Pseudopod projection and cell spreading of passive leukocytes in response to fluid shear stress

Recent evidence suggests that circulating leukocytes respond to physiological levels of fluid shear stress. This study was designed to examine the shear stress response of individual leukocytes adhering passively to a glass surface. Human leukocytes were exposed to a step fluid shear stress with amplitude between 0.2 and 4 dyn/cm(2) and duration between 1 and 20 min. The response of the cells was determined in the form of projected cell area measurements by high-resolution observation before, during, and after fluid shear application. All cells selected initially had a round morphology. After application of fluid shear many cells projected pseudopodia and spread on the glass surface. The number of leukocytes responding with pseudopod projection and the extent of cell spreading increased with increasing amplitude and duration of fluid shear stress. Pseudopod projection after exposure to a step fluid shear occurs following a delay that is insensitive to the shear stress amplitude and duration. Leukocytes that did not project pseudopodia and spread in response to low shear stress could be shown to respond to a second shear step of higher amplitude. The spreading response requires an intact actin network and activated myosin molecules. Depleting the cell glycocalyx with protease treatment enhances the spreading response in sheared leukocytes. These results indicate that passive leukocytes respond to fluid shear stress with active pseudopod projection and cell spreading. This behavior may contribute to cell spreading on endothelium and other cells as well as to transendothelial migration of leukocytes in the microcirculation.     

The fluid shear stress distribution on the membrane of leukocytes in the microcirculation

Recent in-vivo and in-vitro evidence indicates that fluid shear stress on the membrane of leukocytes has a powerful control over several aspects of their cell function. This evidence raises a question about the magnitude of the fluid shear stress on leukocytes in the circulation. The flow of plasma on the surface of a leukocyte at a very low Reynolds number is governed by the Stokes equation for the motion of a Newtonian fluid. We numerically estimated the distribution of fluid shear stress on a leukocyte membrane in a microvessel for the cases when the leukocyte is freely suspended, as well as rolling along or attached to a microvessel wall. The results indicate that the fluid shear stress distribution on the leukocyte membrane is nonuniform with a sharp increase when the leukocyte makes membrane attachment to the microvessel wall. In a microvessel (10 microns diameter), the fluid shear stress on the membrane of a freely suspended leukocyte (8 microns diameter) is estimated to be several times larger than the wall shear stress exerted by the undisturbed Poiseuille flow, and increases on an adherent leukocyte up to ten times. High temporal stress gradients are present in freely suspended leukocytes in shear flow due to cell rotation, which are proportional to the local shear rate. In comparison, the temporal stress gradients are reduced on the membrane of leukocytes that are rolling or firmly adhered to the endothelium. High temporal gradients of shear stress are also present on the endothelial wall. At a plasma viscosity of 1 cPoise, the peak shear stresses for suspended and adherent leukocytes are of the order of 10 dyn/cm2 and 100 dyn/cm2, respectively.     

