A model for shear stress-induced deformation of a flow sensor on the surface of vascular endothelial cells

Fluid mechanical shear stress elicits humoral, metabolic, and structural responses in vascular endothelial cells (ECs); however, the mechanisms involved in shear stress sensing and transduction remain incompletely understood. Beyond being responsive to shear stress, ECs distinguish among and respond differently to different types of shear stress. Recent observations suggest that endothelial shear stress sensing may occur through direct interaction of the flow with cell-surface structures that act as primary flow sensors. This paper presents a mathematical model for the shear stress-induced deformation of a flow sensor on the EC surface. The sensor is modeled as a cytoskeleton-coupled viscoelastic structure exhibiting standard linear solid behavior. Since ECs respond differently to different types of flow, the deformation and resulting velocity of the sensor in response to steady, non-reversing pulsatile, and oscillatory flow have been studied. Furthermore, the sensitivity of the results to changes in various model parameters including the magnitude of applied shear stress, the constants that characterize the viscoelastic behavior, and the pulsatile flow frequency (f) has been investigated. The results have demonstrated that in response to a suddenly applied shear stress, the sensor exhibits a level of instantaneous deformation followed by gradual creeping to the long-term response. The peak deformation increases linearly with the magnitude of the applied shear stress and decreases for viscoelastic constants that correspond to stiffer sensors. While the sensor deformation depends on f for low f values, the deformation becomes f -independent above a critical threshold frequency. Finally, the peak sensor deformation is considerably larger for steady and non-reversing pulsatile flow than for oscillatory flow. If the extent of sensor deformation correlates with the intensity of flow-mediated endothelial signaling, then our results suggest possible mechanisms by which ECs distinguish among steady, non-reversing pulsatile, and oscillatory shear stress.     

The influence of link protein stabilization on the viscometric properties of proteoglycan aggregate solutions

The dynamic, steady-shear and transient shear flow properties of precisely prepared link-stable (s0 136, 66% aggregate) and link-free (s0 93, 59% aggregate) proteoglycan aggregate solutions at concentrations ranging from 10 to 50 mg/ml were determined using a cone-on-plate viscometer in a mechanical spectrometer. All proteoglycan solutions tested possessed: (1) linear viscoelastic properties - as measured by the dynamic complex modulus under small amplitude steady oscillatory conditions (1 less than or equal to omega less than or equal to 100 rad/s) - and (2) nonlinear shear-rate dependent apparent viscosities and primary normal stress difference under steady shearing conditions (0.25 less than or equal to gamma less than or equal to 250 s-1). Our transient flow data show that all proteoglycan aggregate solutions exhibited transient stress overshoot effects in shear stress and normal stress. From these steady and transient flow data, we conclude that link protein stabilized aggregates have significant effects on their dynamic and steady-shear properties as well as transient flow properties. The transient stress overshoot data provide a measure of the energy per unit volume of fluid required to overcome the proteoglycan networks in solution from a resting state. Thus we found that link-stable aggregates form much stronger networks than link-free aggregates. This is corroborated by the fact that link-stable aggregates form more elastic (lower than delta) and stiffer (higher [G*]) networks than link-free aggregates. The complete spectrum of viscometric flow data is entirely compatible with the proposed role of link protein in adding structural stability to the proteoglycan-hyaluronate bond. In cartilage, the enhanced strength of the networks formed by link-stable aggregates may play an important role in determining the material properties of the tissue and thereby contribute to the functional capacity of cartilage in diarthrodial joints.     

Time-dependent deformations in bone cells exposed to fluid flow in vitro: investigating the role of cellular deformation in fluid flow-induced signaling

