Model for Probing Membrane-Cortex Adhesion by Micropipette Aspiration and Fluctuation Spectroscopy

We propose a model for membrane-cortex adhesion that couples membrane deformations, hydrodynamics, and kinetics of membrane-cortex ligands. In its simplest form, the model gives explicit predictions for the critical pressure for membrane detachment and for the value of adhesion energy. We show that these quantities exhibit a significant dependence on the active acto-myosin stresses. The model provides a simple framework to access quantitative information on cortical activity by means of micropipette experiments. We also extend the model to incorporate fluctuations and show that detailed information on the stability of membrane-cortex coupling can be obtained by a combination of micropipette aspiration and fluctuation spectroscopy measurements.     

Stability analysis of micropipette aspiration of neutrophils

During micropipette aspiration, neutrophil leukocytes exhibit a liquid-drop behavior, i.e., if a neutrophil is aspirated by a pressure larger than a certain threshold pressure, it flows continuously into the pipette. The point of the largest aspiration pressure at which the neutrophil can still be held in a stable equilibrium is called the critical point of aspiration. Here, we present a theoretical analysis of the equilibrium behavior and stability of a neutrophil during micropipette aspiration with the aim to rigorously characterize the critical point. We take the energy minimization approach, in which the critical point is well defined as the point of the stability breakdown. We use the basic liquid-drop model of neutrophil rheology extended by considering also the neutrophil elastic area expansivity. Our analysis predicts that the behavior at large pipette radii or small elastic area expansivity is close to the one predicted by the basic liquid-drop model, where the critical point is attained slightly before the projection length reaches the pipette radius. The effect of elastic area expansivity is qualitatively different at smaller pipette radii, where our analysis predicts that the critical point is attained at the projection lengths that may significantly exceed the pipette radius.     

Single Cell Adhesion Assay Using Computer Controlled Micropipette

Cell adhesion is a fundamental phenomenon vital for all multicellular organisms. Recognition of and adhesion to specific macromolecules is a crucial task of leukocytes to initiate the immune response. To gain statistically reliable information of cell adhesion, large numbers of cells should be measured. However, direct measurement of the adhesion force of single cells is still challenging and today’s techniques typically have an extremely low throughput (5–10 cells per day). Here, we introduce a computer controlled micropipette mounted onto a normal inverted microscope for probing single cell interactions with specific macromolecules. We calculated the estimated hydrodynamic lifting force acting on target cells by the numerical simulation of the flow at the micropipette tip. The adhesion force of surface attached cells could be accurately probed by repeating the pick-up process with increasing vacuum applied in the pipette positioned above the cell under investigation. Using the introduced methodology hundreds of cells adhered to specific macromolecules were measured one by one in a relatively short period of time (∼30 min). We blocked nonspecific cell adhesion by the protein non-adhesive PLL-g-PEG polymer. We found that human primary monocytes are less adherent to fibrinogen than their in vitro differentiated descendants: macrophages and dendritic cells, the latter producing the highest average adhesion force. Validation of the here introduced method was achieved by the hydrostatic step-pressure micropipette manipulation technique. Additionally the result was reinforced in standard microfluidic shear stress channels. Nevertheless, automated micropipette gave higher sensitivity and less side-effect than the shear stress channel. Using our technique, the probed single cells can be easily picked up and further investigated by other techniques; a definite advantage of the computer controlled micropipette. Our experiments revealed the existence of a sub-population of strongly fibrinogen adherent cells appearing in macrophages and highly represented in dendritic cells, but not observed in monocytes.     

Squeezing and detachment of living cells

The interaction of living cells with their environment is linked to their adhesive and elastic properties. Even if the mechanics of simple lipid membranes is fairly well understood, the analysis of single cell experiments remains challenging in part because of the mechanosensory response of cells to their environment. To study the mechanical properties of living cells we have developed a tool that borrows from micropipette aspiration techniques, atomic force microscopy, and the classical Johnson-Kendall-Roberts test. We show results from a study of the adhesion properties of living cells, as well as the elastic response and relaxation. We present models that are applied throughout the different stages of an experiment, which indicate that the contribution of the different components of the cell are active at various stages of compression, retraction, and detachment. Finally, we present a model that attempts to elucidate the surprising logarithmic relaxation observed when the cell is subjected to a given deformation.     

