Thermodynamics of cell adhesion. II. Freely mobile repellers

Physical biology of the cancer cell glycocalyx

The glycocalyx coating the outside of most cells is a polymer meshwork comprising proteins and complex sugar chains called glycans. From a physical perspective, the glycocalyx has long been considered a simple 'slime' that protects cells from mechanical disruption or against pathogen interactions, but the great complexity of the structure argues for the evolution of more advanced functionality: the glycocalyx serves as the complex physical environment within which cell-surface receptors reside and operate. Recent studies have demonstrated that the glycocalyx can exert thermodynamic and kinetic control over cell signalling by serving as the local medium within which receptors diffuse, assemble and function. The composition and structure of the glycocalyx change markedly with changes in cell state, including transformation. Notably, cancer-specific changes fuel the synthesis of monomeric building blocks and machinery for production of long-chain polymers that alter the physical and chemical structure of the glycocalyx. In this Review, we discuss these changes and their physical consequences on receptor function and emergent cell behaviours.

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.

A numerical analysis of forces exerted by laminar flow on spreading cells in a parallel plate flow chamber assay

Exposure of spreading anchorage-dependent cells to laminar flow is a common technique to measure the strength of cell adhesion. Since cells protrude into the flow stream, the force exerted by the fluid on the cells is a function of cell shape. To assess the relationship between cell shape and the hydrodynamic force on adherent cells, we obtained numerical solutions of the velocity and stress fields around bovine aortic endothelial cells during various stages of spreading and calculated the force required to detach the cells. Morphometric parameters were obtained from light and scanning electron microscopy measurements. Cells were assumed to have a constant volume, but the surface area increased during spreading until the membrane was stretched taut. Two-dimensional models of steady flow were generated using the software packages ANSYS (mesh generation) and FIDAP (problem solution). The validity of the numerical results was tested by comparison with published results for a semicircle in contact with the surface. The drag force and torque were greatest for round cells making initial contact with the surface. During spreading, the drag force and torque declined by factors of 2 and 20, respectively. The calculated forces and moments were used in adhesion models to predict the wall shear stress at which the cells detached. Based upon published values for the bond force and receptor number, round cells should detach at shear stresses between 2.5 and 6 dyn/cm(2), whereas substantially higher stresses are needed to detach spreading and fully spread cells. Results from the simulations indicate that (1) the drag force varies little with cell shape whereas the torque is very sensitive to cell shape, and (2) the increase in the strength of adhesion during spreading is due to increased contact area and receptor densities within the contact area.

Integrin clustering is driven by mechanical resistance from the glycocalyx and the substrate

Integrins have emerged as key sensory molecules that translate chemical and physical cues from the extracellular matrix (ECM) into biochemical signals that regulate cell behavior. Integrins function by clustering into adhesion plaques, but the molecular mechanisms that drive integrin clustering in response to interaction with the ECM remain unclear. To explore how deformations in the cell-ECM interface influence integrin clustering, we developed a spatial-temporal simulation that integrates the micro-mechanics of the cell, glycocalyx, and ECM with a simple chemical model of integrin activation and ligand interaction. Due to mechanical coupling, we find that integrin-ligand interactions are highly cooperative, and this cooperativity is sufficient to drive integrin clustering even in the absence of cytoskeletal crosslinking or homotypic integrin-integrin interactions. The glycocalyx largely mediates this cooperativity and hence may be a key regulator of integrin function. Remarkably, integrin clustering in the model is naturally responsive to the chemical and physical properties of the ECM, including ligand density, matrix rigidity, and the chemical affinity of ligand for receptor. Consistent with experimental observations, we find that integrin clustering is robust on rigid substrates with high ligand density, but is impaired on substrates that are highly compliant or have low ligand density. We thus demonstrate how integrins themselves could function as sensory molecules that begin sensing matrix properties even before large multi-molecular adhesion complexes are assembled.

