velocities in the model, we estimate the coefficient of frictional coupling between T Cell receptors or LFA-1 and the actin cytoskeleton. Our results provide for the first time, to our knowledge, a quantitative framework bridging T cell-specific biology with concepts developed for integrin-based mechanisms of spreading.     

Avidin-biotin interactions at vesicle surfaces: adsorption and binding, cross-bridge formation, and lateral interactions.

Densely packed domains of membrane proteins are important structures in cellular processes that involve ligand-receptor binding, receptor-mediated adhesion, and macromolecule aggregation. We have used the biotin-avidin interaction at lipid vesicle surfaces to mimic these processes, including the influence of a surface grafted polymer, polyethyleneglycol (PEG). Single vesicles were manipulated by micropipette in solutions of fluorescently labeled avidin to measure the rate and give an estimate of the amount of avidin binding to a biotinylated vesicle as a function of surface biotin concentration and surface-grafted PEG as PEG-lipid. The rate of avidin adsorption was found to be four times less with 2 mol% PEG750 than for the unmodified surface, and 10 mol% PEG completely inhibited binding of avidin to biotin for a 2-min incubation. Using two micropipettes, an avidin-coated vesicle was presented to a biotinylated vesicle. In this vesicle-vesicle adhesion test, the accumulation of avidin in the contact zone was observed, again by using fluorescent avidin. More importantly, by controlling the vesicle membrane tension, this adhesion test provided a direct measure of the spreading pressure of the biotin-avidin-biotin cross-bridges confined in the contact zone. Assuming ideality, this spreading pressure gives the concentration of avidin cross-bridges in the contact zone. The rate of cross-bridge accumulation was consistent with the diffusion of the lipid-linked "receptors" into the contact zone. Once adherent, the membranes failed in tension before they could be peeled apart. PEG750 did not influence the mechanical equilibrium because it was not compressed in the contact zone, but it did perform an important function by eliminating all nonspecific adhesion. This vesicle-vesicle adhesion experiment, with a lower tension limit of 0.01 dyn/cm, now provides a new and useful method with which to measure the spreading pressures and therefore colligative properties of a range of membrane-bound macromolecules.     

A role for syndecan-1 in coupling fascin spike formation by thrombospondin-1

An important role of cell matrix adhesion receptors is to mediate transmembrane coupling between extracellular matrix attachment, actin reorganization, and cell spreading. Thrombospondin (TSP)-1 is a modulatory component of matrix expressed during development, immune response, or wound repair. Cell adhesion to TSP-1 involves formation of biochemically distinct matrix contacts based on stable fascin spikes. The cell surface adhesion receptors required have not been identified. We report here that antibody clustering of syndecan-1 proteoglycan specifically transduces organization of cortical actin and fascin bundles in several cell types. Transfection of COS-7 cells with syndecan-1 is sufficient to stimulate cell spreading, fascin spike assembly, and extensive protrusive lateral ruffling on TSP-1 or on syndecan-1 antibody. The underlying molecular mechanism depends on glycosaminoglycan (GAG) modification of the syndecan-1 core protein at residues S45 or S47 for cell membrane spreading and on the VC2 region of the cytoplasmic domain for spreading and fascin spike formation. Expression of the VC2 deletion mutant or GAG-negative syndecan-1 showed that syndecan-1 is necessary in spreading and fascin spike formation by C2C12 cells on TSP-1. These results establish a novel role for syndecan-1 protein in coupling a physiological matrix ligand to formation of a specific matrix contact structure.     

