Correlation between local cell membrane displacements and filterability of human red blood cells.

Local mechanical fluctuations of the cell membrane of human erythrocytes were shown to involve MgATP- and Mg(2+)-driven fast membrane displacements. We propose that these local bending deformations of the cell membrane are important for cell passage through capillaries. In order to verify this hypothesis, we examined cell membrane fluctuations and filterability of erythrocytes over a wide range of medium osmolalities (180-675 mosmol/kg H2O). The results indicate the existence of a positive correlation between the amplitude of local cell membrane displacements and cell filterability. We suggest that the occurrence of metabolically driven membrane displacements on the side surface of the red blood cell diminishes its bending stiffness and enables it to fold more efficiently upon entrance into blood capillaries. Thus, local cell membrane displacements seem to play an important role in microcirculation.     

The Local Forces Acting on the Mechanotransduction Channel in Hair Cell Stereocilia

In hair cells, mechanotransduction channels are located in the membrane of stereocilia tips, where the base of the tip link is attached. The tip-link force determines the system of other forces in the immediate channel environment, which change the channel open probability. This system of forces includes components that are out of plane and in plane relative to the membrane; the magnitude and direction of these components depend on the channel environment and arrangement. Using a computational model, we obtained the major forces involved as functions of the force applied via the tip link at the center of the membrane. We simulated factors related to channels and the membrane, including finite-sized channels located centrally or acentrally, stiffness of the hypothesized channel-cytoskeleton tether, and bending modulus of the membrane. Membrane forces are perpendicular to the directions of the principal curvatures of the deformed membrane. Our approach allows for a fine vectorial picture of the local forces gating the channel; membrane forces change with the membrane curvature and are themselves sufficient to affect the open probability of the channel.     

The Local Forces Acting on the Mechanotransduction Channel in Hair Cell Stereocilia

In hair cells, mechanotransduction channels are located in the membrane of stereocilia tips, where the base of the tip link is attached. The tip-link force determines the system of other forces in the immediate channel environment, which change the channel open probability. This system of forces includes components that are out of plane and in plane relative to the membrane; the magnitude and direction of these components depend on the channel environment and arrangement. Using a computational model, we obtained the major forces involved as functions of the force applied via the tip link at the center of the membrane. We simulated factors related to channels and the membrane, including finite-sized channels located centrally or acentrally, stiffness of the hypothesized channel-cytoskeleton tether, and bending modulus of the membrane. Membrane forces are perpendicular to the directions of the principal curvatures of the deformed membrane. Our approach allows for a fine vectorial picture of the local forces gating the channel; membrane forces change with the membrane curvature and are themselves sufficient to affect the open probability of the channel.     

A multiscale approach to the elastic moduli of biomembrane networks

We develop equilibrium fluctuation formulae for the isothermal elastic moduli of discrete biomembrane models at different scales. We account for the coupling of large stretching and bending strains of triangulated network models endowed with harmonic and dihedral angle potentials, on the basis of the discrete-continuum approach presented in Schmidt and Fraternali (J Mech Phys Solids 60:172-180, 2012). We test the proposed equilibrium fluctuation formulae with reference to a coarse-grained molecular dynamics model of the red blood cell (RBC) membrane (Marcelli et al. in Biophys J 89:2473-2480, 2005; Hale et al. in Soft Matter 5:3603-3606, 2009), employing a local maximum-entropy regularization of the fluctuating configurations (Fraternali et al. in J Comput Phys 231:528-540, 2012). We obtain information about membrane stiffening/softening due to stretching, curvature, and microscopic undulations of the RBC model. We detect local dependence of the elastic moduli over the RBC membrane, establishing comparisons between the present theory and different approaches available in the literature.     

Atrial natriuretic peptide: direct effects on human red blood cell dynamics.

The ability to deform is an important feature of red blood cells (RBCs) for performing their function of oxygen delivery. Little is known about the hormonal regulation of RBC deformability. Here we report that human atrial natriuretic peptide (ANP) acts directly on human RBCs leading to the elevation of local bending fluctuations of the cell membrane. These changes are accompanied by an increase in the filterability of RBCs. These ANP effects were mimicked by cyclic GMP analogues, suggesting modulation of local membrane bending fluctuations and RBC filterability via a cyclic GMP-dependent pathway. The effect of ANP on the mechanical properties of RBCs suggests that ANP may increase the passage red blood cells through capillaries resulting in an improved oxygen delivery to the tissues.     

