Receptor-mediated cell attachment and detachment kinetics. I. Probabilistic model and analysis.

The kinetics of receptor-mediated cell adhesion to a ligand-coated surface play a key role in many physiological and biotechnology-related processes. We present a probabilistic model of receptor-ligand bond formation between a cell and surface to describe the probability of adhesion in a fluid shear field. Our model extends the deterministic model of Hammer and Lauffenburger (Hammer, D.A., and D.A. Lauffenburger. 1987. Biophys. J. 52:475-487) to a probabilistic framework, in which we calculate the probability that a certain number of bonds between a cell and surface exists at any given time. The probabilistic framework is used to account for deviations from ideal, deterministic behavior, inherent in chemical reactions involving relatively small numbers of reacting molecules. Two situations are investigated: first, cell attachment in the absence of fluid stress; and, second, cell detachment in the presence of fluid stress. In the attachment case, we examine the expected variance in bond formation as a function of attachment time; this also provides an initial condition for the detachment case. Focusing then on detachment, we predict transient behavior as a function of key system parameters, such as the distractive fluid force, the receptor-ligand bond affinity and rate constants, and the receptor and ligand densities.(ABSTRACT TRUNCATED AT 250 WORDS)     

Simulation of detachment of specifically bound particles from surfaces by shear flow.

The receptor-mediated adhesion of cells to ligand-coated surfaces is important in many physiological and biotechnological processes. Previously, we measured the detachment of antibody-coated spheres from counter-antibody- and protein A-coated substrates using a radial-flow detachment assay and were able to relate mechanical adhesion strength to chemical binding affinity (Kuo and Lauffenburger, Biophys. J. 65:2191-2200 (1993)). In this paper, we use "adhesive dynamics" to simulate the detachment of antibody-coated hard spheres from a ligand-coated substrate. We modeled the antibody-ligand (either counter-antibody or protein A) bonds as adhesive springs. In the simulation as in the experiments, beads attach to the substrate under static conditions. Flow is then initiated, and detachment is measured by the significant displacement of previously bound particles. The model can simulate the effects of many parameters on cell detachment, including hydrodynamic stresses, receptor number, ligand density, reaction rates between receptor and ligand, and stiffness and reactive compliance of the adhesive springs. The simulations are compared with experimental detachment data, thus relating measured bead adhesion strength to molecular properties of the adhesion molecules. The simulations accurately recreated the logarithmic dependence of adhesion strength on affinity of receptor-ligand recognition, which was seen in experiments and predicted by analytic theory. In addition, we find the value of the reactive compliance, the parameter which relates the strain of a bond to its rate of breakage, that gives the best match between theory and experiment to be 0.01. Finally, we analyzed the effect of varying either the forward or reverse rate constants as different ways to achieve the same affinity, and showed that adhesion strength depends uniquely on the equilibrium affinity, not on the kinetics of binding. Given that attachment is independent of affinity, detachment and attachment are distinct adhesive phenomena.     

Receptor-mediated adhesion phenomena. Model studies with the Radical-Flow Detachment Assay.

Receptor-mediated cell adhesion phenomena play a vital role in many physiological and biotechnology-related processes. To investigate the physical and chemical factors that influence the cell/surface interaction, we have used a radial flow device, a so-called Radial-Flow Detachment Assay (RFDA). The RFDA allows us to make direct observations of the detachment process under specified experimental conditions. In results reported here, we have studied the detachment of receptor-coated latex beads (prototype cells) from ligand-coated glass surfaces. The receptors and ligands used in this work are complementary antibodies. The beads enable us to examine several aspects of the adhesion process with particles having uniform properties that can be varied systematically. Advantages of the RFDA are many, especially direct observation of cell detachment over a range of shear stresses with quantitative measurement of the adhesive force. We focus our studies on the effects of ligand and receptor densities, along with the influence of pH and ionic strength of the medium. These data are analyzed with a mathematical model based on the theoretical framework of Bell, G. I. (1978. Science [Wash. DC]. 200:618-627) and Hammer, D. A. and D. A. Lauffenburger (1987. Biophys. J. 52:475-487). We demonstrate experimental validation of a theoretical expression for the critical shear stress for particle detachment, and show that it is consistent with reasonable estimates for the receptor-ligand bond affinity.     

