Intermonolayer friction and surface shear viscosity of lipid bilayer membranes

The flow behavior of lipid bilayer membranes is characterized by a surface viscosity for in-plane shear deformations, and an intermonolayer friction coefficient for slip between the two leaflets of the bilayer. Both properties have been studied for a variety of coarse-grained double-tailed model lipids, using equilibrium and nonequilibrium molecular dynamics simulations. For lipids with two identical tails, the surface shear viscosity rises rapidly with tail length, while the intermonolayer friction coefficient is less sensitive to the tail length. Interdigitation of lipid tails across the bilayer midsurface, as observed for lipids with two distinct tails, strongly enhances the intermonolayer friction coefficient, but hardly affects the surface shear viscosity. The simulation results are compared against the available experimental data.     

Lateral mobility of integral proteins in red blood cell tethers.

The red blood cell membrane is a complex material that exhibits both solid- and liquidlike behavior. It is distinguished from a simple lipid bilayer capsule by its mechanical properties, particularly its shear viscoelastic behavior and by the long-range mobility of integral proteins on the membrane surface. Subject to sufficiently large extension, the membrane loses its shear rigidity and flows as a two-dimensional fluid. These experiments examine the change in integral protein mobility that accompanies the mechanical phenomenon of extensional failure and liquidlike flow. A flow channel apparatus is used to create red cell tethers, hollow cylinders of greatly deformed membrane, up to 36-microns long. The diffusion of proteins within the surface of the membrane is measured by the technique of fluorescence redistribution after photobleaching (FRAP). Integral membrane proteins are labeled directly with a fluorescein dye (DTAF). Mobility in normal membrane is measured by photobleaching half of the cell and measuring the rate of fluorescence recovery. Protein mobility in tether membrane is calculated from the fluorescence recovery rate after the entire tether has been bleached. Fluorescence recovery rates for normal membrane indicate that more than half the labeled proteins are mobile with a diffusion coefficient of approximately 4 x 10(-11) cm2/s, in agreement with results from other studies. The diffusion coefficient for proteins in tether membrane is greater than 1.5 x 10(-9) cm2/s. This dramatic increase in diffusion coefficient indicates that extensional failure involves the uncoupling of the lipid bilayer from the membrane skeleton.     

Experimental Study of a Starting Vortex Ring Generated by a Thin Circular Disk

The formation process of vortex ring generated by a thin circular disk was studied experimentally in this paper. A thin circular disk installed a linear motion stage was used to generate the vortex rings. Digital Particle Image Velocimetry (DPIV) was used to measure the velocity and vorticity fields. The finite-time Lyapunov exponent field corresponding to the vortex flow was computed to identify Lagrangian coherent structures of the starting vortex. The results reveal the existence of a flux window between repelling Lagrangian Coherent Structures (rLCS) and attracting Lagrangian Coherent Structures (aLCS), through which the shear flow is entrained into the vortex. The flux window is closed gradually during the starting process. Once the flux window shut down, the formation process of the vortex ring finishes, as the shear flow with vorticity cannot be entrained in the vortex ring.     

Red blood cell orientation in orbit C = 0.

