Classification of Functional Movement Disorders with Resting-State Functional Magnetic Resonance Imaging

Introduction: Functional movement disorder (FMD) is a type of functional neurological disorder characterized by abnormal movements that patients do not perceive as self-generated. Prior imaging studies show a complex pattern of altered activity, linking regions of the brain involved in emotional responses, motor control, and agency. This study aimed to better characterize these relationships by building a classifier using a support vector machine to accurately distinguish between 61 FMD patients and 59 healthy controls using features derived from resting-state functional magnetic resonance imaging. Materials and Methods: First, we selected 66 seed regions based on prior related studies, then we calculated the full correlation matrix between them before performing recursive feature elimination to winnow the feature set to the most predictive features and building the classifier. Results: We identified 29 features of interest that were highly predictive of the FMD condition, classifying patients and controls with 80% accuracy. Several key features included regions in the right sensorimotor cortex, left dorsolateral prefrontal cortex, left cerebellum, and left posterior insula. Conclusions: The features selected by the model highlight the importance of the interconnected relationship between areas associated with emotion, reward, and sensorimotor integration, potentially mediating communication between regions associated with motor function, attention, and executive function. Exploratory machine learning was able to identify this distinctive abnormal pattern, suggesting that alterations in functional linkages between these regions may be a consistent feature of the condition in many FMD patients. Clinical-Trials.gov ID: NCT00500994 Impact statement Our research presents novel results that further elucidate the pathophysiology of functional movement disorder (FMD) with a machine learning model that classifies FMD and healthy controls correctly 80% of the time. Herein, we demonstrate how known differences in resting-state functional magnetic resonance imaging connectivity in FMD patients can be leveraged to better understand the complex pattern of neural changes in these patients. Knowing that there are measurable predictable differences in brain activity in patients with FMD may help both clinicians and patients conceptualize and better understand the illness at the point of diagnosis and during treatment. Our methods demonstrate how an effective combination of machine learning and qualitative approaches to analyzing functional brain connectivity can enhance our understanding of abnormal patterns of brain activity in FMD patients.

Longitudinal changes in network homogeneity in presymptomatic C9orf72 mutation carriers

The risk for carriers of repeat expansion mutations in C9orf72 to develop amyotrophic lateral sclerosis and frontotemporal dementia increases with age. Functional magnetic resonance imaging studies have shown reduced connectivity in symptomatic carriers, but it is not known whether connectivity declines throughout life as an acceleration of the normal aging pattern. In this study, we examined intra-network homogeneity (NeHo) in 5 functional networks in 15 presymptomatic C9+ carriers over an 18-month period and compared to repeated scans in 34 healthy controls and 27 symptomatic C9+ carriers. The longitudinal trajectory of NeHo in the somatomotor, dorsal attention, and default mode networks in presymptomatic carriers differed from aging controls and symptomatic carriers. In somatomotor networks, NeHo increased over time in regions adjacent to regions where symptomatic carriers had reduced NeHo. In the default network, the posterior cingulate exhibited age-dependent increases in NeHo. These findings are evidence against the proposal that the decline in functional connectivity seen in symptomatic carriers represents a lifelong acceleration of the healthy aging process.

Augmenting visual analysis in single-case research with hierarchical linear modeling

The purpose of this article is to demonstrate how hierarchical linear modeling (HLM) can be used to enhance visual analysis of single-case research (SCR) designs. First, the authors demonstrated the use of growth modeling via HLM to augment visual analysis of a sophisticated single-case study. Data were used from a delayed multiple baseline design, across groups of participants, with an embedded changing criterion design in a single-case literacy project for students with moderate intellectual disabilities (MoID). Visual analysis revealed a functional relation between instruction and sight-word acquisition for all students. Growth HLM quantified relations at the group level and revealed additional information that included statistically significant variability among students at initial-baseline probe and also among growth trajectories within treatment subphases. Growth HLM showed that receptive vocabulary was a significant predictor of initial knowledge of sight words, and print knowledge significantly predicted growth rates in both treatment subphases. Next, to show the benefits of combining these methodologies to examine a different behavioral topography within a more commonly used SCR design, the authors used repeated-measures HLM and visual analysis to examine simulated data within an ABAB design. Visual analysis revealed a functional relation between a hypothetical intervention (e.g., token reinforcement) and a hypothetical dependent variable (e.g., performance of a target response). HLM supported the existence of a functional relation through tests of statistical significance and detected significant variance among participants' response to the intervention that would be impossible to identify visually. This study highlights the relevance of these procedures to the identification of evidence-based interventions.

Effects of error correction during assessment probes on the acquisition of sight words for students with moderate intellectual disabilities

Simultaneous prompting is an errorless learning strategy designed to reduce the number of errors students make; however, research has shown a disparity in the number of errors students make during instructional versus probe trials. This study directly examined the effects of error correction versus no error correction during probe trials on the effectiveness and efficiency of simultaneous prompting on the acquisition of sight words by three middle school students with moderate intellectual disabilities. A single-case adapted alternating treatments (Sindelar, Rosenberg, & Wilson, 1985) embedded in a multiple baseline across word sets design was employed to examine the effects of error correction during probe trials in order to reduce error rates. A functional relation was established for two of the three students for the use of error correction during probe sessions to reduce error rates. Error correction during assessment probes required fewer sessions to criterion, resulted in fewer probe errors, resulted in a higher percentage of correct responding on the next subsequent trial, and required less total probe time. For two of the three students, probes with error correction resulted in a more rapid acquisition rate requiring fewer sessions to criterion.

Teaching the reading of connected text through sight-word instruction to students with moderate intellectual disabilities

Sight-word instruction is the most common method of reading instruction for students with Moderate Intellectual Disabilities reported in the research literature. The purpose of this study was to go beyond instruction of single word units to instruction of multiple-word phrases. This study demonstrated the instruction of reading and comprehending individual words and connected text through the use of simultaneous prompting. Instruction progressed through a series of phases which systematically introduced various parts of speech and combinations of parts of speech. Following acquisition, students demonstrated generalization across connected text found in community environments and leisure-reading materials.