Critical cell decisions, including whether to live, proliferate, or assemble into tissue structures, are directed by cues from the extracellular matrix, the external protein scaffold that surrounds cells. Integrin receptors on the cell surface bind to the extracellular matrix and cluster into complexes that translate matrix cues into the set of instructions a cell follows. Using a newly developed model of the cell-matrix interface, in this work we detail a simple yet efficient mechanism by which integrins could “sense” important matrix properties, including chemical composition and mechanical stiffness, and cluster appropriately. This mechanism relies on mechanical resistance to integrin-matrix interaction provided by the glycocalyx, the slimy sugar and protein coating on the cell, as well as the stiffness of the matrix and the cell itself. In general, the resistance alters integrin-ligand reaction rates, such that integrin clustering is favored for many physiologically relevant conditions. Interestingly, the mechanical properties of the cell and ECM are altered in many prevalent diseases, such as cancer, and our work suggests how these mechanical perturbations might adversely influence integrin function.

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.

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.

Nucleation of membrane adhesions

Recent experimental and theoretical studies of biomimetic membrane adhesions [Bruinsma, Phys. Rev. E 61, 4253 (2000); Boulbitch, Biophys. J. 81, 2743 (2001)] suggested that adhesion mediated by receptor interactions is due to the interplay between membrane undulations and a double-well adhesion potential, and should be a first-order transition. We study the nucleation of membrane adhesion by finding the minimum-energy path on the free energy surface constructed from the bending free energy of the membrane and the double-well adhesion potential. We find a nucleation free energy barrier around 20k(B)T for adhesion of flexible membranes, which corresponds to fast nucleation kinetics with a time scale of the order of seconds. For cell membranes with a larger bending rigidity due to the actin network, the nucleation barrier is higher and may require active processes such as the reorganization of the cortex network to overcome this barrier. Our scaling analysis suggests that the geometry of the membrane shapes of the adhesion contact is controlled by the adhesion length that is determined by the membrane rigidity, the barrier height, and the length scale of the double-well potential, while the energetics of adhesion is determined by the depths of the adhesion potential. These results are verified by numerical calculations.

Influence of substratum surface chemistry/energy and topography on the human fetal osteoblastic cell line hFOB 1.19: Phenotypic and genotypic responses observed in vitro

Time-dependent phenotypic response of a model osteoblast cell line (hFOB 1.19, ATCC, and CRL-11372) to substrata with varying surface chemistry and topography is reviewed within the context of extant cell-adhesion theory. Cell-attachment and proliferation kinetics are compared using morphology as a leading indicator of cell phenotype. Expression of (alpha2, alpha3, alpha4, alpha5, alphav, beta1, and beta3) integrins, vinculin, as well as secretion of osteopontin (OP) and type I collagen (Col I) supplement this visual assessment of hFOB growth. It is concluded that significant cell-adhesion events-contact, attachment, spreading, and proliferation-are similar on all surfaces, independent of substratum surface chemistry/energy. However, this sequence of events is significantly delayed and attenuated on hydrophobic (poorly water-wettable) surfaces exhibiting characteristically low-attachment efficiency and long induction periods before cells engage in an exponential-growth phase. Results suggest that a 'time-cell-substratum-compatibility-superposition principle' is at work wherein similar bioadhesive outcomes can be ultimately achieved on all surface types with varying hydrophilicity, but the time required to arrive at this outcome increases with decreasing cell-substratum-compatibility. Genomic and proteomic tools offer unprecedented opportunity to directly measure changes in the cellular machinery that lead to observed cell responses to different materials. But for the purpose of measuring structure-property relationships that can guide biomaterial development, genomic/proteomic tools should be applied early in the adhesion/spreading process before cells have an opportunity to significantly remodel the cell-substratum interface, effectively erasing cause and effect relationships between cell-substratum-compatibility and substratum properties. IMPACT STATEMENT: This review quantifies relationships among cell phenotype, substratum surface chemistry/energy, topography, and cell-substratum contact time for the model osteoblast cell line hFOB 1.19, revealing that genomic/proteomic tools are most useful in the pursuit of understanding cell adhesion if applied early in the adhesion/spreading process.

Molecular mechanics and dynamics of leukocyte recruitment during inflammation

Discovery of new genes and proteins directly supporting leukocyte adhesion is waning, whereas there is heightened interest in the cell mechanics and receptor dynamics that lead from transient tethering via selectins to affinity shifts and adhesion strengthening through integrins. New optical tools enable real-time imaging of leukocyte rolling and arrest in parallel plate flow channels (PPFCs), and detection of single-molecule force spectroscopy provides an inner view of the intercellular adhesive contact region. Leukocyte recruitment during acute inflammation is triggered by ligation of G protein-coupled chemotactic receptors (GPCRs) and clustering of selectins. This, in turn, activates beta(2)-integrin (CD18), which facilitates cell capture and arrest in shear flow. This review provides a conceptual model for the molecular events supporting leukocyte recruitment.

