Richard E. Waugh

Elastic area compressibility modulus of red cell membrane.

Micropipette measurements of isotropic tension vs. area expansion in pre-swollen single human red cells gave a value of 288 +/- 50 SD dyn/cm for the elastic, area compressibility modulus of the total membrane at 25 degrees C. This elastic constant, characterizing the resistance to area expansion or compression, is about 4 X 10(4) times greater than the elastic modulus for shear rigidity; therefore, in situations where deformation of the membrane does not require large isotropic tensions (e.g., in passage through normal capillaries), the membrane can be treated by a simple constitutive relation for a two-dimensionally, incompressible material (i.e. fixed area). The tension was found to be linear and reversible for the range of area changes observed (within the experimental system resolution of 10%). The maximum fractional area expansion required to produce lysis was uniformly distributed between 2 and 4% with 3% average and 0.7% SD. By heating the cells to 50 degrees C, it appears that the structural matrix (responsible for the shear rigidity and most of the strength in isotropic tension) is disrupted and primarily the lipid bilayer resists lysis. Therefore, the relative contributions of the structural matrix and lipid bilayer to the elastic, area compressibility could be estimated. The maximum isotropic tension at 25 degrees C is 10-12 dyn/cm and at 50 degrees C is between 3 and 4 dyn/cm. From this data, the respective compressibilities are estimated at 193 dyn/cm and 95 dyn/cm for structural network and bilayer. The latter value correlates well with data on in vitro, monolayer surface pressure versus area curves at oil-water interfaces.

A Microcantilever Device to Assess the Effect of Force on the Lifetime of Selectin-Carbohydrate Bonds

A microcantilever technique was used to apply force to receptor-ligand molecules involved in leukocyte rolling on blood vessel walls. E-selectin was adsorbed onto 3-microm-diameter, 4-mm-long glass fibers, and the selectin ligand, sialyl Lewis(x), was coupled to latex microspheres. After binding, the microsphere and bound fiber were retracted using a computerized loading protocol that combines hydrodynamic and Hookean forces on the fiber to produce a range of force loading rates (force/time), r(f). From the distribution of forces at failure, the average force was determined and plotted as a function of ln r(f). The slope and intercept of the plot yield the unstressed reverse reaction rate, k(r)(o), and a parameter that describes the force dependence of reverse reaction rates, r(o). The ligand was titrated so adhesion occurred in approximately 30% of tests, implying that >80% of adhesive events involve single bonds. Monte Carlo simulations show that this level of multiple bonding has little effect on parameter estimation. The estimates are r(o) = 0.048 and 0.016 nm and k(r)(o) = 0.72 and 2.2 s(-1) for loading rates in the ranges 200-1000 and 1000-5000 pN s(-1), respectively. Levenberg-Marquardt fitting across all values of r(f) gives r(o) = 0.034 nm and k(r)(o) = 0.82 s(-1). The values of these parameters are in the range required for rolling, as suggested by adhesive dynamics simulations.

Passive mechanical behavior of human neutrophils: power-law fluid.

The mechanical behavior of the neutrophil plays an important role in both the microcirculation and the immune system. Several laboratories in the past have developed mechanical models to describe different aspects of neutrophil deformability. In this study, the passive mechanical properties of normal human neutrophils have been further characterized. The cellular mechanical properties were assessed by single cell micropipette aspiration at fixed aspiration pressures. A numerical simulation was developed to interpret the experiments in terms of cell mechanical properties based on the Newtonian liquid drop model (Yeung and Evans, Biophys. J., 56: 139-149, 1989). The cytoplasmic viscosity was determined as a function of the ratio of the initial cell size to the pipette radius, the cortical tension, aspiration pressure, and the whole cell aspiration time. The cortical tension of passive neutrophils was measured to be about 2.7 x 10(-5) N/m. The apparent viscosity of neutrophil cytoplasm was found to depend on aspiration pressure, and ranged from approximately 500 Pa.s at an aspiration pressure of 98 Pa (1.0 cm H2O) to approximately 50 Pa.s at 882 Pa (9.0 cm H2O) when tested with a 4.0-micron pipette. These data provide the first documentation that the neutrophil cytoplasm exhibits non-Newtonian behavior. To further characterize the non-Newtonian behavior of human neutrophils, a mean shear rate gamma m was estimated based on the numerical simulation. The apparent cytoplasmic viscosity appears to decrease as the mean shear rate increases. The dependence of cytoplasmic viscosity on the mean shear rate can be approximated as a power-law relationship described by mu = mu c(gamma m/gamma c)-b, where mu is the cytoplasmic viscosity, gamma m is the mean shear rate, mu c is the characteristic viscosity at characteristic shear rate gamma c, and b is a material coefficient. When gamma c was set to 1 s-1, the material coefficients for passive neutrophils were determined to be mu c = 130 +/- 23 Pa.s and b = 0.52 +/- 0.09 for normal neutrophils. The power-law approximation has a remarkable ability to reconcile discrepancies among published values of the cytoplasmic viscosity measured using different techniques, even though these values differ by nearly two orders of magnitude. Thus, the power-law fluid model is a promising candidate for describing the passive mechanical behavior of human neutrophils in large deformation. It can also account for some discrepancies between cellular behavior in single-cell micromechanical experiments and predictions based on the assumption that the cytoplasm is a simple Newtonian fluid.

