Bending stiffness of lipid bilayers: IV. Interpretation of red cell shape change.

Two mechanisms are operative when the resting shape of human red cells is changed into an echinocyte or a stomatocyte. The first (bilayer couple) is a differential change in the surface area of the two monolayers. It rests on the two-dimensional isotropic elasticity of the two monolayers and their fixed distance. The second (single layer) is a change in the average cone angle of the molecules comprising a monolayer. It rests on the intrinsic bending elasticity of each single layer. With a few exceptions the first mechanism has been quoted to interpret experimentally observed shape changes. To reconsider this preference two types of spontaneous curvatures (in bilayer couple bending and in single-layer bending) are defined. It is shown that (a) disregarding the single-layer mechanism is not justified and (b) there is too little basic information for quantitative interpretations of shape change.     

Interaction of the antivirus agents remantadine and amantadine with lipid membranes and the influence on the curvature of human red cells

Surface potential difference, conductance, and elasticity changes of bilayer lipid membranes induced by the antivirus drugs amantadine and remantadine were measured. An influence on the human erythrocyte shape was shown. Both drugs are stomatocytogenic. The adsorption at the cytoplasmatic membrane was electrophoretically proved. The heat-induced vesiculation is partly inhibited. No microvesicles were observed. Instead, large tails which did not detach from the cell body were seen. The general conclusion is that these amphiphilic adamantane derivatives are membrane agents which modify membrane interaction processes, possibly by influencing the bending properties.     

A mechanism of formation of protein-free regions in the red cell membrane: the rupture of the membrane skeleton

The process of rupture and redistribution of the red cell membrane skeleton is analyzed theoretically. Following the emergence of the rupture the spectrin-actin network is redistributed on the cytoplasmic surface of the membrane bilayer. Due to the interaction of the membrane skeleton and integral proteins the redistribution of the spectrin-actin network leads to the release of purely lipid regions of the membrane. The scale of the protein redistribution caused by the rupture of the membrane skeleton and the size of the lipid domains produced depend on the shape of the membrane and the value of the electrical interaction of the membrane proteins. The lipid domains occurring as a result of the rupture and relaxation of the spectrinactin network can spontaneously increase or decrease its area. The criteria determining the conditions which result in the system's evolutions leading to the domain growth have been obtained. The character of the evolution is determined by the shape of the membrane region in which the rupture occurs as well as the relation between the effective linear tension of the rupture boundary and the modulus of elasticity of the spectrin-actin network.     

Numerical simulation of a single cell passing through a narrow slit

The narrow slit between endothelial cells that line the microvessel wall is the principal pathway for tumor cell extravasation to the surrounding tissue. To understand this crucial step for tumor hematogenous metastasis, we used dissipative particle dynamics method to investigate an individual cell passing through a narrow slit numerically. The cell membrane was simulated by a spring-based network model which can separate the internal cytoplasm and surrounding fluid. The effects of the cell elasticity, cell shape, nucleus and slit size on the cell transmigration through the slit were investigated. Under a fixed driving force, the cell with higher elasticity can be elongated more and pass faster through the slit. When the slit width decreases to 2/3 of the cell diameter, the spherical cell becomes jammed despite reducing its elasticity modulus by 10 times. However, transforming the cell from a spherical to ellipsoidal shape and increasing the cell surface area by merely 9.3 % can enable the cell to pass through the narrow slit. Therefore, the cell shape and surface area increase play a more important role than the cell elasticity in cell passing through the narrow slit. In addition, the simulation results indicate that the cell migration velocity decreases during entrance but increases during exit of the slit, which is qualitatively in agreement with the experimental observation.     

Remodeling the shape of the skeleton in the intact red cell.