Biomechanical Properties of Insect Wings: The Stress Stiffening Effects on the Asymmetric Bending of the Allomyrina dichotoma Beetle's Hind Wing

Although the asymmetry in the upward and downward bending of insect wings is well known, the structural origin of this asymmetry is not yet clearly understood. Some researchers have suggested that based on experimental results, the bending asymmetry of insect wings appears to be a consequence of the camber inherent in the wings. Although an experimental approach can reveal this phenomenon, another method is required to reveal the underlying theory behind the experimental results. The finite element method (FEM) is a powerful tool for evaluating experimental measurements and is useful for studying the bending asymmetry of insect wings. Therefore, in this study, the asymmetric bending of the Allomyrina dichotoma beetle''s hind wing was investigated through FEM analyses rather than through an experimental approach. The results demonstrated that both the stressed stiffening of the membrane and the camber of the wing affect the bending asymmetry of insect wings. In particular, the chordwise camber increased the rigidity of the wing when a load was applied to the ventral side, while the spanwise camber increased the rigidity of the wing when a load was applied to the dorsal side. These results provide an appropriate explanation of the mechanical behavior of cambered insect wings, including the bending asymmetry behavior, and suggest an appropriate approach for analyzing the structural behavior of insect wings.     

The effect of local bending on gating of MscL using a representative volume element and finite element simulation

Many physiological processes such as cell division, endocytosis and exocytosis cause severe local curvature of the cell membrane. Local curvature has been shown experimentally to modulate numerous mechanosensitive (MS) ion channels. In order to quantify the effects of local curvature we introduced a coarse grain representative volume element for the bacterial mechanosensitive ion channel of large conductance (MscL) using continuum elasticity. Our model is designed to be consistent with the channel conformation in the closed and open states to capture its major continuum rheological behavior in response to the local membrane curvature. Herein we show that change in the local curvature of the lipid bilayer can modulate MscL activity considerably by changing both bilayer thickness and lateral pressure profile. Intriguingly, although bending in any direction results in almost the same free-energy cost, inward (cytoplasmic) bending favors channel opening, whereas outward (periplasmic) bending facilitates closing of the narrowest part of the MscL pore. This quantitative study using MscL as a model channel may have wide reaching consequences for the effect of local curvature on the physiological function of other types of prokaryotic and eukaryotic membrane proteins.     

The effect of local bending on gating of MscL using a representative volume element and finite element simulation

Many physiological processes such as cell division, endocytosis and exocytosis cause severe local curvature of the cell membrane. Local curvature has been shown experimentally to modulate numerous mechanosensitive (MS) ion channels. In order to quantify the effects of local curvature we introduced a coarse grain representative volume element for the bacterial mechanosensitive ion channel of large conductance (MscL) using continuum elasticity. Our model is designed to be consistent with the channel conformation in the closed and open states to capture its major continuum rheological behavior in response to the local membrane curvature. Herein we show that change in the local curvature of the lipid bilayer can modulate MscL activity considerably by changing both bilayer thickness and lateral pressure profile. Intriguingly, although bending in any direction results in almost the same free-energy cost, inward (cytoplasmic) bending favors channel opening, whereas outward (periplasmic) bending facilitates closing of the narrowest part of the MscL pore. This quantitative study using MscL as a model channel may have wide reaching consequences for the effect of local curvature on the physiological function of other types of prokaryotic and eukaryotic membrane proteins.     

Local and nonlocal curvature elasticity in bilayer membranes by tether formation from lecithin vesicles.

Bilayer membranes exhibit an elastic resistance to changes in curvature. This resistance depends both on the intrinsic stiffness of the constituent monolayers and on the curvature-induced expansion or compression of the monolayers relative to each other. The monolayers are constrained by hydrophobic forces to remain in contact, but they are capable of independent lateral redistribution to minimize the relative expansion or compression of each leaflet. Therefore, the magnitude of the expansion and compression of the monolayers relative to each other depends on the integral of the curvature over the entire membrane capsule. The coefficient characterizing the membrane stiffness resulting from relative expansion is the nonlocal bending modulus kr. Both the intrinsic (local) bending modulus (kc) and the nonlocal bending modulus (kr) can be measured by the formation of thin cylindrical membrane strands (tethers) from giant phospholipid vesicles. Previously, we reported measurements of kc based on measurements of tether radius as a function of force (Song and Waugh, 1991, J. Biomech. Engr. 112:233). Further analysis has revealed that the contribution from the nonlocal bending stiffness can be detected by measuring the change in the aspiration pressure required to establish equilibrium with increasing tether length. Using this approach, we obtain a mean value for the nonlocal bending modulus kr of approximately 4.1 x 10(-19)J. The range of values is broad (1.1-10.1 x 10(-19)J) and could reflect contributions other than simple mechanical equilibrium. Inclusion of the nonlocal bending stiffness in the calculation of kc results in a value for that modulus of approximately 1.20 +/- 0.17 x 10(-19)J, in close agreement with values obtained by other methods.     