Image correlation microscopy for uniform illumination

Image cross-correlation microscopy is a technique that quantifies the motion of fluorescent features in an image by measuring the temporal autocorrelation function decay in a time-lapse image sequence. Image cross-correlation microscopy has traditionally employed laser-scanning microscopes because the technique emerged as an extension of laser-based fluorescence correlation spectroscopy. In this work, we show that image correlation can also be used to measure fluorescence dynamics in uniform illumination or wide-field imaging systems and we call our new approach uniform illumination image correlation microscopy. Wide-field microscopy is not only a simpler, less expensive imaging modality, but it offers the capability of greater temporal resolution over laser-scanning systems. In traditional laser-scanning image cross-correlation microscopy, lateral mobility is calculated from the temporal de-correlation of an image, where the characteristic length is the illuminating laser beam width. In wide-field microscopy, the diffusion length is defined by the feature size using the spatial autocorrelation function. Correlation function decay in time occurs as an object diffuses from its original position. We show that theoretical and simulated comparisons between Gaussian and uniform features indicate the temporal autocorrelation function depends strongly on particle size and not particle shape. In this report, we establish the relationships between the spatial autocorrelation function feature size, temporal autocorrelation function characteristic time and the diffusion coefficient for uniform illumination image correlation microscopy using analytical, Monte Carlo and experimental validation with particle tracking algorithms. Additionally, we demonstrate uniform illumination image correlation microscopy analysis of adhesion molecule domain aggregation and diffusion on the surface of human neutrophils.

Abnormalities in the membrane material properties of hereditary spherocytes

Mechanical measurements of intrinsic membrane material properties are used to characterize the defect in hereditary spherocyte membrane at a continuum level. The value of the surface elastic shear modulus is two-thirds as large as normal values, and the value of the yield shear resultant is one-third as large as normal values. The viscosity of the surface above the elastic-plastic transition appears normal. Under similar geometric conditions, the force required to fragment a hereditary spherocyte is about one-third as large as the force required to fragment a normal cell.

Using simultaneous prompting to teach sounds and blending skills to students with moderate intellectual disabilities

The purpose of this study was to examine the effects of simultaneous prompting on acquisition of letter-sound correspondences and blending skills of previously taught words for three elementary students with moderate intellectual disabilities, and to measure generalization of those skills to untaught words. The three students were first taught to read five nouns using sight-word instruction. After acquisition of the five words the students were taught letter-sound correspondences and to blend the sounds in order to apply word-analysis skills. All the students demonstrated application of letter-sound correspondences and blending skills to read the five sight words and the untaught, generalization words. This study took place across two partial academic school years and therefore provides regression and recoupment data for the students.

Neutrophil adhesive contact dependence on impingement force

Neutrophil capture and recruitment from the circulation requires the formation of specific receptor/ligand bonds under hydrodynamic forces. In the present study we examine bond formation between beta2-integrins on neutrophils and immobilized ICAM-1 while using micropipettes to control the force of contact between the cell and substrate. Magnesium was used to induce the high affinity conformation of the integrins, and bond formation was assessed by measuring the probability of adhesion during repeated contacts. Increasing the impingement force caused an increase in the contact area and led to a proportional increase in adhesion probability (from approximately 20 to 50%) over the range of forces tested (50-350 pN). In addition, different-sized beads were used to change the force per unit area in the contact zone (contact stress). We conclude that for a given contact stress, the rate of bond formation increases linearly with contact area, but that increasing contact stress results in higher intrinsic rates of bond formation.

Rheological analysis and measurement of neutrophil indentation

Aspects of neutrophil mechanical behavior relevant to the formation of adhesive contacts were assessed by measuring the dependence of the contact area between the cell and a spherical substrate under controlled loading. Micropipettes were used to bring neutrophils into contact with spherical beads under known forces, and the corresponding contact area was measured over time. The neutrophil was modeled as a viscous liquid drop with a constant cortical tension. Both the equilibrium state and the dynamics of the approach to equilibrium were examined. The equilibrium contact area increased monotonically with force in a manner consistent with a cell cortical tension of 16-24 pN/microm. The dynamic response matched predictions based on a model of the cell as a growing drop using published values for the effective viscosity of the cell. The contact pressure between the cell and substrate at equilibrium is predicted to depend on the curvature of the contacting substrate, but to be independent of the impingement force. The approach to equilibrium was rapid, such that the time-averaged stress for a two-second impingement was within 20% of the equilibrium value. These results have implications for the role of mechanical force in the formation of adhesive contacts.

Elastic properties of the red blood cell membrane that determine echinocyte deformability

The natural biconcave shape of red blood cells (RBC) may be altered by injury or environmental conditions into a spiculated form (echinocyte). An analysis is presented of the effect of such a transformation on the resistance of RBC to entry into capillary sized cylindrical tubes. The analysis accounts for the elasticity of the membrane skeleton in dilation and shear, and the local and nonlocal resistance of the bilayer to bending, the latter corresponding to different area strains in the two leaflets of the bilayer. The shape transformation is assumed to be driven by the equilibrium area difference (delta A(0), the difference between the equilibrium areas of the bilayer leaflets), which also affects the energy of deformation. The cell shape is approximated by a parametric model. Shape parameters, skeleton shear deformation, and the skeleton density of deformed membrane relative to the skeleton density of undeformed membrane are obtained by minimization of the corresponding thermodynamic potential. Experimentally, delta A(0) is modified and the corresponding discocyte-echinocyte shape transition obtained by high-pressure aspiration into a narrow pipette, and the deformability of the resulting echinocyte is examined by whole cell aspiration into a larger pipette. We conclude that the deformability of the echinocyte can be accounted for by the mechanical behavior of the normal RBC membrane, where the equilibrium area difference delta A(0) is modified.