The role of the membrane skeleton in determining the shape of the human red cell was probed by weakening it in situ with urea, a membrane-permeable perturbant of spectrin. Urea by itself did not alter the biconcave disk shape of the red cell; however, above threshold conditions (1.5 M, 37 degrees C, 10 min), it caused an 18% reduction in the membrane elastic shear modulus. It also potentiated the spiculation of cells by lysophosphatidylcholine. These findings suggest that the contour of the resting cell is not normally dependent on the elasticity of or tension in the membrane skeleton. Rather, the elasticity of the skeleton stabilizes membranes against deformation. Urea treatment also caused the projections induced both by micropipette aspiration and by lysophosphatidylcholine to become irreversible. Furthermore, urea converted the axisymmetric conical spicules induced by lysophosphatidylcholine into irregular, curved and knobby spicules; i.e., echinocytosis became acanthocytosis. Unlike controls, the ghosts and membrane skeletons obtained from urea-generated acanthocytes were imprinted with spicules. These data suggest that perturbing interprotein associations with urea in situ allowed the skeleton to evolve plastically to accommodate the contours imposed upon it by the overlying membrane.     

Red blood cell shapes as explained on the basis of curvature elasticity.

Assuming that the shape of red blood cells is controlled by the curvature elasticity of the surrounding membrane, we fit theoretical shapes to the contours Evans and co-workers determined by interference microscopy. Very good agreement is obtained for disc shapes. The fit is not so good for less common shapes, which may result from Evans' parametric representation and from the interference of shear elasticity.     

Elastic Free Energy Drives the Shape of Prevascular Solid Tumors

It is well established that the mechanical environment influences cell functions in health and disease. Here, we address how the mechanical environment influences tumor growth, in particular, the shape of solid tumors. In an in vitro tumor model, which isolates mechanical interactions between cancer tumor cells and a hydrogel, we find that tumors grow as ellipsoids, resembling the same, oft-reported observation of in vivo tumors. Specifically, an oblate ellipsoidal tumor shape robustly occurs when the tumors grow in hydrogels that are stiffer than the tumors, but when they grow in more compliant hydrogels they remain closer to spherical in shape. Using large scale, nonlinear elasticity computations we show that the oblate ellipsoidal shape minimizes the elastic free energy of the tumor-hydrogel system. Having eliminated a number of other candidate explanations, we hypothesize that minimization of the elastic free energy is the reason for predominance of the experimentally observed ellipsoidal shape. This result may hold significance for explaining the shape progression of early solid tumors in vivo and is an important step in understanding the processes underlying solid tumor growth.     

Mechanics of curved plasma membrane vesicles: resting shapes, membrane curvature, and in-plane shear elasticity

Highly curved cell membrane structures, such as plasmalemmal vesicles (caveolae) and clathrin-coated pits, facilitate many cell functions, including the clustering of membrane receptors and transport of specific extracellular macromolecules by endothelial cells. These structures are subject to large mechanical deformations when the plasma membrane is stretched and subject to a change of its curvature. To enhance our understanding of plasmalemmal vesicles we need to improve the understanding of the mechanics in regions of high membrane curvatures. We examine here, theoretically, the shapes of plasmalemmal vesicles assuming that they consist of three membrane domains: an inner domain with high curvature, an outer domain with moderate curvature, and an outermost flat domain, all in the unstressed state. We assume the membrane properties are the same in these domains with membrane bending elasticity as well as in-plane shear elasticity. Special emphasis is placed on the effects of membrane curvature and in-plane shear elasticity on the mechanics of vesicle during unfolding by application of membrane tension. The vesicle shapes were computed by minimization of bending and in-plane shear strain energy. Mechanically stable vesicles were identified with characteristic membrane necks. Upon stretch of the membrane, the vesicle necks disappeared relatively abruptly leading to membrane shapes that consist of curved indentations. While the resting shape of vesicles is predominantly affected by the membrane spontaneous curvatures, the membrane shear elasticity (for a range of values recorded in the red cell membrane) makes a significant contribution as the vesicle is subject to stretch and unfolding. The membrane tension required to unfold the vesicle is sensitive with respect to its shape, especially as the vesicle becomes fully unfolded and approaches a relative flat shape.     

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.     