Numerous experiments have shown fluid flow to be a potent stimulator of bone cells in vitro, suggesting that fluid flow is an important physical signal in bone mechanotransduction. In fluid flow experiments, bone cells are exposed to both time-dependent (e.g., oscillating or pulsing) and time-independent (e.g., steady) flow profiles. Interestingly, the signaling response of bone cells shows dependence on loading frequency and/or rate that has been postulated to be due to viscoelastic behavior. Thus, the objective of this study was to investigate the time-dependent deformations of bone cells exposed to fluid flow in vitro. Specifically, our goal was to characterize the mechanical response of bone cells exposed to oscillatory flow from 0.5 to 2.0 Hz and steady flow, since these flow profiles have previously been shown to induce different morphological and biochemical responses in vitro. By tracking cell-bound sulfate and collagen coated fluorescent beads of varying sizes, we quantified the normalized peak deformation (peak displacement normalized by the maximum peak displacement observed for all frequencies) and phase lag in bone cells exposed to 1.0 Pa oscillating flow at frequencies of 0.5-2.0 Hz. The phase lag was small (3-10 degrees ) and frequency dependent, while the normalized peak displacements decreased as a weak power law of frequency ( approximately f(-0.2)). During steady flow, the cells exhibited a nearly instantaneous deformation, followed by creep. Our results suggest that while substantial viscous deformation may occur during steady flow (compared to oscillating flow at approximately 1 Hz), bone cells behave primarily as elastic bodies when exposed to flow at frequencies associated with habitual loading.     

The mechanical response of the active human triceps brachii muscle to very rapid stretch and shortening

Very rapid, small amplitude, ramp-and-hold rotations were imposed on the braced forearms of three normal adult male subjects who were isometrically contracting their elbow extensors. By carefully accounting for inertial and viscoelastic coupling effects in the experimental system it was possible to compute the time course of the muscle-moment evoked by these mechanical perturbations. The muscle-moment responses, and their dependence on rotation amplitude and direction, as well as tonic contraction level, are described. These responses are also compared to the predictions of a simple muscle model which we have proposed previously on the basis of frequency-response tests. The results indicate that: at a given tonic contraction level, triceps may be stiffer in an isometric state than in an oscillatory steady state, and high frequency fluctuations in the myoelectric activity are very ineffective in generating corresponding muscle-force fluctuations.     

Strain-dependent viscoelastic behaviour and rupture force of single chondrocytes and chondrons under compression

The chondron in articular cartilage includes the chondrocyte and its surrounding pericellular matrix (PCM). Single chondrocytes and chondrons were compressed between two parallel surfaces by a micromanipulation technique to investigate their biomechanical properties and to discover the mechanical significance of the PCM. The force imposed on the cells was measured directly during deformation at various compression speeds and deformations up to cell rupture. When the deformation at the end of compression was 50%, relaxation showed that the cells were viscoelastic, but this viscoelasticity was generally insignificant at 30% deformation or lower. When the deformation was 70%, the cells had deformed plastically. Chondrons ruptured at a mean deformation of 85 ± 1%, whilst chondrocytes ruptured at a mean deformation of 78 ± 1%. Chondrons were generally stiffer than chondrocytes and showed less viscoelastic behaviour than chondrocytes. Thus, the PCM significantly influences the mechanical properties of the cells.     

Osteopontin gene regulation by oscillatory fluid flow via intracellular calcium mobilization and activation of mitogen-activated protein kinase in MC3T3-E1 osteoblasts

Recently fluid flow has been shown to be a potent physical stimulus in the regulation of bone cell metabolism. However, most investigators have applied steady or pulsing flow profiles rather than oscillatory fluid flow, which occurs in vivo because of mechanical loading. Here oscillatory fluid flow was demonstrated to be a potentially important physical signal for loading-induced changes in bone cell metabolism. We selected three well known biological response variables including intracellular calcium (Ca(2+)i), mitogen-activated protein kinase (MAPK) activity, and osteopontin (OPN) mRNA levels to examine the response of MC3T3-E1 osteoblastic cells to oscillatory fluid flow with shear stresses ranging from 2 to -2 Newtons/m(2) at 1 Hz, which is in the range expected to occur during routine physical activities. Our results showed that within 1 min, oscillatory flow induced cell Ca(2+)i mobilization, whereas two MAPKs (ERK and p38) were activated over a 2-h time frame. However, there was no activation of JNK. Furthermore 2 h of oscillatory fluid flow increased steady-state OPN mRNA expression levels by approximately 4-fold, 24 h after exposure to fluid flow. The presence of both ERK and p38 inhibitors and thapsigargin completely abolished the effect of oscillatory flow on steady-state OPN mRNA levels. In addition, experiments using a variety of pharmacological agents suggest that oscillatory flow induces Ca(2+)i mobilization via the L-type voltage-operated calcium channel and the inositol 1,4,5-trisphosphate pathway.     