Fractional occurrence of defects in membranes and mechanically driven interleaflet phospholipid transport

The picture of biological membranes as uniform, homogeneous bileaflet structures has been revised in recent times due to the growing recognition that these structures can undergo significant fluctuations both in local curvature and in thickness. In particular, evidence has been obtained that a temporary, localized disordering of the lipid bilayer structure (defects) may serve as a principal pathway for movement of lipid molecules from one leaflet of the membrane to the other. How frequently these defects occur and how long they remain open are important unresolved questions. In this report, we calculate the rate of molecular transport through a transient defect in the membrane and compare this result to measurements of the net transbilayer flux of lipid molecules measured in an experiment in which the lipid flux is driven by differences between the mechanical stress in the two leaflets of the membrane bilayer. Based on this comparison, we estimate the frequency of defect occurrence in the membrane. The occurrence of defects is rare: the probability of finding a defect in 1.0 microm2 of a lecithin membrane is estimated to be approximately 6.0x10(-6). Based on this fractional occurrence of defects, the free energy of defect formation is estimated to be approximately 1.0x10(-19) J. The calculations provide support for a model in which interleaflet transport in membranes is accelerated by mechanically driven lipid flow.

Membrane instability in late-stage erythropoiesis

During maturation of the red blood cell (RBC) from the nucleated normoblast stage to the mature biconcave discocyte, both the structure and mechanical properties of the cell undergo radical changes. The development of the mechanical stability of the membrane reflects underlying changes in the organization of membrane-associated cytoskeletal proteins, and so provides an assessment of the time course of the development of membrane structural organization. Membrane stability in maturing erythrocytes was assessed by measuring forces required to form thin, tubular, lipid strands (tethers) from the surfaces of mononuclear cells obtained from fresh human marrow samples, marrow reticulocytes, circulating reticulocytes, and mature erythrocytes. Cells were biotinylated and manipulated with a micropipette to form an adhesive contact with a glass microcantilever, which gave a measure of the tethering force. The cell was withdrawn at controlled velocity and aspiration pressure to form a tether from the cell surface. The mean force required to form tethers from marrow reticulocytes and normoblasts was 27 +/- 9 pN, compared to 54 +/- 14 pN for mature cells. The energy of dissociation of the bilayer from the underlying skeleton increases 4-fold between the marrow reticulocyte stage and the mature cell, demonstrating that the mechanical stability of the membrane is not completely established until the very last stages of RBC maturation.

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.

Adaptation and survival of surface-deprived red blood cells in mice

The consequences of lost membrane area for long-term erythrocyte survival in the circulation were investigated. Mouse red blood cells were treated with lysophosphatidylcholine to reduce membrane area, labeled fluorescently, reinfused into recipient mice, and then sampled periodically for 35 days. The circulating fraction of the modified cells decreased on an approximately exponential time course, with time constants ranging from 2 to 14 days. The ratio of volume to surface area of the surviving cells, measured using micropipettes, decreased rapidly over the first 5 days after infusion to within 5% of normal. This occurred by both preferential removal of the most spherical cells and modification of others, possibly due to membrane stress developed during transient trapping of cells in the microvasculature. After 5 days, the cell area decreased with time in the circulation, but the ratio of volume to surface area remained essentially constant. These results demonstrate that the ratio of cell volume to surface area is a major determinant of the ability of erythrocytes to circulate properly.

Theoretical analysis of the effect of the transbilayer movement of phospholipid molecules on the dynamic behavior of a microtube pulled out of an aspirated vesicle

Observations over extended times of a lipid microtube (tether) formed from a lecithin vesicle have shown that under constant external loads the tether exhibits a continuous slow growth. It is considered that this growth is a consequence of the net transbilayer movement of phospholipid molecules in a direction which relieves the membrane strain resulting from the elastic deformation of the vesicle. The elastic deformation mode responsible for this effect is identified as the relative expansion of the two membrane layers reflecting the non-local contribution to membrane bending. An equation for the consequent rate of transbilayer movement of phospholipid molecules is derived. The dynamic behavior of the system is modeled by including frictional contributions due to interlayer slip and Stokes drag on the glass bead used to form the tether. The general numerical solution reveals a complex dependence of the tether growth rate on the system parameters and a continuous increase in the rate of tether growth at long times. Closed form expressions approximating the system behavior are derived and the conditions under which they can be applied are specified. Modeling the mechanically-driven lipid transport as a simple, stochastic, thermal process, allows the rate of lipid translocation to be related to the equilibrium transbilayer exchange rate of phospholipid molecules. Consideration of experimental results shows that the time constant for mechanically-driven translocation is shorter than the time for diffusion-driven translocation by approximately two orders of magnitude, indicating that lipid translocation is not a simple diffusive process.

Passive mechanical behavior of human neutrophils: effects of colchicine and paclitaxel

The role of microtubules in determining the mechanical rigidity of neutrophils was assessed. Neutrophils were treated with colchicine to disrupt microtubules, or with paclitaxel to promote formation of microtubules. Paclitaxel caused an increase in the number of microtubules in the cells as assessed by immunofluorescence, but it had no effect on the presence or organization of actin filaments or on cellular mechanical properties. Colchicine at concentrations <1.0 microM caused disruption of microtubular structures, but had little effect on either F-actin or on cellular mechanical properties. Higher concentrations of colchicine disrupted microtubular structure, but also caused increased actin polymerization and increases in cell rigidity. Treatment with 10 microM colchicine increased F-actin content by 17%, the characteristic cellular viscosity by 30%, the dependence of viscosity on shear rate by 10%, and the cortical tension by 18%. At 100 microM colchicine the corresponding increases were F-actin, 25%; characteristic viscosity, 50%; dependence of viscosity on shear rate, 20%; and cortical tension, 21%. These results indicate that microtubules have little influence on the mechanical properties of neutrophils, and that increases in cellular rigidity caused by high concentrations of colchicine are due to a secondary effect that triggers actin polymerization. This study supports the conclusion that actin filaments are the primary structural determinants of neutrophil mechanical properties.

