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

Locomotive forces produced by single leukocytes in vivo and in vitro

We report here the first time-resolved measurements of the forces produced during the migration of single leukocytes in vivo and in vitro. Pulmonary macrophages from hamsters and mice, in vitro, and Nembutal (pentobarbital sodium)-anesthetized hamster neutrophils, in vivo, generated maximum locomotive forces ranging from 1.9 to 10.7 nN or tenths of microdynes. Force production was periodic and correlated with the length of the leading lamellipod but not with generalized cell ruffling. Although the extension of the leading lamella is critical to locomotive force generation, these direct measurements suggest that lamellar extension may not arise from the same contractile processes driving forward motion of the cell mass. Indeed, cell ruffling, lamellar extension, and locomotive force generation may be differentially controlled and have different origins. This technique may be extended to test numerous hypotheses of how these and other nonmuscle cells crawl.

Motility and substratum adhesion of Dictyostelium wild-type and cytoskeletal mutant cells: a study by RICM/bright-field double-view image analysis

To investigate the dynamics of cell-substratum adhesion during locomotion, a double-view optical technique and computer-assisted image analysis has been developed which combines reflection interference contrast microscopy (RICM) with bright-field imaging. The simultaneous recording of cell-substratum contact and cell body contour has been applied to aggregation-competent cells of Dictyostelium discoideum. These cells are distinguished from cells at earlier stages of development by small areas of contact to a substratum. Three questions have been addressed in analysing the locomotion of aggregation-competent cells. (1) What is the relationship between changes in the shape of cells and their contact to a substratum during a chemotactic response? (2) What is the relationship between protrusion and retraction of the cell body, and between local attachment and detachment? (3) Are there differences between wild-type and mutant cells that lack certain cytoskeletal proteins? During a chemotactic response the front region of the amoeba can bend towards the gradient of attractant without being supported by its contact with a surface, which excludes the necessity for gradients of adhesion for the response. The finding that in locomoting cells protrusion of the leading edge often precedes retraction establishes a pioneer role for the front region. The finding that gain of contact area precedes loss provides evidence for the coordination of interactions between the cell surface and a substratum. For comparison with wild-type, aggregation-competent triple mutant cells have been used that lack two F-actin crosslinking proteins, alpha-actinin and 120 kDa gelation factor, and an actin filament fragmenting protein, severin. Disturbances in the spatial and temporal control of cytoskeletal activities have been unravelled in the mutant by RICM and quantified by cross-correlation analysis of attachment and detachment vectors. In order to detect these disturbances, it was essential to analyse cell locomotion on the weakly adhesive surface of freshly cleaved mica.

Physics of actin networks. I. Rheology of semi-dilute F-actin

The mechanical properties of cytoplasm are considered to be of underlying importance in the mechanism of cell movement and are to a large extent determined by an actin-containing cytoskeleton. Several laboratories have begun to accumulate data on the mechanical or rheologic properties of protein systems derived from the actin cytoskeleton. The focus of this manuscript is to attempt to reproduce the experimentally determined mechanical properties of non-cross-linked F-actin from theoretical considerations. It was found that a mechanical spectrum for 1 mg/ml F-actin could be calculated, which approximated experimental data, from a relaxation spectrum consisting of a long range rotational diffusion motion and short range bending motion, assuming an exponential distribution of filament lengths with a weight average length of 4 mu. The calculated spectrum underestimated the dynamic moduli at high frequencies, suggesting that a more complex actin structure is present that enhances the high frequency component.