Receptor-mediated cell attachment and detachment kinetics. II. Experimental model studies with the radial-flow detachment assay.

Quantitative information regarding the kinetics of receptor-mediated cell adhesion to a ligand-coated surface are crucial for understanding the role of certain key parameters in many physiological and biotechnology-related processes. Here, we use the probabilistic attachment and detachment models developed in the preceding paper to interpret transient data from well-defined experiments. These data are obtained with a simple model cell system that consists of receptor-coated latex beads (prototype cells) and a Radial-Flow Detachment Assay (RFDA) using a ligand-coated glass disc. The receptors and ligands used in this work are complementary antibodies. The beads enable us to examine transient behavior with particles that possess fairly uniform properties that can be varied systematically, and the RFDA is designed for direct observation of adhesion to the ligand-coated glass surface over a range of shear stresses. Our experiments focus on the effects of surface shear stress, receptor density, and ligand density. These data provide a crucial test of the probabilistic framework. We show that these data can be explained with the probabilistic analyses, whereas they cannot be readily interpreted on the basis of a deterministic analysis. In addition, we examine transient data on cell adhesion reported from other assays, demonstrating the consistency of these data with the predictions of the probabilistic models.     

A stochastic description of Dictyostelium chemotaxis

Chemotaxis, the directed motion of a cell toward a chemical source, plays a key role in many essential biological processes. Here, we derive a statistical model that quantitatively describes the chemotactic motion of eukaryotic cells in a chemical gradient. Our model is based on observations of the chemotactic motion of the social ameba Dictyostelium discoideum, a model organism for eukaryotic chemotaxis. A large number of cell trajectories in stationary, linear chemoattractant gradients is measured, using microfluidic tools in combination with automated cell tracking. We describe the directional motion as the interplay between deterministic and stochastic contributions based on a Langevin equation. The functional form of this equation is directly extracted from experimental data by angle-resolved conditional averages. It contains quadratic deterministic damping and multiplicative noise. In the presence of an external gradient, the deterministic part shows a clear angular dependence that takes the form of a force pointing in gradient direction. With increasing gradient steepness, this force passes through a maximum that coincides with maxima in both speed and directionality of the cells. The stochastic part, on the other hand, does not depend on the orientation of the directional cue and remains independent of the gradient magnitude. Numerical simulations of our probabilistic model yield quantitative agreement with the experimental distribution functions. Thus our model captures well the dynamics of chemotactic cells and can serve to quantify differences and similarities of different chemotactic eukaryotes. Finally, on the basis of our model, we can characterize the heterogeneity within a population of chemotactic cells.     

Cell population-based model of dermal wound invasion with heterogeneous intracellular signaling properties

A deterministic model of dermal wound invasion, which accounts for the platelet-derived growth factor (PDGF) gradient sensing mechanism in fibroblasts mediated by cell surface receptors and the phosphoinositide 3-kinase (PI3K) signal transduction pathway, was previously described (Biophys J 2006; 90:2297-2308). Here, we extend that work and implement a hybrid modeling strategy that treats fibroblasts as discrete entities endowed with heterogeneous properties, namely receptor, PI3K and 3’ phosphoinositide phosphatase expression levels. Analysis of the model suggests that the wound environment fosters the advancement of cells within the population that are better fit to migrate and/or proliferate in response to PDGF stimulation. Thus, cell-to-cell variability results in a significantly higher rate of wound invasion as compared with the deterministic model, in a manner that depends on the way in which individual cell properties are sampled or inherited upon cell division.     

Interrupting autocrine ligand-receptor binding: comparison between receptor blockers and ligand decoys.

Stimulation of cell behavioral functions by ligand/receptor binding can be accomplished in autocrine fashion, where cells secrete ligand capable of binding to receptors on their own surfaces. This proximal secretion of autocrine ligands near the surface receptors on the secreting cell suggests that control of these systems by inhibitors of receptor/ligand binding may be more difficult than for systems involving exogenous ligands. Hence, it is of interest to predict the conditions under which successful inhibition of cell receptor binding by the autocrine ligand can be expected. Previous theoretical work using a compartmentalized model for autocrine cells has elucidated the conditions under which addition of solution decoys for the autocrine ligand can interrupt cell receptor/ligand binding via competitive binding of the secreted molecules (Forsten, K. E., and D. A. Lauffenburger. 1992. Biophys. J. 61:1-12.) We now apply a similar modeling approach to examine the addition of solution blockers targeted against the cell receptor. Comparison of the two alternative inhibition strategies reveals that a significantly lower concentration of receptor blockers, compared to ligand decoys, will obtain a high degree of inhibition. The more direct interruption scheme characteristic of the receptor blockers may make them a preferred strategy when feasible.     

