Distinct roles of frontal and rear cell-substrate adhesions in fibroblast migration.

Cell migration involves complex physical and chemical interactions with the substrate. To probe the mechanical interactions under different regions of migrating 3T3 fibroblasts, we have disrupted cell-substrate adhesions by local application of the GRGDTP peptide, while imaging stress distribution on the substrate with traction force microscopy. Both spontaneous and GRGDTP-induced detachment of the trailing edge caused extensive cell shortening, without changing the overall level of traction forces or the direction of migration. In contrast, disruption of frontal adhesions caused dramatic, global loss of traction forces before any significant shortening of the cell. Although traction forces and cell migration recovered within 10-20 min of transient frontal treatment, persistent treatment with GRGDTP caused the cell to develop traction forces elsewhere and reorient toward a new direction. We conclude that contractile forces of a fibroblast are transmitted to the substrate through two distinct types of adhesions. Leading edge adhesions are unique in their ability to transmit active propulsive forces. Their functions cannot be transferred directly to existing adhesions upon detachment. Trailing end adhesions create passive resistance during cell migration and readily redistribute their loads upon detachment. Our results indicate the distinct nature of mechanical interactions at the leading versus trailing edges, which together generate the mechanical interactions for fibroblast migration.

Aspiration of human neutrophils: effects of shear thinning and cortical dissipation.

It is generally accepted that the human neutrophil can be mechanically represented as a droplet of polymeric fluid enclosed by some sort of thin slippery viscoelastic cortex. Many questions remain however about the detailed rheology and chemistry of the interior fluid and the cortex. To address these quantitative issues, we have used a finite element method to simulate the dynamics of neutrophils during micropipet aspiration using various plausible assumptions. The results were then systematically compared with aspiration experiments conducted at eight different combinations of pipet size and pressure. Models in which the cytoplasm was represented by a simple Newtonian fluid (i.e., models without shear thinning) were grossly incapable of accounting for the effects of pressure on the general time scale of neutrophil aspiration. Likewise, models in which the cortex was purely elastic (i.e., models without surface viscosity) were unable to explain the effects of pipet size on the general aspiration rate. Such models also failed to explain the rapid acceleration of the aspiration rate during the final phase of aspiration nor could they account for the geometry of the neutrophil during various phases of aspiration. Thus, our results indicate that a minimal mechanical model of the neutrophil needs to incorporate both shear thinning and surface viscosity to remain valid over a reasonable range of conditions. At low shear rates, the surface dilatation viscosity of the neutrophil was found to be on the order of 100 poise-cm, whereas the viscosity of the interior cytoplasm was on the order of 1000 poise. Both the surface viscosity and the interior viscosity seem to decrease in a similar fashion when the shear rate exceeds approximately 0.05 s(-1). Unfortunately, even models with both surface viscosity and shear thinning studied are still not sufficient to fully explain all the features of neutrophil aspiration. In particular, the very high rate of aspiration during the initial moments after ramping of pressure remains mysterious.

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.

Nascent focal adhesions are responsible for the generation of strong propulsive forces in migrating fibroblasts.

Fibroblast migration involves complex mechanical interactions with the underlying substrate. Although tight substrate contact at focal adhesions has been studied for decades, the role of focal adhesions in force transduction remains unclear. To address this question, we have mapped traction stress generated by fibroblasts expressing green fluorescent protein (GFP)-zyxin. Surprisingly, the overall distribution of focal adhesions only partially resembles the distribution of traction stress. In addition, detailed analysis reveals that the faint, small adhesions near the leading edge transmit strong propulsive tractions, whereas large, bright, mature focal adhesions exert weaker forces. This inverse relationship is unique to the leading edge of motile cells, and is not observed in the trailing edge or in stationary cells. Furthermore, time-lapse analysis indicates that traction forces decrease soon after the appearance of focal adhesions, whereas the size and zyxin concentration increase. As focal adhesions mature, changes in structure, protein content, or phosphorylation may cause the focal adhesion to change its function from the transmission of strong propulsive forces, to a passive anchorage device for maintaining a spread cell morphology.

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.

Substrate flexibility regulates growth and apoptosis of normal but not transformed cells.

One of the hallmarks of oncogenic transformation is anchorage-independent growth (27). Here we demonstrate that responses to substrate rigidity play a major role in distinguishing the growth behavior of normal cells from that of transformed cells. We cultured normal or H-ras-transformed NIH 3T3 cells on flexible collagen-coated polyacrylamide substrates with similar chemical properties but different rigidity. Compared with cells cultured on stiff substrates, nontransformed cells on flexible substrates showed a decrease in the rate of DNA synthesis and an increase in the rate of apoptosis. These responses on flexible substrates are coupled to decreases in cell spreading area and traction forces. In contrast, transformed cells maintained their growth and apoptotic characteristics regardless of substrate flexibility. The responses in cell spreading area and traction forces to substrate flexibility were similarly diminished. Our results suggest that normal cells are capable of probing substrate rigidity and that proper mechanical feedback is required for regulating cell shape, cell growth, and survival. The loss of this response can explain the unregulated growth of transformed cells.