Inhibition of Intercellular Adhesion in Herpex Simplex Virus Infection by Glycyrrhizin

Herpes simplex virus (HSV) is one of the most common viruses infecting humans and animals. Cellular adhesion is increased in HSV and plays a role in pathogenesis of inflammatory response during this viral infection. In our study, we studied a potential role of glycyrrhizin in disrupting cellular adhesion in HSV. We isolated rat cerebral capillary vessel endothelial cells (CCECs) and polymorphonuclear leukocytes (PMN) and evaluated intercellular adhesion between these cells by micropipette aspiration technique. The adhesion force and stress between CCEC and PMN were significantly (P < 0.01) increased in HSV infection. Glycyrrhizin perfusion significantly (P < 0.01) reduced adhesion force and stress between CCEC and PMN. In conclusion, glycyrrhizin may attenuate inflammatory responses in HSV by inhibition of adhesion between CCEC and PMN.     

A power-law rheology-based finite element model for single cell deformation

Physical forces can elicit complex time- and space-dependent deformations in living cells. These deformations at the subcellular level are difficult to measure but can be estimated using computational approaches such as finite element (FE) simulation. Existing FE models predominantly treat cells as spring-dashpot viscoelastic materials, while broad experimental data are now lending support to the power-law rheology (PLR) model. Here, we developed a large deformation FE model that incorporated PLR and experimentally verified this model by performing micropipette aspiration on fibroblasts under various mechanical loadings. With a single set of rheological properties, this model recapitulated the diverse micropipette aspiration data obtained using three protocols and with a range of micropipette sizes. More intriguingly, our analysis revealed that decreased pipette size leads to increased pressure gradient, potentially explaining our previous counterintuitive finding that decreased pipette size leads to increased incidence of cell blebbing and injury. Taken together, our work leads to more accurate rheological interpretation of micropipette aspiration experiments than previous models and suggests pressure gradient as a potential determinant of cell injury.     

On the use of ultrasounds to quantify the longitudinal threshold force to detach osteoblastic cells from a conditioned glass substrate

Cell adhesion on a biomaterial is an important phase of the cell-material interactions and the quality of this phase governs the success of the biomaterial integration. Understanding of the phenomena of cell adhesion and in particular understanding of cell adhesion on biomaterials is of crucial importance for the development of new biomaterials with excellent biocompatibility. One of the physical quantitative indexes to evaluate the quality of cell-material adhesion is its strength. Determining the strength of adhesive bonds requires applying external forces to the cells. Thus, a few methods have been developed to evaluate the strength of cell-material adhesion (micropipette, microplates, microcantilever, ...). These methods apply shear forces on adherent cells. The aim of our work is the development of a new ultrasonic characterization method of cellular adhesion on substrates. With our method, longitudinal acoustic waves are applied on cell culture to impose a longitudinal strain on cells. Only the cells subjected to a sufficient level of strain will be detached from the substrate. The idea is to correlate cell detachment rate to the longitudinal strain threshold supported by cells. From this result, we can deduce the critical force just sufficient to detach the cell. This global method can be adapted for different cell types and for different substrates. This method can provide an evaluation of the effect of functionalization on substrates. The technique is investigated for the 200 kHz ultrasound frequency. An insonificator adapted to the use of cell culture boxes was developed and calibrated. Tests were carried out on a glass substrate with or without biological conditioning. We used the MC3T3-E1 osteoblastic cell line. Our results to date provide the value of the necessary force to detach with reproducibility osteoblastic cells from glass.     

Effects of pressure on red blood cell geometry during micropipette aspiration

Micropipette aspiration is a potentially useful and accurate technique to measure red blood cell (RBC) geometry. Individual RBCs are partially aspirated and from the resulting sphere diameter, total cell length, and pipette diameter, membrane area and cell volume can be calculated. In this study we have focused on possible shape artifacts associated with the aspirated portion of RBC. We observed that the apparent RBC geometry (calculated area and volume) changed markedly (P < 0.001) with the applied aspiration pressure; for normal human RBC the area increased by 5.6 +/- 0.6% and volume decreased by 4.7 +/- 0.6% when the aspiration pressure was increased from 20 to 100 mm water. The calculated membrane area dilation modulus was 7.4 dyn/ cm, which is far below the expected value, and microscopic observations revealed a membrane folding artifact as a possible artifact. These assumptions were strengthened by using a short-duration (3 s) pressure peak of 20-100-20 mm water. The folding then disappeared permanently, but a small (0.31 +/- 0.09%; P < 0.001) area decrease was detected which yields a realistic dilation modulus of 215 dyn/cm. We conclude that membrane folding can critically affect RBC micropipette measurements and that a transient pressure peak can unfold the RBC membrane, thus allowing accurate measurements of RBC geometry.     

Receptor-mediated cell attachment and detachment kinetics. I. Probabilistic model and analysis.