Two modes of behavior of single human red cells in a shear field have been described. It is known that in low viscosity media and at shear rates less than 20 s-1, the cells rotate with a periodically varying angular velocity, in accord with the theory of Jeffery (1922) for oblate spheroids. In media of viscosity greater than approximately 5 mPa s and sufficiently high shear rates, the cells align themselves at a constant angle to the direction of flow with the membrane undergoing tank-tread motion. Also, in low viscosity media, as the shear rate is increased, more and more cells lie in the plane of shear, undergoing spin with their axes of symmetry aligned with the vorticity axis of the shear field in an orbit "C = 0" (Goldsmith and Marlow, 1972). We have explored this latter phenomenon using two experimental methods. First, the erythrocytes were observed in the rheoscope and their diameters measured. Forward light scattering patterns were correlated with the red cell orientation mode. Light flux variations after flow onset or stop were measured, and the characteristic times of erythrocyte orientation and disorientation were assessed. The characteristic time of erythrocyte orientation in Orbit C = 0 is proportional to the inverse of the shear rate. The corresponding coefficient of proportionality depends on the suspending medium viscosity eta o. The disorientation time tau D, after flow has been stopped, is such that the ratio tau D/eta o is independent of the initial applied shear stress. However, tau D is much shorter than one would expect if pure Brownian motion were involved. The proportion of erythrocytes in orbit C = 0 was also measured. It was found that this proportion is a function of both the shear rate and eta o. At low values of eta o, the proportion increases with increasing shear rate and then reaches a plateau. For higher values of eta o (5 to 10 mPa s), the proportion of RBC in orbit C = 0 is a decreasing function of the shear stress. A critical transition between orbit C = 0 and parallel alignment was observed at high values of eta o, when the shear stress is on the order of 1 N/m2. Finally, the effect of altering membrane viscoelastic properties (by heat or diamide treatment) was tested. The proportion of oriented cells is a steep decreasing function of red cell rigidity.     

Differences in the modulation of collective membrane motions by ergosterol, lanosterol, and cholesterol: a dynamic light scattering study

A dynamic light scattering setup was used to study the undulations of freely suspended planar lipid bilayers, the so-called black lipid membranes, over a previously inaccessible range of frequency and wave number. A pure synthetic lecithin bilayer, 1,2-dielaidoyl-sn-3-glycero-phoshatidylcholine (DEPC), and binary mixtures of DEPC with 40 mol % of cholesterol, ergosterol, or lanosterol were studied. By analyzing the dynamic light scattering data (oscillation and damping curves) in terms of transverse shear motion, we extracted the lateral tension and surface viscosity of the composite bilayers for each sterol. Cholesterol gave the strongest increase in lateral tension (approximately sixfold) with respect to the DEPC control, followed by lanosterol (approximately twofold), and ergosterol (1.7-fold). Most interestingly, only cholesterol simultaneously altered the surface viscosity of the bilayer by almost two orders of magnitude, whereas the other two sterols did not affect this parameter. We interpret this unique behavior of cholesterol as a result of its previously established out-of-plane motion which allows the molecule to cross the bilayer midplane, thereby effectively coupling the bilayer leaflets to form a highly flexible but more stable composite membrane.     

Measuring Material Microstructure Under Flow Using 1-2 Plane Flow-Small Angle Neutron Scattering

A new small-angle neutron scattering (SANS) sample environment optimized for studying the microstructure of complex fluids under simple shear flow is presented. The SANS shear cell consists of a concentric cylinder Couette geometry that is sealed and rotating about a horizontal axis so that the vorticity direction of the flow field is aligned with the neutron beam enabling scattering from the 1-2 plane of shear (velocity-velocity gradient, respectively). This approach is an advance over previous shear cell sample environments as there is a strong coupling between the bulk rheology and microstructural features in the 1-2 plane of shear. Flow-instabilities, such as shear banding, can also be studied by spatially resolved measurements. This is accomplished in this sample environment by using a narrow aperture for the neutron beam and scanning along the velocity gradient direction. Time resolved experiments, such as flow start-ups and large amplitude oscillatory shear flow are also possible by synchronization of the shear motion and time-resolved detection of scattered neutrons. Representative results using the methods outlined here demonstrate the useful nature of spatial resolution for measuring the microstructure of a wormlike micelle solution that exhibits shear banding, a phenomenon that can only be investigated by resolving the structure along the velocity gradient direction. Finally, potential improvements to the current design are discussed along with suggestions for supplementary experiments as motivation for future experiments on a broad range of complex fluids in a variety of shear motions.     

Is the surface area of the red cell membrane skeleton locally conserved?