Cell movement is guided by the rigidity of the substrate.

Directional cell locomotion is critical in many physiological processes, including morphogenesis, the immune response, and wound healing. It is well known that in these processes cell movements can be guided by gradients of various chemical signals. In this study, we demonstrate that cell movement can also be guided by purely physical interactions at the cell-substrate interface. We cultured National Institutes of Health 3T3 fibroblasts on flexible polyacrylamide sheets coated with type I collagen. A transition in rigidity was introduced in the central region of the sheet by a discontinuity in the concentration of the bis-acrylamide cross-linker. Cells approaching the transition region from the soft side could easily migrate across the boundary, with a concurrent increase in spreading area and traction forces. In contrast, cells migrating from the stiff side turned around or retracted as they reached the boundary. We call this apparent preference for a stiff substrate "durotaxis." In addition to substrate rigidity, we discovered that cell movement could also be guided by manipulating the flexible substrate to produce mechanical strains in the front or rear of a polarized cell. We conclude that changes in tissue rigidity and strain could play an important controlling role in a number of normal and pathological processes involving cell locomotion.

Separation of propulsive and adhesive traction stresses in locomoting keratocytes.

Strong, actomyosin-dependent, pinching tractions in steadily locomoting (gliding) fish keratocytes revealed by traction imaging present a paradox, since only forces perpendicular to the direction of locomotion are apparent, leaving the actual propulsive forces unresolved. When keratocytes become transiently "stuck" by their trailing edge and adopt a fibroblast-like morphology, the tractions opposing locomotion are concentrated into the tail, leaving the active pinching and propulsive tractions clearly visible under the cell body. Stuck keratocytes can develop approximately 1 mdyn (10,000 pN) total propulsive thrust, originating in the wings of the cell. The leading lamella develops no detectable propulsive traction, even when the cell pulls on its transient tail anchorage. The separation of propulsive and adhesive tractions in the stuck phenotype leads to a mechanically consistent hypothesis that resolves the traction paradox for gliding keratocytes: the propulsive tractions driving locomotion are normally canceled by adhesive tractions resisting locomotion, leaving only the pinching tractions as a resultant. The resolution of the traction pattern into its components specifies conditions to be met for models of cytoskeletal force production, such as the dynamic network contraction model (Svitkina, T.M., A.B. Verkhovsky, K.M. McQuade, and G.G. Borisy. 1997. J. Cell Biol. 139:397-415). The traction pattern associated with cells undergoing sharp turns differs markedly from the normal pinching traction pattern, and can be accounted for by postulating an asymmetry in contractile activity of the opposed lateral wings of the cell.

Cytoplasm dynamics and cell motion: two-phase flow models.

The motion of amoeboid cells is characterized by cytoplasmic streaming and by membrane protrusions and retractions which occur even in the absence of interactions with a substratum. Cell translocation requires, in addition, a transmission mechanism wherein the power produced by the cytoplasmic engine is applied to the substratum in a highly controlled fashion through specific adhesion proteins. Here we present a simple mechano-chemical model that tries to capture the physical essence of these complex biomolecular processes. Our model is based on the continuum equations for a viscous and reactive two-phase fluid model with moving boundaries, and on force balance equations that average the stochastic interactions between actin polymers and membrane proteins. In this paper we present a new derivation and analysis of these equations based on minimization of a power functional. This derivation also leads to a clear formulation and classification of the kinds of boundary conditions that should be specified at free surfaces and at the sites of interaction of the cell and the substratum. Numerical simulations of a one-dimensional lamella reveal that even this extremely simplified model is capable of producing several typical features of cell motility. These include periodic 'ruffle' formation, protrusion-retraction cycles, centripetal flow and cell-substratum traction forces.

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.

Hydrodynamics of micropipette aspiration.

The dynamics of human neutrophils during micropipette aspiration are frequently analyzed by approximating these cells as simple slippery droplets of viscous fluid. Here, we present computations that reveal the detailed predictions of the simplest and most idealized case of such a scheme; namely, the case where the fluid of the droplet is homogeneous and Newtonian, and the surface tension of the droplet is constant. We have investigated the behavior of this model as a function of surface tension, droplet radius, viscosity, aspiration pressure, and pipette radius. In addition, we have tabulated a dimensionless factor, M, which can be utilized to calculate the apparent viscosity of the slippery droplet. Computations were carried out using a low Reynolds number hydrodynamics transport code based on the finite-element method. Although idealized and simplistic, we find that the slippery droplet model predicts many observed features of neutrophil aspiration. However, there are certain features that are not observed in neutrophils. In particular, the model predicts dilation of the membrane past the point of being continuous, as well as a reentrant jet at high aspiration pressures.

