Influence of cell deformation on leukocyte rolling adhesion in shear flow

Blood cell interaction with vascular endothelium is important in microcirculation, where rolling adhesion of circulating leukocytes along the surface of endothelial cells is a prerequisite for leukocyte emigration under flow conditions. HL-60 cell rolling adhesion to surface-immobilized P-selectin in shear flow was investigated using a side-view flow chamber, which permitted measurements of cell deformation and cell-substrate contact length as well as cell rolling velocity. A two-dimensional model was developed based on the assumption that fluid energy input to a rolling cell was essentially distributed into two parts: cytoplasmic viscous dissipation, and energy needed to break adhesion bonds between the rolling cell and its substrate. The flow fields of extracellular fluid and intracellular cytoplasm were solved using finite element methods with a deformable cell membrane represented by an elastic ring. The adhesion energy loss was calculated based on receptor-ligand kinetics equations. It was found that, as a result of shear-flow-induced cell deformation, cell-substrate contact area under high wall shear stresses (20 dyn/cm2) could be as much as twice of that under low stresses (0.5 dyn/cm2). An increase in contact area may cause more energy dissipation to both adhesion bonds and viscous cytoplasm, whereas the fluid energy input may decrease due to the flattened cell shape. Our model predicts that leukocyte rolling velocity will reach a plateau as shear stress increases, which agrees with both in vivo and in vitro experimental observations.     

Biomechanics of cell rolling: shear flow, cell-surface adhesion, and cell deformability

The mechanics of leukocyte (white blood cell; WBC) deformation and adhesion to endothelial cells (EC) has been investigated using a novel in vitro side-view flow assay. HL-60 cell rolling adhesion to surface-immobilized P-selectin was used to model the WBC-EC adhesion process. Changes in flow shear stress, cell deformability, or substrate ligand strength resulted in significant changes in the characteristic adhesion binding time, cell-surface contact and cell rolling velocity. A 2-D model indicated that cell-substrate contact area under a high wall shear stress (20 dyn/cm2) could be nearly twice of that under a low stress (0.5 dyn/cm2) due to shear flow-induced cell deformation. An increase in contact area resulted in more energy dissipation to both adhesion bonds and viscous cytoplasm, whereas the fluid energy that inputs to a cell decreased due to a flattened cell shape. The model also predicted a plateau of WBC rolling velocity as flow shear stresses further increased. Both experimental and computational studies have described how WBC deformation influences the WBC-EC adhesion process in shear flow.     

Kinematics of cytoplasmic deformation in neutrophils during active motion

A procedure is proposed to measure the cytoplasmic deformation in active motile neutrophils in the form of cytoplasmic strains and strain rates. Three neighboring microspheres in a local region of the cytoplasm serve as markers for local motion. Their positions are tracked by means of a high resolution light microscope and serve to compute nonlinear measures of strains and strain rates together with the principal strains and principal directions. Active neutrophils exhibit large cytoplasmic strains both during periodic pseudopod projections and during continuous locomotion in a polarized shape. The cytoplasmic motion is often synchronized with the whole cell deformation. The local cytoplasmic strains exceed the strains estimated for the whole cell and are not reversible except in some cases of single pseudopod projections. Large strains are observed both in attached and freely suspended cells. Strain rates are relatively constant but show an increase during the pseudopod retraction phase. Local cytoplasmic strains in neutrophils are inhomogeneous and reach large values during passage of the contraction rings. Neutrophils rendered passive by treatment with cytochalasin or EDTA show a random motion of microspheres with much smaller displacements. These observations suggest that the cytoplasm of active neutrophil exhibits large cytoplasmic strains and strain rates in the absence of an external stress resulting in a high degree of intracellular mixing. The proposed technique may be applied to a wide range of problems in cell biology.     

A Mathematical Model of Spatial Self-Organization in a Mechanically Active Cellular Medium