The incompressibility of the lipid bilayer keeps the total surface area of the red cell membrane constant. Local conservation of membrane surface area requires that each surface element of the membrane skeleton keeps its area when its aspect ratio is changed. A change in area would require a flow of lipids past the intrinsic proteins to which the skeleton is anchored. in fast red cell deformations, there is no time for such a flow. Consequently, the bilayer provides for local area conservation. In quasistatic deformations, the extent of local change in surface area is the smaller the larger the isotropic modulus of the skeleton in relation to the shear modulus. Estimates indicate: (a) the velocity of relative flow between lipid and intrinsic proteins is proportional to the gradient in normal tension within the skeleton and inversely proportional to the viscosity of the bilayer; (b) lateral diffusion of lipids is much slower than this flow; (c) membrane tanktreading at frequencies prevailing in vivo as well as the release of a membrane tongue from a micropipette are fast deformations; and (d) the slow phase in micropipette aspiration may be dominated by a local change in skeleton surface.     

Transient shear stresses on a suspension cell in turbulence

A model flow field representative of Kolmogorov eddies in turbulence is proposed, and its two parameters are expressed in terms of the known bioreactor variables epsilon, the rate of turbulent power dissipation, and nu, the fluid kinematic viscosity. The trajectory through this flow field of a small sphere representing a cell is determined, and from that the time-varying local shear rate can be found. This allows calculation of the shear stress at any point on the sphere's surface as it rotates in and moves through the model eddy. The maximum shear stress imposed on the cell by the surrounding turbulence has a range of 0.5-5 dyn/cm(2), and can be estimated by 5.33rho(epsilonnu)(1/2). The shear stress has two major frequency components with ranges of 1-4 and 20-80 s(-1); the higher frequency component is estimated by 0.678(epsilon/nu)(1/2). The rotation of the direction of the shear stress vector at each point on the cell's surface is also discussed. Two ways in which external stresses might affect cell growth are proposed.     

Modeling of orthokinetic flocculation of Saccharomyces cerevisiae.

This study examined the flocculation behavior of two Saccharomyces cerevisiae strains expressing either Flo1 (LCC1209) genotype or NewFlo (LCC125) phenotype in a laminar flow field by measurement of the fundamental flocculation parameter, the orthokinetic capture coefficient. This orthokinetic capture coefficient was measured as a function of shear rate (5.95-223 s(-1)) and temperature (5-45 degrees C). The capture coefficients of these suspensions were directly proportional to the inverse of shear rate, and exhibited an increase as the temperature was increased to 45 degrees C. The capture coefficient of pronase-treated cells was also measured over similar shear rate and temperature range. A theory, which predicts capture coefficient values due to zymolectin interactions, was simplified from that developed by Long et al. [Biophys. J. 76: (1999) 1112]. This new modified theory uses estimates of: (1) cell wall densities of zymolectins and carbohydrate ligands; (2) cell wall collision contact area; and (3) the forward rate coefficient of binding to predict theoretical capture coefficients. A second model that involves both zymolectin interactions and DLVO forces was used to describe the phenomenon of yeast flocculation at intermediate shear ranges, to explain yeast flocculation in laminar flow.     

In vivo demonstration of flow recirculation and turbulence downstream of graded stenoses in canine arteries

The velocity field around arterial stenoses was investigated using a pulsed doppler velocimeter in vivo. Asymmetric zones of recirculation were identified by systolic flow reversal in the post-stenotic field in carotid and iliac arteries of anesthetised dogs. There was a close correlation between shear intensity and turbulence as estimated by the velocity difference between the jet and the recirculation zone and by maximum spectral width respectively. Under the conditions of these experiments, stenosis grade (% diameter reduction) dominated hemodynamic variables such as Reynolds number, oscillation and pulsatility in determining the intensity of turbulence. The method used does not appear to have sufficient resolution to distinguish between turbulence and discrete oscillating velocities (vorticity) nor to allow determination of wall shear stress though the pattern of change of the latter is similar to that found downstream of axisymmetric stenosis in models using steady flow.     