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.

[Breath-hold 3D MR urography with 2 ml Gd-DTPA injection].

Breath-hold gadolinium-enhanced 3D MR urography was performed in five healthy volunteers. Enhanced 3D fast gradient-echo with a spectral IR pulse sequence was used for depicting MR urography, which was obtained 5-10 minutes after the injection of 2 ml of gadopentate dimeglumine (0.013-0.02 mmol/kg). The urinary tract was depicted as a high-signal intensity area, and detectability of the non-dilated urinary tracts was superior to that of heavy T2-weighted images. At the same time, comparison between the urinary tract and vascular structure could be made using breath-hold contrast-enhanced 3D MR angiography with an additional Gd-DTPA injection.

On the mechanics of the first cleavage division of the sea urchin egg.

We describe a continuum model of the sea urchin egg during the first cleavage division. Using estimated values of the relevant mechanical parameters we then carry out numerical simulations of cytokinesis and conduct a systematic comparison of these computations with a variety of published experimental data.

Modeling the reversible kinetics of neutrophil aggregation under hydrodynamic shear.

Neutrophil emigration into inflamed tissue is mediated by beta 2-integrin and L-selectin adhesion receptors. Homotypic neutrophil aggregation is also dependent on these molecules, and it provides a model system in which to study adhesion dynamics. In the current study we formulated a mathematical model for cellular aggregation in a linear shear field based on Smoluchowski's two-body collision theory. Neutrophil suspensions activated with chemotactic stimulus and sheared in a cone-plate viscometer rapidly aggregate. Over a range of shear rates (400-800 s-1), approximately 90% of the single cells were recruited into aggregates ranging from doublets to groupings larger than sextuplets. The adhesion efficiency fit to these kinetics reached maximum levels of > 70%. Formed aggregates remained intact and resistant to shear up to 120 s, at which time they spontaneously dissociated back to singlets. The rate of cell disaggregation was linearly proportional to the applied shear rate, and it was approximately 60% lower for doublets as compared to larger aggregates. By accounting for the time-dependent changes in adhesion efficiency, disaggregation rate, and the effects of aggregate geometry, we succeeded in predicting the reversible kinetics of aggregation over a wide range of shear rates and cell concentrations. The combination of viscometry with flow cytometry and mathematical analysis as presented here represents a novel approach to differentiating between the effects of hydrodynamics and the intrinsic biological processes that control cell adhesion.

Numerical simulation of oil-droplet cleavage by surfactant.

We present numerical computations of the deformation of an oil-droplet under the influence of a surface tension gradient generated by the surfactant released at the poles (the Greenspan experiment). We find this deformation to be very small under the pure surface tension gradient. To explain the large deformation of oil droplets observed in Greenspan's experiments, we propose the existence of a phoretic force generated by the concentration gradient of the surfactant. We show that this hypothesis successfully explains the available experimental data and we propose some further tests.

Imaging the traction stresses exerted by locomoting cells with the elastic substratum method.

The cytoskeletal activity of motile or adherent cells is frequently seen to induce detectable displacements of sufficiently compliant substrata. The physics of this phenomenon is discussed in terms of the classical theory of small-strain, plane-stress elasticity. The main results of such analysis is a transform expressing the displacement field of the elastic substrate as an integral over the traction field. The existence of this transform is used to derive a Bayesian method for converting noisy measurements of substratum displacement into "images" of the actual traction forces exerted by adherent or locomoting cells. Finally, the Monte Carlo validation of the statistical method is discussed, some new rheological studies of films are presented, and a practical application is given.

Modeling chemoattractant-elicited relocalization of myosin filaments in Dictyostelium.

Dictyostelium myosin is able to assemble into filaments that, when visualized under normal conditions, appear to be uniformly distributed throughout the cytoplasm. After stimulation by the chemoattractant cAMP, these filaments quickly diminish in the cellular medulla and accumulate in the cortex. A general hypothesis to explain the mechanism of this relocalization proposes that one or more of the chemical coefficients governing filament polymerization is precisely regulated by some sort of intracellular second messenger. To investigate this hypothesis we formulated a simple theoretical model of myosin polymerization and then used this model to analyze the resting state of the cell and various scenarios for initializing a transition to the activated state. In general, we found that the relocalization of filaments could be realized if a second messenger increased the elongation and (or) the nucleation coefficients for filament assembly in cortical ectoplasm and (or) if the messenger decreased these parameters in the cellular medulla. By comparing these limiting cases with experimental observations, we concluded that models in which redistribution of myosin is achieved by decreasing filament stability in the medulla are the most likely candidates.