Perception of Elasticity in the Kinetic Illusory Object with Phase Differences in Inducer Motion

Background

It is known that subjective contours are perceived even when a figure involves motion. However, whether this includes the perception of rigidity or deformation of an illusory surface remains unknown. In particular, since most visual stimuli used in previous studies were generated in order to induce illusory rigid objects, the potential perception of material properties such as rigidity or elasticity in these illusory surfaces has not been examined. Here, we elucidate whether the magnitude of phase difference in oscillation influences the visual impressions of an object''s elasticity (Experiment 1) and identify whether such elasticity perceptions are accompanied by the shape of the subjective contours, which can be assumed to be strongly correlated with the perception of rigidity (Experiment 2).

Methodology/Principal Findings

In Experiment 1, the phase differences in the oscillating motion of inducers were controlled to investigate whether they influenced the visual impression of an illusory object''s elasticity. The results demonstrated that the impression of the elasticity of an illusory surface with subjective contours was systematically flipped with the degree of phase difference. In Experiment 2, we examined whether the subjective contours of a perceived object appeared linear or curved using multi-dimensional scaling analysis. The results indicated that the contours of a moving illusory object were perceived as more curved than linear in all phase-difference conditions.

Conclusions/Significance

These findings suggest that the phase difference in an object''s motion is a significant factor in the material perception of motion-related elasticity.     

The role of mucus viscoelasticity in cough clearance

The relationships between mucus rheology, depth of mucus layer and clearance by simulated cough were examined in a study employing a model plexiglass trachea lined with gels formed from locust bean gum crosslinked with sodium tetraborate. The viscoelastic properties of the mucus simulants were determined by magnetic rheometry at 100 rad/s and expressed as mechanical impedance (dynamic stress/strain ratio) and loss tangent. Cough was simulated by opening a solenoid valve connecting the model trachea to a pressurized tank, using an upstream flow-constrictive element to shape the flow profile to approximate the pattern seen in a normal adult. Mucus clearance was quantitated by observing the movement of contrasting marker particles placed in the mucus layer. The median particle displacement was defined as the clearance index, Cl. For any initial depth of mucus, Cl increased with driving pressure in the tank, and for a given driving pressure, Cl increased linearly with increasing mucus depth. For a given driving pressure and depth, Cl decreased with increasing mechanical impedance of the mucus. At constant mechanical impedance, Cl increased with increasing loss tangent, in other words, cough clearance was impeded more by elasticity than viscosity. Mucus clearance was associated with transient wave formation in the lining layer. Thus dependence on viscoelasticity is consistent with observations that airflow-mucus interaction and wave formation are impeded by elasticity. The clearance vs. loss tangent relationship for cough is opposite to that found for ciliary clearance (Biorheology 1980, 17, 249), suggesting a natural balance in viscosity and elasticity for mucus to be cleared by both mechanisms.(ABSTRACT TRUNCATED AT 250 WORDS)     

Interaction of plasma lipoproteins and apolipoproteins with lipid bilayer membranes

It was shown that the interaction of lipoproteins (LP) with bilayer lipid membranes (BLM) resulted in some changes in the physical-chemical properties of the membranes. Adsorption of very low and low density lipoproteins (VLDL and LDL) at concentrations of 5-8 g protein/ml increased the surface potential difference and decreased transversal elasticity module of the bilayer. LP concentrations higher than the mentioned ones increased BLM conductance and caused instability and disruption of the membranes. The same effects were revealed for high density lipoproteins (HDL) at higher concentrations--15-20 micrograms protein/ml. The effect of apolipoproteins in the interaction of LP with BLM was investigated. It is proposed that apolipoproteins and especially apo B are the main factor which affects the nonreceptor interactions of LP with the membranes.     

