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.

Mechanical compliance is emerging as an important environmental cue that can influence certain cell behaviors, such as morphology and motility. Recent in vitro studies have shown that cells preferentially migrate from less stiff to more stiff substrates; however, much of this phenomenon, termed durotaxis, remains ill-defined. To address this problem, we studied the morphology and motility of vascular smooth muscle cells on well-defined stiffness gradients. Baselines for cell spreading, polarization, and random motility on uniform gels with moduli ranging from 5 to 80 kPa were found to increase with increasing stiffness. Subsequent analysis of the behavior of vascular smooth muscle cells on gradient substrata (0-4 kPa/100 mum, with absolute moduli of 1-80 kPa) demonstrated that the morphology on gradient gels correlated with the absolute modulus. In contrast, durotaxis (evaluated quantitatively as the tactic index for a biased persistent random walk) and cell orientation with respect to the gradient both increased with increasing magnitude of gradient, but were independent of the absolute modulus. These observations provide a foundation for establishing quantitative relationships between gradients in substrate stiffness and cell response. Moreover, these results reveal common features of phenomenological cell response to chemotactic and durotactic gradients, motivating further mechanistic studies of how cells integrate and respond to multiple complex signals.

Blends of biodegradable polymers, poly(caprolactone) and poly(D, L-lactic-co-glycolic acid), have been examined as scaffolds for applications in bone tissue engineering. Hydroxyapatite granules have been incorporated into the blends and porous discs were prepared. Mechanical properties and degradation rates in vitro of the composites were determined. The discs were seeded with rabbit bone marrow or cultured bone marrow stromal cells and incubated under physiological conditions. Polymer/ceramic scaffolds supported cell growth throughout the scaffold for 8 weeks. Scanning and transmission electron microscopy, and histological analyses were used to characterize the seeded composites. This study suggests the feasibility of using novel polymer/ceramic composites as scaffold in bone tissue engineering applications.