Control of neutrophil pseudopods by fluid shear: role of Rho family GTPases

Blood vessels and blood cells are under continuous fluid shear. Studies on vascular endothelium and smooth muscle cells have shown the importance of this mechanical stress in cell signal transduction, gene expression, vascular remodeling, and cell survival. However, in circulating leukocytes, shear-induced signal transduction has not been investigated. Here we examine in vivo and in vitro the control of pseudopods in leukocytes under the influence of fluid shear stress and the role of the Rho family small GTPases. We used a combination of HL-60 cells differentiated into neutrophils (1.4% dimethyl sulfoxide for 5 days) and fresh leukocytes from Rac knockout mice. The cells responded to shear stress (5 dyn/cm²) with retraction of pseudopods and reduction of their projected cell area. The Rac1 and Rac2 activities were decreased by fluid shear in a time- and magnitude-dependent manner, whereas the Cdc42 activity remained unchanged (up to 5 dyn/cm²). The Rho activity was transiently increased and recovered to static levels after 10 min of shear exposure (5 dyn/cm²). Inhibition of either Rac1 or Rac2 slightly but significantly diminished the fluid shear response. Transfection with Rac1-positive mutant enhanced the pseudopod formation during shear. Leukocytes from Rac1-null and Rac2-null mice had an ability to form pseudopods in response to platelet-activating factor but did not respond to fluid shear in vitro. Leukocytes in wild-type mice retracted pseudopods after physiological shear exposure, whereas cells in Rac1-null mice showed no retraction during equal shear. On leukocytes from Rac2-null mice, however, fluid shear exerted a biphasic effect. Leukocytes with extended pseudopods slightly decreased in length, whereas initially round cells increased in length after shear application. The disruption of Rac activity made leukocytes nonresponsive to fluid shear, induced cell adhesion and microvascular stasis, and decreased microvascular density. These results suggest that deactivation of Rac activity by fluid shear plays an important role in stable circulation of leukocytes. microcirculation; mechanotransduction; actin polymerization; transgenic mouse; leukocyte     

G protein-coupled receptors serve as mechanosensors for fluid shear stress in neutrophils

Many cells respond to fluid shear stress but in a cell type-specific fashion. Fluid shear stress applied to leukocytes serves to control pseudopod formation, migration, and other functions. Specifically, fresh neutrophils or neutrophilic leukocytes derived from differentiated HL60 cells respond to fluid shear stress by cytoplasmic pseudopod retraction. The membrane elements that sense fluid shear and induce such a specific response are still unknown, however. We hypothesized that membrane receptors may serve as fluid shear sensors. We found that fluid shear decreased the constitutive activity of G protein-coupled receptors (GPCRs). Inhibition of GPCR constitutive activity by inverse agonists abolished fluid shear stress-induced cell area reduction. Among the GPCRs in neutrophils, the formyl peptide receptor (FPR) exhibits relatively high constitutive activity. Undifferentiated HL60 cells that lacked FPR formed few pseudopods and showed no detectable response to fluid shear stress, whereas expression of FPR in undifferentiated HL60 cells caused pseudopod projection and robust pseudopod retraction during fluid shear. FPR small interfering RNA-transfected differentiated HL60 cells exhibited no response to fluid shear stress. These results suggest that GPCRs serve as mechanosensors for fluid shear stress in neutrophils by decreasing its constitutive activity and reducing pseudopod projection. leukocyte; constitutive activity; mechanotransduction; formyl peptide receptor     

Short-Term Shear Stress Induces Rapid Actin Dynamics in Living Endothelial Cells

Hemodynamic shear stress guides a variety of endothelial phenotype characteristics, including cell morphology, cytoskeletal structure, and gene expression profile. The sensing and processing of extracellular fluid forces may be mediated by mechanotransmission through the actin cytoskeleton network to intracellular locations of signal initiation. In this study, we identify rapid actin-mediated morphological changes in living subconfluent and confluent bovine aortic endothelial cells (ECs) in response to onset of unidirectional steady fluid shear stress (15 dyn/cm²). After flow onset, subconfluent cells exhibited dynamic edge activity in lamellipodia and small ruffles in the downstream and side directions for the first 12 min; activity was minimal in the upstream direction. After 12 min, peripheral edge extension subsided. Confluent cell monolayers that were exposed to shear stress exhibited only subtle increases in edge fluctuations after flow onset. Addition of cytochalasin D to disrupt actin polymerization served to suppress the magnitude of flow-mediated actin remodeling in both subconfluent confluent EC monolayers. Interestingly, when subconfluent ECs were exposed to two sequential flow step increases (1 dyn/cm² followed by 15 dyn/cm² 12 min later), actin-mediated edge activity was not additionally increased after the second flow step. Thus, repeated flow increases served to desensitize mechanosensitive structural dynamics in the actin cytoskeleton.     