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.

Surface area and volume changes during maturation of reticulocytes in the circulation of the baboon

Changes in the surface area and volume of reticulocytes were measured in vivo during late stage maturation. Baboons were treated with erythropoietin to produce mild reticulocytosis. Reticulocyte-rich cohorts of cells were obtained from whole blood by density gradient centrifugation. The cohorts were labeled with biotin, reinfused into the animal, and recovered from whole blood samples by panning on avidin supports. Changes in the surface area, volume, and membrane deformability were measured using micropipettes during the 2 to 6 weeks subsequent to reinfusion. For the entire cohort, the membrane area decreased by 10% to 15% and the cell volume decreased by approximately 8.5%, mostly within 24 hours after reinfusion. Estimates of the cellular dimensions of the reticulocyte subpopulation within this cohort indicated larger reductions in the mean cell area (12% to 30%) and mean cell volume (approximately 15%) of the reticulocytes themselves. Two weeks after reinfusion, the distribution of cell size for the cohort was indistinguishable from that of whole blood. There was evidence of slightly elevated membrane shear rigidity in some reticulocytes before reinfusion, but this slight increase disappeared within 24 hours after reinfusion. These are the first direct measurements of changes in the membrane physical properties of an identifiable cohort of reticulocytes as they mature in vivo.

Effects of lost surface area on red blood cells and red blood cell survival in mice

The effects of removing area from mouse red blood cells on the fate of the cells after reinfusion were investigated. When cells were made nearly spherical (by reducing cell area by approximately 35%) and then reinfused into the animal, most were cleared from the circulation within 1-2 h, although approximately 20% of the cells survived for 4 h or longer. When only 20% of the area was removed (leaving a 15% excess), more than 90% of the cells continued to circulate for 4 h. After reinfusion, the mean surface area of the surviving cells remained constant (73-75 microns2), but the mean volume decreased, from 56.6 +/- 2.1 to 19.1 +/- 1.5 microns3 (+/- SD of 5 replicates) over 4 h. These changes did not occur in cells suspended in plasma but not reinfused into the animal. Thus a loss of surface area results in a decrease in cell volume, as if to maintain a requisite degree of deformability. The results support the hypothesis that the increase in cell density associated with increasing cell age may be a consequence of surface area loss.

Combined use of fluorescence microscopy and micromechanical measurement to assess cell and membrane properties

The combined use of fluorescence microscopy and micromanipulation provides a powerful approach for understanding the mechanochemistry of cell membranes. Fluorescent labeling of erythrocytes has been used to identify particular populations of cells to assess the effects of abnormal deformability on cell survival. It was found that cells deprived of surface area are either eliminated rapidly from the circulation or undergo a reduction in volume to improve cellular deformability. Fluorescence microscopy can also be used to assess the distribution of specific membrane components during mechanical deformation and fragmentation of cell membranes and so lead to more fundamental understanding of the physical association between the membrane bilayer and the underlying membrane cytoskeleton.

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 expected to be proportional to the square root of the membrane tension, with a constant of proportionality containing Kc. 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 of 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 of Kc for 10 different vesicles was 1.17 x 10(-19) J (SD = 0.08 x 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 determining Kc.

Accelerated interleaflet transport of phosphatidylcholine molecules in membranes under deformation

Biological membranes are lamellar structures composed of two leaflets capable of supporting different mechanical stresses. Stress differences between leaflets were generated during micromechanical experiments in which long thin tubes of lipid (tethers) were formed from the surfaces of giant phospholipid vesicles. A recent dynamic analysis of this experiment predicts the relaxation of local differences in leaflet stress by lateral slip between the leaflets. Differential stress may also relax by interleaflet transport of lipid molecules ("flip-flop"). In this report, we extend the former analysis to include interleaflet lipid transport. We show that transmembrane lipid flux will evidence itself as a linear increase in tether length with time after a step reduction in membrane tension. Multiple measurements were performed on 24 different vesicles composed of stearoyl-oleoyl-phosphatidylcholine plus 3% dinitrophenol-linked di-oleoyl-phosphatidylethanolamine. These tethers all exhibited a linear phase of growth with a mean value of the rate of interlayer permeation, cp = 0.009 s-1. This corresponds to a half-time of approximately 8 min for mechanically driven interleaflet transport. This value is found to be consistent with longer times obtained for chemically driven transport if the lipids cross the membrane via transient, localized defects in the bilayer.

Cell cycle-dependence of HL-60 cell deformability

In this study, the role of cytoskeleton in HL-60 deformability during the cell cycle was investigated. G1, S, and G2/M cell fractions were separated by centrifugal elutriation. Cell deformability was evaluated by pipette aspiration. Tested at the same aspiration pressures, S cells were found to be less deformable than G1 cells. Moreover, HL-60 cells exhibited power-law fluid behavior: mu = mu c(gamma m/ gamma c)-b, where mu is cytoplasmic viscosity, gamma m is mean shear rate, mu c is the characteristic viscosity at the characteristic shear rate gamma c, and b is a material constant. At a given shear rate, S cells (mu c = 276 +/- 14 Pa.s, b = 0.51 +/- 0.03) were more viscous than G1 cells (mu c = 197 +/- 25, b = 0.53 +/- 0.02). To evaluate the relative importance of different cytoskeletal components in these cell cycle-dependent properties, HL-60 cells were treated with 30 microM dihydrocytochalasin B (DHB) to disrupt F-actin or 100 microM colchicine to collapse microtubules. DHB dramatically softened both G1 and S cells, which reduced the material constants mu c by approximately 65% and b by 20-30%. Colchicine had a limited effect on G1 cells but significantly reduced mu c of S cells (approximately 25%). Thus, F-actin plays the predominate role in determining cell mechanical properties, but disruption of microtubules may also influence the behavior of proliferating cells in a cell cycle-dependent fashion.