The superposition of steady on oscillatory shear and its effect on the viscoelasticity of human blood and a blood-like model fluid

To understand the pulsatility of human blood flow in vivo, it is necessary to separately investigate (1) steady shear and oscillatory flow, and (2) the superposition of steady shear flow on oscillatory flow performed under in vitro conditions. In this study a variable steady shear rate was superimposed in parallel on oscillatory shear at a constant frequency (0.5 Hz) for human blood (45% hematocrit), and an aqueous polyacrylamide polymer solution (AP 30E, concentration 300 ppm). The effect of superposition of the above two shear flows on the viscoelasticity of blood was more pronounced for the elastic (η′') than for the viscous (η′) component of viscoelasticity. With increasing superimposed shear rate, both η′ and η′' decreased, especially at the low shear region. This behavior can be explained by the viscoelastic properties of blood and the phenomena of blood aggregation and disaggregation. Quantitatively, the dependence of the viscous component of complex viscosity on superimposed shear for both blood and polymer solution is described by a modified Carreau equation. The elastic component of complex viscosity decreased exponentially with increasing superimposed shear, and it is described by an exponential model. © 1997 Elsevier Science Ltd     

A constitutive model for the time-dependent,nonlinear stress response of fibrin networks

Blood clot formation is important to prevent blood loss in case of a vascular injury but disastrous when it occludes the vessel. As the mechanical properties of the clot are reported to be related to many diseases, it is important to have a good understanding of their characteristics. In this study, a constitutive model is presented that describes the nonlinear viscoelastic properties of the fibrin network, the main structural component of blood clots. The model is developed using results of experiments in which the fibrin network is subjected to a large amplitude oscillatory shear (LAOS) deformation. The results show three dominating nonlinear features: softening over multiple deformation cycles, strain stiffening and increasing viscous dissipation during a deformation cycle. These features are incorporated in a constitutive model based on the Kelvin–Voigt model. A network state parameter is introduced that takes into account the influence of the deformation history of the network. Furthermore, in the period following the LAOS deformation, the stiffness of the networks increases which is also incorporated in the model. The influence of cross-links created by factor XIII is investigated by comparing fibrin networks that have polymerized for 1 and 2 h. A sensitivity analysis provides insights into the influence of the eight fit parameters. The model developed is able to describe the rich, time-dependent, nonlinear behavior of the fibrin network. The model is relatively simple which makes it suitable for computational simulations of blood clot formation and is general enough to be used for other materials showing similar behavior.     

Oscillatory Flow Accelerates Autocrine Signaling due to Nonlinear Effect of Convection on Receptor-Related Actions

We study effects of oscillatory convective flow in extracellular space on the velocity of chemical signal propagation having a form of a front wave above a cellular layer. We found that the time-averaged propagation velocity under oscillatory flow for a particular Péclet number amplitude is slower than the velocity under steady laminar flow regime for the same value of the Péclet number, but significantly faster than under no-flow conditions. We derive asymptotic values of the propagation velocity and asymptotic characteristics of the corresponding concentration fronts in high- and low-frequency regimes and show that the reason for the observed velocity increase under the oscillatory flow stems from a nonlinear dependence of the propagation velocity on the Péclet number, particularly from the convex character of the dependence. Our findings suggest that the specific responses of cellular cultures to different flow conditions in the extracellular space (for example, expression of atherosclerosis protective genes under steady laminar flow but not under oscillatory flow) is a consequence of a nonlinear coupling between the extracellular transport and complex intracellular reaction cascades forming a positive feedback loop of the autocrine signaling. This mechanism can operate independently of, or in conjunction with, a direct stress-sensing due to mechanotransduction.     