A mechanical function of myosin II in cell motility

Myosin II mutant Dictyostelium amoebae crawl more slowly than wild-type cells. Thus, myosin II must contribute to amoeboid locomotion. We propose that contractile forces generated by myosin II help the cell's rear edge to detach from the substratum and retract, allowing the cell to continue forward. To test this hypothesis, we measured the speed of wild-type and myosin II null mutant Dictyostelium cells on surfaces of varying adhesivity. As substratum adhesivity increased, the speed of myosin II null mutant cells decreased substantially compared to wild-type cells, suggesting that the mutant is less able to retract from sticky surfaces. Furthermore, interference reflection microscopy revealed a myosin-II-dependent contraction in wild-type but not null mutant cells that is consistent with a balance of adhesive and contractile forces in retraction. Although myosin II null mutant cells have a defect in retraction, pseudopod extension does not cause the cells to become elongated on sticky surfaces. This suggests a mechanism, based possibly on cytoskeletal tension, for regulating cell shape in locomotion. The tension would result from the transmission of tractional forces through the cytoskeletal network, providing the myosin II null mutant with a limited means of retraction and cell division on a surface.

Simulation of integrin-cytoskeletal interactions in migrating fibroblasts

Cell migration is a dynamic phenomenon requiring a physical interaction between the internal cell motile machinery and the external substratum in which adhesion receptors, such as integrins, serve as the transmembrane link. To analyze quantitatively this interaction, we apply a modified Brownian dynamics algorithm to simulate cytoskeleton-mediated transport of integrin on the dorsal surfaces of migrating fibroblasts. Previously, we experimentally demonstrated that integrin is transported in an intermittent fashion, with directed excursions interspersed by diffusive periods, preferentially toward the cell edge where the integrin is likely used in the formation of nascent adhesions. Integrins containing mutations in the cytoskeleton-binding region of the cytoplasmic domain display statistically different degrees of directed transport, indicating that this phenomenon is dependent on cytoskeletal associations. In the present work, we develop a computer algorithm generating simulated integrin transport trajectories, given estimates for the rate constants defining coupling (kc) and uncoupling (ku) of integrin with cytoskeletal components. Other parameters supplied to the program, the diffusion coefficient (D) for integrin in the membrane and the instantaneous velocity (vi) of the integrin/cytoskeleton complex, have been measured independently in our experimental system. By comparing the simulated trajectories with those obtained experimentally, we are able to estimate the coupling and uncoupling rate constants for the interaction of integrin with cytoskeletal elements in vivo. We find that integrin couples with cytoskeletal elements at a rate approximately 10 times slower than its rate of uncoupling (kc = 0.3 s-1, ku = 3 s-1). Comparison of these rate constants with an equivalent rate constant for diffusion, k+ = 0.4 s-1, indicates that the coupling interaction is likely a diffusion-limited process, as is typically expected for membrane processes. We further show by calculation that directed transport is necessary for integrin to traverse the length of an extending lamellipod to its leading edge; diffusion alone is not sufficiently fast to supply adhesion receptors to points of new cell/substratum contact.

Integrin-binding peptide in solution inhibits or enhances endothelial cell migration, predictably from cell adhesion

We have examined the effects of an integrin-binding competitor, echistatin, in solution on adhesion and migration of rat microvessel endothelial cells on fibronectin in vitro. A biphasic dependence of cell motility on fibronectin surface density was observed, with a peak random motility coefficient of about 8 x 10(-9) cm2/sec occurring below 0.3 microgram/cm2 fibronectin. In the presence of echistatin at 0.5 microM, the peak random motility coefficient was similar but occurred at the significantly greater fibronectin surface density of 1.2 micrograms/cm2. Hence, the same concentration of this soluble integrin-binding competitor inhibited migration on low fibronectin densities but enhanced migration on high fibronectin densities. At the same time, echistatin decreased adhesiveness on all fibronectin surface densities. When motility was correlated explicitly with adhesiveness, a single biphasic relationship was obtained for both absence and presence of echistatin with peak motility occurring in both cases at identical adhesiveness. Both the inhibiting and enhancing effects of the soluble integrin-binding competitor on motility are predictable from its effect on adhesion, consistent with the theoretical models of Lauffenburger (15) and DiMilla et al. (3).