Elastic energy of curvature-driven bump formation on red blood cell membrane

Model calculations were performed to explore quantitative aspects of the discocyte-echinocyte shape transformation in red blood cells. The shape transformation was assumed to be driven by changes in the preferred curvature of the membrane bilayer and opposed by the elastic shear rigidity of the membrane skeleton. The energy required for echinocyte bump formation was calculated for a range of bump shapes for different preferred curvatures. Energy minima corresponding to nonzero bump heights were found when the stress-free area difference between the membrane leaflets or the spontaneous curvature of the membrane became sufficiently large, but the calculations predict that the membrane can tolerate significant differences in the resting areas of the inner and outer leaflets or significant spontaneous curvature without visible changes in shape. Thus, if the cell is near the threshold for bump formation, the calculations predict that small changes in membrane properties would produce large changes in cellular geometry. These results provide a rational framework for interpreting observations of shape transformations in red cells and for understanding the mechanism by which small changes in membrane elastic properties might lead to significant changes in geometry.

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.

Changes in HL-60 cell deformability during differentiation induced by DMSO

We have investigated changes in cellular deformability during promyelocytic leukemic HL-60 cell maturation. HL-60 cells were induced to mature with 1.25% dimethyl sulfoxide. Cellular deformability was evaluated by single-cell micropipette aspiration at one day, four days and seven days after induction. HL-60 cells were found to decrease in size and increase in deformability with maturation. When tested under the same aspiration pressures (0.5-1.3 kPa), cytoplasmic viscosity was found to vary from 210 to 85 Pa.s for cells prior to induction; it varied from 85 to 40 Pa.s for cells seven days after induction. Further, cytoplasmic viscosity exhibits power-law dependence on shear rate, mu = mu c (gamma m/gamma c)-b, where mu is cytoplasmic viscosity, gamma m is mean shear rate during cell entry, mu c is the characteristic viscosity at the characteristic shear rate, gamma c, and b is a material coefficient. Cells of all maturities showed similar dependence on shear rate (b approximately 0.5), but the characteristic viscosity decreased with maturation except for Day 1. When gamma c was set to 1 s-1, mu c = 236 +/- 5 Pa.s for cells prior to induction, mu c = 239 +/- 7, 209 +/- 7 and 175 +/- 14 Pa.s for cells on Days 1, 4 and 7 of induction, respectively.

Physical measurements of bilayer-skeletal separation forces

Bilayer membranes are intrinsically fluid in character and require stabilization by association with an underlying cytoskeleton. Instability either in the membrane-associated cytoskeleton or in the association between the bilayer and the skeleton can lead to loss of membrane bilayer and premature cell death. In this report measurements of the physical strength of the association between membrane bilayer and the membrane-associated skeleton in red blood cells are reported. These measurements involve the mechanical formation of long, thin cylinders of membrane bilayer (tethers) from the red cell surface. Ultrastructural evidence is presented indicating that these tethers do not contain membrane skeleton and, furthermore, that they are deficient in at least some integral membrane proteins. By measuring the forces on the cell as the tether is formed and the dimensions of the tether, the energy associated with its formation can be calculated. The minimum force to form a tether was found to be approximately 50 pN corresponding to an energy of dissociation of 0.2-0.3 mJ/m2. Such measurements enable critical evaluation of potential physical mechanisms for the stabilization of the membrane bilayer by the underlying cytoskeleton. It is postulated that an important contribution to the energy of association between bilayer and skeleton comes from the increase in chemical potential due to the lateral segregation of lipids and integral proteins.

Passive mechanical behavior of human neutrophils: effect of cytochalasin B

Actin is a ubiquitous protein in eukaryotic cells. It plays a major role in cell motility and in the maintenance and control of cell shape. In this article, we intend to address the contribution of actin to the passive mechanical properties of human neutrophils. As a framework for assessing this contribution, the neutrophil is modeled as a simple viscous fluid drop with a constant cortical ("surface") tension. The reagent cytochalasin B (CTB) was used to disrupt the F-actin structure, and the neutrophil cortical tension and cytoplasmic viscosity were evaluated by single-cell micropipette aspiration. The cortical tension was calculated by simple force balance, and the viscosity was calculated according to a numerical analysis of the cell entry into the micropipette. CTB reduced the cell cortical tension in a dose-dependent fashion: by 19% at a concentration of 3 microM and by 49% at 30 microM. CTB also reduced the cytoplasmic viscosity by approximately -25% at a concentration of 3 microM and by approximately 65% at a concentration of 30 microM when compared at the same aspiration pressures. All three groups of neutrophils, normal cells, and cells treated with either 3 or 30 microM CTB, exhibited non-Newtonian behavior, in that the apparent viscosity decreased with increasing shear rate. The dependence of the cytoplasmic viscosity on deformation rate can be described empirically by mu = mu c(gamma m/gamma c)-b, where mu is cytoplasmic viscosity, gamma m is mean shear rate, mu c is the characteristic viscosity at the characteristic shear rate gamma c, and b is a material coefficient. The shear rate dependence of the cytoplasmic viscosity was reduced by CTB treatment. This is reflected by the changes in the material coefficients. When gamma c was set to 1 s-1, pc = 130 +/- 23 Pa.s and b = 0.52 +/- 0.09 for normal neutrophils and pc = 54 +/- 15 Pa.S and b = 0.26 +/- 0.05 for cells treated with 30 micro M CTB. These results provide the first quantitative assessment of the role that Pa-s-actin structure plays in the passive mechanical properties of human neutrophils.