A theory of blood flow in skeletal muscle

A theoretical analysis of blood flow in the microcirculation of skeletal muscle is provided. The flow in the microvessels of this organ is quasi steady and has a very low Reynolds number. The blood is non-Newtonian and the blood vessels are distensible with viscoelastic properties. A formulation of the problem is provided using a viscoelastic model for the vessel wall which was recently derived from measurements in the rat spinotrapezius muscle (Skalak and Schmid-Sch?nbein, 1986b). Closed form solutions are derived for several physiologically important cases, such as perfusion at steady state, transient and oscillatory flows. The results show that resting skeletal muscle has, over a wide range of perfusion pressures an almost linear pressure-flow curve. At low flow it exhibits nonlinearities. Vessel distensibility and the non-Newtonian properties of blood both have a strong influence on the shape of the pressure-flow curve. During oscillatory flow the muscle exhibits hysteresis. The theoretical results are in qualitative agreement with experimental observations.     

Oscillatory Flow Accelerates Autocrine Signaling due to Nonlinear Effect of Convection on Receptor-Related Actions

We study effects of oscillatory convective flow in extracellular space on the velocity of chemical signal propagation having a form of a front wave above a cellular layer. We found that the time-averaged propagation velocity under oscillatory flow for a particular Péclet number amplitude is slower than the velocity under steady laminar flow regime for the same value of the Péclet number, but significantly faster than under no-flow conditions. We derive asymptotic values of the propagation velocity and asymptotic characteristics of the corresponding concentration fronts in high- and low-frequency regimes and show that the reason for the observed velocity increase under the oscillatory flow stems from a nonlinear dependence of the propagation velocity on the Péclet number, particularly from the convex character of the dependence. Our findings suggest that the specific responses of cellular cultures to different flow conditions in the extracellular space (for example, expression of atherosclerosis protective genes under steady laminar flow but not under oscillatory flow) is a consequence of a nonlinear coupling between the extracellular transport and complex intracellular reaction cascades forming a positive feedback loop of the autocrine signaling. This mechanism can operate independently of, or in conjunction with, a direct stress-sensing due to mechanotransduction.     

Viscoelastic properties of aqueous solutions of an exocellular polysaccharide from cyanobacteria

The viscoelastic properties of aqueous solutions of the exocellular polysaccharide of Cyanospira capsulata have been studied, over a wide range of polymer concentrations, using small deformation oscillatory, steady and transient shear methods. The viscoelastic spectra generally resemble those of an entangled network, although notable deviations can be observed in the low frequency dependence of G′ and G″. At higher polymer concentrations, the viscoelastic spectrum shows solid-like behaviour over a wide range of frequencies. The superposition of η^*(ω) and η( ) curves occurs only at low frequencies, at higher frequencies the slope of η^*(ω) is lower than that of η( ). By studying the time evolution of shear stress after the inception of a steady shear rate (stress overshoot), the recovery of non-linear properties after steady shearing flow is seen to occur after times of c. 10³ s (in the case of 1·1% w/v solutions).

The overall viscoelastic properties appear original in comparison with those of the two structurally limiting types of polysaccharide, the ‘ordered’ chain xanthan and the ‘random coil’ guar. A rationale for this ‘anomalous’ viscoelastic behaviour can be tentatively proposed in terms of flickering intermolecular cross-interactions between semi-flexible segments, which occur in addition to the usual topological constraints.     

EXPERIMENTS BEARING ON THE NATURE OF INTRACELLULAR INCLUSIONS IN PLANT VIRUS DISEASES

The intracellular changes resultant on infection with aucuba mosaic and Hy. III diseases are described and are compared with the cytological effects of tobacco mosaic virus. With the two former viruses, inclusion bodies are formed by the aggregation and fusion of minute particles which appear in the cytoplasmic stream. With tobacco mosaic disease an amoeba-like body is produced and this persists for some weeks before suddenly disappearing again. It is accompanied by striate material all of which ultimately fuses into one large body.
Attempts have been made to parallel these conditions in healthy cells of Solanaceous plants by treatment with substances known to coagulate protoplasm. Almost all the reagents used induced stimulation of the cytoplasmic stream similar to the initial sign of virus infection. With salts of molybdic acid, all the cytological abnormalities due to aucuba mosaic or Hy. III disease have been imitated. Treatment with lactic acid induces the formation of amoeboid bodies like the X-bodies of tobacco mosaic, but these bodies persist for only a few hours.
Attempts have also been made to inhibit the formation of inclusion bodies induced by several different diseases in a number of hosts but no success was obtained.
The experiments support the view that the intracellular inclusions of plant virus diseases are essentially products of the host cell.     