Consequences of chemosensory phenomena for leukocyte chemotactic orientation

The stochastic nature of cell surface receptor-ligand binding is known to limit the accuracy of detection of chemoattractant gradients by leukocytes, thus limiting the orientation ability that is crucial to the chemotactic response in host defense. The probabilistic cell orientation model of Lauffenburger is extended here to assess the consequences of recently discovered receptor phenomena: "down-regulation" of total surface receptor number, spatial asymmetry of surface receptors, and existence of a higher-affinity receptor subpopulation. In general, a reduction in orientation accuracy is predicted by inclusion of these phenomena. An orientation signal based on a simple model of chemosensory adaptation (i.e., a spatial difference in relative receptor occupancy) is found to be functionally different from the signal suggested by an experimental correlation (i.e., a spatial difference in absolute receptor occupancy). However, in the context of receptor "signal noise," the signal based on adaptation yields predictions in better qualitative agreement with the experimental orientation data of Zigmond. From this cell orientation model we can estimate the effective time-averaging period required for noise diminution to a level allowing orientation predictions to match observed levels. This time-averaging period presumably reflects the time constant for receptor signal transduction and locomotory response.     

Cell population-based model of dermal wound invasion with heterogeneous intracellular signaling properties

A deterministic model of dermal wound invasion, which accounts for the platelet-derived growth factor (PDGF) gradient sensing mechanism in fibroblasts mediated by cell surface receptors and the phosphoinositide 3-kinase (PI3K) signal transduction pathway, was previously described (Biophys J 2006; 90:2297–308). Here, we extend that work and implement a hybrid modeling strategy that treats fibroblasts as discrete entities endowed with heterogeneous properties, namely receptor, PI3K and 3′ phosphoinositide phosphatase expression levels. Analysis of the model suggests that the wound environment fosters the advancement of cells within the population that are better fit to migrate and/or proliferate in response to PDGF stimulation. Thus, cell-to-cell variability results in a significantly higher rate of wound invasion as compared with the deterministic model, in a manner that depends on the way in which individual cell properties are sampled or inherited upon cell division.Key words: wound healing, chemotaxis, gradient sensing, mathematical model, stochastic, signal transduction, phosphoinositide 3-kinase, PDGF     

Consequences of chemosensory phenomena for leukocyte chemotactic orientation

The stochastic nature of cell surface receptor-ligand binding is known to limit the accuracy of detection of chemoattractant gradients by leukocytes (11, 12), thus limiting the orientation ability that is crucial to the chemotactic response in host defense. The probabilistic cell orientation model of Lauffenburger (11) is extended here to assess the consequences of recently discovered receptor phenomena: “down-regulation” of total surface receptor number, spatial asymmetry of surface receptors, and existence of a higher-affinity receptor subpopulation. In general, a reduction in orientation accuracy is predicted by inclusion of these phenomena. An orientation signal based on a simple model of chemosensory adaptation (i.e., a spatial difference inrelative receptor occupancy) is found to be functionally different from the signal suggested by an experimental correlation (i.e., a spatial difference inabsolute receptor occupancy). However, in the context of receptor “signal noise,” the signal based on adaptation yields predictions in better qualitative agreement with the experimental orientation data of Zigmond (10). From this cell orientation model we can estimate the effective timeaveraging period required for noise diminution to a level allowing orientation predictions to match observed levels. This time-averaging period presumably reflects the time constant for receptor signal transduction and locomotory response.     

High voltage redox properties of cytochrome c oxidase.

In earlier studies evidence was obtained for the existence of both high and low redox potential forms of cytochrome a3 (Hendler et al. 1986. Biophys. J. 49:717-729; Hendler and Sidhu. 1988. Biophys. J. 54:121-133). The current paper describes additional experiments that support this conclusion and then reviews a large number of experimental observations that appear to be consistent with the view that cytochrome a3 displays at least (see Sidhu and Hendler. 1990. Biophys. J. 57:1125-1140) two different forms, which are distinguishable by their redox potentials, spectra, and reactivity with CO.     