Cooperative Effects of Matrix Stiffness and Fluid Shear Stress on Endothelial Cell Behavior

Arterial hemodynamic shear stress and blood vessel stiffening both significantly influence the arterial endothelial cell (EC) phenotype and atherosclerosis progression, and both have been shown to signal through cell-matrix adhesions. However, the cooperative effects of fluid shear stress and matrix stiffness on ECs remain unknown. To investigate these cooperative effects, we cultured bovine aortic ECs on hydrogels matching the elasticity of the intima of compliant, young, or stiff, aging arteries. The cells were then exposed to laminar fluid shear stress of 12 dyn/cm². Cells grown on more compliant matrices displayed increased elongation and tighter EC-cell junctions. Notably, cells cultured on more compliant substrates also showed decreased RhoA activation under laminar shear stress. Additionally, endothelial nitric oxide synthase and extracellular signal-regulated kinase phosphorylation in response to fluid shear stress occurred more rapidly in ECs cultured on more compliant substrates, and nitric oxide production was enhanced. Together, our results demonstrate that a signaling cross talk between stiffness and fluid shear stress exists within the vascular microenvironment, and, importantly, matrices mimicking young and healthy blood vessels can promote and augment the atheroprotective signals induced by fluid shear stress. These data suggest that targeting intimal stiffening and/or the EC response to intima stiffening clinically may improve vascular health.     

Role of shear forces and adhesion molecule distribution on P-selectin-mediated leukocyte rolling in postcapillary venules

Rolling on the venular endothelium is a critical step in the recruitment of leukocytes during the inflammatory response. P-selectin is a key mediator of leukocyte rolling, which is an early event in the inflammatory cascade; this rolling is likely to be directly regulated by both local fluid shear forces and P-selectin site densities in the microvasculature. However, neither the spatial pattern of P-selectin expression in postcapillary venules nor the effect of local expression patterns on rolling behavior in intact functional venules is known. We investigated the influence of local shear forces and the spatial distribution of endothelial P-selectin in intact blood perfused post capillary venules in anesthetized mice using intravital confocal microscopy, high temporal resolution particle tracking, and immunofluorescent labeling. We demonstrated a shear-dependent increase in average leukocyte rolling velocity that was attributable to a shear-dependent increase in the occurrence of transient leukocyte detachments from the endothelial surface: translational velocity during leukocyte contact with the vessel wall remained constant. P-selectin expression was not different in venules with characteristically different shear rates or diameters but varied significantly within individual venules. In postcapillary venules, regions of high P-selectin expression correlated with regions of slow leukocyte rolling. Thus the characteristically variable leukocyte rolling in vivo is a function of the spatial heterogeneity in P-selectin expression. The study shows how the local hydrodynamic forces and the nonuniform pattern of P-selectin expression affect the behavior of interacting leukocytes, providing direct evidence for the local variation of adhesion molecule expression as a mechanism for the regulation of leukocyte recruitment.     

Threshold Levels of Fluid Shear Promote Leukocyte Adhesion through Selectins (CD62L,P,E)

Leukocyte adhesion through L-selectin to peripheral node addressin (PNAd, also known as MECA-79 antigen), an L-selectin ligand expressed on high endothelial venules, has been shown to require a minimum level of fluid shear stress to sustain rolling interactions (Finger, E.B., K.D. Puri, R. Alon, M.B. Lawrence, V.H. von Andrian, and T.A. Springer. 1996. Nature (Lond.). 379:266–269). Here, we show that fluid shear above a threshold of 0.5 dyn/cm² wall shear stress significantly enhances HL-60 myelocyte rolling on P- and E-selectin at site densities of 200/μm² and below. In addition, gravitational force is sufficient to detach HL60 cells from P- and E-selectin substrates in the absence, but not in the presence, of flow. It appears that fluid shear–induced torque is critical for the maintenance of leukocyte rolling. K562 cells transfected with P-selectin glycoprotein ligand-1, a ligand for P-selectin, showed a similar reduction in rolling on P-selectin as the wall shear stress was lowered below 0.5 dyn/cm². Similarly, 300.19 cells transfected with L-selectin failed to roll on PNAd below this level of wall shear stress, indicating that the requirement for minimum levels of shear force is not cell type specific. Rolling of leukocytes mediated by the selectins could be reinitiated within seconds by increasing the level of wall shear stress, suggesting that fluid shear did not modulate receptor avidity. Intravital microscopy of cremaster muscle venules indicated that the leukocyte rolling flux fraction was reduced at blood centerline velocities less than 1 mm/s in a model in which rolling is mediated by L- and P-selectin. Similar observations were made in L-selectin–deficient mice in which leukocyte rolling is entirely P-selectin dependent. Leukocyte adhesion through all three selectins appears to be significantly enhanced by a threshold level of fluid shear stress.     