Systematic measurements of interleaflet friction in supported bilayers

When lipid membranes curve or are subjected to strong shear forces, the two apposed leaflets of the bilayer slide past each other. The drag that one leaflet creates on the other is quantified by the coefficient of interleaflet friction, b. Existing measurements of this coefficient range over several orders of magnitude, so we used a recently developed microfluidic technique to measure it systematically in supported lipid membranes. Fluid shear stress was used to force the top leaflet of a supported membrane to slide over the stationary lower leaflet. Here, we show that this technique yields a reproducible measurement of the friction coefficient and is sensitive enough to detect differences in friction between membranes made from saturated and unsaturated lipids. Adding cholesterol to saturated and unsaturated membranes increased interleaflet friction significantly. We also discovered that fluid shear stress can reversibly induce gel phase in supported lipid bilayers that are close to the gel-transition temperature.     

Approximating hemodynamics of cerebral aneurysms with steady flow simulations

Computational fluid dynamics (CFD) simulations can be employed to gain a better understanding of hemodynamics in cerebral aneurysms and improve diagnosis and treatment. However, introduction of CFD techniques into clinical practice would require faster simulation times. The aim of this study was to evaluate the use of computationally inexpensive steady flow simulations to approximate the aneurysm's wall shear stress (WSS) field. Two experiments were conducted. Experiment 1 compared for two cases the time-averaged (TA), peak systole (PS) and end diastole (ED) WSS field between steady and pulsatile flow simulations. The flow rate waveform imposed at the inlet was varied to account for variations in heart rate, pulsatility index, and TA flow rate. Consistently across all flow rate waveforms, steady flow simulations accurately approximated the TA, but not the PS and ED, WSS field. Following up on experiment 1, experiment 2 tested the result for the TA WSS field in a larger population of 20 cases covering a wide range of aneurysm volumes and shapes. Steady flow simulations approximated the space-averaged WSS with a mean error of 4.3%. WSS fields were locally compared by calculating the absolute error per node of the surface mesh. The coefficient of variation of the root-mean-square error over these nodes was on average 7.1%. In conclusion, steady flow simulations can accurately approximate the TA WSS field of an aneurysm. The fast computation time of 6 min per simulation (on 64 processors) could help facilitate the introduction of CFD into clinical practice.     

A numerical study of flow in curved tubes simulating coronary arteries

Numerical simulations of pulsatile flow in coronary arteries which take into account the curvature associated with the bending of arteries over the surface of the heart are presented for resting, excited and drug induced states. The study was motivated by reported observations of atherosclerotic plaque localization on the inner curvature of coronary arteries. The simulated flow field appears quasi-steady under resting conditions with wall shear stress always highest on the outside wall and only a single secondary flow vortex in the half tube. However, reversal of wall shear stress direction at the inside wall does occur under resting flow conditions and this is not a quasi-steady characteristic. The flow field is markedly unsteady under excited conditions with wall shear stress sometimes peaking on the inside wall and an increase in the magnitude of wall shear stress reversal on the inside wall. However, only a single secondary flow vortex in the half tube is observed. Implications of the simulations for the role of fluid mechanics in coronary artery atherosclerosis are also discussed.     

Two-dimensional microelectrophoresis in supported lipid bilayers

We report the application of supported bilayers for two-dimensional microelectrophoresis. This method allows the lateral separation and accumulation of charged amphiphilic molecular probes in bilayers by application of an electric field parallel to the bilayer surface. Diffusion coefficient and mobility of the fluorescent probes are determined by observation of the fluorescence recovery after photobleaching (pattern bleaching). The diffusion coefficients and the mobilities of oppositely charged fluorescent probes in one bilayer can be determined independently from a single measurement. By analysis of the motion of charged and uncharged probes in one membrane one can distinguish between the motion caused by the electric field acting on the charge of individual probes and that caused by frictional forces due to electroosmosis.     