Flow properties of N-(carboxymethyl) chitosan aqueous systems in the sol and gel domains

The flow behaviour and the viscoelastic properties of N-(carboxymethyl) chitosan aqueous systems in the sol and gel domains have been investigated by means of dynamic, steady and transient shear techniques. For polymer concentrations Cp up to 1%, a typical response of moderately concentrated polymer solutions was observed under continuous and oscillatory shear conditions. No time-dependent properties were detected during transient shear experiments. On the other hand, for all the samples with Cp greater than 1%, the rheological properties were more similar to those of a weak gel system. The continuous shear flow behaviour was of the plastic type and the viscoelastic quantities G' and G" were parallel to each other and slightly dependent on the frequency of oscillation omega. Stress overshoots were observed during transient shear experiments, and the kinetics of the structural breakdown and build-up processes were found to be dependent both on the polymer concentration and the applied shear rate.     

Elastic versus brittle mechanical responses predicted for dimeric cadherin complexes

Cadherins are a superfamily of adhesion proteins involved in a variety of biological processes that include the formation of intercellular contacts, the maintenance of tissue integrity, and the development of neuronal circuits. These transmembrane proteins are characterized by ectodomains composed of a variable number of extracellular cadherin (EC) repeats that are similar but not identical in sequence and fold. E-cadherin, along with desmoglein and desmocollin proteins, are three classical-type cadherins that have slightly curved ectodomains and engage in homophilic and heterophilic interactions through an exchange of conserved tryptophan residues in their N-terminal EC1 repeat. In contrast, clustered protocadherins are straighter than classical cadherins and interact through an antiparallel homophilic binding interface that involves overlapped EC1 to EC4 repeats. Here we present molecular dynamics simulations that model the adhesive domains of these cadherins using available crystal structures, with systems encompassing up to 2.8 million atoms. Simulations of complete classical cadherin ectodomain dimers predict a two-phased elastic response to force in which these complexes first softly unbend and then stiffen to unbind without unfolding. Simulated α, β, and γ clustered protocadherin homodimers lack a two-phased elastic response, are brittle and stiffer than classical cadherins and exhibit complex unbinding pathways that in some cases involve transient intermediates. We propose that these distinct mechanical responses are important for function, with classical cadherin ectodomains acting as molecular shock absorbers and with stiffer clustered protocadherin ectodomains facilitating overlap that favors binding specificity over mechanical resilience. Overall, our simulations provide insights into the molecular mechanics of single cadherin dimers relevant in the formation of cellular junctions essential for tissue function.     

Mechanical properties of brain tubulin and microtubules

We measured the elasticity and viscosity of brain tubulin solutions under various conditions with a cone and plate rheometer using both oscillatory and steady shearing modes. Microtubules composed of purified tubulin, purified tubulin with taxol and 3x cycled microtubule protein from pig, cow, and chicken behaved as mechanically indistinguishable viscoelastic materials. Microtubules composed of pure tubulin and heat stable microtubule-associated proteins were also similar but did not recover their mechanical properties after shearing like other samples, even after 60 min. All of the other microtubule samples were more rigid after flow orientation, suggesting that the mechanical properties of anisotropic arrays of microtubules may be substantially greater than those of randomly arranged microtubules. These experiments confirm that MAPs do not cross link microtubules. Surprisingly, under conditions where microtubule assembly is strongly inhibited (either 5 degrees or at 37 degrees C with colchicine or Ca++) tubulin was mechanically indistinguishable from microtubules at 10-20 microM concentration. By electron microscopy and ultracentrifugation these samples were devoid of microtubules or other obvious structures. However, these mechanical data are strong evidence that tubulin will spontaneously assemble into alternate structures (aggregates) in nonpolymerizing conditions. Because unpolymerized tubulin is found in significant quantities in the cytoplasm, it may contribute significantly to the viscoelastic properties of cytoplasm, especially at low deformation rates.     