Effective adhesion strength of specifically bound vesicles

A theoretical approach has been undertaken in order to model the thermodynamic equilibrium of a 3D vesicle adhering to a flat substrate. The vesicle is treated in a canonical description with a fixed number of sites. A finite number of these sites are occupied by mobile ligands that are capable of interacting with a discrete number of receptors immobilized on the substrate. Explicit consideration of the bending energy of the vesicle shape has shown that the problem of the vesicle shape can be decoupled from the determination of the optimum allocation of ligands over the vesicle. The allocation of bound and free ligands in the vesicle can be determined as a function of the size of the contact zone, the ligand-receptor binding strength, and the concentration of the system constituents. Several approximate solutions for different regions of system parameters are determined and in particular, the distinction between receptor- and ligand-dominated equilibria is found to be important. The crossover between these two types of solutions is found to occur at a critical size of the contact zone. The presented approach enables the calculation of the effective adhesion strength of the vesicle and thus permits meaningful comparisons with relevant experiments as well as connecting the presented model with the proven success of the continuum approach for modeling the shapes of adhering vesicles. The behavior of the effective adhesion strength is analyzed in detail and several approximate expressions for it are given.

Specific recognition of macroscopic objects by the cell surface: evidence for a receptor density threshold revealed by micrometric particle binding characteristics

The establishment of specific molecular bonds between a cell and a facing surface is involved in many physiological and technological situations. Using micrometric magnetic particles, we have explored the formation of specific molecular bonds between the cell and surfaces bearing complementary ligands under passive conditions. Streptavidin-coated particles were targeted to the cell surface of a B-cell line through a specific biotinylated antibody against the CD19 receptor. Flow cytometry, optical microscopy, and micropipette experimental techniques have been used. Main findings have been that cell surface receptor density acted like a switch for particle capture with a threshold value found here equal to 1.6 x 10(3) receptor/ microm(2). This led to exclusion from binding of the cells of lowest receptor density. The density threshold was modulated by the length of the binding link and the physics of the cell/particle collision. We suggest that the shear stress is one of the main determinants of the characteristics of binding. We also show that several thousand receptors were involved in the cell particle contact at the end of the binding process, although only eight bonds are required for the initial capture of a particle. A passive binding inhibition process due to link concentration by the initial contact was proposed to account for the small number of particles per cell.

Equilibrium thermodynamics of cell-cell adhesion mediated by multiple ligand-receptor pairs

In many situations, cell-cell adhesion is mediated by multiple ligand-receptor pairs. For example, the interaction between T cells and antigen-presenting cells of the immune system is mediated not only by T cell receptors and their ligands (peptide-major histocompatibility complex) but also by binding of intracellular adhesion molecules. Interestingly, these binding pairs have different resting lengths. Fluorescent labeling reveals segregation of the longer adhesion molecules from the shorter T cell receptors in this case. Here, we explore the thermal equilibrium of a general cell-cell interaction mediated by two ligand-receptor pairs to examine competition between the elasticity of the cell wall, nonspecific intercellular repulsion, and bond formation, leading to segregation of bonds of different lengths at equilibrium. We make detailed predictions concerning the relationship between physical properties of the membrane and ligand-receptor pairs and equilibrium pattern formation, and suggest experiments to refine our understanding of the system. We demonstrate our model by application to the T cell/antigen-presenting-cell system and outline applications to natural killer cell adhesion.

Measuring the forces that control protein interactions

Although the force fields and interaction energies that control protein behavior can be inferred indirectly from equilibrium and kinetic measurements, recent developments have made it possible to quantify directly (a) the ranges, magnitudes, and time dependence of the interaction energies and forces between biological materials; (b) the mechanical properties of isolated proteins; and (c) the strength of single receptor-ligand bonds. This review describes recent results obtained by using the atomic force microscope, optical tweezers, the surface force apparatus, and micropipette aspiration to quantify short-range protein-ligand interactions and the long-range, nonspecific forces that together control protein behavior. The examples presented illustrate the power of force measurements to quantify directly the force fields and energies that control protein behavior.