MICROTUBULE ARMS AND CYTOPLASMIC STREAMING AND MICROTUBULE BENDING AND STRETCHING OF INTERTUBULE LINKS IN THE FEEDING TENTACLE OF THE SUCTORIAN CILIATE TOKOPHRYA

Microtubules attached to the pellicle at the tips of tentacles pivot through about 140° on these attachments, splay apart, and bend along their longitudinal axes when feeding occurs. The tubules could be bending in response to pellicular contractions; active bending, sliding, or contraction of the tubules may not be involved. Intertubule links apparently prevent tubules from splaying apart at certain levels. These links are probably under tension during feeding. They stretch; they sometimes become half as thick and eight times as long as they are before feeding. Often, tubules joined together by these links also change in shape; they become slightly flattened and elliptical in cross section. Cytoplasm from the ciliate Tetrahymena is drawn down a feeding tentacle inside an invagination of the Tokophrya cell membrane from the tentacle tip. The positions of arm-bearing microtubules around such invaginations indicate that arms are involved in moving invaginations along. The edges of the perforated Tetrahymena cell membrane are "sealed" to the cell membrane of Tokophrya around each feeding tentacle tip.     

Spectroscopic Investigation of Local Mechanical Impedance of Living Cells

We studied nanoscale mechanical properties of PC12 living cells with a Force Feedback Microscope using two experimental approaches. The first one consists in measuring the local mechanical impedance of the cell membrane while simultaneously mapping the cell morphology at constant force. As the interaction force is increased, we observe the appearance of the sub-membrane cytoskeleton. We compare our findings with the outcome of other techniques. The second experimental approach consists in a spectroscopic investigation of the cell while varying the tip indentation into the membrane and consequently the applied force. At variance with conventional dynamic Atomic Force Microscopy techniques, here it is not mandatory to work at the first oscillation eigenmode of the cantilever: the excitation frequency of the tip can be chosen arbitrary leading then to new spectroscopic AFM techniques. We found in this way that the mechanical response of the PC12 cell membrane is found to be frequency dependent in the 1 kHz - 10 kHz range. In particular, we observe that the damping coefficient consistently decreases when the excitation frequency is increased.     

Mechanical properties of pore-spanning lipid bilayers probed by atomic force microscopy

We measure the elastic response of a free-standing lipid membrane to a local indentation by using an atomic force microscope. Starting point is a planar gold-coated alumina substrate with a chemisorbed 3-mercaptopropionic acid monolayer displaying circular pores of very well defined and tunable size, over which bilayers composed of N,N,-dimethyl-N,N,-dioctadecylammonium bromide or 1,2-dioleoyl-3-trimethylammonium-propane chloride were spread. Centrally indenting these "nanodrums" with an atomic force microscope tip yields force-indentation curves, which we quantitatively analyze by solving the corresponding shape equations of continuum curvature elasticity. Since the measured response depends in a known way on the system geometry (pore size, tip radius) and on material parameters (bending modulus, lateral tension), this opens the possibility to monitor local elastic properties of lipid membranes in a well-controlled setting.     

Mapping correlated membrane pulsations and fluctuations in human cells

The cell membrane and cytoskeleton are dynamic structures that are strongly influenced by the thermo-mechanical background in addition to biologically driven mechanical processes. We used atomic force microscopy (AFM) to measure the local membrane motion of human foreskin fibroblasts (HFFs) which were found to be governed by random and non-random correlated mechanical processes. Interphase cells displayed distinct membrane pulsations in which the membrane was observed to slowly contract upwards followed by a recovery to its initial position. These pulsations occurred one to three times per minute with variable amplitudes (20-100 pN) separated by periods of random baseline fluctuations with amplitudes of <20 pN. Cells were exposed to actin and microtubule (MT) destabilizing drugs and induced into early apoptosis. Mechanical pulsations (20-80 pN) were not prevented by actin or MT depolymerization but were prevented in early apoptotic cells which only displayed small amplitude baseline fluctuations (<20 pN). Correlation analysis revealed that the cell membrane motion is largely random; however several non-random processes, with time constants varying between approximately 2 and 35 s are present. Results were compared to measured cardiomyocyte motion which was well defined and highly correlated. Employing automated positioning of the AFM tip, interphase HFF correlation time constants were also mapped over a 10 microm2 area above the nucleus providing some insights into the spatial variability of membrane correlations. Here, we are able to show that membrane pulsations and fluctuations can be linked to physiological state and cytoskeletal dynamics through distinct sets of correlation time constants in human cells.     