Oscillatory deformation of human erythrocytes in sinusoidally modulated shear flow

The red cell deformation under oscillatory shear stress was studied. Shear stress was sinusoidally modulated between 8 and 32 dyn/cm2, thus, the extent of cellular deformation altered sinusoidally. At a low modulation frequency (less than 1.8 Hz), intact red cells perfectly responded to the shear stress applied on cells, and they could deform as much as the deformation in stationary shear flow. Above 2 Hz, the cellular deformation could not follow changes in shear stress along up-phase in the shear stress cycle. As decreasing the intracellular hemoglobin concentration, the cellular response to oscillatory shear stress became better. Treatment of cells with low concentrations of diamide impaired the response of intact cells to oscillatory shear stress, but unaffected the response of partially hemolyzed cells. These data suggest that the cellular response to oscillatory shear stress is determined by the cytoskeletal structure and the intracellular viscosity.     

Preparation and properties of stretched polytene chromosomes. 2. Mechanism of stretching]

Isolated polytene chromosomes were stretched in a 0.125 M NaCl solution with constant speed, by constant force and by cyclically changing force. For each regime, the dependence of chromosome length on the time and force magnitude were recorded. From this it may be concluded that three processes are involved in chromosome stretching: viscoelastic deformation, viscous flow of DNP segments, and cristallization, i.e. intermolecular cross-linking of neighbour segments. At a high rate stretching (V greater than Vo) chromosome may be torn like at small deformation; when rate is V greater than Vo chromosome deformation is mostly viscoelastic; at rates V approximately Vo viscous flow of DNP segments if predominant. We estimate Vo approximately less than 3--6 mum/s. Electron microscopy shows that during chromosome stretching its DNP fibers are oriented along chromosome axis without detectable breaks.     

Steady and pulsatile shear stress induce different three-dimensional endothelial networks through pseudopodium formation

Control of angiogenesis is a major challenge to promotion of vascularization in the field of tissue engineering. In particular, shear stress is recognized as an important mechanical factor controlling new vessel formation. However, the effects of steady and pulsatile shear stress on endothelial cell (EC) network formation remain unclear. Here, we systematically investigated their effects. Compared with pulsatile shear stress, steady shear stress at 1.0 Pa increased cell numbers in EC networks as well as the distribution of networks and pseudopodia in the deep range after 48 h. To further investigate the process of EC network growth, we focused on the effect of flow frequency on network elongation dynamics. Pulsatile shear stress at 1.0 Pa increased the extension and retraction velocities and separation of networks, resulting in the formation of unstable EC networks. In contrast, steady shear stress application resulted in the formation of extended and stable EC networks composed of many cells. Thus, two types of three-dimensional network growth were observed, depending on flow pulsatility. A combination of the type of ECs, such as aortic and microvascular ECs, and flow characteristics, such as flow magnitude and frequency, may have important implications for the construction of well-developed three-dimensional EC networks.     

Effect of combined cyclic stretch and fluid shear stress on endothelial cell morphological responses

Endothelial cells in vivo are normally subjected to multiple mechanical stimuli such as stretch and fluid shear stress (FSS) but because each stimulus induces magnitude-dependent morphologic responses, the relative importance of each stimulus in producing the normal in vivo state is not clear Using cultured human aortic endothelial cells, this study first determined equipotent levels of cyclic stretch, steady FSS, and oscillatory FSS with respect to the time course of cell orientation. We then tested whether these levels of stimuli were equipotent in combination with each other by imposing simultaneous cyclic stretch and steady FSS or cyclic stretch and oscillatory FSS so as to reinforce or counteract the cells' orientation responses. Equipotent levels of the three stimuli were 2% cyclic stretch at 2%/s, 80 dynes/cm2 steady FSS and 20 +/- 10 dynes/cm2 oscillatory FSS at 20 dyne/cm2-s. When applied in reinforcing fashion, cyclic stretch and oscillatory, but not steady, FSS were additive. Both pairs of stimuli canceled when applied in counteracting fashion. These results indicate that this level of cyclic stretch and oscillatory FSS sum algebraically so that they are indeed equipotent. In addition, oscillatory FSS is a stronger stimulus than steady FSS for inducing cell orientation. Moreover, arterial endothelial cells in vivo are likely receiving a stronger stretch than FSS stimulus.