A general continual model of a medium composed of mechanically active cells is proposed. The medium is considered to be formed by three phases: cells, extracellular fluid, and an additional phase that is responsible for active interaction forces between cells and, for instance, may correspond to a system of protrusions that provide the development of active contractile forces. The deformation of the medium, which is identified with the deformation of the cell phase, consists of two components: elastic deformation of individual cells and cell rearrangements. The elastic deformation is associated with stresses in the cell phase. The spherical component of the stress tensor describes the nonlinear resistance of the cellular medium, which leads to the impossibility of its excessive compression. The constitutive equation for pressure in the cell phase is taken in the form of a nonlinear dependence on the volume cell density. The rearrangement of cells is considered as a flow controlled by stresses in the cell phase, active stresses, and fluid pressure. The tensor of active stresses is assumed to be spherical and nonlocally dependent on the cell density. Assuming that the process of biological tissue deformation is slow, we obtained a reduced model that neglects the elastic deformation of cells, compared to the inelastic deformation. A linear stability analysis of a spatially uniform steady-state solution was performed. The hydrostatic pressure of fluid is present among the parameters that are responsible for the loss of stability of the steady-state solution: an increase in it has a destabilizing effect owing to the action of the component of the interphase interaction force that is determined by the fluid pressure. The model we obtained can be used to describe the process of cavity formation in an initially homogeneous cell spheroid. The role of local and nonlocal mechanisms of active stress generation in the formation of cavity is investigated.     

One-dimensional steady continuum model of retraction of pseudopod in leukocytes

A one-dimensional steady state continuum mechanics model of retraction of pseudopod in leukocytes is developed. The retracting pseudopod is assumed to move bodily toward the main cell body, the bulk motion of which can be represented by cytoplasmic flow within a typical stream tube through the leukocyte. The stream tube is approximated by a frictionless tube with prescribed geometry. The passive rheological properties of cytoplasm in the main cell body and in the pseudopod are modeled, respectively, by Maxwell fluid and Hookean solid. The two regions are assumed to be separated by a sharp interface at which actin gel solates and thereby changes its rheological properties as it flows from the pseudopod to the main cell body. The driving mechanism responsible for the active retraction motion is hypothesized to be a spontaneous deformation of the actin gel, analogous but not necessarily equal to the well known actin-myosin interaction. This results in an active contractile stress being developed in the pseudopod as well as in the cell cortex. The transverse traction pulls against the inclined wall of the stream tube and is transduced into an axial stress gradient, which in turn drives the flow. The tension on the tube wall is picked up by the prestressed cortical shell. Governing equations and boundary conditions are derived. A solution is obtained. Sample data are computed. Comparison of the theory with experiments shows that the model is compatible to the observations.     

A computational model of ameboid deformation and locomotion

Traditional continuum models of ameboid deformation and locomotion are limited by the computational difficulties intrinsic in free boundary conditions. A new model using the immersed boundary method overcomes these difficulties by representing the cell as a force field immersed in fluid domain. The forces can be derived from a direct mechanical interpretation of such cell components as the cell membrane, the actin cortex, and the transmembrane adhesions between the cytoskeleton and the substratum. The numerical cytoskeleton, modeled as a dynamic network of immersed springs, is able to qualitatively model the passive mechanical behavior of a shear-thinning viscoelastic fluid (Bottino 1997). The same network is used to generate active protrusive and contractile forces. When coordinated with the attachment-detachment cycle of the cell's adhesions to the substratum, these forces produce directed locomotion of the model ameba. With this model it is possible to study the effects of altering the numerical parameters upon the motility of the model cell in a manner suggestive of genetic deletion experiments. In the context of this ameboid cell model and its numerical implementation, simulations involving multicellular interaction, detailed internal signaling, and complex substrate geometries are tractable. Received: 5 January 1998 / Revised version: 23 March 1998 / Accepted: 26 March 1998     

A semianalytical model to study the effect of cortical tension on cell rolling

Cell rolling on the vascular endothelium plays an important role in trafficking of leukocytes, stem cells, and cancer cells. We describe a semianalytical model of cell rolling that focuses on the microvillus as the unit of cell-substrate interaction and integrates microvillus mechanics, receptor clustering, force-dependent receptor-ligand kinetics, and cortical tension that enables incorporation of cell body deformation. Using parameters obtained from independent experiments, the model showed excellent agreement with experimental studies of neutrophil rolling on P-selectin and predicted different regimes of cell rolling, including spreading of the cells on the substrate under high shear. The cortical tension affected the cell-surface contact area and influenced the rolling velocity, and modulated the dependence of rolling velocity on microvillus stiffness. Moreover, at the same shear stress, microvilli of cells with higher cortical tension carried a greater load compared to those with lower cortical tension. We also used the model to obtain a scaling dependence of the contact radius and cell rolling velocity under different conditions of shear stress, cortical tension, and ligand density. This model advances theoretical understanding of cell rolling by incorporating cortical tension and microvillus extension into a versatile, semianalytical framework.     