Effects of external pressures on the pressure-volume relation of the left ventricle

The effects of ventricular geometry, muscle mass, muscle elasticity and external pressures on the pressure-volume and muscle stiffness-stress relations have been quantitated on the basis of a theoretical model. Data taken from patients before and after interventions with nitroprusside and angiotensin were applied to the model in order to explain the possible causes for the marked shifts in the pressure-volume relations. The results indicate that (a) ventricular geometry does not markedly alter the pressure-volume and stiffness-stress relations unless there is a drastic change from a spherical shape to an ellipsoidal shape orvice versa, (b) increases in muscle mass and muscle elasticity of the order of 30% result in significant alterations in the P-V relations but are not the cause for the parallel shifts unless accompanied by substantial external pressures, (c) the parallel shifts in the pressure-volume relations can be accounted for entirely by the presence of external pressures without changes in muscle mass or muscle elasticity. Thus manipulation of right ventricular pressures or pericardial pressures by drug interventions may be useful in the treatment of left heart disease and the presence of such pressures must be considered in the analysis of ventricular function curves.     

Chained vesicles in vascular endothelial cells.

There is extensive ultrastructural evidence in endothelium for the presence of chained vesicles or clusters of attached vesicles, and they are considered to be involved in specific transport mechanisms, such as the formation of trans-endothelial channels. However, few details are known about their mechanical characteristics. In this study, the formation mechanism and mechanical aspects of vascular endothelial chained vesicles are investigated theoretically, based on membrane bending strain energy analysis. The shape of the axisymmetric vesicles was computed on the assumption that the cytoplasmic side of the vesicle has a molecular layer or cytoskeleton attached to the lipid bilayer, which induces a spontaneous curvature in the resting state. The bending strain energy is the only elasticity involved, while the shear elasticity is assumed to be negligible. The surface area of the membrane is assumed to be constant due to constant lipid bilayer thickness. Mechanically stable shapes of chained vesicles are revealed, in addition to a cylindrical tube shape. Unfolding of vesicles into a more flattened shape is associated with increase in bending energy without a significant increase in membrane tension. These results provide insights into the formation mechanism and mechanics of the chained vesicle.     

Characterization of a potent platelet aggregation inhibitor from Agkistrodon rhodostoma snake venom

By means of CM-Sephadex C-50 column chromatography and gel filtration on Sephadex G-75 and G-50 columns, a potent platelet aggregation inhibitor was purified and characterized. It was a glycoprotein with a molecular weight of 31,000. It was devoid of phospholipase A, ADPase, esterase and fibrino(geno)lytic activities. It inhibited dose-dependently the aggregation of washed platelets induced by collagen, thrombin, sodium arachidonate, platelet activating factor and ionophore A23187 with a similar IC50 (5-10 micrograms/ml). It was also active in platelet-rich plasma, with an IC50 of 10-15 micrograms/ml. The venom inhibitor reduced the elasticity of whole blood clot and inhibited the thrombin-induced clot retraction of platelet-rich plasma. These activities were related to its inhibitory activity on platelet aggregation rather than blood coagulation. The venom inhibitor had various effects on [14C]serotonin release stimulated by aggregation agonists. It had no effect on thromboxane B2 formation of platelets stimulated by sodium arachidonate, collagen and ionophore A23187. The presence of this venom inhibitor prior to the initiation of aggregation was a prerequisite for the maintenance of its maximal activity. It showed a similar inhibitory effect on collagen or thrombin-induced aggregation even when it was added after the platelets had undergone the shape change. High fibrinogen levels partially antagonized its activity. The venom inhibitor completely inhibited the fibrinogen-induced aggregation of alpha-chymotrypsin-treated platelets. It is concluded that this venom inhibitor interferes with the interaction of fibrinogen with fibrinogen receptors, leading to inhibition of aggregation.     