Melanoma cell CD44 interaction with the alpha 1(IV)1263-1277 region from basement membrane collagen is modulated by ligand glycosylation

Invasion of the basement membrane is believed to be a critical step in the metastatic process. Melanoma cells have been shown previously to bind distinct triple-helical regions within basement membrane (type IV) collagen. Additionally, tumor cell binding sites within type IV collagen contain glycosylated hydroxylysine residues. In the present study, we have utilized triple-helical models of the type IV collagen alpha1(IV)1263-1277 sequence to (a) determine the melanoma cell receptor for this ligand and (b) analyze the results of single-site glycosylation on melanoma cell recognition. Receptor identification was achieved by a combination of methods, including (a) cell adhesion and spreading assays using triple-helical alpha1(IV)1263-1277 and an Asp(1266)Abu variant, (b) inhibition of cell adhesion and spreading assays, and (c) triple-helical alpha1(IV)1263-1277 affinity chromatography with whole cell lysates and glycosaminoglycans. Triple-helical alpha1(IV)1263-1277 was bound by melanoma cell CD44/chondroitin sulfate proteoglycan receptors and not by the collagen-binding integrins or melanoma-associated proteoglycan. Melanoma cell adhesion to and spreading on the triple-helical alpha1(IV)1263-1277 sequence was then compared for glycosylated (replacement of Lys(1265) with Hyl(O-beta-d-galactopyranosyl)) versus non-glycosylated ligand. Glycosylation was found to strongly modulate both activities, as adhesion and spreading were dramatically decreased due to the presence of galactose. CD44/chondroitin sulfate proteoglycan did not bind to glycosylated alpha1(IV)1263-1277. Overall, this study (a) is the first demonstration of the prophylactic effects of glycosylation on tumor cell interaction with the basement membrane, (b) provides a rare example of an apparent unfavorable interaction between carbohydrates, and (c) suggests that sugars may mask "cryptic sites" accessible to tumor cells with cell surface or secreted glycosidase activities.     

Substrate Compliance versus Ligand Density in Cell on Gel Responses

Substrate stiffness is emerging as an important physical factor in the response of many cell types. In agreement with findings on other anchorage-dependent cell lineages, aortic smooth muscle cells are found to spread and organize their cytoskeleton and focal adhesions much more so on “rigid” glass or “stiff” gels than on “soft” gels. Whereas these cells generally show maximal spreading on intermediate collagen densities, the limited spreading on soft gels is surprisingly insensitive to adhesive ligand density. Bell-shaped cell spreading curves encompassing all substrates are modeled by simple functions that couple ligand density to substrate stiffness. Although smooth muscle cells spread minimally on soft gels regardless of collagen, GFP-actin gives a slight overexpression of total actin that can override the soft gel response and drive spreading; GFP and GFP-paxillin do not have the same effect. The GFP-actin cells invariably show an organized filamentous cytoskeleton and clearly indicate that the cytoskeleton is at least one structural node in a signaling network that can override spreading limits typically dictated by soft gels. Based on such results, we hypothesize a central structural role for the cytoskeleton in driving the membrane outward during spreading whereas adhesion reinforces the spreading.     

Modulation of triple-helical stability and subsequent melanoma cellular responses by single-site substitution of fluoroproline derivatives

Collagen is a multifunctional protein, serving as a structural scaffold and a modulator of cellular responses. Prior work has identified distinct regions from several collagen types that promote cell adhesion, spreading, migration, and signal transduction. One of these regions, alpha1(IV)1263-1277 from type IV collagen, mediates these responses via melanoma cell CD44-chondrotin sulfate proteoglycan receptors. In the study presented here, we have used a triple-helical model of alpha1(IV)1263-1277 to evaluate (a) conformational stability and (b) cellular responses based on single-site incorporation of trans-4-fluoro-L-proline (trans-Flp) or cis-4-fluoro-L-proline (cis-Flp) for trans-4-hydroxy-L-proline (trans-Hyp). The structural effects of cis-Flp and trans-Flp substitution were studied by circular dichroism and NMR spectroscopies. The peptide containing a single trans-Flp instead of trans-Hyp was slightly more thermally stable than the parent peptide (T(m) = 37 vs 34 degrees C), while the peptide containing cis-Flp was considerably less stable than the parent peptide (T(m) = 30 degrees C). Melanoma cell adhesion and spreading were examined under conditions where the trans-Hyp-, trans-Flp-, and cis-Flp-containing ligands were approximately 15, <10, and approximately 65% denatured, respectively. Adhesion to each of the three ligands was remarkably sensitive to the respective ligand conformation, with EC(50) values of approximately 2.5, approximately 0.35, and >5.0 microM for the trans-Hyp-, trans-Flp-, and cis-Flp-containing ligands, respectively. Melanoma cell spreading was quantitated over a ligand concentration range of 0.01-50 microM and, in a fashion similar to adhesion, was more extensive on the trans-Flp ligand than on the trans-Hyp ligand. Very low levels of spreading were observed with the cis-Flp-containing ligand at all concentrations tested. Melanoma cell adhesion to and spreading on the three ligands suggested the dramatic biological consequence of even subtle changes in relative triple-helical content. Such subtle changes may model those occurring in the basement membrane during the tumor cell invasion process, and thus provide mechanistic insight into this stage of metastasis.     