Mechanical Modelling of Confined Cell Migration Across Constricted-curved Micro-channels

Confined migration is a crucial phenomenon during embryogenesis, immune response and cancer. Here, a two-dimensional finite element model of a HeLa cell migrating across constricted–curved micro-channels is proposed. The cell is modelled as a continuum with embedded cytoplasm and nucleus, which are described by standard Maxwell viscoelastic models. The decomposition of the deformation gradient is employed to define the cyclic active strains of protrusion and contraction, which are synchronized with the adhesion forces between the cell and the substrate. The micro-channels are represented by two rigid walls and exert an additional viscous force on the cell boundaries. Five configurations have been tested: 1) top constriction, 2) top-bottom constriction, 3) shifted top-bottom constriction, 4) embedded obstacle and 5) bending micro-channel. Additionally, for the first four micro-channels both sub-cellular and sub-nuclear constrictions have been obtained, while for the fifth micro-channel three types of bending have been investigated (‘curved’, ‘sharp’ and ‘sharper’). For each configuration, several parameters such as the cell behaviour, the covered distance, the migration velocity, the ratio between the cell and the nucleus area as well as the cell-substrate and cell-channel surfaces forces have been evaluated. The results show once more the fundamental role played by mechanics of both the cell and the environment.     

Cell-substrate interaction with cell-membrane-stress dependent adhesion

Cell-substrate interaction is examined in a two-dimensional mechanics model. The cell and substrate are treated as a shell and an elastic solid, respectively. Their interaction through adhesion is treated using nonlinear springs. Compared to previous cell mechanics models, the present model introduces a cohesive force law that is dependent not only on cell-substrate distance but also on internal cell-membrane stress. It is postulated that a living cell would establish focal adhesion sites with density dependent on the cell-membrane stress. The formulated mechanics problem is numerically solved using coupled finite elements and boundary elements for the cell and the substrate, respectively. The nodes in the adhesion zone from either side are linked by the cohesive springs. The specific cases of a cell adhering to a homogeneous substrate and a heterogeneous bimaterial substrate are examined. The analyses show that the substrate stiffness affects the adhesion behavior significantly and regulates the direction of cell adhesion, in good agreement with the experimental results in the literature. By introducing a reactive parameter (i.e., cell-membrane stress) linking biological responses of a living cell to a mechanical environment, the present model offers a unified mechanistic vehicle for characterization and prediction of living cell responses to various kinds of mechanical stimuli including local extracellular matrix and neighboring cells.     

How Listeria exploits host cell actin to form its own cytoskeleton. II. Nucleation, actin filament polarity, filament assembly, and evidence for a pointed end capper

Processes such as cell locomotion and morphogenesis depend on both the generation of force by cytoskeletal elements and the response of the cell to the resulting mechanical loads. Many widely accepted theoretical models of processes involving cell shape change are based on untested hypotheses about the interaction of these two components of cell shape change. I have quantified the mechanical responses of cytoplasm to various chemical environments and mechanical loading regimes to understand better the mechanisms of cell shape change and to address the validity of these models. Measurements of cell mechanical properties were made with strands of cytoplasm submerged in media containing detergent to permeabilize the plasma membrane, thus allowing control over intracellular milieu. Experiments were performed with equipment that generated sinusoidally varying length changes of isolated strands of cytoplasm from Physarum polycephalum. Results indicate that stiffness, elasticity, and viscosity of cytoplasm all increase with increasing concentration of Ca2+, Mg2+, and ATP, and decrease with increasing magnitude and rate of deformation. These results specifically challenge assumptions underlying mathematical models of morphogenetic events such as epithelial folding and cell division, and further suggest that gelation may depend on both actin cross-linking and actin polymerization.     

Vahlkampfia sp: structural observations of cultured trophozoites

Some structural observations on cultured Vahlkampfia sp. trophozoites are reported. Trophozoites are active and pleomorphic, producing large cell protrusions related to locomotion such as lamellipodia, filopodia and endocytic structures formed by hyaline cytoplasm, in which actin provides a framework that allows rapid changes in morphology. As observed by transmission electron microscopy, the cytoplasm is highly granular masking some cell organelles and the major cytoplasmic membrane systems. The structure of cell organelles such as the nucleus, endoplasmic reticulum, and digestive vacuoles is described. A common finding was the presence of 50 nm electron-dense round granules that are not limited by a membrane and that appear scattered in the cytoplasm, and whose function remains unknown. Apparently, the cell reserve material is glycogen, since complete trophozoites were positive to Schiff periodic-acid technique.     