Morphology of epidermoid carcinoma A431 cells spread on immobilized ligands

Cell interaction with extracellular matrix is a multi-step process characterized by cell attachment to substrata with subsequent cell spreading accompanied by actin cytoskeleton and cellular membrane receptor reorganization. It has been shown elsewhere that epidermoid carcinoma A431 cells, spread on solid substrata coated with fibronectin, laminin-2/4 or antibodies to EGF receptor, form specific actin filament structures typical for each particular ligand. Here quantitative analysis of heterogeneous A431 cell population spread on the above ligands has been reported. Cells were subdivided into morphological classes, according to their shape and actin filament structure, and the relationship among classes under various experimental conditions were quantitatively estimated for every ligand. We studied the influence of cell detachment pattern, short-term and long-term starvation, and cell incubation in suspended state in the medium before plating on the cell population composition. It was possible to recognize the modal morphological class of cells with typical actin cytoskeleton structure dominating for the ligand in the population. Long-term starvation and incubation in suspension before cell spreading are considered as the crucial experimental parameters leading to dramatic changes in cell population.     

Simulation of cell rolling and adhesion on surfaces in shear flow: general results and analysis of selectin-mediated neutrophil adhesion.

The receptor-mediated adhesion of cells to ligand-coated surfaces in viscous shear flow is an important step in many physiological processes, such as the neutrophil-mediated inflammatory response, lymphocyte homing, and tumor cell metastasis. This paper describes a calculational method which simulates the interaction of a single cell with a ligand-coated surface under flow. The cell is idealized as a microvilli-coated hard sphere covered with adhesive springs. The distribution of microvilli on the cell surface, the distribution of receptors on microvilli tips, and the forward and reverse reaction between receptor and ligand are all simulated using random number sampling of appropriate probability functions. The velocity of the cell at each time step in the simulation results from a balance of hydrodynamic, colloidal and bonding forces; the bonding force is derived by summing the individual contributions of each receptor-ligand tether. The model can simulate the effect of many parameters on adhesion, such as the number of receptors on microvilli tips, the density of ligand, the rates of reaction between receptor and ligand, the stiffness of the resulting receptor-ligand springs, the response of springs to strain, and the magnitude of the bulk hydrodynamic stresses. The model can successfully recreate the entire range of expected and observed adhesive phenomena, from completely unencumbered motion, to rolling, to transient attachment, to firm adhesion. Also, the method can generate meaningful statistical measures of adhesion, including the mean and variance in velocity, rate constants for cell attachment and detachment, and the frequency of adhesion. We find a critical modulating parameter of adhesion is the fractional spring slippage, which relates the strain of a bond to its rate of breakage; the higher the slippage, the faster the breakage for the same strain. Our analysis of neutrophil adhesive behavior on selectin-coated (CD62-coated) surfaces in viscous shear flow reported by Lawrence and Springer (Lawrence, M.B., and T.A. Springer 1991. Cell. 65:859-874) shows the fractional spring slippage of the CD62-LECAM-1 bond is likely below 0.01. We conclude the unique ability of this selectin bond to cause neutrophil rolling under flow is a result of its unique response to strain. Furthermore, our model can successfully recreate data on neutrophil rolling as function of CD62 surface density.     

The influence of doubly attached crossbridges on the mechanical behavior of skeletal muscle fibers under equilibrium conditions.

A simple model of a double-headed crossbridge is introduced to explain the retardation of force decay after an imposed stretch in skeletal muscle fibers under equilibrium conditions. The critical assumption in the model is that once one of the heads of a crossbridge is attached to one of the available actin sites, the attachment of the second head will be restricted to a level of strain determined by the attachment of the first head. The crossbridge structure, namely the connection of both heads of a crossbridge to the same tail region, is assumed to impose this constraint on the spatial configurations of crossbridge heads. The unique feature of the model is the prediction that, in the presence of a ligand (PPi, ADP, AMP-PNP) and absence of Ca2+, the halftime of force decay is many times larger than the inverse rate of detachment of a crossbridge head measured in solution. This prediction is in agreement with measured values of half-times of force decay in fibers under similar conditions (Schoenberg, M., and E. Eisenberg. 1985. Biophys. J. 48:863-871f). It is predicted that a crossbridge head is more likely to re-attach to its previously strained position than remain unattached while the other head is attached, leading to the slow decay of force. Our computations also show that the apparent cooperativity in crossbridge binding observed in experiments (Brenner, B., L. C. Yu, L. E. Greene, E. Eisenberg, and M. Schoenberg. 1986. Biophys. J. 50:1101-1108) can be partially accounted by the double-headed crossbridge attachment.(ABSTRACT TRUNCATED AT 250 WORDS)     

