Micah Dembo

Stresses at the Cell-to-Substrate Interface during Locomotion of Fibroblasts

Recent technological improvements in the elastic substrate method make it possible to produce spatially resolved measurements of the tractions exerted by single motile cells. In this study we have applied these developments to produce maps of the tractions exerted by 3T3 fibroblasts during steady locomotion. The resulting images have a spatial resolution of approximately 5 micrometers and a maximum intensity of approximately 10(2) kdyn/cm2 (10(4) pN/micrometers2). We find that the propulsive thrust for fibroblast locomotion, approximately 0.2 dyn, is imparted to the substratum within 15 micrometers of the leading edge. These observations demonstrate that the lamellipodium of the fibroblast is able to generate intense traction stress. The cell body and posterior seem to be mechanically passive structures pulled forward entirely by this action.

Cell adhesion. Competition between nonspecific repulsion and specific bonding

We develop a thermodynamic calculus for the modeling of cell adhesion. By means of this approach, we are able to compute the end results of competition between the formation of specific macromolecular bridges and nonspecific repulsion arising from electrostatic forces and osmotic (steric stabilization) forces. Using this calculus also allows us to derive in a straightforward manner the effects of cell deformability, the Youngs modulus for stretching of bridges, diffusional mobility of receptors, heterogeneity of receptors, variation in receptor number, and the strength of receptor-receptor binding. The major insight that results from our analysis concerns the existence and characteristics of two phase transitions corresponding, respectively, to the onset of stable cell adhesion and to the onset of maximum cell-cell or cell-substrate contact. We are also able to make detailed predictions of the equilibrium contact area, equilibrium number of bridges, and the cell-cell or cell-substrate separation distance. We illustrate how our approach can be used to improve the analysis of experimental data, by means of two concrete examples.

Analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice Boltzmann BGK model

In this paper we analytically solve the velocity of the lattice Boltzmann BGK equation (LBGK) for several simple flows. The analysis provides a framework to theoretically analyze various boundary conditions. In particular, the analysis is used to derive the slip velocities generated by various schemes for the nonslip boundary condition. We find that the slip velocity is zero as long as Σαfαeα=0 at boundaries, no matter what combination of distributions is chosen. The schemes proposed by Nobleet al. and by Inamuroet al. yield the correct zeroslip velocity, while some other schemes, such as the bounce-back scheme and the equilibrium distribution scheme, would inevitably generate a nonzero slip velocity. The bounce-back scheme with the wall located halfway between a flow node and a bounce-back node is also studied for the simple flows considered and is shown to produce results of second-order accuracy. The momentum exchange at boundaries seems to be highly related to the slip velocity at boundaries. To be specific, the slip velocity is zero only when the momentum dissipated by boundaries is equal to the stress provided by fluids.

Traction force microscopy of migrating normal and H-ras transformed 3T3 fibroblasts.

Mechanical interactions between cell and substrate are involved in vital cellular functions from migration to signal transduction. A newly developed technique, traction force microscopy, makes it possible to visualize the dynamic characteristics of mechanical forces exerted by fibroblasts, including the magnitude, direction, and shear. In the present study such analysis is applied to migrating normal and transformed 3T3 cells. For normal cells, the lamellipodium provides almost all the forces for forward locomotion. A zone of high shear separates the lamellipodium from the cell body, suggesting that they are mechanically distinct entities. Timing and distribution of tractions at the leading edge bear no apparent relationship to local protrusive activities. However, changes in the pattern of traction forces often precede changes in the direction of migration. These observations suggest a frontal towing mechanism for cell migration, where dynamic traction forces at the leading edge actively pull the cell body forward. For H-ras transformed cells, pockets of weak, transient traction scatter among small pseudopods and appear to act against one another. The shear pattern suggests multiple disorganized mechanical domains. The weak, poorly coordinated traction forces, coupled with weak cell-substrate adhesions, are likely responsible for the abnormal motile behavior of H-ras transformed cells.

Focal adhesion kinase is involved in mechanosensing during fibroblast migration

Focal adhesion kinase (FAK) is a non-receptor protein tyrosine kinase localized at focal adhesions and is believed to mediate adhesion-stimulated effects. Although ablation of FAK impairs cell movement, it is not clear whether FAK might be involved in the guidance of cell migration, a role consistent with its putative regulatory function. We have transfected FAK-null fibroblasts with FAK gene under the control of the tetracycline repression system. Cells were cultured on flexible polyacrylamide substrates for the detection of traction forces and the application of mechanical stimulation. Compared with control cells expressing wild-type FAK, FAK-null cells showed a decrease in migration speed and directional persistence. In addition, whereas FAK-expressing cells responded to exerted forces by reorienting their movements and forming prominent focal adhesions, FAK-null cells failed to show such responses. Furthermore, FAK-null cells showed impaired responses to decreases in substrate flexibility, which causes control cells to generate weaker traction forces and migrate away from soft substrates. Cells expressing Y397F FAK, which cannot be phosphorylated at a key tyrosine site, showed similar defects in migration pattern and force-induced reorientation as did FAK-null cells. However, other aspects of F397-FAK cells, including the responses to substrate flexibility and the amplification of focal adhesions upon mechanical stimulation, were similar to that of control cells. Our results suggest that FAK plays an important role in the response of migrating cells to mechanical input. In addition, phosphorylation at Tyr-397 is required for some, but not all, of the functions of FAK in cell migration.

Extending the range of rate constants available from BIACORE: interpreting mass transport-influenced binding data.