Probing Cell Structure Responses Through a Shear and Stretching Mechanical Stimulation Technique

Cells are complex, dynamic systems that respond to various in vivo stimuli including chemical, mechanical, and scaffolding alterations. The influence of mechanics on cells is especially important in physiological areas that dictate what modes of mechanics exist. Complex, multivariate physiological responses can result from multi-factorial, multi-mode mechanics, including tension, compression, or shear stresses. In this study, we present a novel device based on elastomeric materials that allowed us to stimulate NIH 3T3 fibroblasts through uniaxial strip stretching or shear fluid flow. Cell shape and structural response was observed using conventional approaches such as fluorescent microscopy. Cell orientation and actin cytoskeleton alignment along the direction of applied force were observed to occur after an initial 3 h time period for shear fluid flow and static uniaxial strip stretching experiments although these two directions of alignment were oriented orthogonal relative to each other. This response was then followed by an increasingly pronounced cell and actin cytoskeleton alignment parallel to the direction of force after 6, 12, and 24 h, with 85% of the cells aligned along the direction of force after 24 h. These results indicate that our novel device could be implemented to study the effects of multiple modes of mechanical stimulation on living cells while probing their structural response especially with respect to competing directions of alignment and orientation under these different modes of mechanical stimulation. We believe that this will be important in a diversity of fields including cell mechanotransduction, cell–material interactions, biophysics, and tissue engineering.     

Endothelial actin cytoskeleton remodeling during mechanostimulation with fluid shear stress

Fluid shear stress stimulation induces endothelial cells to elongate and align in the direction of applied flow. Using the complementary techniques of photoactivation of fluorescence and fluorescence recovery after photobleaching, we have characterized endothelial actin cytoskeleton dynamics during the alignment process in response to steady laminar fluid flow and have correlated these results to motility. Alignment requires 24 h of exposure to fluid flow, but the cells respond within minutes to flow and diminish their movement by 50%. Although movement slows, the actin filament turnover rate increases threefold and the percentage of total actin in the polymerized state decreases by 34%, accelerating actin filament remodeling in individual cells within a confluent endothelial monolayer subjected to flow to levels used by dispersed nonconfluent cells under static conditions for rapid movement. Temporally, the rapid decrease in filamentous actin shortly after flow stimulation is preceded by an increase in actin filament turnover, revealing that the earliest phase of the actin cytoskeletal response to shear stress is net cytoskeletal depolymerization. However, unlike static cells, in which cell motility correlates positively with the rate of filament turnover and negatively with the amount polymerized actin, the decoupling of enhanced motility from enhanced actin dynamics after shear stress stimulation supports the notion that actin remodeling under these conditions favors cytoskeletal remodeling for shape change over locomotion. Hours later, motility returned to pre-shear stress levels but actin remodeling remained highly dynamic in many cells after alignment, suggesting continual cell shape optimization. We conclude that shear stress initiates a cytoplasmic actin-remodeling response that is used for endothelial cell shape change instead of bulk cell translocation. atherosclerosis; cytoskeletal dynamics; endothelial cells; mechanotransduction     

Spatiotemporal analysis of flow-induced intermediate filament displacement in living endothelial cells