Determination of bilayer membrane bending stiffness by tether formation from giant, thin-walled vesicles

The curvature elastic modulus (bending stiffness) of stearoyloleoyl phosphatidylcholine (SOPC) bilayer membrane is determined from membrane tether formation experiments. R. E. Waugh and R. M. Hochmuth 1987. Biophys. J. 52:391-400) have shown that the radius of a bilayer cylinder (tether) is inversely related to the force supported along its axis. The coefficient that relates the axial force on the tether to the tether radius is the membrane bending stiffness. Thus, the bending stiffness can be calculated directly from measurements of the tether radius as a function of force. Giant (10-50-microns diam) thin-walled vesicles were aspirated into a micropipette and a tether was pulled out of the surface by gravitational forces on small glass beads that had adhered to the vesicle surface. Because the vesicle keeps constant surface area and volume, formation of the tether requires displacement of material from the projection of the vesicle in the pipette. Tethers can be made to grow longer or shorter or to maintain equilibrium by adjusting the aspiration pressure in the micropipette at constant tether force. The ratio of the change in the length of the tether to the change in the projection length is proportional to the ratio of the pipette radius to the tether radius. Thus, knowing the density and diameter of the glass beads and measuring the displacement of the projection as a function of tether length, independent determinations of the force on the tether and the tether radius were obtained. The bending stiffness for an SOPC bilayer obtained from these data is approximately 2.0 x 10(-12) dyn cm, for tether radii in the range of 20-100 nm. An equilibrium relationship between pressure and tether force is derived which closely matches experimental observation.

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.

ENERGY OF DISSOCIATION OF LIPID BILAYER FROM THE MEMBRANE SKELETON OF RED BLOOD CELLS

The association between the lipid bilayer and the membrane skeleton is important to cell function. In red blood cells, defects in this association can lead to various forms of hemolytic anemia. Although proteins involved in this association have been well characterized biochemically, the physical strength of this association is only beginning to be studied. Formation of a small cylindrical strand of membrane material (tether) from the membrane involves separation of the lipid bilayer from the membrane skeleton. By measuring the force required to form a tether, and knowing the contribution to the force due to the deformation of a lipid bilayer, it is possible to calculate the additional contribution to the work of tether formation due to the separation of membrane skeleton from the lipid bilayer. In the present study, we measured the tethering force during tether formation using a microcantilever (a thin, flexible glass fiber) as a force transducer. Numerical calculations of the red cell contour were performed to examine how the shape of the contour affects the calculation of tether radius, and subsequently separation work per unit area W(sk) and bending stiffness k(c). At high aspiration pressure and small external force, the red cell contour can be accurately modeled as a sphere, but at low aspiration pressure and large external force, the contour deviates from a sphere and may affect the calculation. Based on an energy balance and numerical calculations of the cell contour, values of the membrane bending stiffness k(c) = 2.0 x 10(-19) Nm and the separation work per unit area W(sk) = 0.06 mJ/m2 were obtained.

A piconewton force transducer and its application to measurement of the bending stiffness of phospholipid membranes.

The bending stiffness of a phospholipid bilayer (kc) was measured by forming thin bilayer cylinders (tethers) from giant phospholipid vesicles. Based on the balance of forces, the tether force was expeeted to be proportional to the square root of the membrane tension, with a constant of proportionality containingk>c. The membrane tension was controlled via the aspiration pressure in a micropipette used to hold the vesicle. The force on the tether was generated by an electromagnet acting on a paramagnetic bead attached to the vesicle surface. The magnitude of the force was determined from measurements on the magnet current which was adjusted to maintain the position of the bead. Measurements were performed on vesicles composed of stearoyl-oleoyl-phosphatidylcholine plus 5% (by mole) biotinylated phosphatidylethanolamine to mediate adhesion to streptavidin-coated beads. From each vesicle, tethers were formed repeatedly at different values of the membrane tension. The expected relationship between membrane tension and tether force was observed. The mean value ofkc for 10 different vesicles was 1.17×10−19 J (SD=0.08×10−19 J). The precision of these data demonstrates the reliability of this approach, which avoids uncertainties of interpretation and measurement that may be associated with other methods for determiningkc.