A dynamical model for receptor-mediated cell adhesion to surfaces in viscous shear flow

We present a dynamical model for receptor-mediated cell adhesion to surfaces in viscous shear flow when the surfaces are coated with ligand molecules complementary to receptors in the cell membrane. This model considers the contact area between the cell and the surface to be a small, homogeneous region that mediates the initial attachment of the cell to the surface. Using a phase plane analysis for a system of nonlinear ordinary differential equations that govern the changes in free receptor density and bond density within the contact area with time, we can predict the conditions for which adhesion between the cell and the surface will take place. Whether adhesion occurs depends on values of dimensionless quantities that characterize the interaction of the cell and its receptors with the surface and its ligand, such as the bond formation rate, the receptor-ligand affinity, the fluid mechanical force, the receptor mobility, and the contact area. A key result is that there are two regimes in which different chemical and physical forces dominate: a rate-controlled high affinity regime and an affinity-controlled low affinity regime. Many experimental observations, including the effects of temperature and receptor mobility on adhesiveness, can be explained by understanding which of these regimes is appropriate. We also provide simple approximate analytical solutions, relating adhesiveness to cell and surface properties as well as fluid forces, which allow convenient testing of model predictions by experiment.     

A dynamical model for receptor-mediated cell adhesion to surfaces.

We present a dynamical model for receptor-mediated adhesion of cells in a shear field of viscous fluid to surfaces coated with ligand molecules complementary to receptors in the cell membrane. We refer to this model as the "point attachment model" because it considers the contact area between the cell and the surface to be a small, homogeneous region that mediates the initial attachment of the cell to the surface. Using a phase plane analysis of a system of nonlinear ordinary differential equations which govern the changes in free receptor density and bond density within the contact area with time, we can predict the conditions for which adhesion between the cell and the surface will take place. Whether adhesion occurs depends on values of dimensionless quantities that characterize the interaction of the cell and its receptors with the surface and its ligand, such as the bond formation rate, the receptor-ligand affinity, the fluid mechanical force, the receptor mobility, and the contact area. A key result is that there are two regimes in which different chemical and physical forces dominate: a rate-controlled high affinity regime and an affinity-controlled low-affinity regime. Many experimental observations can be explained by understanding which of these regimes is appropriate. We also provide simple approximate analytical solutions, relating adhesiveness to cell and surface properties as well as fluid forces, which allow convenient testing of model predictions by experiment.     

The relative importance of topography and RGD ligand density for endothelial cell adhesion

The morphology and function of endothelial cells depends on the physical and chemical characteristics of the extracellular environment. Here, we designed silicon surfaces on which topographical features and surface densities of the integrin binding peptide arginine-glycine-aspartic acid (RGD) could be independently controlled. We used these surfaces to investigate the relative importance of the surface chemistry of ligand presentation versus surface topography in endothelial cell adhesion. We compared cell adhesion, spreading and migration on surfaces with nano- to micro-scaled pyramids and average densities of 6×10(2)-6×10(11) RGD/mm(2). We found that fewer cells adhered onto rough than flat surfaces and that the optimal average RGD density for cell adhesion was 6×10(5) RGD/mm(2) on flat surfaces and substrata with nano-scaled roughness. Only on surfaces with micro-scaled pyramids did the topography hinder cell migration and a lower average RGD density was optimal for adhesion. In contrast, cell spreading was greatest on surfaces with 6×10(8) RGD/mm(2) irrespectively of presence of feature and their size. In summary, our data suggest that the size of pyramids predominately control the number of endothelial cells that adhere to the substratum but the average RGD density governs the degree of cell spreading and length of focal adhesion within adherent cells. The data points towards a two-step model of cell adhesion: the initial contact of cells with a substratum may be guided by the topography while the engagement of cell surface receptors is predominately controlled by the surface chemistry.     