The kinetics of receptor-mediated cell adhesion to a ligand-coated surface play a key role in many physiological and biotechnology-related processes. We present a probabilistic model of receptor-ligand bond formation between a cell and surface to describe the probability of adhesion in a fluid shear field. Our model extends the deterministic model of Hammer and Lauffenburger (Hammer, D.A., and D.A. Lauffenburger. 1987. Biophys. J. 52:475-487) to a probabilistic framework, in which we calculate the probability that a certain number of bonds between a cell and surface exists at any given time. The probabilistic framework is used to account for deviations from ideal, deterministic behavior, inherent in chemical reactions involving relatively small numbers of reacting molecules. Two situations are investigated: first, cell attachment in the absence of fluid stress; and, second, cell detachment in the presence of fluid stress. In the attachment case, we examine the expected variance in bond formation as a function of attachment time; this also provides an initial condition for the detachment case. Focusing then on detachment, we predict transient behavior as a function of key system parameters, such as the distractive fluid force, the receptor-ligand bond affinity and rate constants, and the receptor and ligand densities.(ABSTRACT TRUNCATED AT 250 WORDS)     

Quantifying Shear-Induced Deformation and Detachment of Individual Adherent Sickle Red Blood Cells

Vaso-occlusive crisis, a common painful complication of sickle cell disease, is a complex process triggered by intercellular adhesive interactions among blood cells and the endothelium in all human organs (e.g., the oxygen-rich lung as well as hypoxic systems such as liver and kidneys). We present a combined experimental-computational study to quantify the adhesive characteristics of sickle mature erythrocytes (SMEs) and irreversibly sickled cells (ISCs) under flow conditions mimicking those in postcapillary venules. We employed an in vitro microfluidic cell adherence assay, which is coated uniformly with fibronectin. We investigated the adhesion dynamics of SMEs and ISCs in pulsatile flow under well-controlled hypoxic conditions, inferring the cell adhesion strength by increasing the flow rate (or wall shear stress (WSS)) until the onset of cell detachment. In parallel, we performed simulations of individual SMEs and ISCs under shear. We introduced two metrics to quantify the adhesion process, the cell aspect ratio (AR) as a function of WSS and its rate of change (the dynamic deformability index). We found that the AR of SMEs decreases significantly with the increase of WSS, consistent between the experiments and simulations. In contrast, the AR of ISCs remains constant in time and independent of the flow rate. The critical WSS value for detaching a single SME in oxygenated state is in the range of 3.9–5.5 Pa depending on the number of adhesion sites; the critical WSS value for ISCs is lower than that of SMEs. Our simulations show that the critical WSS value for SMEs in deoxygenated state is above 6.2 Pa (multiple adhesion sites), which is greater than their oxygenated counterparts. We investigated the effect of cell shear modulus on the detachment process; we found that for the same cell adhesion spring constant, the higher shear modulus leads to an earlier cell detachment from the functionalized surface. These findings may aid in the understanding of individual roles of sickle cell types in sickle cell disease vaso-occlusion.     

Cell Adhesion Strength Is Controlled by Intermolecular Spacing of Adhesion Receptors

Spatial patterning of biochemical cues on the micro- and nanometer scale controls numerous cellular processes such as spreading, adhesion, migration, and proliferation. Using force microscopy we show that the lateral spacing of individual integrin receptor-ligand bonds determines the strength of cell adhesion. For spacings ≥90 nm, focal contact formation was inhibited and the detachment forces as well as the stiffness of the cell body were significantly decreased compared to spacings ≤50 nm. Analyzing cell detachment at the subcellular level revealed that rupture forces of focal contacts increase with loading rate as predicted by a theoretical model for adhesion clusters. Furthermore, we show that the weak link between the intra- and extracellular space is at the intracellular side of a focal contact. Our results show that cells can amplify small differences in adhesive cues to large differences in cell adhesion strength.     

Leukocyte rolling on P-selectin: a three-dimensional numerical study of the effect of cytoplasmic viscosity

Rolling leukocytes deform and show a large area of contact with endothelium under physiological flow conditions. We studied the effect of cytoplasmic viscosity on leukocyte rolling using our three-dimensional numerical algorithm that treats leukocyte as a compound droplet in which the core phase (nucleus) and the shell phase (cytoplasm) are viscoelastic fluids. The algorithm includes the mechanical properties of the cell cortex by cortical tension and considers leukocyte microvilli that deform viscoelastically and form viscous tethers at supercritical force. Stochastic binding kinetics describes binding of adhesion molecules. The leukocyte cytoplasmic viscosity plays a critical role in leukocyte rolling on an adhesive substrate. High-viscosity cells are characterized by high mean rolling velocities, increased temporal fluctuations in the instantaneous velocity, and a high probability for detachment from the substrate. A decrease in the rolling velocity, drag, and torque with the formation of a large, flat contact area in low-viscosity cells leads to a dramatic decrease in the bond force and stable rolling. Using values of viscosity consistent with step aspiration studies of human neutrophils (5-30 Pa·s), our computational model predicts the velocities and shape changes of rolling leukocytes as observed in vitro and in vivo.     