Effect of receptor-ligand affinity on the strength of endothelial cell adhesion

The objective of this study was to determine the effect of receptor-ligand affinity on the strength of endothelial cell adhesion. Linear and cyclic forms of the fibronectin (Fn) cell-binding domain peptide Arg-Gly-Asp (RGD) were covalently immobilized to glass, and Fn was adsorbed onto glass slides. Bovine aortic endothelial cells attached to the surfaces for 15 min. The critical wall shear stress at which 50% of the cells detached increased nonlinearly with ligand density and was greater with immobilized cyclic RGD than with immobilized linear RGD or adsorbed Fn. To directly compare results for the different ligand densities, the receptor-ligand dissociation constant and force per bond were estimated from data for the critical shear stress and contact area. Total internal reflection fluorescence microscopy was used to measure the contact area as a function of separation distance. Contact area increased with increasing ligand density. Contact areas were similar for the immobilized peptides but were greater on surfaces with adsorbed Fn. The dissociation constant was determined by nonlinear regression of the net force on the cells to models that assumed that bonds were either uniformly stressed or that only bonds on the periphery of the contact region were stressed (peeling model). Both models provided equally good fits for cells attached to immobilized peptides whereas the peeling model produced a better fit of data for cells attached to adsorbed Fn. Cyclic RGD and linear RGD both bind to the integrin alpha v beta 3, but immobilized cyclic RGD exhibited a greater affinity than did linear RGD. Receptor affinities of Fn adsorbed to glycophase glass and Fn adsorbed to glass were similar. The number of bonds was calculated assuming binding equilibrium. The peeling model produced good linear fits between bond force and number of bonds. Results of this study indicate that 1) bovine aortic endothelial cells are more adherent on immobilized cyclic RGD peptide than linear RGD or adsorbed Fn, 2) increased adhesion is due to a greater affinity between cyclic RGD and its receptor, and 3) the affinity of RGD peptides and adsorbed Fn for their receptors is increased after immobilization.

Hybridoma screening for cell adhesion molecules using multiple parallel comparisons in conditions of flow

Cell adhesion is a complex biophysical process that plays a central role in immunophysiology. Because of the complex force-energy relationships involved, insights into the mechanism of cell adhesion largely depend on comparative measurements. In this report, we describe a comparative approach to the measurement of cell adhesion under conditions of flow. The assay system perfuses fluorescently labeled lymphocytes over a cell monolayer in commercially available multiwell culture plates. The fluorescently labeled cells demonstrate a reproducible flow pattern within the well. Videomicroscopic recordings of cell movement have demonstrated rolling behavior over a wide range of cell velocities. This technique permits the measurement of cell adhesion over a variety of flow velocities, time courses, and treatment conditions. The ability to vary treatment conditions and provide multiple parallel conditions suggests the utility of this approach in the development of monoclonal antibodies (MAb) recognizing cell adhesion molecules.

Molecular analysis of antigen-independent adhesion forces between T and B lymphocytes

The low-affinity interactions underlying antigen recognition by T-cell receptors (TCRs) are thought to involve antigen-independent adhesion mechanisms. Using a hydrodynamic approach, we found that antigen-independent adhesion occurred between human B cells and resting T cells in a transient and temperature-dependent fashion. The mean cell-cell adhesion force was 0.32 x 10(-9) N and was generated by similar contributions (0.16 x 10(-9) N) of the LFA-1- and CD2-dependent adhesion pathways. After T-cell stimulation with a phorbol ester, the force contributed by LFA-1 was drastically increased, while that of CD2 was unaffected. We propose that weak receptor-mediated adhesion initiates antigen-independent intercellular contacts required for antigen recognition by the TCR and is upregulated following TCR engagement. The method used permits adhesion forces between living cells to be resolved at the molecular level and should prove valuable for the rapid assessment of interaction forces between various types of cells and cell-sized particles.