Cytoplasmic desmosomes and intermediate filament disturbance following acrylamide treatment in cultured rat keratinocytes

The present paper describes disturbances in the organization of tonofilaments and desmosomes of rat lingual and epidermal keratinocytes after treatment of the cells with acrylamide in culture. This treatment induced changes in cell shape, reduction of intercellular adhesion and a perinuclear accumulation of cytoplasmic organelles. Using specific antibodies for cytokeratins, the filaments were disorganized particularly in the perinuclear region. In untreated cells, keratin filament labelling was very weak or absent above and below the nucleus thus leaving a black nuclear space in fluorescine microscopy. Following acrylamide treatment, the keratin filament labelling covered the nuclear space which indicated the accumulation of these filaments all around the nucleus. Furthermore, the desmosomal junctions were often associated with thick keratin bundles. Antibodies for desmoplakins revealed a reduction in intercellular labelling and stronger cytoplasmic labelling. Ultrastructurally, well-developed long tonofilaments were found to associate with large desmosomal junctions. Furthermore, small-sized desmosomal structures were identified within the cytoplasm. Morphologically, these were identical to cell surface desmosomes and were almost always associated with well-developed tonofilaments. The effect of acrylamide on the protein kinase A activity might be implicated in the disturbances of the desmosome-intermediate filament complex and in the initiation of contractile forces necessary for perinuclear accumulation of intermediate filaments and for the formation of intact cytoplasmic desmosomes. The acrylamide-induced intermediate filament and desmosomal changes may provide valuable information on the mechanism of intact cytoplasmic desmosome formation in several skin diseases and in squamous cell carcinoma.

Integrin-cytoskeletal interactions in migrating fibroblasts are dynamic, asymmetric, and regulated

We have used laser optical trapping and nanometer-level motion analysis to investigate the cytoskeletal associations and surface dynamics of beta 1 integrin, a cell-substrate adhesion molecule, on the dorsal surfaces of migrating fibroblast cells. A single-beam optical gradient trap (laser tweezers) was used to restrain polystyrene beads conjugated with anti-beta 1 integrin mAbs and place them at desired locations on the cell exterior. This technique was used to demonstrate a spatial difference in integrin-cytoskeleton interactions in migrating cells. We found a distinct increase in the stable attachment of beads, and subsequent rearward flow, on the lamellipodia of locomoting cells compared with the retracting portions. Complementary to the enhanced linkage of integrin at the cell lamellipodium, the membrane was more deformable at the rear versus the front of moving cells while nonmotile cells did not exhibit this asymmetry in membrane architecture. Video microscopy and nanometer-precision tracking routines were used to study the surface dynamics of integrin on the lamellipodia of migrating cells by monitoring the displacements of colloidal gold particles coated with anti-beta 1 integrin mAbs. Small gold aggregates were rapidly transported preferentially to the leading edge of the lamellipod where they resumed diffusion restricted along the edge. This fast transport was characterized by brief periods of directed movement ("jumps") having an instantaneous velocity of 37 +/- 15 microns/min (SD), separated by periods of diffusion. In contrast, larger aggregates of gold particles and the large latex beads underwent slow, steady rearward movement (0.85 +/- 0.44 micron/min) (SD) at a rate similar to that reported for other capping events and for migration of these cells. Cell lines containing mutated beta 1 integrins were used to show that the cytoplasmic domain is essential for an asymmetry in attachment of integrin to the underlying cytoskeletal network and is also necessary for rapid, intermittent transport. However, enhanced membrane deformability at the cell rear does not require integrin-cytoskeletal interactions. We also demonstrated that posttranslational modifications of integrin could potentially play a role in these phenomena. These results suggest a scheme for the role of dynamic integrin-mediated adhesive interactions in cell migration. Integrins are transported preferentially to the cell front where they form nascent adhesions. These adhesive structures grow in size and associate with the cytoskeleton that exerts a rearward force on them. Dorsal aggregates more rearward while those on the ventral side remain fixed to the substrate allowing the cell body to move forward. Detachment of the cell rear occurs by at least two modes: (a) weakened integrin-cytoskeleton interactions, potentially mediated by local modifications of linkage proteins, which lead to weakened cell-substratum interactions and (b) ripping of integrins and the highly deformable membrane from the cell body.