Reductions of erythrocyte membrane viscoelastic coefficients reflect spectrin deficiencies in hereditary spherocytosis

Hereditary spherocytosis is a common hemolytic anemia associated with deficiencies in spectrin, the principal structural protein of the erythrocyte membrane-skeleton. We have examined 20 different individuals from 10 spherocytosis kindreds and 2 elliptocytosis kindreds to determine the effects of different levels of spectrin deficiency on the viscoelastic properties of the erythrocyte membrane. Micropipettes were used to perform single-cell micromechanical measurements of approximately 1,000 individual cells to determine the membrane elastic shear modulus, the apparent membrane bending stiffness, and whole cell recovery time constant for the different cell populations. The membrane viscosity was calculated by the product of the shear modulus and the recovery time constant. Results show correlation between the fractional reduction in shear modulus and the fractional reduction in spectrin content (determined by spectrin radioimmunoassay) and spectrin density (determined by the ratios of spectrin to band 3 on electrophoresis gels) suggesting that membrane shear elasticity is directly proportional to the surface density of spectrin on the membrane (P less than 0.001). The apparent membrane bending stiffness is also reduced in proportion to the density of spectrin (P less than 0.001). The membrane viscosity is reduced relative to control (P less than 0.001), but the nature of the relationship between spectrin density and membrane viscosity is less clearly defined. These studies document striking relationships between partial deficiencies of erythrocyte spectrin and specific viscoelastic properties of the mutant membranes.

Mechanical equilibrium of thick, hollow, liquid membrane cylinders

The mechanical equilibrium of bilayer membrane cylinders is analyzed. The analysis is motivated by the observation that mechanically formed membrane strands (tethers) can support significant axial loads and that the tether radius varies inversely with the axial force. Previously, thin shell theory has been used to analyze the tether formation process, but this approach is inadequate for describing and predicting the equilibrium state of the tether itself. In the present work the membrane is modeled as two adjacent, thick, anisotropic liquid shells. The analysis predicts an inverse relationship between axial force and tether radius, which is consistent with experimental observation. The area expansivity modulus and bending stiffness of the tether membrane are calculated using previously measured values of tether radii. These calculated values are consistent with values of membrane properties measured previously. Application of the analysis to precise measurements of the relationship between tether radius and axial force will provide a novel method for determining the mechanical properties of biomembrane.

LFA-1 and Mac-1 Define Characteristically Different Intralumenal Crawling and Emigration Patterns for Monocytes and Neutrophils In Situ

To exit blood vessels, most (∼80%) of the lumenally adhered monocytes and neutrophils crawl toward locations that support transmigration. Using intravital confocal microscopy of anesthetized mouse cremaster muscle, we separately examined the crawling and emigration patterns of monocytes and neutrophils in blood-perfused unstimulated or TNF-α–activated venules. Most of the interacting cells in microvessels are neutrophils; however, in unstimulated venules, a greater percentage of the total monocyte population is adherent compared with neutrophils (58.2 ± 6.1% versus 13.6 ± 0.9%, adhered/total interacting), and they crawl for significantly longer distances (147.3 ± 13.4 versus 61.8 ± 5.4 μm). Intriguingly, after TNF-α activation, monocytes crawled for significantly shorter distances (67.4 ± 9.6 μm), resembling neutrophil crawling. Using function-blocking Abs, we show that these different crawling patterns were due to CD11a/CD18 (LFA-1)- versus CD11b/CD18 (Mac-1)-mediated crawling. Blockade of either Mac-1 or LFA-1 revealed that both LFA-1 and Mac-1 contribute to monocyte crawling; however, the LFA-1–dependent crawling in unstimulated venules becomes Mac-1 dependent upon inflammation, likely due to increased expression of Mac-1. Mac-1 alone was responsible for neutrophil crawling in both unstimulated and TNF-α–activated venules. Consistent with the role of Mac-1 in crawling, Mac-1 block (compared with LFA-1) was also significantly more efficient in blocking TNF-α–induced extravasation of both monocytes and neutrophils in cremaster tissue and the peritoneal cavity. Thus, mechanisms underlying leukocyte crawling are important in regulating the inflammatory responses by regulating the numbers of leukocytes that transmigrate.