Direct force measurements of specific and nonspecific protein interactions

Streptavidin-biotin (receptor-ligand) interaction forces were measured directly as a function of their intermolecular separation in various salt solutions and at various temperatures with a surface forces apparatus. Electrostatic and van der Waals forces were found to dominate the long-range streptavidin-biotin interaction at > 20 A. At intermediate separations, down to approximately 10 A, the interaction is governed by repulsive steric and attractive van der Waals and hydrophobic forces. A much stronger short-range attraction giving rise to the strong, specific adhesive binding was measured at molecular separations of less than 5 A. A decrease in the pH from 7.2 to 6.0 resulted in complete charge reversal on the binding surface of streptavidin (pK approximately 6) from net negative to net positive, while leaving the negatively charged biotin surface (pK approximately 3.0) unchanged, and the long-range interaction switched from repulsive to attractive. This observed behavior can be attributed to the titration of two histidines on the biotin binding surface of streptavidin. These results reveal a strong sensitivity of the long-range interaction forces to the detailed amino acid composition of the biotin binding surface. They also demonstrate the powerful regulatory potential conferred by small changes in local surface ionic conditions on protein interaction forces over different distance regimes. The effects of temperature on receptor-ligand dynamics and on the strength of intermembrane adhesion forces were studied by measuring the long-range force profiles and short-range adhesion forces above and below the chain melting temperature (Tc approximately 30 degrees C) of the lipids in the supporting bilayers. Increased bilayer fluidity due to a temperature increase to 33 degrees C (T > Tc) increased short-range adhesion by 7-fold relative to bilayers in the gel state at 25 degrees C (T < Tc). This effect was attributed to the enhanced rates of lateral diffusion and molecular rearrangements on the more fluid bilayer surfaces, which resulted in greater and more rapid intermembrane bond formation. A change in the rates of molecular rearrangements was also found to affect the repulsive part of the interaction potential at intermediate separations (10-20 A) via modulation of the steric repulsion between streptavidin and the highly flexible, polymer-like biotin molecules. This is expected to have a large effect on the association rates of receptor-ligand binding, even if it does not change the equilibrium binding energy.(ABSTRACT TRUNCATED AT 250 WORDS)

Kinetics of ligand binding to a cluster of membrane-associated receptors

The process of ligand binding to a cluster of membrane-associated receptors is examined theoretically. The theoretical model proposed involves the diffusion of ligands from the solution to the disc-like cluster of receptors on the surface of the spherical cell. When the ligand hits the internal part of the disc-like cluster, it begins to move laterally until it leaves the disc through its outer surface or is bound by one of the receptors inside the disc. If the ligand leaves the cluster, it returns to the solution and hits the disc again after a certain period, etc. According to our model the transition from a diffusion-limited to a reaction-limited process of binding is determined by the dimensionless parameter lambda identical to Dtc/a2, where D is the lateral diffusion coefficient, tc is the characteristic time of reaction, and a is the radius of the disc-like cluster. The forward rate constant kf turns out to be a function of lambda. Comparing the results of our calculations of kf with some experimental data we found that agreement is achieved at high lambda, i.e. the process of ligand binding by clustered receptors is predominantly reaction-limited.

Morphology of cell-substratum adhesion. Influence of receptor heterogeneity and nonspecific forces

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.

A thermodynamic and biomechanical theory of cell adhesion. Part I: General formulism

The equilibrium thermodynamics calculus of cell adhesion developed by Bell et al. (1984, Biophys. J. 45, 1051-1064) has been extended to the general non-equilibrium case. In contrast to previous models which could only compute the end results of equilibrium states, the present theory is able to calculate the kinetic process of evolution of adhesion, which may or may not approach towards equilibrium. Starting from a basic constitutive hypothesis for Helmholtz free energy, equations of balance of normal forces, energy balance at the edge of the contact area and rate of entropy production are derived using an irreversible thermodynamics approach, in which the restriction imposed by the Second Law of Thermodynamics takes the place of free energy minimization used by Bell et al. (1984). An explicit expression for adhesion energy density is derived for the general transient case as the difference of the usable work transduced from chemical energy liberation from bond formation of specific crosslinking molecules and the repulsive potential of non-specific interactions. This allows the energy balance to be used as an independent boundary equation rather than a practical way of computing the adhesion energy. Jump conditions are obtained from the conservation of crosslinking molecules across the edge of adhesion region which is treated as a singular curve. The bond formation and lateral motion of the crosslinking molecules are assumed to obey a set of reaction-diffusion equations. These equations and the force balance equation within the contact area, plus the jump conditions and the energy balance equation at the edge form a well-posed moving boundary problem which determines the propagation of the adhesion boundary, the separation distance between the two cell membranes over the contact area as well as the distributions of the crosslinking molecules on the cell surfaces. The behavior of the system depends on the relative importance of virtual convection, lateral diffusion and bond formation of the crosslinking molecules at the edge of the adhesion region, according to which two types of rate limiting cases are discussed, viz, reaction-limited and diffusion-limited processes.