Relationship between receptor/ligand binding affinity and adhesion strength

Receptor-mediated cell adhesion is a central phenomenon in many physiological and biotechnological processes. Mechanical strength of adhesion is generally presumed to be related to chemical affinity of receptor/ligand bonds, but no experimental study has been previously directed toward this issue. Here we investigate the dependence of receptor/ligand adhesion strength on bond affinity using a radial fluid flow chamber assay to measure the force needed to detach polystyrene beads covalently coated with immunoglobulin G from glass surfaces covalently coated with protein A. A spectrum of animal species sources for immunoglobulin G permits examination of three decades of protein A/immunoglobulin G binding affinity. Our results for this model system demonstrate that adhesion strength varies with the logarithm of the binding affinity, consistent with a prediction from the theoretical model by Dembo et al. (Dembo, M., D.C. Torney, K. Saxman, and D. Hammer. 1988. Proc. R. Soc. Lond. Ser. B 234:55-83).

Maximal migration of human smooth muscle cells on fibronectin and type IV collagen occurs at an intermediate attachment strength

Although a biphasic dependence of cell migration speed on cell-substratum adhesiveness has been predicted theoretically, experimental data directly demonstrating a relationship between these two phenomena have been lacking. To determine whether an optimal strength of cell-substratum adhesive interactions exists for cell migration, we measured quantitatively both the initial attachment strength and migration speed of human smooth muscle cells (HSMCs) on a range of surface concentrations of fibronectin (Fn) and type IV collagen (CnIV). Initial attachment strength was measured in order to characterize short time-scale cell-substratum interactions, which may be representative of dynamic interactions involved in cell migration. The critical fluid shear stress for cell detachment, determined in a radial-flow detachment assay, increased linearly with the surface concentrations of adsorbed Fn and CnIV. The detachment stress required for cells on Fn, 3.6 +/- 0.2 x 10(-3) mu dynes/absorbed molecule, was much greater than that on CnIV, 5.0 +/- 1.4 x 10(-5) mu dynes/absorbed molecule. Time-lapse videomicroscopy of individual cell movement paths showed that the migration behavior of HSMCs on these substrates varied with the absorbed concentration of each matrix protein, exhibiting biphasic dependence. Cell speed reached a maximum at intermediate concentrations of both proteins, with optimal concentrations for migration at 1 x 10(3) molecules/micron2 and 1 x 10(4) molecules/micron2 on Fn and CnIV, respectively. These optimal protein concentrations represent optimal initial attachment strengths corresponding to detachment shear stresses of 3.8 mu dyne/micron2 on Fn and 1.5 mu dyne/micron2 on CnIV. Thus, while the optimal absorbed protein concentrations for migration on Fn and CnIV differed by an order of magnitude, the optimal initial attachment strengths for migration on these two proteins were very similar. Further, the same minimum strength of initial attachment, corresponding to a detachment shear stress of approximately 1 mu dyne/micron2, was required for movement on either protein. These results suggest that initial cell-substratum attachment strength is a central variable governing cell migration speed, able to correlate observations of motility on substrata differing in adhesiveness. They also demonstrate that migration speed depends in biphasic manner on attachment strength, with maximal migration at an intermediate level of cell-substratum adhesiveness.