Detailed mechanics of membrane-membrane adhesion and separation. I. Continuum of molecular cross-bridges

The mechanics of membrane-membrane adhesion are developed for the approximation that the molecular cross-bridging forces are continuously distributed as a normal stress (force per unit area). The significance of the analysis is that the finite range of the cross-bridging forces and the microscopic contact angle are not assumed negligible. Since the cross-bridging and adhesion forces are finite range interactions, there are two membrane regions: a free zone where the membranes are not subject to attractive forces; and an adherent zone where the membranes are held together by attractive stresses. The membrane is treated as an elastic continuum. The approach is to analyze the mechanics for each zone separately and then to require continuity of the solutions at the interface between the zones. Final solution yields the membrane contour and stresses proximal to and within the contact zone as well as the microscopic contact angle at the edge of the contact zone. It is demonstrated that the classical Young equation is consistent with this model. The results show that the microscopic contact angle becomes appreciable when the strength of adhesion is large or the length of the cross-bridge is large; however, the microscopic contact angle approaches zero as the membrane elastic stiffness increases. The solution predicts the width of the contact zone over which molecular bonds are stretched. It is this boundary region where increased biochemical activity is expected. In the classical model presented here, the level of tension necessary to oppose spreading of the contact is equal to the minimal level of tension required to separate the adherent membranes. This behavior is in contrast with that derived for the case of discrete molecular cross-bridges where the possibility of different levels of tension associated with adhesion and separation is introduced. The discrete cross-bridge case is the subject of a companion paper.     

Incorporation of integrins into artificial planar lipid membranes: characterization by plasmon-enhanced fluorescence spectroscopy

An optimized peptide-tethered artificial lipid membrane system has been developed. Integrins (cell adhesion receptors) were functionally incorporated into this membrane model and integrin-ligand interactions were analyzed by surface plasmon-enhanced fluorescence spectroscopy (SPFS). The transmembrane receptors alpha(v)beta(3) and alpha(1)beta(1) of the integrin superfamily were incorporated into a lipid-functionalized peptide layer by vesicle spreading. Consecutive layer formations were monitored by surface plasmon spectroscopy (SPS). Orientation and accessibility of the membrane receptor alpha(v)beta(3) was reliably assessed by specific and reproducible binding of selective antibodies. Moreover, full retention of the functional properties of this receptor was verified by specific and reversible binding of natural ligands. Functional integrity of incorporated integrins was maintained over a time period of 72 h. The integrin/extracellular matrix ligand complexes, whose formations are known to depend on the presence of divalent cations, were lost upon addition of ethylenediaminetetraacetate. Therefore, regeneration of the surface for further binding experiments with minimized unspecific ligand association was possible. These results demonstrate that integrins can be functionally incorporated into peptide-tethered artificial membranes. In combination with the SPS/SPFS method, this artificial membrane system provides a reliable experimental platform for investigation of isolated membrane proteins under experimental conditions resembling those of their native environment.     

Distinct functions for integrins alpha 3 beta 1 in focal adhesions and alpha 6 beta 4/bullous pemphigoid antigen in a new stable anchoring contact (SAC) of keratinocytes: relation to hemidesmosomes