Regulation of polarity in cells devoid of actin bundle system after treatment with inhibitors of myosin II activity

Interplay of two cytoskeletal systems--microfilaments and microtubules is essential for directional cell movement. To better understand the role of those cytoskeletal systems in polarization of cells, rat fibroblasts were incubated with drugs inhibiting activity of myosin II: blebbistatin and Y-27632. Both drugs led to disappearance of actin-myosin bundles and mature focal cell-matrix adhesions but did not affect polarization and directional motility. The rate of motility even increased after inhibitor treatment. The characteristic feature of inhibitor-treated fibroblasts was collapse of the cytoplasm accompanied by bundling of microtubules that led to transformation of lamellae into long immobile tails. The only exception was the leading anterior lamella which was not transformed into the tail and supported directional movement of the cell. The tail at the cell rear determined the position of anterior lamella and direction of locomotion. Depolymerization of microtubules by colcemid stopped directional locomotion of inhibitor-treated cells. These data show that integrity of the microtubular system provides the basic mechanism of polarization and orientation which is only modified by interactions with actin-myosin system and cell-substrate adhesions. We suggest that the position of bundled tail microtubules and dispersed microtubules in leading lamella determine polarization in cells lacking stress fibers and focal adhesions. Thus, polarization is based on microtubule-dependent mechanisms both in non-contractile and contractile cells. These mechanisms could switch dependent on circumstances as fibroblasts may acquire non-contractile phenotype, not only after direct inhibition of myosin II but also in certain conditions of microenvironment.     

Determination of binding strength and kinetics of binding initiation. A model study made on the adhesive properties of P388D1 macrophage-like cells

The adhesive properties of the mouse P388D1 macrophage-like line were explored. Cells were deposited in glass capillary tubes, and the kinetics of adhesion and spreading were studied. Binding involved the cell metabolism since it was decreased by cold, azide, or a divalent cation chelator. Glass-adherent cells were subjected to calibrated laminar shear flows with a highly viscous dextran solution. A tangential force of about 5 X 10(-3) dyn/cell was required to achieve substantial detachment. The duration of application of the shearing force strongly influenced cell-substrate separation when this was varied from 1-10 s. Further, this treatment resulted in marked cell deformation, with the appearance of an elongated shape. Hence, cell-substrate separation is a progressive process, and binding strength is expected to be influenced by cell deformability. The minimum time required for adhesion was also investigated by making cells adhere under flow conditions. The maximum flow rate compatible with adhesion was about 1000-fold lower than that required to detach glass-bound cells. A simple model was devised to provide a quantitative interpretation for the experimental results of kinetic studies. It is concluded that cell-to-glass adhesion required a cell-substrate contact longer than a few seconds. This first step of adhesion was rapidly followed by a large (about 1000-fold) increase of adhesion strength. It is therefore emphasized that adhesion is heavily dependent on the duration of cell-to-cell encounter, as well as the force used to remove so-called unbound cells.     

Determination of binding strength and kinetics of binding initiation

The adhesive properties of the mouse P388D1 macrophage-like line were explored. Cells were deposited in glass capillary tubes, and the kinetics of adhesion and spreading were studied. Binding involved the cell metabolism since it was decreased by cold, azide, or a divalent cation chelator. Glass-adherent cells were subjected to calibrated laminar shear flows with a highly viscous dextran solution. A tangential force of about 5×10⁻³ dyn/cell was required to achieve substantial detachment. The duration of application of the shearing force strongly influenced cell-substrate separation when this was varied from 1–10 s. Further, this treatment resulted in marked cell deformation, with the appearance of an elongated shape. Hence, cell-substrate separation is a progressive process, and binding strength is expected to be influenced by cell deformability. The minimum time required for adhesion was also investigated by making cells adhere under flow conditions. The maximum flow rate compatible with adhesion was about 1000-fold lower than that required to detach glass-bound cells. A simple model was devised to provide a quantitative interpretation for the experimental results of kinetic studies. It is concluded that cell-to-glass adhesion required a cell-substrate contact longer than a few seconds. This first step of adhesion was rapidly followed by a large (about 1000-fold) increase of adhesion strength. It is therefore emphasized that adhesion is heavily dependent on the duration of cell-to-cell encounter, as well as the force used to remove so-called unbound cells.     

A master relation defines the nonlinear viscoelasticity of single fibroblasts

Cell mechanical functions such as locomotion, contraction, and division are controlled by the cytoskeleton, a dynamic biopolymer network whose mechanical properties remain poorly understood. We perform single-cell uniaxial stretching experiments on 3T3 fibroblasts. By superimposing small amplitude oscillations on a mechanically prestressed cell, we find a transition from linear viscoelastic behavior to power law stress stiffening. Data from different cells over several stress decades can be uniquely scaled to obtain a master relation between the viscoelastic moduli and the average force. Remarkably, this relation holds independently of deformation history, adhesion biochemistry, and intensity of active contraction. In particular, it is irrelevant whether force is actively generated by the cell or externally imposed by stretching. We propose that the master relation reflects the mechanical behavior of the force-bearing actin cytoskeleton, in agreement with stress stiffening known from semiflexible filament networks.     