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.

Bending rigidity of SOPC membranes containing cholesterol

Bilayer membranes in the fluid state exhibit a large resistance to changes in surface area, negligible resistance to surface shear deformation, and a small but finite resistance to bending. The presence of cholesterol in the membrane is known to increase its resistance to area dilation. In this report, a new method for measuring bilayer membrane bending stiffness has been used to investigate the effect of cholesterol on the bending rigidity of SOPC (1,stearoyl-2,oleoyl-phosphatidylcholine) membranes. The curvature elasticity (kc) for membranes saturated with cholesterol was measured to be 3.3 x 10(-19) J, approximately 3-fold larger than that the modulus for cholesterol-free SOPC membrane. These findings are consistent with previous measurements of bending stiffness based on thermal fluctuations, which showed a similar approximately 3-fold increase in the modulus with cholesterol addition (Evans and Rawicz, 1990, Phys. Rev. Lett. 64:2094) and provide further substantiation of the important contribution that cholesterol makes to membrane cohesion and stability.

Role of lamellar membrane structure in tether formation from bilayer vesicles

A theoretical analysis is presented of the formation of membrane tethers from micropipette-aspirated phospholipid vesicles. In particular, it is taken into account that the phospholipid membrane is composed of two layers which are in contact but unconnected. The elastic energy of the bilayer is taken to be the sum of contributions from area expansivity, relative expansivity of the two monolayers, and bending. The vesicle is aspirated into a pipette and a constant point force is applied at the opposite side in the direction away from the pipette. The shape of the vesicle in approximated as a cylindrical projection into the pipette with a hemispherical cap, a spherical section, and a cylindrical tether with a hemispherical cap. The dimensions of the different regions of the vesicle are obtained by minimizing its elastic energy subject to the condition that the volume of the vesicle is fixed. The range of values for the parameters of the system is determined at which the existence of a tether is possible. Stability analysis is performed showing which of these configurations are stable. The importance of the relative expansion and compression of the constituent monolayers is established by recognizing that local bending energy by itself does not stabilize the vesicle geometry, and that in the limit as the relative expansivity modulus becomes infinitely large, a tether cannot be formed. Predictions are made for the functional relationships among experimentally observable quantities. In a companion report, the results of this analysis are applied to experimental measurements of tether formation, and used to calculate values for the membrane material coefficients.

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.

Rheologic properties of senescent erythrocytes: loss of surface area and volume with red blood cell age

The rheologic properties of senescent erythrocytes have been examined using two models of red blood cell (RBC) aging. In the rabbit, aged erythrocytes were isolated after biotinylation, in vivo aging, and subsequent recovery on an avidin support. Aged RBCs from the mouse were obtained using the Ganzoni hypertransfusion model that suppresses erythropoiesis for prolonged periods of time allowing preexisting cells to age in vivo. In both cases, the aged erythrocytes were found by ektacytometry to have decreased deformability due to diminished surface area and cellular dehydration. The aged rabbit erythrocytes were further characterized by micropipette methods that documented an average surface area decrease of 10.5% and a volume decrease of 8.4% for the cells that were 50 days old. Because both the surface area and volume decreased with cell age, there was little change in surface-to-volume ratio (sphericity) during aging. The aged cells were found to have normal membrane elasticity. In addition, human RBCs were fractionated over Stractan density gradients and the most dense cells were found to have rheologic properties similar to those reported for the aged RBCs from rabbits and mice, although the absolute magnitude of the changes in surface area and volume were considerably greater for the human cells. Thus, stringent density fractionation protocols that result in isolation of the most dense 1% of cells can produce a population of human cells with rheologic properties similar to senescent cells obtained in other species. The data indicate that progressive loss of cell area and cell dehydration are characteristic features of cell aging.

Reticulocyte rigidity and passage through endothelial-like pores

The importance of cell rigidity in regulating the release of reticulocytes from the bone marrow has been investigated in a model system. Reticulocytes were obtained from phlebotomized rabbits and separated from whole blood by discontinuous density gradient centrifugation. The mechanical properties of the cells were tested. Using single-cell micromechanical techniques, the membrane elastic rigidity and the viscoelastic response of reticulocyte and mature cell populations were measured. The reticulocyte membranes were more rigid than the mature membranes, but the reticulocyte properties were heterogeneous, and some cells exhibited behavior indistinguishable from the mature cells. The mean time constant for viscoelastic recovery was the same for reticulocytes as for mature cells, but the variability within the reticulocyte population was greater. The possible influence of this increased rigidity on cell egress from the bone marrow was tested using an in vitro model of the thin endothelial pores found within the marrow. A silicon wafer approximately 0.1 microns in thickness and containing a small (1.2-microns diameter) pore in its center was cemented over the tip of a large (15.0-microns ID) micropipette. The passage of cells through the pore was observed as a function of the pressure across the pore. Consistent with the difference in mechanical properties, the reticulocytes required greater pressures (as great as 4.0 mm Hg compared with less than 1.0 mm Hg) and took longer to traverse the pore. These measurements support the postulate that deformability is important in the regulation of the release of cells from bone marrow.

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.

Flexural rigidity of marginal bands isolated from erythrocytes of the newt

The marginal band is a bundle of microtubules residing at the periphery of nucleated erythrocytes of nonmammalian vertebrates and some invertebrates. Marginal bands from erythrocytes of the newt (Notopthalmus viridescens) were isolated from the cells as intact structures by treatment with detergent and either mild protease or high salt. Isolated bands were subjected to mechanical testing by stretching the band between a glass microhook and a calibrated glass fiber. The deflection of the fiber provided a measure of the force on the band. The flexural rigidity of the band was determined from measurements of the band deformation as a function of applied force. Bands isolated with either of two proteases (pepsin or elastase) or with high salt exhibited elastic behavior with a flexural rigidity of approximately 9.0 X 10(-12) dyn.cm2. Treatment of bands with chymopapain caused an increase in band rigidity and inelastic behavior. Estimates of the contribution of the band to cellular rigidity are made based on the measurements of the structural properties of the isolated band. The band provides the cell with a large resistance to indentations at the rim and to large extensions, while maintaining a high degree of flexibility in small extensions or flexure.