The distribution of hemodynamic shear stress throughout the arterial tree is transduced by the endothelium into local cellular responses that regulate vasoactivity, vessel wall remodeling, and atherogenesis. Although the exact mechanisms of mechanotransduction remain unknown, the endothelial cytoskeleton has been implicated in transmitting extracellular force to cytoplasmic sites of signal generation via connections to the lumenal, intercellular, and basal surfaces. Direct observation of intermediate filament (IF) displacement in cells expressing green fluorescent protein-vimentin has suggested that cytoskeletal mechanics are rapidly altered by the onset of fluid shear stress. Here, restored images from time-lapse optical sectioning fluorescence microscopy were analyzed as a four-dimensional intensity distribution function that represented IF positions. A displacement index, related to the product moment correlation coefficient as a function of time and subcellular spatial location, demonstrated patterns of IF displacement within endothelial cells in a confluent monolayer. Flow onset induced a significant increase in IF displacement above the nucleus compared with that measured near the coverslip surface, and displacement downstream from the nucleus was larger than in upstream areas. Furthermore, coordinated displacement of IF near the edges of adjacent cells suggested the existence of mechanical continuity between cells. Thus, quantitative analysis of the spatiotemporal patterns of flow-induced IF displacement suggests redistribution of intracellular force in response to alterations in hemodynamic shear stress acting at the lumenal surface.     

Leukocytes rolling and recruitment by endothelial cells: hemorheological experiments and numerical simulations

The recruitment of leukocytes from the blood stream and their subsequent adhesion to endothelial walls are essential stages to the immune response system during inflammation. The precise dynamic mechanisms by which molecular mediators facilitate leukocyte arrests are still unknown. In this study combined experimental results and computer simulations are used to investigate localized hydrodynamics of individual and collective behavior of clusters of leukocytes. Leukocyte-endothelial cell interactions in post-capillary venules of Wistar rats cremaster muscle were monitored by intravital microscopy. From these experiments the hemorheologic and hemodynamical measured parameters were used in time dependent three-dimensional computer simulations, using a mesoscopic lattice Boltzmann flow solver for shear thinning fluids. The dynamics of leukocyte clusters under generalized Newtonian blood flow with shear thinning viscosity was computed and discussed. In this paper we present quantified distributions of velocity and shear stress on the surface of leukocytes and near vessel wall attachment points. We have observed one region of maximum shear stress and two regions of minimum shear stress on the surface of leukocytes close to the endothelial wall. We verified that the collective hydrodynamic behavior of the cluster of recruited leukocytes establishes a strong motive for additional leukocyte recruitment. It was found that the lattice Boltzmann solver used here is fully adaptive to the measured experimental parameters. This study suggests that the influence of the leukocytes rolling on the increase of the endothelial wall shear stress may support the activation of more signalling mediators during inflammation.     

Mapping the dynamics of shear stress-induced structural changes in endothelial cells

Hemodynamic shear stress regulates endothelial cell biochemical processes that govern cytoskeletal contractility, focal adhesion dynamics, and extracellular matrix (ECM) assembly. Since shear stress causes rapid strain focusing at discrete locations in the cytoskeleton, we hypothesized that shear stress coordinately alters structural dynamics in the cytoskeleton, focal adhesion sites, and ECM on a time scale of minutes. Using multiwavelength four-dimensional fluorescence microscopy, we measured the displacement of rhodamine-fibronectin and green fluorescent protein-labeled actin, vimentin, paxillin, and/or vinculin in aortic endothelial cells before and after onset of steady unidirectional shear stress. In the cytoskeleton, the onset of shear stress increased actin polymerization into lamellipodia, altered the angle of lateral displacement of actin stress fibers and vimentin filaments, and decreased centripetal remodeling of actin stress fibers in subconfluent and confluent cell layers. Shear stress induced the formation of new focal complexes and reduced the centripetal remodeling of focal adhesions in regions of new actin polymerization. The structural dynamics of focal adhesions and the fibronectin matrix varied with cell density. In subconfluent cell layers, shear stress onset decreased the displacement of focal adhesions and fibronectin fibrils. In confluent monolayers, the direction of fibronectin and focal adhesion displacement shifted significantly toward the downstream direction within 1 min after onset of shear stress. These spatially coordinated rapid changes in the structural dynamics of cytoskeleton, focal adhesions, and ECM are consistent with focusing of mechanical stress and/or strain near major sites of shear stress-mediated mechanotransduction.     