A model for the mechanism of tip extension in pollen tubes

Three main mechanisms are proposed to account for the tip growth of pollen tubes. (1) The tip region is supported against the internal osmotic pressure of the cell by a fibrillar network, composed mainly of microfilaments, that is stabilized by calcium ions. Tip extension is promoted by a lowering of the local cytoplasmic calcium ion concentration, through uptake by the mitochondria and/or endoplasmic reticulum, which leads to a weakening of the fibrillar network. (2) Vesicles, derived from dictyosomes in the main body of the tube, fuse with the apical plasma membrane, providing new membrane and further carbohydrate for the wall. The rate of fusion is proportional to the rate of diffusion of calcium ion across the plasma membrane at the tip. (3) The callose lining present in the pollen tube wall, except at the tip, renders the wall impermeable and restricts entry of calcium ions to the apical plasma membrane. This restriction limits the rate of vesicle fusion, and tube growth, to the tip.This model is discussed in the light of previous observations on the growth and structure of pollen tubes under normal and experimental conditions.     

Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests.

Observation of cell membrane buckling and cell folding in micropipette aspiration experiments was used to evaluate the bending rigidity of the red blood cell membrane. The suction pressure required to buckle the membrane surface initially was found to be about one-half to two-thirds of the pressure that caused the cell to fold and move up the pipet. A simple analytical model for buckling of a membrane disk supported at inner and outer radii correlates well with the observed buckling pressures vs. pipet radii. The buckling pressure is predicted to increase in inverse proportion to the cube of the pipet radius; also, the buckling pressure depends inversely on the radial distance to the toroidal rim of the cell, normalized by the pipet radius. As such, the pressure required to buckle the membrane with 1 X 10(-4) cm diam pipet would be about four times greater than with a 2 X 10(-4) cm pipet. This is the behavior observed experimentally. Based on analysis of the observed buckling data, the membrane bending or curvature elastic modulus is calculated to be 1.8 X 10(-12) dyn-cm.     

Serine and threonine residues bend alpha-helices in the chi(1) = g(-) conformation

The relationship between the Ser, Thr, and Cys side-chain conformation (chi(1) = g(-), t, g(+)) and the main-chain conformation (phi and psi angles) has been studied in a selection of protein structures that contain alpha-helices. The statistical results show that the g(-) conformation of both Ser and Thr residues decreases their phi angles and increases their psi angles relative to Ala, used as a control. The additional hydrogen bond formed between the O(gamma) atom of Ser and Thr and the i-3 or i-4 peptide carbonyl oxygen induces or stabilizes a bending angle in the helix 3-4 degrees larger than for Ala. This is of particular significance for membrane proteins. Incorporation of this small bending angle in the transmembrane alpha-helix at one side of the cell membrane results in a significant displacement of the residues located at the other side of the membrane. We hypothesize that local alterations of the rotamer configurations of these Ser and Thr residues may result in significant conformational changes across transmembrane helices, and thus participate in the molecular mechanisms underlying transmembrane signaling. This finding has provided the structural basis to understand the experimentally observed influence of Ser residues on the conformational equilibrium between inactive and active states of the receptor, in the neurotransmitter subfamily of G protein-coupled receptors.     

Rapid local oscillations of the surface of the human erythrocyte

The transverse displacements of the human erythrocyte surface with amplitude 300-400 nm in the frequency range 0.2-30 Hz are recorded on the minimal area erythrocyte rim (approximately 0.5 X 0.5 microns). These local oscillations of the surface are diminished at hypoosmotic erythrocyte swelling, on addition of substances which increase the membrane rigidity (0.01% glutaraldehyde, 0.5 mM 4-hydroxymercuribenzoate, cell membrane stain--0.002% Heliogen Blue) and on discocyte--echinocyte transformation due to addition of 1-2 mM 2,4-dinitrophenol. The amplitude of transverse displacements is reduced by 1.7-2 times on erythrocytes of patients with inherent microspherocytosis. These erythrocytes have inherent defects in spectrin. It is suggested that spectrin is important for rapid local oscillations of the human erythrocyte surface.     