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.

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.

Effects of intracellular Ca2+ and proteolytic digestion of the membrane skeleton on the mechanical properties of the red blood cell membrane

Intracellular Ca2+ at concentrations ranging from 0 to 10 mumol/l increases the shear modulus of surface elasticity (mu) and the surface viscosity (eta) of human red blood cells by 20% and 70%, respectively. K+ selective channels in the red cell membrane become activated by Ca2+. The activation still occurs to the same extent when the membrane skeleton is degraded by incorporation of trypsin into resealed red cell ghosts, suggesting that the channel activation is not controlled by the proteins of the membrane skeleton and is independent of mu and eta. Incorporation of trypsin at concentrations ranging from 0 to 100 ng/ml into red cell ghosts leads to a graded digestion of spectrin, a cleavage of the band 3 protein and a release of the binding proteins ankyrin and band 4.1. These alterations are accompanied by an increase of the lateral mobility of the band 3 protein which, at 40 ng/ml trypsin, reaches a plateau value where the rate of lateral diffusion is enhanced by about two orders of magnitude above the rate measured in controls without trypsin. Proteolytic digestion by 10-20 ng/ml trypsin leads to a degradation of more than 40% of the spectrin and increases the rate of lateral diffusion to about 20-70% of the value observed at the plateau. Nevertheless, mu and eta remain virtually unaltered. However, the stability of the membrane is decreased to the point where a slight mechanical extension, or the shear produced by centrifugation results in disintegration and vesiculation, precluding measurements of eta and mu in ghosts treated with higher concentrations of trypsin. These findings indicate that alterations of the structural integrity of the membrane skeleton exert drastically different effects on mu and eta on the one hand and on the stability of the membrane on the other.

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.

Effects of inherited membrane abnormalities on the viscoelastic properties of erythrocyte membrane

Several workers have identified molecular abnormalities associated with inherited blood disorders. The present work examines how these alterations in molecular structure affect the viscoelastic properties of the red blood cell membrane. Changes in the membrane shear modulus, the membrane viscosity, and the apparent membrane bending stiffness were observed in cells of eight patients having a variety of disorders: Two had reductions in the number of high-affinity ankyrin binding sites, two had abnormalities associated with the protein band 4.1, and six were known to be deficient in spectrin. The data suggest that the membrane shear modulus is proportional to the density of spectrin on the membrane and support the view that spectrin is primarily responsible for membrane shear elasticity. Although membranes having abnormalities associated with the function of ankyrin or band 4.1 exhibited reduced elasticity, the degree of mechanical dysfunction was quantitatively inconsistent with the extent of the molecular abnormality. This indicates that these skeletal components do not play a primary role in determining membrane shear elasticity. The membrane viscosity was reduced in seven of the eight patients studied. The reduction in viscosity was usually greater than the reduction in shear modulus, but the degree of reduction in viscosity was variable and did not correlate well with the degree of molecular abnormality.

Measurement of the extensional and flexural rigidities of a subcellular structure: marginal bands isolated from erythrocytes of the newt

The elastic properties of marginal band, a microtubular structure isolated from the newt (notophthalmus viridescens) have been measured. Bands were isolated using Triton X-100 and pepsin at pH 6.8 according to the method of Cohen (1978). Isolated bands were manipulated with a glass microhook in a buffer-filled chamber under the microscope. Single bands were stretched between the hook and a thin glass fiber. The fiber was calibrated so that the force on the band could be calculated from the displacement of the fiber. The data pairs of force versus band deflection were analyzed according to the theoretical work of Libai and Simmonds (1983) to obtain the flexural and extensional rigidities of the band. Band dimensions calculated from the data were consistent with microscopically determined values. The average flexural rigidity of the bands (EI) was 5.3 X 10(-13) dyn X cm2 and the average extensional rigidity (EA) was 0.017 dyn. Compared to the cell membrane, the marginal band is nearly inextensible and has a much greater resistance to bending, indicating that the band makes an important contribution to the deformability of the circulating cell.

An in vitro model of erythroid egress in bone marrow

An in vitro system has been developed that mimics the passage of erythrocytes from the bone marrow to the circulation. Bone marrow egress and its proper regulation are vital physiologic processes. However, because of the inaccessibility of the marrow, it is difficult to evaluate the various factors important in controlling these processes or even to define the precise mechanism by which egress occurs. The in vitro system has been designed to evaluate the importance of different physical parameters in regulating egress. It consists of a thin silicon wafer (thickness approximately equal to 1.0 micron) cemented over the tip of a large (15.0 micron ID) micropipette. The wafer contains a single circular pore. Cells were observed under the microscope as they passed through the pore under controlled pressures. The rate and duration of passage were obtained from videorecordings of the experiment. The measured passage times agreed well with the predictions of a simple analytical model of a cell passing through a thin aperture. The experimental results confirm the conclusion reached from the analysis that the pressures needed to drive a cell through the pore are well within the physiologic range, and the time needed to complete egress is typically less than 1.0 seconds. These results support the hypothesis that erythrocyte egress may be driven by a hydrostatic pressure difference across the pore.