Measurements of growth cone adhesion to culture surfaces by micromanipulation

Neurons were grown on plastic surfaces that were untreated, or treated with polylysine, laminin, or L1 and their growth cones were detached from their culture surface by applying known forces with calibrated glass needles. This detachment force was taken as a measure of the force of adhesion of the growth cone. We find that on all surfaces, lamellipodial growth cones require significantly greater detachment force than filopodial growth cones, but this differences is, in general, due to the greater area of lamellipodial growth cones compared to filopodial growth cones. That is, the stress (force/unit area) required for detachment was similar for growth cones of lamellipodial and filopodial morphology on all surfaces, with the exception of lamellipodial growth cones on L1-treated surfaces, which had a significantly lower stress of detachment than on other surfaces. Surprisingly, the forces required for detachment (760-3,340 mudynes) were three to 15 times greater than the typical resting axonal tension, the force exerted by advancing growth cones, or the forces of retraction previously measured by essentially the same method. Nor did we observe significant differences in detachment force among growth cones of similar morphology on different culture surfaces, with the exception of lamellipodial growth cones on L1-treated surfaces. These data argue against the differential adhesion mechanism for growth cone guidance preferences in culture. Our micromanipulations revealed that the most mechanically resistant regions of growth cone attachment were confined to quite small regions typically located at the ends of filopodia and lamellipodia. Detached growth cones remained connected to the substratum at these regions by highly elastic retraction fibers. The closeness of contact of growth cones to the substratum as revealed by interference reflection microscopy (IRM) did not correlate with our mechanical measurements of adhesion, suggesting that IRM cannot be used as a reliable estimator of growth cone adhesion.     

The human erythrocyte membrane skeleton may be an ionic gel. III. Micropipette aspiration of unswollen erythrocytes

We have carried out a theoretical analysis of micropipette aspiration of unswollen erythrocytes using the protein-gel-lipid-bilayer membrane model and taking into account that the modulus of area compression of the membrane skeleton may depend on the environmental conditions. Our analysis shows that the aspiration pressure needed to obtain a certain membrane projection length is strongly dependent on the ratio between the membrane skeleton modulus of area compression and the elastic shear modulus. Our analysis therefore predicts that micropipette aspiration of unswollen erythrocytes may be a sensitive method for detection of changes in this ratio. The analysis thus also shows that micropipette aspiration of unswollen erythrocytes can not be used to determine the membrane shear modulus unless something is known about the membrane skeleton modulus of area compression.     

The reaction-limited kinetics of membrane-to-surface adhesion and detachment

Biological adhesion is frequently mediated by specific membrane proteins (adhesion molecules). Starting with the notion of adhesion molecules, we present a simple model of the physics of membrane-to-surface attachment and detachment. This model consists of coupling the equations for deformation of an elastic membrane with equations for the chemical kinetics of the adhesion molecules. We propose a set of constitutive laws relating bond stress to bond strain and also relating the chemical rate constants of the adhesion molecules to bond strain. We derive an exact formula for the critical tension. We also describe a fast and accurate finite difference algorithm for generating numerical solutions of our model. Using this algorithm, we are able to compute the transient behaviour during the initial phases of adhesion and detachment as well as the steady-state geometry of adhesion and the velocity of the contact. An unexpected consequence of our model is the predicted occurrence of states in which adhesion cannot be reversed by application of tension. Such states occur only if the adhesion molecules have certain constitutive properties (catch-bonds). We discuss the rational for such catch-bonds and their possible biological significance. Finally, by analysis of numerical solutions, we derive an accurate and general expression for the steady-state velocity of attachment and detachment. As applications of the theory, we discuss data on the rolling velocity of granulocytes in post-capillary venules and data on lectin-mediated adhesion of red cells.     