Model for the alignment of actin filaments in endothelial cells subjected to fluid shear stress

Cultured vascular endothelial cells undergo significant morphological changes when subjected to sustained fluid shear stress. The cells elongate and align in the direction of applied flow. Accompanying this shape change is a reorganization at the intracellular level. The cytoskeletal actin filaments reorient in the direction of the cells' long axis. How this external stimulus is transmitted to the endothelial cytoskeleton still remains unclear. In this article. we present a theoretical model accounting for the cytoskeletal reorganization under the influence of fluid shear stress. We develop a system of integro-partial-differential equations describing the dynamics of actin filaments, the actin-binding proteins, and the drift of transmembrane proteins due to the fluid shear forces applied on the plasma membrane. Numerical simulations of the equations show that under certain conditions, initially randomly oriented cytoskeletal actin filaments reorient in structures parallel to the externally applied fluid shear forces. Thus, the model suggests a mechanism by which shear forces acting on the cell membrane can be transmitted to the entire cytoskeleton via molecular interactions alone.     

Deformation mechanism of leukocyte adhering to vascular surface under steady shear flow

The adhesion of leukocytes to vascular surface is an important biomedical problem and has drawn extensive attention. In this study, we propose a compound drop model to simulate a leukocyte with a nucleus adhering to the surface of blood vessel under steady shear flow. A two-dimensional computational fluid dynamics (CFD) is conducted to determine the local distribution of pressure on the surface of the adherent model cell. By introducing the parameter of deformation index (DI), we investigate the deformation of the leukocyte and its nucleus under controlled conditions. Our numerical results show that: (i) the leukocyte is capable of deformation under external exposed flow field. The deformation index increases with initial contact angle and Reynolds number of external exposed flow. (ii) The nucleus deforms with the cell, and the deformation index of the leukocyte is greater than that of the nucleus. The leukocyte is more deformable while the nucleus is more capable of resisting external shear flow. (iii) The leukocyte and the nucleus are not able to deform infinitely with the increase of Reynolds number because the deformation index reaches a maximum. (iv) Pressure distribution confirms that there exists a region downstream of the cell, which produces high pressure to retard continuous deformation and provide a positive lift force on the cell. Meanwhile, we have measured the deformation of human leukocytes exposed to shear flow by using a flow chamber system. We found that the numerical results are well consistent with those of experiment. We conclude that the nucleus with high viscosity plays a particular role in leukocyte deformation.     

Deformation mechanism of leukocyte adhering to vascular surface under steady shear flow

~~Deformation mechanism of leukocyte adhering to vascular surface under steady shear flow~~     

Mechanotransduction in leukocyte activation: a review

We review recent evidence which suggests that leukocytes in the circulation and in the tissue may readily respond to physiological levels of fluid shear stress in the range between about 1 and 10 dyn/cm 2, a range that is below the level to achieve a significant passive, viscoelastic response. The response of activated neutrophilic leukocytes to fluid shear consists of a rapid retraction of lamellipodia with membrane detachment from integrin binding sites. In contrast, a subgroup of non-activated neutrophils may project pseudopods after exposure to fluid shear stress. The evidence suggests that G-protein coupled receptor downregulation by fluid shear with concomitant downregulation of Rac-related small GTPases and depolymerization of F-actin serves to retract the lamellipodia in conjunction with proteolytic cleavage of beta 2 integrin to facilitate membrane detachment. Furthermore, there exists a mechanism to up- and down-regulate the fluid shear-response, which involves nitric oxide and the second messenger cyclic guanosine monophosphate (cGMP). Many physiological activities of circulating leukocytes are under the influence of fluid shear stress, including transendothelial migration of lymphocytes. We describe a disease model with chronic hypertension that suffers from an attenuated fluid shear-response with far reaching implications for microvascular blood flow.     