Analytical approximations for the orientation distribution of small dipolar particles in steady shear flows

 Analytic approximations are obtained to solutions of the steady Fokker-Planck equation describing the probability density functions for the orientation of dipolar particles in a steady, low-Reynolds-number shear flow and a uniform external field. Exact computer algebra is used to solve the equation in terms of a truncated spherical harmonic expansion. It is demonstrated that very low orders of approximation are required for spheres but that spheroids introduce resolution problems in certain flow regimes. Moments of the orientation probability density function are derived and applications to swimming cells in bioconvection are discussed. A separate asymptotic expansion is performed for the case in which spherical particles are in a flow with high vorticity, and the results are compared with the truncated spherical harmonic expansion. Agreement between the two methods is excellent. Received 10 February 1997; received in revised form 26 May 1997     

Shear-Induced Migration of a Transmembrane Protein within a Vesicle

Biomembranes feature phospholipid bilayers and serve as the interface between cells or organelles and the extracellular and/or cellular environment. Lipids can move freely throughout the membrane; the lipid bilayer behaves like a fluid. Such fluidity is important in terms of the actions of membrane transport proteins, which often mediate biological functions; membrane protein motion has attracted a great deal of attention. Because the proteins are small, diffusion phenomena are often in play, but flow-induced transport has rarely been addressed. Here, we used a dissipative particle dynamics approach to investigate flow-induced membrane protein transport. We analyzed the drift of a membrane protein located within a vesicle. Under the influence of shear flow, the protein gradually migrated toward the vorticity axis via a random walk, and the probability of retention around the axis was high. To understand the mechanism of protein migration, we varied both shear strength and protein size. Protein migration was induced by the balance between the drag and thermodynamic diffusion forces and could be represented by the Péclet number. These results improve our understanding of flow-induced membrane protein transport.     

Membrane viscoplastic flow.

In this paper, a theory of viscoplasticity formulated by Prager and Hohenemser is developed for a two-dimensional membrane surface and applied to the analysis of the flow of "microtethers" pulled from red blood cells attached to glass substrates. The viscoplastic flow involves two intrinsic material constants: yield shear and surface viscosity. The intrinsic viscosity for plastic flow of membrane is calculated to be 1 X 10(-2) dyn-s/cm from microtether flow experiments, three orders of magnitude greater than surface viscosities of lipid membrane components. The fluid dissipation is dominated by the flow of a structural matrix which has exceeded its yield shear. The yield shear is the maximum shear resultant that the membrane can sustain before it begins to deform irreversibly. The yield shear is found to be in the range 2-8 X 10(-2) dyn/cm, two or three orders of magnitude smaller than the isotropic tension required to lyse red cells.     

Rheology and ultrasound scattering from aggregated red cell suspensions in shear flow

The shear flow dynamics of reversible red cell aggregates in dense suspensions were investigated by ultrasound scattering, to study the shear disruption processes of Rayleigh clusters and examine the effective mean field approximation used in microrheological models. In a first section, a rheo-acoustical model, in the Rayleigh scattering regime, is proposed to describe the shear stress dependence of the low frequency scattered power in relation to structural parameters. The fractal scattering regime characterizing the anisotropic scattering from flocs of size larger than the ultrasound wavelength is further discussed. In the second section, we report flow-dependent changes in the low-frequency scattering coefficient in a plane-plane flow geometry to analyze the shear disruption processes of hardened or deformable red cell aggregates in neutral dextran polymer solution. Rheo-acoustical experiments are examined on the basis of the rheo-acoustical model and the effective medium approximation. The ability of ultrasound scattering technique to determine the critical disaggregation shear stress and to give quantitative information on particle surface adhesive energy is analyzed. Lastly, the shear-thinning behavior of weakly aggregated hardened or deformable red cells is described.