Micropipette aspiration on the outer hair cell lateral wall

The mechanical properties of the lateral wall of the guinea pig cochlear outer hair cell were studied using the micropipette aspiration technique. A fire-polished micropipette with an inner diameter of approximately 4 microm was brought into contact with the lateral wall and negative pressure was applied. The resulting deformation of the lateral wall was recorded on videotape and subjected to morphometric analysis. The relation between the length of the aspirated portion of the cell and aspiration pressure is characterized by the stiffness parameter, K(s) = 1.07 +/- 0.24 (SD) dyn/cm (n = 14). Values of K(s) do not correlate with the original cell length, which ranges from 29 to 74 microm. Theoretical analysis based on elastic shell theory applied to the experimental data yields an estimate of the effective elastic shear modulus, mu = 15.4 +/- 3.3 dyn/cm. These data were obtained at subcritical aspiration pressures, typically less than 10 cm H2O. After reaching a critical (vesiculation) pressure, the cytoplasmic membrane appeared to separate from the underlying structures, a vesicle with a length of 10-20 microm was formed, and the cytoplasmic membrane resealed. This vesiculation process was repeated until a cell-specific limit was reached and no more vesicles were formed. Over 20 vesicles were formed from the longest cells in the experiment.     

Enforced detachment of red blood cells adhering to surfaces: statics and dynamics

We investigated the mechanical strength of adhesion and the dynamics of unbinding of red blood cells to solid surfaces. Two different situations were tested: 1), native red blood cells nonspecifically adhered to glass surfaces coated with positively charged polymers and 2), biotinylated red blood cells specifically adhered to glass surfaces decorated with streptavidin, which has a high binding affinity for biotin. We used micropipette manipulation for forming and subsequently breaking the adhesive contact through a stepwise micromechanical procedure. Analysis of cell deformations provided the relation between force and contact radius, which was found to be in good agreement with theoretical predictions. We further demonstrated that the separation energy could be precisely derived from the measure of rupture forces and the cell shape. Finally, the dynamics of detachment was analyzed as a function of the applied force and the initial size of the adhesive patch. Our experiments were supported by original theoretical predictions, which allowed us to correlate the measured separation times with the molecular parameters (e.g., activation barrier, receptor-ligand characteristic length) derived from force measurements at the single bond level.     

Simulation of cell rolling and adhesion on surfaces in shear flow. Microvilli-coated hard spheres with adhesive springs.

The adhesion of cells to ligand-coated surfaces in viscous shear flow is an important step in many physiological processes, such as the neutrophil-mediated inflammatory response, lymphocyte homing, and tumor cell metastasis. This article describes a calculational method that allows simulation of the interaction of a single cell with a ligand-coated surface. The cell is idealized as a microvilli-coated hard sphere covered with adhesive springs. The distribution of microvilli on the cell surface, the distribution of receptors on microvilli tips, and the forward and reverse reaction between receptor and ligand are all simulated using random number sampling of appropriate probability functions. The velocity of the cell at each time step in the simulation results from a balance of hydrodynamic, colloidal, and bonding forces; the bonding force is derived by summing the individual contributions of each receptor-ligand tether. The model can simulate the effect of many parameters on adhesion, such as the number of receptors on microvilli tips, the density of ligand, the rates of reaction between receptor and ligand, the stiffness of the springs, the response of springs to extension, and the magnitude of hydrodynamic stresses. By varying these parameters, the model can successfully recreate the entire range of expected and observed adhesive phenomena, from completely unencumbered motion, to rolling, to transient attachment, to firm adhesion. Also, the model can provide meaningful statistical measures of adhesion, including the mean and variance in velocity, rate constants for cell attachment and detachment, and the frequency of adhesion. We find a critical modulating parameter of adhesion is the fractional spring slippage, which relates the extension of a bond to its rate of breakage; the higher the slippage, the faster the breakage for the same extension. Changes in the fractional spring slippage can radically change the adhesive behavior of a cell. We show that stiffer springs will only serve to increase adhesion if the fractional slippage remains small. In addition, our simulations emphasize the importance of reaction rates between receptor and ligand, rather than affinity, as being the key determinant of adhesion under flow. These results suggest reaction rates and response to stress of adhesion molecules must be independently measured to understand how adhesion is controlled at the molecular level.     

A Computational Study of Stress Fiber-Focal Adhesion Dynamics Governing Cell Contractility

We apply a recently developed model of cytoskeletal force generation to study a cell’s intrinsic contractility, as well as its response to external loading. The model is based on a nonequilibrium thermodynamic treatment of the mechanochemistry governing force in the stress fiber-focal adhesion system. Our computational study suggests that the mechanical coupling between the stress fibers and focal adhesions leads to a complex, dynamic, mechanochemical response. We collect the results in response maps whose regimes are distinguished by the initial geometry of the stress fiber-focal adhesion system, and by the external load on the cell. The results from our model connect qualitatively with recent studies on the force response of smooth muscle cells on arrays of polymeric microposts.