3D finite element analyses of insertion of the Nucleus standard straight and the Contour electrode arrays into the human cochlea

Previous experimental studies of insertion of the Nucleus standard straight and the Contour arrays into the scala tympani have reported that the electrode arrays cause damage to various cochlear structures. However, the level of insertion-induced damage by these electrode arrays to cochlear structures (the spiral ligament, the basilar membrane and the osseous spiral lamina) has not been quantified. Although it has been suggested that rotation can overcome this resistance and prevent the basilar membrane from being pierced by the tip of the Nucleus standard straight array, there has not been any attempt to study the relationship between the rotation and the reduction of damage to the basilar membrane. In this study, 3D finite element analyses of insertions of the Nucleus standard straight array and the Contour array into the scala tympani have been undertaken. The perforation of the basilar membrane by the tip of the Nucleus standard straight array at the region of 11-14 mm from the round window appears to be compounded by the geometry of the spiral passage of the scala tympani. Anti-clockwise rotations between 25 degrees and 90 degrees applied at the basal end of the electrode array (for the right cochlea) were shown to significantly reduce the contact stresses exerted by the tip on the basilar membrane which support the practice of applying small rotation partway through insertion of electrode array to minimize damage to the basilar membrane. Although the Contour array (with its stylet intact) is stiffer than the Nucleus standard straight array, a slight withdrawal of the stylet from the Contour array before insertion was found to significantly reduce damage by the electrode array to the spiral ligament and the basilar membrane.     

Adhesively-tensed cell membranes: lysis kinetics and atomic force microscopy probing

Membrane tension underlies a range of cell physiological processes. Strong adhesion of the simple red cell is used as a simple model of a spread cell with a finite membrane tension-a state which proves useful for studies of both membrane rupture kinetics and atomic force microscopy (AFM) probing of native structure. In agreement with theories of strong adhesion, the cell takes the form of a spherical cap on a substrate densely coated with poly-L-lysine. The spreading-induced tension, sigma, in the membrane is approximately 1 mN/m, which leads to rupture over many minutes; and sigma is estimated from comparable rupture times in separate micropipette aspiration experiments. Under the sharpened tip of an AFM probe, nano-Newton impingement forces (10-30 nN) are needed to penetrate the tensed erythrocyte membrane, and these forces increase exponentially with tip velocity ( approximately nm/ms). We use the results to clarify how tapping-mode AFM imaging works at high enough tip velocities to avoid rupturing the membrane while progressively compressing it to a approximately 20-nm steric core of lipid and protein. We also demonstrate novel, reproducible AFM imaging of tension-supported membranes in physiological buffer, and we describe a stable, distended network consistent with the spectrin cytoskeleton. Additionally, slow retraction of the AFM tip from the tensed membrane yields tether-extended, multipeak sawtooth patterns of average force approximately 200 pN. In sum we show how adhesive tensioning of the red cell can be used to gain novel insights into native membrane dynamics and structure.     

Bilayer membrane bending stiffness by tether formation from mixed PC-PS lipid vesicles

Recently, a new approach to measure the bending stiffness (curvature elastic modulus) of lipid bilayer membrane was developed (Biophys. J., Vol. 55; pp. 509-517, 1989). The method involves the formation of cylindrical membrane strands (tethers) from bilayer vesicles. The bending stiffness (B) can be calculated from measurements of the tether radius (Rt) as a function of the axial force (f) on the tether: B = f.Rt/2 pi. In the present report, we apply this method to determine the bending stiffness of bilayer membranes composed of mixtures of SOPC (1-stearoyl-2-oleoyl phosphatidyl choline) and POPS (1-palmitoyl-2-oleoyl phosphatidyl serine). Three different mixtures were tested: pure SOPC, SOPC plus 2 percent (mol/mol) POPS, and SOPC plus 16 percent POPS. The bending stiffness determined for these three different lipid mixtures were not significantly different (1.6-1.8 x 10(-12) ergs). Because POPS carries a net negative charge, these results indicate that changes in the density of the membrane surface charge have no effect on the intrinsic rigidity of the membrane. The values we obtain are consistent with published values for the bending stiffness of other membranes determined by different methods. Measurements of the aspiration pressure, tether radius and the tether force were used to verify a theoretical relationship among these quantities at equilibrium. The ratio of the theoretical force to the measured force was 1.12 +/- 0.17.