Basal cells of stratified epidermis are anchored to the basement membrane zone (BMZ) of skin via hemidesmosomes. We previously identified integrin alpha 3 beta 1, in focal adhesions (FAs), of cultured human keratinocytes (HFKs) as a mediator of HFK adhesion to secreted BMZ-like extracellular matrix (ECM; Carter, W.G., E.A. Wayner, T.S. Bouchard, and P. Kaur. 1990. J. Cell Biol. 110: 1387-1404). Here, we have examined the relation of integrins alpha 6 beta 4 and alpha 3 beta 1, to bullous pemphigoid antigen (BPA), a component of hemidesmosomes. We conclude that alpha 6 beta 4 in HFKs localizes in a new stable anchoring contact (SAC) that cooperates with alpha 3 beta 1- FAs to mediate adhesion to ECM, based on the following. (a) Comparison of secreted ECM, with exogenous laminin, fibronectin and collagen identified ECM as the preferred ligand for HFK adhesion and spreading and for formation of both alpha 6 beta 4-SACs and alpha 3 beta 1-FAs. (b) Inhibition of HFK adhesion with combined anti-alpha 3 beta 1 (P1B5) and anti-alpha 6 beta 4 (GoH3) antibodies indicated that both receptors were functional in adhesion to ECM while alpha 3 beta 1 played a dominant role in spreading. (c) alpha 6 beta 4 colocalized with BPA in SACs that were proximal to but excluded from FAs. Both alpha 6 beta 4- SACs and alpha 3 beta 1-FAs were in contact with the adhesion surface as indicated by antibody exclusion and interference reflection microscopy. (d) In contrast to alpha 3 beta 1-FAs, alpha 6 beta 4-SACs were present only in nonmotile cells, not associated with stress fibers, and were relatively stable to detergents and urea, suggesting a nonmotile, or anchoring function for SACs and motility functions for alpha 3 beta 1-FAs. (e) alpha 6 beta 4 formed a detergent-insoluble complex with exogenous ECM in an affinity isolation procedure, confirming the ability of an unidentified ECM ligand to interact with alpha 6 beta 4. (f) We suggest that alpha 6 beta 4/BPA-SACs in culture restrict migration of HFKs on ECM while alpha 3 beta 1-FAs form dynamic adhesions in spreading and migrating cells. alpha 6 beta 4/BPA-SACs in culture bear functional and compositional similarities to hemidesmosomes in skin.     

Mechanics of spreading cells probed by atomic force microscopy

Cellular adhesion and motility are fundamental processes in biological systems such as morphogenesis and tissue homeostasis. During these processes, cells heavily rely on the ability to deform and supply plasma membrane from pre-existing membrane reservoirs, allowing the cell to cope with substantial morphological changes. While morphological changes during single cell adhesion and spreading are well characterized, the accompanying alterations in cellular mechanics are scarcely addressed. Using the atomic force microscope, we measured changes in cortical and plasma membrane mechanics during the transition from early adhesion to a fully spread cell. During the initial adhesion step, we found that tremendous changes occur in cortical and membrane tension as well as in membrane area. Monitoring the spreading progress by means of force measurements over 2.5 h reveals that cortical and membrane tension become constant at the expense of excess membrane area. This was confirmed by fluorescence microscopy, which shows a rougher plasma membrane of cells in suspension compared with spread ones, allowing the cell to draw excess membrane from reservoirs such as invaginations or protrusions while attaching to the substrate and forming a first contact zone. Concretely, we found that cell spreading is initiated by a transient drop in tension, which is compensated by a decrease in excess area. Finally, all mechanical parameters become almost constant although morphological changes continue. Our study shows how a single cell responds to alterations in membrane tension by adjusting its overall membrane area. Interference with cytoskeletal integrity, membrane tension and excess surface area by administration of corresponding small molecular inhibitors leads to perturbations of the spreading process.     