A stochastic model for adhesion-mediated cell random motility and haptotaxis

The active migration of blood and tissue cells is important in a number of physiological processes including inflammation, wound healing, embryogenesis, and tumor cell metastasis. These cells move by transmitting cytoplasmic force through membrane receptors which are bound specifically to adhesion ligands in the surrounding substratum. Recently, much research has focused on the influence of the composition of extracellular matrix and the distribution of its components on the speed and direction of cell migration. It is commonly believed that the magnitude of the adhesion influences cell speed and/or random turning behavior, whereas a gradient of adhesion may bias the net direction of the cell movement, a phenomenon known as haptotaxis. The mechanisms underlying these responses are presently not understood. A stochastic model is presented to provide a mechanistic understanding of how the magnitude and distribution of adhesion ligands in the substratum influence cell movement. The receptor-mediated cell migration is modeled as an interrelation of random processes on distinct time scales. Adhesion receptors undergo rapid binding and transport, resulting in a stochastic spatial distribution of bound receptors fluctuating about some mean distribution. This results in a fluctuating spatio-temporal pattern of forces on the cell, which in turn affects the speed and turning behavior on a longer time scale. The model equations are a system of nonlinear stochastic differential equations (SDE's) which govern the time evolution of the spatial distribution of bound and free receptors, and the orientation and position of the cell. These SDE's are integrated numerically to simulate the behavior of the model cell on both a uniform substratum, and on a gradient of adhesion ligand concentration. Furthermore, analysis of the governing SDE system and corresponding Fokker-Planck equation (FPE) yields analytical expressions for indices which characterize cell movement on multiple time scales in terms of cell cytomechanical, morphological, and receptor binding and transport parameters. For a uniform adhesion ligand concentration, this analysis provides expressions for traditional cell movement indices such as mean speed, directional persistence time, and random motility coefficient. In a small gradient of adhesion, a perturbation analysis of the FPE yields a constitutive cell flux expression which includes a drift term for haptotactic directional cell migration. The haptotactic drift contains terms identified as contributions from directional orientation bias (taxis), kinesis, and orthotaxis, of which taxis appears to be predominant given estimates of the model parameters.

New physical concepts for cell amoeboid motion

Amoeboid motion of cells is an essential mechanism in the function of many biological organisms (e.g., the regiment of scavenger cells in the immune defense system of animals). This process involves rapid chemical polymerization (with numerous protein constituents) to create a musclelike contractile network that advances the cell over the surface. Significant progress has been made in the biology and biochemistry of motile cells, but the physical dynamics of cell spreading and contraction are not well understood. The reason is that general approaches are formulated from complex mass, momentum, and chemical reaction equations for multiphase-multicomponent flow with the nontrivial difficulty of moving boundaries. However, there are strong clues to the dynamics that allow bold steps to be taken in simplifying the physics of motion. First, amoeboid cells often exhibit exceptional kinematics, i.e., steady advance and retraction of local fixed-shape patterns. Second, recent evidence has shown that cell projections "grow" by polymerization along the advancing boundary of the cell. Together, these characteristics represent a local growth process pinned to the interfacial contour of a contractile network. As such, the moving boundary becomes tractable, but subtle features of the motion lead to specific requirements for the chemical nature of the boundary polymerization process. To demonstrate these features, simple examples for limiting conditions of substrate interaction (i.e., "strong" and "weak" adhesion) are compared with data from experimental studies of yeast particle engulfment by blood granulocytes and actin network dynamics in fishscale keratocytes.

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.

