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

Abstract. 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 (CnlV). 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 CnlV. The detachment stress required for cells on Fn, 3.6 + 0.2 x 10 -3 ttdynes/absorbed molecule, was much greater than that on CnlV, 5.0 + 1.4 x 10 -5 #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 × 103 molecules//zm 2 and 1 x 104 molecules/#m 2 on Fn and CnlV, respectively. These optimal protein concentrations represent optimal initial attachment strengths corresponding to detachment shear stresses of 3.8/~dyne//~m 2 on Fn and 1.5 /zdyne/#m 2 on CnlV. Thus, while the optimal absorbed protein concentrations for migration on Fn and CnlV 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 ~,,1 #dyne//~m 2, 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.

Integrin adhesion receptors play a crucial role in regulating interactions between cells and extracellular matrix (ECM). Integrin activation initiates multiple intracellular signaling pathways and results in regulation of cell functions such as motility, proliferation and differentiation. Two key observations regarding the biophysical nature of integrin-mediated cell-matrix interactions motivated the present study: (1) cell motility can be regulated by modulating the magnitude of cell-substratum adhesion, by varying cell integrin expression level, integrin-ECM binding affinity or substratum ECM surface density; and (2) integrin clustering enables assembly of multiple cytoplasmic regulatory and structural proteins at sites of aggregated integrin cytoplasmic domains, activating certain intracellular signalling pathways. Here, using a minimal integrin adhesion ligand, YGRGD, we test the hypothesis that ligand clustering can affect cell migration in a manner related to its modulation of cell-substratum adhesion. We employ a synthetic polymer-linking method, which allows us to independently and systematically vary both the average surface density and the local (approx. 50 nm scale) spatial distribution of the YGRGD peptide, against a background otherwise inert with respect to cell adhesion. In this system, the ligand was presented in three alternative spatial distributions: singly, in clusters with an average of five ligands per cluster, or in clusters with an average of nine ligands per cluster; for each of these spatial distributions, a range of average ligand densities (1,000-200,000 ligands/micrometer(2)) were examined. Cluster spacing was adjusted in order to present equivalent average ligand densities independently of cluster size. The murine NR6 fibroblast cell line was used as a model because its migration behavior on ECM in the presence and absence of growth factors has been well-characterized and it expresses integrins known to interact with the YGRGD peptide. Using time-lapse videomicroscopy and analysis of individual cell movement paths, we find that NR6 cells can migrate on substrata where adhesion is mediated solely by the YGRGD peptide. As previously observed for migration of NR6 cells on fibronectin, migration speed on YGRGD is a function of the average surface ligand density. Strikingly, clustering of ligand significantly reduced the average ligand density required to support cell migration. In fact, non-clustered integrin ligands support cell attachment but neither full spreading nor haptokinetic or chemokinetic motility. In addition, by quantifying the strength of cell-substratum adhesion, we find that the variation of cell speed with spatial presentation of YGRGD is mediated via its effect on cell adhesion. These effects on motility and adhesion are also observed in the presence of epidermal growth factor (EGF), a known motility-regulating growth factor. Variation in YGRGD presentation also affects the organization of actin filaments within the cell, with a greater number of cells exhibiting stress fibers at higher cluster sizes of YGRGD. Our observations demonstrate that cell motility may be regulated by varying ligand spatial presentation at the nanoscale level, and suggest that integrin clustering is required to support cell locomotion.

Abstract. We have used laser optical trapping and nanometer-level motion analysis to investigate the cytoskeletal associations and surface dynamics of/31 integrin, a cell-substrate adhesion molecule, on the dorsal surfaces of migrating fibroblast cells. A singlebeam optical gradient trap (laser tweezers) was used to restrain polystyrene beads conjugated with anti-/5'l 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-/31 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 #m/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 #m/min) (SD) at a rate similar to that reported for other capping events and for migration of these cells. Cell lines containing mutated/~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 move 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. contacts between the cell and its surroundings, a...

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