Effects of 2,3-diphosphoglycerate on the mechanical properties of erythrocyte membrane

Investigation by Schindler et al and Sheetz and Casaly have indicated that high (approximately 10 mmol/L) concentrations of 2,3-diphosphoglycerate (2,3-DPG) have a destabilizing effect on erythrocyte membrane and the membrane skeleton. We have investigated changes in the membrane mechanical properties that occur at elevated 2,3-DPG levels in both intact cells and ghosts. The membrane shear modulus, viscoelastic recovery time constant, critical force, "plastic" viscosity, and material relaxation time constant were measured by standard micropipette and flow channel techniques. Intact cells showed no change in properties at physiologic ionic strength and 2,3-DPG concentrations of about 20 mmol/L, except for an increase in membrane viscosity resulting from an increased cellular hemoglobin concentration that occurs when the 2,3-DPG concentration is elevated. At ionic strengths 20% below physiologic and 2,3-DPG concentrations of approximately 20 mmol/L, decreases in membrane shear modulus and membrane viscosity were observed. In ghosts, no changes in these properties were observed at a 2,3-DPG concentration of 10 mmol/L and ionic strengths as low as 25% below physiologic, but a decrease in the force required to form tethers (critical force) was observed at physiologic ionic strength. The decrease in membrane shear modulus and viscosity of intact cells and the reduced critical force in ghosts are consistent with the results of other investigators. However, the difference in the effects of 2,3-DPG on ghosts and intact cells indicates that the effects of 2,3-DPG depend strongly on the conditions of the experiment. It appears unlikely that 2,3-DPG affects erythrocyte membrane material properties under physiologic conditions.

Effects of abnormal cytoskeletal structure on erythrocyte membrane mechanical properties

Measurements of the mechanical properties of the erythrocyte membrane provide a direct assessment of the proper function of its structural components. To assess the effects of alterations in molecular structure on membrane mechanical properties, measurements have been performed on cells from six individuals whose membranes contain inherited, biochemically characterized structural defects. Because the contribution of the membrane skeleton to the mechanical behavior of the membrane is most evident in shear deformation, mechanical experiments were performed to measure the material constants which characterize the response of the membrane to shear force resultants. The surface elastic shear modulus characterizes the elastic response of the membrane; the yield shear resultant is the maximum shear force resultant which the membrane can support elastically; and the plastic viscosity coefficient characterizes the rate of membrane deformation when the elastic limit has been exceeded. Generally, it was found that when the molecular defect is found to occur in a region of the skeleton which is stress-supporting, the maximum elastic strength of the membrane is reduced. However, the magnitude of the reduction can be quite different for membranes having similar or even identical defects. In some cases the differences can be attributed to the removal of the most fragile cells of the population by the spleen, but other results indicate that the biochemical description of the defects may be incomplete. These results emphasize the need for further refinements both in the biochemical characterization of membrane skeleton structure and in the description and measurement of membrane mechanical properties.

Temperature dependence of the yield shear resultant and the plastic viscosity coefficient of erythrocyte membrane. Implications about molecular events during membrane failure

Structural failure of the erythrocyte membrane in shear deformation occurs when the maximum shear resultant (force/length) exceeds a critical value, the yield shear resultant. When the yield shear resultant is exceeded, the membrane flows with a rate of deformation characterized by the plastic viscosity coefficient. The temperature dependence of the yield shear resultant and the plastic viscosity coefficient have been measured over the temperature range 10-40 degrees C. Over this range the yield shear resultant does not change significantly (+/- 15%), but the plastic viscosity coefficient changes exponentially from a value of 1.3 X 10(-2) surface poise (dyn s/cm) at 10 degrees C to a value of 6.2 X 10(-4) surface poise (SP) at 40 degrees C. The different temperature dependence of these two parameters is not surprising, inasmuch as they characterize different molecular events. The yield shear resultant depends on the number and strength of intermolecular connections within the membrane skeleton, whereas the plastic viscosity depends on the frictional interactions between molecular segments as they move past one another in the flowing surface. From the temperature dependence of the plastic viscosity, a temperature-viscosity coefficient, E, can be calculated: eta p = constant X exp(--E/RT). This quantity (E) is related to the probability that a molecular segment can "jump" to its next location in the flowing network. The temperature-viscosity coefficient for erythrocyte membrane above the elastic limit is calculated to be 18 kcal/mol, which is similar to coefficients for other polymeric materials.

Surface viscosity measurements from large bilayer vesicle tether formation. II. Experiments

A mechanical experiment has been developed that measures an upper bound for the viscosity of a lipid bilayer membrane. In this experiment, strands of membrane (tethers) are formed from phospholipid vesicles attached to micropipettes by subjecting the vesicles to fluid drag. The rate of tether formation is measured as a function of the velocity of the suspending fluid. The surface viscosity can be calculated from this data using a theoretical relationship derived in a companion paper. Because of the multilamellar character of the vesicles, these values provide an upper bound for the viscosity of a single bilayer. The smallest values obtained in these measurements fell in the range 5.0-13.0 x 10(-6) dyn s/cm. These values are in relatively good agreement with the values calculated from lateral and rotational mobility measurements.

Surface viscosity measurements from large bilayer vesicle tether formation. I. Analysis

Recent observations indicate that it is possible to form tethers from large phospholipid vesicles. The process of tether formation is analyzed using a continuum mechanical approach to obtain the surface viscosity of the bilayer in terms of experimentally measurable parameters. The membrane is treated as a two-dimensional isotropic material which deforms a constant area. The constitutive equation relates the maximum surface shear resultant to the rate of deformation via the surface viscosity coefficient. The force which acts to increase the tether length is generated by fluid moving past the vesicle. The magnitude of the force is estimated from Stoke's drag equation. The analysis predicts that there is a critical force necessary to produce an increase in the tether length. A dimensionless tether growth parameter is defined, and its value is obtained as a function of the ratio of the applied force on the vesicle to the critical force. This relationship is independent of both the size of the vesicle and the radius of the tether. Knowing the force on the vesicle, the critical force, and the rate of tether growth, the surface viscosity can be calculated.