Direct determination of crystallographic phases for diffraction data from lipid bilayers. I. Reliability and phase refinement.

Direct analysis of lipid lamellar packing based on the probabilistic estimate of sigma 1- and sigma 2-triplet phase invariants is evaluated here for a large variety of bilayer structures than examined in an original study of this problem (Dorset, D.L., 1990. Biophys. J. 58:1077-1087). Using x-ray crystal structures of five phospholipids, three glycerides and two cerebrosides, lamellar diffraction data were generated at the approximately 3 A resolution often found experimentally from oriented multilayers. For structures where no significant density occurs at the unit cell origin, the ab initio phase determination is successful for six of the ten structures. A seventh structure can be solved if a limited set of sigma 2-triples are used to determine the initial phase set based on the hierarchy of the A2 values. Bilayers, e.g., with solvent at the origin, can be analyzed if a modified criterion for accepting phase estimates for sigma 1-triples is used, as suggested by the distribution of normalized structure factors and the number of probable single-valued phase domains. In all cases, partial phase determinations can be refined effectively by density modification ("flattening") of the hydrocarbon region in real space. A figure of merit suggested by Luzzati et al. (Luzzati, V., A. Tardieu, and D. Taupin. 1972. J. Mol. Biol. 64:269-286) used to evaluate the success of such refinement can be supplemented by an evaluation of density smoothness, which can also detect the presence of near structure homomorphs not identified by the former test for density flatness.     

Persistence and Dissemination of Introduced Bacteria in Freshwater Microcosms

Abstract Genetically engineered microorganisms (GEMs) released into the environment may persist and spread, depending on their features and conditions encountered. In streams, the extent of dispersion depends largely on cycles of attachment to, and detachment from, biofilms, because distribution of microorganisms is limited only by stream flow and settling rates, and because biofilms are the primary generator of bacterial cells. To simulate dissemination of introduced bacteria, multiple antibiotic-resistant bacteria (Chryseobacterium (Flavobacterium) indologenes) were introduced into microcosms containing water, sediments, and leaves. Marked bacteria reached greatest abundances in sediments, and contributions of bacteria from sediments to other habitats was relatively low. Bacterial attachment and detachment occurred rapidly, but the ability of marked bacteria to successfully exploit receiving habitats was comparatively low. Current speed influenced bacterial dissemination. A mechanistic model, using mortality and attachment/detachment rates, determined experimentally, was developed to predict bacterial exchanges in nature. The model was predictive of experimental results when only 5% of bacteria in sediments were available for detachment. Based on model results, an introduced bacterial strain, with mortality rates comparable to those of the model strain, is predicted to maintain highest abundances in sediments. However, within a month, abundance was predicted to be reduced by 98%; long-term persistence is possible if these low population sizes can be sustained. Received: 11 August 1997; Accepted: 9 December 1997     

Specific adhesion of glycophorin liposomes to a lectin surface in shear flow.

The adhesion of cells to other cells or to surfaces by receptor-ligand binding in a shear field is an important aspect of many different biological processes and various cell separation techniques. The purpose of this study was to observe the adhesion of model cells with receptor molecules embedded in their surfaces to a ligand-coated surface under well-defined flow conditions in a parallel plate flow chamber. Liposomes containing glycophorin were used as the model cells to permit a variation in the adhesion parameters and then to observe the effect on adhesion. A mathematical model for cell sedimentation was created to predict the deposition time and the velocity preceding adhesion for the selection of experimental operating conditions and the methods useful for data analysis. The likelihood of cell attachment was represented by a quantity called the sticking probability which was defined as the inverse of the number of times a liposome made contact with the surface before attachment occurred. The sticking probability decreased as the cell receptor concentration was lowered from approximately 10(4) to 10(2) receptors per 4-microns diam liposome and as the shear rate increased from 5 to 22 s-1. The effect of the wall shear rate and particle diameter on detachment of liposomes from a surface was also observed.     