A GTPase controls cell-substrate adhesion in Xenopus XTC fibroblasts

Cell-substrate adhesion is crucial at various stages of development and for the maintenance of normal tissues. Little is known about the regulation of these adhesive interactions. To investigate the role of GTPases in the control of cell morphology and cell-substrate adhesion we have injected guanine nucleotide analogs into Xenopus XTC fibroblasts. Injection of GTP gamma S inhibited ruffling and increased spreading, suggesting an increase in adhesion. To further investigate this, we made use of GRGDSP, a peptide which inhibits binding of integrins to vitronectin and fibronectin. XTC fibroblasts injected with non-hydrolyzable analogs of GTP took much more time to round up than mock-injected cells in response to treatment with GRGDSP, while GDP beta S-injected cells rounded up in less time than controls. Injection with GTP gamma S did not inhibit cell rounding induced by trypsin however, showing that cell contractility is not significantly affected by the activation of GTPases. These data provide evidence for the existence of a GTPase which can control cell-substrate adhesion from the cytoplasm. Treatment of XTC fibroblasts with the phorbol ester 12-o-tetradecanoylphorbol-13-acetate reduced cell spreading and accelerated cell rounding in response to GRGDSP, which is essentially opposite to the effect exerted by non-hydrolyzable GTP analogs. These results suggest the existence of at least two distinct pathways controlling cell-substrate adhesion in XTC fibroblasts, one depending on a GTPase and another one involving protein kinase C.

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.

Quantification of human neutrophil motility in three-dimensional collagen gels. Effect of collagen concentration

Leukocytes must migrate through tissues to fulfill their role in the immune response, but direct methods for observing and quantifying cell motility have mostly been limited to migration on two-dimensional surfaces. We have now developed methods for examining neutrophil movement in a three-dimensional gel containing 0.1 to 0.7 mg/ml rat tail tendon collagen. Neutrophil-populated collagen gels were formed within flat glass capillary tubes, permitting direct observation with light microscopy. By following the tracks of individual cells over a 13.5-min observation period and comparing them to a stochastic model of cell movement, we quantified cell speed within a given gel by estimating a random motility coefficient (mu) and persistence time (P). The random motility coefficient changed significantly with collagen concentration in the gel, varying from 1.6 to 13.3 x 10(-9) cm2/s, with the maximum occurring at a collagen gel concentration of 0.3 mg/ml. The methods described may be useful for studying tissue dynamics and for evaluating the mechanism of cell movement in three-dimensional gels of extracellular matrix (ECM) molecules.

Three-dimensional motility cycle in leukocytes

A 3-dimensional dynamic image analyzing system (3D-DIAS) has been developed in which a translocating cell is optically sectioned in the z-axis within a 2 sec period; the perimeter of the cell in each section is digitized into the 3D-DIAS data file, and the digitized perimeters are wrapped in order to reconstruct the cell image in three dimensions. Using 3D-DIAS, we have obtained the first dynamic 3-dimensional description of human polymorphonuclear leukocytes (PMN) translocating on a glass surface. A general behavior cycle has emerged which includes two phases. In the first, an ellipsoidal PMN with significant z-axis extends anteriorly and descends to the substratum. When the ventral surface of the anterior end contacts the substratum, there is rapid anterior expansion, which correlates with velocity peaks. In the second phase, the elongate PMN stops translocating along the substratum, the anterior end lifts off of the substratum, sometimes to heights greater than the length of the PMN at the substratum, and finally the PMN retracts into an ellipsoidal morphology still capable of random protrusions. During this second phase, which correlates with velocity troughs, turning usually occurs. The degree of turning is restricted by the continuous integrity of the posterior uropod. The period of the behavior cycle varies from roughly 0.5 to 2 min between PMNs, but is relatively constant within each individual PMN.

Simulation of cell rolling and adhesion on surfaces in shear flow. Microvilli-coated hard spheres with adhesive springs

The 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 article describes a calculational method that allows simulation of the interaction of a single cell with a ligand-coated surface. 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 springs, the response of springs to extension, and the magnitude of hydrodynamic stresses. By varying these parameters, 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 model can provide 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 extension of a bond to its rate of breakage; the higher the slippage, the faster the breakage for the same extension. Changes in the fractional spring slippage can radically change the adhesive behavior of a cell. We show that stiffer springs will only serve to increase adhesion if the fractional slippage remains small. In addition, our simulations emphasize the importance of reaction rates between receptor and ligand, rather than affinity, as being the key determinant of adhesion under flow. These results suggest reaction rates and response to stress of adhesion molecules must be independently measured to understand how adhesion is controlled at the molecular level.