Modulation of the locomotion of polymorphonuclear leukocytes by a synthetic amphiphile, poly(ethyleneglycol) palmitate

To mimic in vitro the effect of biologically active amphipathic molecules on the locomotion of polymorphonuclear leukocytes (PMNL), the interaction and the consequences of the interaction between poly(ethyleneglycol) (PEG) esterified with palmitic acid (P-PEG) and PMNL, was studied. It was shown that P-PEG was more liable to hydrophobic interaction than PEG, and that P-PEG associated to a greater extent than PEG with PMNL. This association was inhibited by decreasing the interaction temperature from 37 to 4 °C, but it was insensitive to inhibitors of glycolysis. P-PEG decreased colchicine-facilitated capping by concanavalin A (ConA). P-PEG also decreased random locomotion of individual as well as population of PMNL. Neither cell viability nor the ability to respond by stimulated locomotion to an attractant was affected. The results indicate that P-PEG modulates PMNL locomotion by altering the membrane structure, e.g. by decreasing the lateral mobility of membrane constituents.     

Quantification of cell surface roughness; a method for studying cell mechanical and adhesive properties

The presence on the surface of nucleated cells of a variety of asperities of different size and shape plays a prominent role in cell-cell and cell-substrate interaction. Also, the organization of these asperities is directly related to cellular cytoskeletal elements. In the present report, we describe a simple and objective method of studying electron micrographs to quantify the roughness of cell contours. Constant-length segments of cell boundaries are compared to reference circular segments with common extremities and enclosing the same area. This procedure was performed with a digitizer connected to a microcomputer, and it was used to analyse model contours or electron micrographs of (i) target tumour cells bound by cytotoxic T lymphocytes and (ii) thymocytes sticking to concanavalin A-coated surfaces. It is shown that this method allows precise quantification of cell deformation in adhesive zones, which may allow absolute evaluation of adhesive stimuli.     

A computational model for the transit of a cancer cell through a constricted microchannel

We propose a three-dimensional computational model to simulate the transient deformation of suspended cancer cells flowing through a constricted microchannel. We model the cell as a liquid droplet enclosed by a viscoelastic membrane, and its nucleus as a smaller stiffer capsule. The cell deformation and its interaction with the suspending fluid are solved through a well-tested immersed boundary lattice Boltzmann method. To identify a minimal mechanical model that can quantitatively predict the transient cell deformation in a constricted channel, we conduct extensive parametric studies of the effects of the rheology of the cell membrane, cytoplasm and nucleus and compare the results with a recent experiment conducted on human leukaemia cells. We find that excellent agreement with the experiment can be achieved by employing a viscoelastic cell membrane model with the membrane viscosity depending on its mode of deformation (shear versus elongation). The cell nucleus limits the overall deformation of the whole cell, and its effect increases with the nucleus size. The present computational model may be used to guide the design of microfluidic devices to sort cancer cells, or to inversely infer cell mechanical properties from their flow-induced deformation.

     

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.     

Finite element analysis of the effects of focal adhesion mechanical properties and substrate stiffness on cell migration

The attachment of cells to the extracellular matrix (ECM) is achieved by the specific binding of cell-surface receptors to ligands present in the ECM. These interactions are important for many biological processes, including cell migration, cancer development, and wound healing. Our objective was to develop a computational model to investigate how focal adhesion mechanical properties, substrate stiffness, and intracellular stresses affect cell-matrix interactions during cell migration on a flat substrate. In our model, the cell-substrate traction was proportional to the bound receptor concentration, relative velocity between the cell and substrate, and the cell-substrate friction coefficient. Simulation results showed that even if the receptor number and ligand density were fixed, the mechanical properties of the focal adhesions still affected cell-ECM interactions. In fact, the cell-substrate traction was biphasic with respect to the friction coefficient, a parameter that can be used to quantify focal adhesion properties. In contrast, the cell speed was a monotonically decreasing function with respect to this parameter. Furthermore, tractions showed greater increases when the maximum intracellular stress was increased from 400 to 600Pa than when substrate stiffness was increased from 0.5 to 100kPa. This mathematical model is able to quantify the effects of focal adhesion mechanical properties, extracellular stiffness, and intracellular stresses on cell-ECM interactions, and should be beneficial to research in cancer development.