Migration of chick blastoderm under the vitelline membrane: the role of fibronectin

In the earliest stages of its development the chick blastoderm is a flattened disc at the surface of the yolk. It gradually increases in diameter, partially because the cells are rapidly proliferating, but also because the cells at the periphery (the margin of overgrowth) are migrating in a centrifugal direction. These cells utilize the inner surface of the vitelline membrane as their substratum. In the normal blastoderm, these cells at the edge of the spreading blastoderm are the only cells which are attached to the vitelline membrane. This investigation is concerned with the possible role played by fibronectin in the interaction between these migrating cells and the vitelline membrane. Chick blastoderms, explanted by the New (1955) technique have been treated with synthetic peptides that mimic the adhesive recognition signal of the fibronectin molecule. The pentapeptide GRGDS (containing the specific RGD cell adhesion sequence) caused the edge cells of the blastoderm to detach within minutes, and the expansion of the blastoderm was inhibited for about 4 hr. After this period there was gradual recovery and the cells reattached and spreading resumed. Examination of the margin of the blastoderm by scanning electron microscopy showed that cell processes were lost soon after treatment with GRGDS but concomitant with reattachment and the resumption of spreading, the cell processes reformed. The pentapeptide GRDGS (with the amino acids G and D inverted) produced a brief inhibition of spreading, but after an hour these blastoderms spread at the same rate as controls. Immunocytochemical staining with anti-fibronectin demonstrated that fibronectin was not only present at the interface of the edge cells and the vitelline membrane, but also between the epiblast and the hypoblast. These results indicate that tissue movement during blastoderm spreading is dependent upon fibronectin and that the specific RGD amino acid sequence, and presumably the VLA/integrin family of receptors, is involved in this embryonic morphogenetic movement.     

A semianalytic model of leukocyte rolling

Rolling allows leukocytes to maintain adhesion to vascular endothelium and to molecularly coated surfaces in flow chambers. Using insights from adhesive dynamics, a computational method for simulating leukocyte rolling and firm adhesion, we have developed a semianalytic model for the steady-state rolling of a leukocyte. After formation in a force-free region of the contact zone, receptor-ligand bonds are transported into the trailing edge of the contact zone. Rolling velocity results from a balance of the convective flux of bonds and the rate of dissociation at the back edge of the contact zone. We compare the model's results to that of adhesive dynamics and to experimental data on the rolling of leukocytes, with good agreement. We calculate the dependence of rolling velocity on shear rate, intrinsic forward and reverse reaction rates, bond stiffness, and reactive compliance, and use the model to calculate a state diagram relating molecular parameters and the dynamic state of adhesion. A dimensionless form of the analytic model permits exploration of the parameters that control rolling. The chemical affinity of a receptor-ligand pair does not uniquely determine rolling velocity. We elucidate a fundamental relationship between off-rate, ligand density, and reactive compliance at the transition between firm and rolling adhesion. The model provides a rapid method for screening system parameters for the potential to mediate rolling.     

Coated pits and asialoglycoprotein receptors redistribute to the substratum during hepatocyte adhesion to galactoside surfaces

Rat hepatocytes bind in a sugar-specific and concentration-dependent manner to flat polyacrylamide matrices containing covalently attached galactosyl (Gal) groups. Previous studies (Weigel, P.H., J. Cell Biol. 87, 855, 1980) concluded that binding was likely mediated by the asialoglycoprotein receptor. Here we confirm that adhesion is mediated by this receptor, since cell binding is inhibited by antireceptor antibody and a threshold binding response is also observed when hepatocytes adhere to surfaces coated with asialoorosomucoid, a ligand for this receptor. Cells that had bound to a Gal surface and were then sheared from the surface left a membrane patch behind on the substratum. The cytoplasmic side of these plasma membrane patches was visualized on the substratum by indirect immunofluorescence using antireceptor antibody or anticlathrin antibody. The density of punctate coated pits, visualized with the latter antibody, was enriched in a circular membrane region of about 4 microns 2 area that mediated cell binding. This zone also contained concentrated receptors, although the staining pattern with antireceptor antibody was more uniform and less punctate. The results show that both asialoglycoprotein receptors and coated pits are redistributed at the substratum interface on hepatocytes bound to Gal surfaces.     