Functional diversity buffers the effects of a pulse perturbation on the dynamics of tritrophic food webs

Biodiversity decline causes a loss of functional diversity, which threatens ecosystems through a dangerous feedback loop: This loss may hamper ecosystems’ ability to buffer environmental changes, leading to further biodiversity losses. In this context, the increasing frequency of human‐induced excessive loading of nutrients causes major problems in aquatic systems. Previous studies investigating how functional diversity influences the response of food webs to disturbances have mainly considered systems with at most two functionally diverse trophic levels. We investigated the effects of functional diversity on the robustness, that is, resistance, resilience, and elasticity, using a tritrophic—and thus more realistic—plankton food web model. We compared a non‐adaptive food chain with no diversity within the individual trophic levels to a more diverse food web with three adaptive trophic levels. The species fitness differences were balanced through trade‐offs between defense/growth rate for prey and selectivity/half‐saturation constant for predators. We showed that the resistance, resilience, and elasticity of tritrophic food webs decreased with larger perturbation sizes and depended on the state of the system when the perturbation occurred. Importantly, we found that a more diverse food web was generally more resistant and resilient but its elasticity was context‐dependent. Particularly, functional diversity reduced the probability of a regime shift toward a non‐desirable alternative state. The basal‐intermediate interaction consistently determined the robustness against a nutrient pulse despite the complex influence of the shape and type of the dynamical attractors. This relationship was strongly influenced by the diversity present and the third trophic level. Overall, using a food web model of realistic complexity, this study confirms the destructive potential of the positive feedback loop between biodiversity loss and robustness, by uncovering mechanisms leading to a decrease in resistance, resilience, and potentially elasticity as functional diversity declines.     

Computational Analysis of Dynamic Interaction of Two Red Blood Cells in a Capillary

The dynamic interaction of two red blood cells (RBCs) in a capillary is investigated computationally by the two-fluid model, including their deformable motion and interaction. For characterization of the deformation, the RBC membrane is treated as a curved two-dimensional shell with finite thickness by the shell model, and allowed to undergo the stretching strain and bending deformation. Moreover, a Morse potential is adopted to model the intercellular interaction for the aggregation behavior, which is characterized as the weak attraction at far distance and strong repulsion at near distance. For validation of the present technique, the dynamic interaction of two RBCs in static blood plasma is simulated firstly, where the RBCs aggregate slowly until a balanced configuration is achieved between the deformation and aggregation forces. The balanced configuration is in good agreement with the results reported previously. Three important effects on the dynamic behavior of RBCs are then analyzed, and they are the initial RBC shape, RBC deformability, and the intercellular interaction strength. It is found that the RBC is less deformed into a well-known parachute shape when the initial RBC shape is larger. Similarly, if the elastic shear modulus and bending stiffness of RBC membrane increase, the RBC resistance to deformation becomes higher, such that the RBC is less deformed. The simulation results also demonstrate that the RBC deformability strongly depends on the intercellular interaction strength. The RBCs deform more easily as the intercellular interaction strength increases.     

Langevin dynamics of conformational transformations induced by the charge–curvature interaction

The role of thermal fluctuations in the conformational dynamics of a single closed filament is studied. It is shown that, due to the interaction between charges and bending degrees of freedom, initially circular chains may undergo transformation to polygonal shape.     

Cell contraction caused by microtubule disruption is accompanied by shape changes and an increased elasticity measured by scanning acoustic microscopy

The state of crosslinking of microfilaments and the state of myosin-driven contraction are the main determinants of the mechanical properties of the cell cortex underneath the membrane, which is significant for the mechanism of shaping cells. Therefore, any change in the contractile state of the actomyosin network would alter the mechanical properties and finally result in shape changes. The relationship of microtubules to the mechanical properties of cells is still obscure. The main problem arises because disruption of microtubules enhances acto-myosin-driven contraction. This reaction and its impact on cell shape and elasticity have been investigated in single XTH-2 cells. Microtubule disruption was induced by colcemid, a polymerization inhibitor. The reaction was biphasic: a change in cell shape from a fried egg shape to a convex surface topography was accompanied by an increase in elastic stiffness of the cytoplasm, measured as longitudinal sound velocity revealed by scanning acoustic microscope. Elasticity increases in the cell periphery and reaches its peak after 30 min. Subsequently while the cytoplasm retracts from the periphery, longitudinal sound velocity (elasticity) decreases. Simultaneously, a two- to threefold increase of F-actin and alignment of stress fibers from the cell center to cell-cell junctions in dense cultures are induced, supposedly a consequence of the increased tension.