Shear stress-induced endothelial cell polarization is mediated by Rho and Rac but not Cdc42 or PI 3-kinases

Shear stress induces endothelial polarization and migration in the direction of flow accompanied by extensive remodeling of the actin cytoskeleton. The GTPases RhoA, Rac1, and Cdc42 are known to regulate cell shape changes through effects on the cytoskeleton and cell adhesion. We show here that all three GTPases become rapidly activated by shear stress, and that each is important for different aspects of the endothelial response. RhoA was activated within 5 min after stimulation with shear stress and led to cell rounding via Rho-kinase. Subsequently, the cells respread and elongated within the direction of shear stress as RhoA activity returned to baseline and Rac1 and Cdc42 reached peak activation. Cell elongation required Rac1 and Cdc42 but not phosphatidylinositide 3-kinases. Cdc42 and PI3Ks were not required to establish shear stress-induced polarity although they contributed to optimal migration speed. Instead, Rho and Rac1 regulated directionality of cell movement. Inhibition of Rho or Rho-kinase did not affect the cell speed but significantly increased cell displacement. Our results show that endothelial cells reorient in response to shear stress by a two-step process involving Rho-induced depolarization, followed by Rho/Rac-mediated polarization and migration in the direction of flow.     

Model of coupled transient changes of Rac, Rho, adhesions and stress fibers alignment in endothelial cells responding to shear stress

Interactions of cell adhesions, Rho GTPases and actin in the endothelial cells' response to external forces are complex and not fully understood, but a qualitative understanding of the mechanosensory response begins to emerge. Here, we formulate a mathematical model of the coupled dynamics of cell adhesions, small GTPases Rac and Rho and actin stress fibers guiding a directional reorganization of the actin cytoskeleton. The model is based on the assumptions that the interconnected cytoskeleton transfers the shear force to the adhesion sites, which in turn transduce the force into a chemical signal that activates integrins at the basal surface of the cell. Subsequently, activated and ligated integrins signal and transiently de-activate Rho, causing the disassembly of actin stress fibers and inhibiting the maturation of focal complexes into focal contacts. Focal complexes and ligated integrins activate Rac, which in turn enhances focal complex assembly. When Rho activity recovers, stress fibers re-assemble and promote the maturation of focal complexes into focal contacts. Merging stress fibers self-align, while the elevated level of Rac activity at the downstream edge of the cell is translated into an alignment of the cells and the newly forming stress fibers in the flow direction. Numerical solutions of the model equations predict transient changes in Rac and Rho that compare well with published experimental results. We report quantitative data on early alignment of the stress fibers and its dependence on cell shape that agrees with the model.     

A mathematical model for the determination of viscoelastic behavior of brain in vivo. II. Relaxation response

In a recent experiment for determining the mechanical response of brain in vivo. a probe, inserted through scalp, skull and dura, is placed in contact with and normal to the brain, given a prescribed motion, and the time variation of corresponding force is measured. In the corresponding continuum mechanical model, brain is idealized as a linear isotropic viscoelastic solid constrained by a rigid skull. At the mating surface, the shear stress and normal displacement vanish everywhere except under the probe which exerts a local radial displacement. This model introduces effective viscoelastic moduli in shear, which is unknown, and in dilatation, which is considered known from other sources. Part II of this study is concerned with stress relaxation induced by a small step displacement of the probe. From the solution of the corresponding quasi-static boundary value problem, a nonlinear Volterra integral equation is established from which the shear stress relaxation function can be solved in terms of measured probe displacement and force. A numerical method of solution is developed.