Modeling of cell adhesion and deformation mediated by receptor–ligand interactions

The current work is devoted to studying adhesion and deformation of biological cells mediated by receptors and ligands in order to enhance the existing models. Due to the sufficient in-plane continuity and fluidity of the phospholipid molecules, an isotropic continuum fluid membrane is proposed for modeling the cell membrane. The developed constitutive model accounts for the influence of the presence of receptors on the deformation and adhesion of the cell membrane through the introduction of spontaneous area dilation. Motivated by physics, a nonlinear receptor–ligand binding force is introduced based on charge-induced dipole interaction. Diffusion of the receptors on the membrane is governed by the receptor–ligand interaction via Fick’s Law and receptor-ligand interaction. The developed model is then applied to study the deformation and adhesion of a biological cell. The proposed model is used to study the role of the material, binding, spontaneous area dilation and environmental properties on the deformation and adhesion of the cell.     

Mathematical model for the effects of adhesion and mechanics on cell migration speed.

Migration of mammalian blood and tissue cells over adhesive surfaces is apparently mediated by specific reversible reactions between cell membrane adhesion receptors and complementary ligands attached to the substratum. Although in a number of systems these receptors and ligand molecules have been isolated and identified, a theory capable of predicting the effects of their properties on cell migration behavior currently does not exist. We present a simple mathematical model for elucidating the dependence of cell speed on adhesion-receptor/ligand binding and cell mechanical properties. Our model can be applied to propose answers to questions such as: does an optimal adhesiveness exist for cell movement? How might changes in receptor and ligand density and/or affinity affect the rate of migration? Can cell rheological properties influence movement speed? This model incorporates cytoskeletal force generation, cell polarization, and dynamic adhesion as requirements for persistent cell movement. A critical feature is the proposed existence of an asymmetry in some cell adhesion-receptor property, correlated with cell polarity. We consider two major alternative mechanisms underlying this asymmetry: (a) a spatial distribution of adhesion-receptor number due to polarized endocytic trafficking and (b) a spatial variation in adhesion-receptor/ligand bond strength. Applying a viscoelastic-solid model for cell mechanics allows us to represent one-dimensional locomotion with a system of differential equations describing cell deformation and displacement along with adhesion-receptor dynamics. In this paper, we solve these equations under the simplifying assumption that receptor dynamics are at a quasi-steady state relative to cell locomotion. Thus, our results are strictly valid for sufficiently slow cell movement, as typically observed for tissue cells such as fibroblasts. Numerical examples relevant to experimental systems are provided. Our results predict how cell speed might vary with intracellular contractile force, cell rheology, receptor/ligand kinetics, and receptor/ligand number densities. A biphasic dependence is shown to be possible with respect to some of the system parameters, with position of the maxima essentially governed by a balance between transmitted contractile force and adhesiveness. We demonstrate that predictions for the two alternative asymmetry mechanisms can be distinguished and could be experimentally tested using cell populations possessing different adhesion-receptor numbers.     

Morphology of cell-substratum adhesion

Many cell types modulate growth, differentiation, and motility through changes in cell substrate adhesion, including regulation of focal contact formation. Clustering of cell surface adhesion receptors is an essential early step in the development of focal contacts, and thus may influence cell physiology. In this paper, we present a theoretical framework to examine how cell surface chemistry affects receptor clustering. Our one-dimensional tape-peeling model couples the equations of mechanical equilibrium for a cell membrane with kinetic receptor-ligand binding relations. We considered two distinct model scenarios: Adhesion mediated by multiple receptor-ligand interactions of different length and specific binding of a single receptor type occurs in the presence of van der Waals attraction and nonspecific repulsion. In each case, nonuniform (wave-like) membrane morphologies are observed in certain parameter ranges that support the clustering of adhesion receptors. The formation of these morphologies is described in terms of a balance of membrane stresses; when cell-surface potential as a function of separation distance is symmetric between two potential energy minima, nonuniform morphologies are obtained. Increases in the chemical binding energy between receptor and ligand (e.g., increases in ligand density) or decreases in the membrane rigidity result in smaller wavelengths for nonuniform interfaces. Additionally, we show wave-like geometries appear only when the mechanical compliance of receptor-ligand bonds is within an intermediate range, and examine how the mobility of “repellers”—glycocalyx molecules that exert a nonspecific repulsive force—influences membrane morphology. We find fully mobile repellers always redistribute to prevent nonuniform morphologies.