Surface-based binding assays are often influenced by the transport of analyte to the sensor surface. Using simulated data sets, we test a simple two-compartment model to see if its description of transport and binding is sufficient to accurately analyze BIACORE data. First we present a computer model that can generate realistic BIACORE data. This model calculates the laminar flow of analyte within the flow cell, its diffusion both perpendicular and parallel to the sensor surface, and the reversible chemical reaction between analyte and immobilized reactant. We use this computer model to generate binding data under a variety of conditions. An analysis of these data sets with the two-compartment model demonstrates that good estimates of the intrinsic reaction rate constants are recovered even when mass transport influences the binding reaction. We also discuss the conditions under which the two-compartment model can be used to determine the diffusion coefficient of the analyte. Our results illustrate that this model can significantly extend the range of association rate constants that can be accurately determined from BIACORE.

Factors underlying spontaneous inactivation and susceptibility to neutralization of human immunodeficiency virus

To determine the factors governing inactivation and neutralization, physical, chemical, and biological assays were performed on a molecular clone of human immunodeficiency type 1 (HIV-1HXB3). This included quantitative electron microscopy, gp120 and p24 enzyme-linked immunosorbent assays, reverse, transcriptase assays, and quantitative infectivity assays. For freshly harvested stocks, the ratio of infectious to noninfectious viral particles ranged from 10(-4) to 10(-7) in viral stocks containing 10(9) to 10(10) physical particles per milliliter. There were relatively few gp120 knobs per HIV particle, mean approximately 10 when averaged over the total particle count. Each HIV particle contained a mean approximately 5 x 10(-17) g of p24 and approximately 2 x 10(-16) g of RNA polymerase, corresponding to about 1200 and 80 molecules, respectively. The spontaneous shedding of gp120 envelope proteins from virions was exponential, with a half-life approximately 30 hr. The loss of RNA polymerase activity in virons was also exponential, with a half-life approximately 40 hr. The physical breakup of virions and the dissolution of p24 core proteins were slow (half-life greater than 100 hr) compared to the gp120 shedding and polymerase loss rates. The decay of HIV-1 infectivity was found to obey superimposed single- and multihit kinetics. At short preincubation times, the loss of infectivity correlated with spontaneous shedding of gp120 from virions. At longer times, an accelerating decay rate indicated that HIV requires a minimal number of gp120 molecules for efficient infection of CD4+ cells. The blocking activity of recombinant soluble CD4 (sCD4) and phosphonoformate (foscarnet) varied with the number of gp120 molecules and number of active RNA polymerase molecules per virion, respectively. These results demonstrate that the physical state of virions greatly influences infectivity and neutralization. The knowledge gained from these findings will improve the reliability of in vitro assays, enhance the study of wild-type strains, and facilitate the evaluation of potential HIV therapeutics and vaccines.

Cell-Cell Mechanical Communication through Compliant Substrates

The role of matrix mechanics on cell behavior is under intense investigation. Cells exert contractile forces on their matrix and the matrix elasticity can alter these forces and cell migratory behavior. However, little is known about the contribution of matrix mechanics and cell-generated forces to stable cell-cell contact and tissue formation. Using matrices of varying stiffness and measurements of endothelial cell migration and traction stresses, we find that cells can detect and respond to substrate strains created by the traction stresses of a neighboring cell, and that this response is dependent on matrix stiffness. Specifically, pairs of endothelial cells display hindered migration on gels with elasticity below 5500 Pa in comparison to individual cells, suggesting these cells sense each other through the matrix. We believe that these results show for the first time that matrix mechanics can foster tissue formation by altering the relative motion between cells, promoting the formation of cell-cell contacts. Moreover, our data indicate that cells have the ability to communicate mechanically through their matrix. These findings are critical for the understanding of cell-cell adhesion during tissue formation and disease progression, and for the design of biomaterials intended to support both cell-matrix and cell-cell adhesion.

Responses of fibroblasts to anchorage of dorsal extracellular matrix receptors

Fibroblasts in 2D cultures differ dramatically in behavior from those in the 3D environment of a multicellular organism. However, the basis of this disparity is unknown. A key difference is the spatial arrangement of anchored extracellular matrix (ECM) receptors to the ventral surface in 2D cultures and throughout the entire surface in 3D cultures. Therefore, we asked whether changing the topography of ECM receptor anchorage alone could invoke a morphological response. By using polyacrylamide-based substrates to present anchored fibronectin or collagen on dorsal cell surfaces, we found that well spread fibroblasts in 2D cultures quickly changed into a bipolar or stellate morphology similar to fibroblasts in vivo. Cells in this environment lacked lamellipodia and large actin bundles and formed small focal adhesions only near focused sites of protrusion. These responses depend on substrate rigidity, calcium ion, and, likely, the calcium-dependent protease calpain. We suggest that fibroblasts respond to both spatial distribution and mechanical input of anchored ECM receptors. Changes in cell shape may in turn affect diverse cellular activities, including gene expression, growth, and differentiation, as shown in numerous previous studies.

Influence of Type I Collagen Surface Density on Fibroblast Spreading, Motility, and Contractility

We examine the relationships of three variables (projected area, migration speed, and traction force) at various type I collagen surface densities in a population of fibroblasts. We observe that cell area is initially an increasing function of ligand density, but that above a certain transition level, increases in surface collagen cause cell area to decline. The threshold collagen density that separates these two qualitatively different regimes, approximately 160 molecules/ microm(2), is approximately equal to the cell surface density of integrin molecules. These results suggest a model in which collagen density induces a qualitative transition in the fundamental way that fibroblasts interact with the substrate. At low density, the availability of collagen binding sites is limiting and the cells simply try to flatten as much as possible by pulling on the few available sites as hard as they can. The force per bond under these conditions approaches 100 pN, approximately equal to the force required for rupture of integrin-peptide bonds. In contrast, at high collagen density adhesion, traction force and motility are limited by the availability of free integrins on the cell surface since so many of these receptors are bound to the surface ligand and the force per bond is very low.