Effects of growth factors on cell cycle arrest in dolichyl phosphate-depleted cultures

Previously we showed that CHO cell growth is arrested in the G1 or G0 phase within 24 h after the biosynthesis of mevalonic acid is blocked. The growth-limiting factor under these conditions appeared to be dolichyl phosphate or one of its glycosylated derivatives with consequent decrease in the synthesis of N-linked glycoproteins (Doyle, J.W., and A.A. Kandutsch, 1988, J. Cell Physiol. 137:133–140; Kabakoff, B., J.W. Doyle, and A.A. Kandutsch, 1990, Arch. Biochem. Biophys. 276:382–389). We show herein that cell surface glycoproteins are depleted in the inhibited cultures and that growth arrest is delayed when supraphysiological concentrations of insulin, insulin-like growth factor-1 (IGF-1) and bFGF are added to the culture medium. Apparently an elevated level of a growth factor increases the length of time during which a threshold level of occupied receptor is maintained as the number of glycosylated receptor molecules declines. The results support the idea that cellular levels of dolichyl phosphate and its derivatives may limit cell division by controlling the numbers of functional receptors for growth factors and of other glycoproteins on the cell surface. © 1993 Wiley-Liss, Inc.     

Effects of domain connection and disconnection on the yields of in-plane bimolecular reactions in membranes.

It has recently been shown (Vaz, W.L.C., E.C.C. Melo, and T.E. Thompson. 1989. Biophys. J. 56:869-875; 1990. Biophys. J. 58:273-275) that in lipid bilayer membranes in which ordered and disordered phases coexist, the ordered phase can form a two-dimensional reticular structure that subdivides the coexisting disordered phase into a disconnected domain structure. Here we consider theoretically the yields of bimolecular reactions between membrane-localized reactants, when both the reactants and products are confined to the disordered phase. It is shown that compartmentalization of reactants in disconnected domains can lead to significant reductions in reaction yields. The reduction in yield was calculated for classical bimolecular processes and for enzyme-catalyzed reactions. These ideas can be used to explain certain experimental observations.     

A theoretical analysis for the effect of focal contact formation on cell-substrate attachment strength.

For many cell types, growth, differentiation, and motility are dependent on receptor-mediated adhesion to ligand-coated surfaces. Focal contacts are strong, specialized, adhesive connections between cell and substrate in which receptors aggregate and connect extracellular ligand to intracellular cytoskeletal molecules. In this paper, we present a mathematical model to examine how focal contact formation affects cellular adhesive strength. To calculate adhesive strength with and without focal contacts, we use a one-dimensional tape peeling analysis to determine the critical tension necessary to peel the membrane. Receptor-ligand bonds are modeled as adhesive springs. In the absence of focal contacts, we derive analytic expressions for the critical tension at low and high ligand densities and show how membrane morphology affects adhesion. Then, focal contacts are modeled as cytoplasmic nucleation centers which bind adhesion receptors. The extent of adhesive strengthening upon focal contact formation depends on the elastic rigidity of the cytoskeletal connections, which determines the structural integrity of the focal contact itself. We consider two limits to this elasticity, very weak and rigid. Rigid cytoskeletal connections give much greater attachment strengths. The dependence of attachment strength on measurable model parameters is quite different in these two limits, which suggests focal contact structure might be deduced from properly performed adhesion experiments. Finally, we compare our model to the adhesive strengthening response reported for glioma cell adhesion to fibronectin (Lotz et al., 1989. J. Cell Biol. 109:1795-1805). Our model successfully predicts the observed detachment forces at 4 degrees C and yields values for the number of fibronectin receptors per glioma cell and the density of cytoskeletal connection molecules (talin) involved in receptor clusters which are consistent with measurements for other cell types. Comparison of the model with data at 37 degrees C suggests that while cytoskeletal cross-linking and clustering of fibronectin receptors significantly increases adhesion strength, specific glioma cell-substratum attachment sites possess little mechanical rigidity and detach through a peeling mechanism, consistent with the view that these sites of < or = 15 nm cell-substrate separation are precursors to fully formed, elastically rigid focal contacts.