Concentration effects on reactions in membranes: rhodopsin and transducin

The reaction rate of two laterally-diffusing species in a biological membrane shows a maximum at some concentration of reactants, because an increase in the concentration of reactants tends to increase the reaction rate by the law of mass action but decreases the diffusion rate of the reactants. The activation of transducin by rhodopsin in the disk membrane of the rod outer segment is described in terms of a steady-state diffusion model with concentration-dependent diffusion coefficients. The optimum concentrations of reactants are obtained from contour plots of the reaction rate as a function of rhodopsin and transducin concentrations, and the sensitivity of the results to the assumed values of the variables is examined. To determine whether the observed concentrations are in fact those yielding the maximum reaction rate, several variables must be known more accurately.

The reaction-limited kinetics of membrane-to-surface adhesion and detachment

Biological adhesion is frequently mediated by specific membrane proteins (adhesion molecules). Starting with the notion of adhesion molecules, we present a simple model of the physics of membrane-to-surface attachment and detachment. This model consists of coupling the equations for deformation of an elastic membrane with equations for the chemical kinetics of the adhesion molecules. We propose a set of constitutive laws relating bond stress to bond strain and also relating the chemical rate constants of the adhesion molecules to bond strain. We derive an exact formula for the critical tension. We also describe a fast and accurate finite difference algorithm for generating numerical solutions of our model. Using this algorithm, we are able to compute the transient behaviour during the initial phases of adhesion and detachment as well as the steady-state geometry of adhesion and the velocity of the contact. An unexpected consequence of our model is the predicted occurrence of states in which adhesion cannot be reversed by application of tension. Such states occur only if the adhesion molecules have certain constitutive properties (catch-bonds). We discuss the rational for such catch-bonds and their possible biological significance. Finally, by analysis of numerical solutions, we derive an accurate and general expression for the steady-state velocity of attachment and detachment. As applications of the theory, we discuss data on the rolling velocity of granulocytes in post-capillary venules and data on lectin-mediated adhesion of red cells.

Thermodynamics of short-term cell adhesion in vitro

A thermodynamic theory of short-term (less than 2 hr) in vitro cell adhesion has been developed which allows calculation of reversible work of adhesion and estimation of a term proportional to cell-substrate contact area. The theory provides a means of determining a parameter related to membrane wetting tension for microscopic cells that does not require special manipulations which might desiccate or denature delicate cell membranes. Semiquantitative agreement between predicted and experimentally-measured cell adhesion obtained for three different cell types (MDCK, RBL-1, and HCT-15) in two different liquid phase compositions of surfactants (Tween-80 and fetal bovine serum) supports concepts and approximations utilized in development of theory. Cell-substrate contact areas were largest for wettable surfaces treated with ionizing corona or plasma discharges and smallest for hydrophobic materials for each cell type studied. Contact area for the continuous dog-kidney cell line MDCK was larger than that of either the leukemic blood cell RBL-1 or the anaplastic human colon cell HCT-15.

Animal glycolipids as attachment sites for microbes

The abundance of carbohydrate at the animal cell surface may explain why microbes have selected primarily carbohydrates as essential attachment sites for colonization or infection. Of the various surface glycoconjugates of interest, primary attention has been given to glycolipids, due in part to an efficient binding assay based on a thin-layer chromatogram with separated glycolipids. In this way the general character of carbohydrate recognition by microbes is being mapped. Mainly two examples are briefly described to illustrate some generalizations: lactosylceramide-recognition by several bacteria, and Gal alpha l----4Gal-binding by Escherichia coli and the Shiga toxin. The unique recognition of internally placed sequences, the often low-affinity binding, and the preference of certain sequences before others are interpreted to be of decisive biological value. The binding to internal parts makes it technically possible to approximate the binding epitope on a receptor glycolipid. For this the binding preferences to glycolipids carrying the binding site in different saccharide environments (isoreceptors) are compared with the computer-calculated preferred conformations (definition of steric hindrances to epitope access). Several binding epitopes dissected with this approach have a common surface character: a nonpolar area of ring hydrogens over one or two sugars, surrounded by polar oxygens or amide. This is in agreement with the recent Lemieux concept for antibody-carbohydrate interaction. This information facilitates a rational synthesis of receptor analogues for potential applications. An outline is finally given of an improved general approach for receptor analysis.