Influence of sickle hemoglobin polymerization and membrane properties on deformability of sickle erythrocytes in the microcirculation.

The rheological properties of normal erythrocytes appear to be largely determined by those of the red cell membrane. In sickle cell disease, the intracellular polymerization of sickle hemoglobin upon deoxygenation leads to a marked increase in intracellular viscosity and elastic stiffness as well as having indirect effects on the cell membrane. To estimate the components of abnormal cell rheology due to the polymerization process and that due to the membrane abnormalities, we have developed a simple mathematical model of whole cell deformability in narrow vessels. This model uses hydrodynamic lubrication theory to describe the pulsatile flow in the gap between a cell and the vessel wall. The interior of the cell is modeled as a Voigt viscoelastic solid with parameters for the viscous and elastic moduli, while the membrane is assigned an elastic shear modulus. In response to an oscillatory fluid shear stress, the cell--modeled as a cylinder of constant volume and surface area--undergoes a conical deformation which may be calculated. We use published values of normal and sickle cell membrane elastic modulus and of sickle hemoglobin viscous and elastic moduli as a function of oxygen saturation, to estimate normalized tip displacement, d/ho, and relative hydrodynamic resistance, Rr, as a function of polymer fraction of hemoglobin for sickle erythrocytes. These results show the transition from membrane to internal polymer dominance of deformability as oxygen saturation is lowered. More detailed experimental data, including those at other oscillatory frequencies and for cells with higher concentrations of hemoglobin S, are needed to apply fully this approach to understanding the deformability of sickle erythrocytes in the microcirculation. The model should be useful for reconciling the vast and disparate sets of data available on the abnormal properties of sickle cell hemoglobin and sickle erythrocyte membranes, the two main factors that lead to pathology in patients with this disease.     

Red Blood Cell Shape and Fluctuations: Cytoskeleton Confinement and ATP Activity

We review recent theoretical work that analyzes experimental measurements of the shape and fluctuations of red blood cells. Particular emphasis is placed on the role of the cytoskeleton and cell elasticity and we contrast the situation of elastic cells with that of fluid-filled vesicles. In red blood cells (RBCs), the cytoskeleton consists of a two-dimensional network of spectrin proteins. Our analysis of the wave vector and frequency dependence of the fluctuation spectrum of RBCs indicates that the spectrin network acts as a confining potential that reduces the fluctuations of the lipid bilayer membrane. However, since the cytoskeleton is only sparsely connected to the bilayer, one cannot regard the composite cytoskeleton membrane as a polymerized object with a shear modulus. The sensitivity of RBC fluctuations and shapes to ATP concentration may reflect the transient defects induced in the cytoskeleton network by ATP.     

Effect of hydroperoxides on red blood cell membrane mechanical properties

We investigate the effect of oxidative stress on red blood cell membrane mechanical properties in vitro using detailed analysis of the membrane thermal fluctuation spectrum. Two different oxidants, the cytosol-soluble hydrogen peroxide and the membrane-soluble cumene hydroperoxide, are used, and their effects on the membrane bending elastic modulus, surface tension, strength of confinement due to the membrane skeleton, and 2D shear elastic modulus are measured. We find that both oxidants alter significantly the membrane elastic properties, but their effects differ qualitatively and quantitatively. While hydrogen peroxide mainly affects the elasticity of the membrane protein skeleton (increasing the membrane shear modulus), cumene hydroperoxide has an impact on both membrane skeleton and lipid bilayer mechanical properties, as can be seen from the increased values of the shear and bending elastic moduli. The biologically important implication of these results is that the effects of oxidative stress on the biophysical properties, and hence the physiological functions, of the cell membrane depend on the nature of the oxidative agent. Thermal fluctuation spectroscopy provides a means of characterizing these different effects, potentially in a clinical milieu.     

A multiscale approach to the elastic moduli of biomembrane networks

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

Exploring mechanochemical processes in the cell with optical tweezers

Force and torque, stress and strain or work are examples of mechanical and elastic actions which are intimately linked to chemical reactions in the cell. Optical tweezers are a light-based method which allows the real-time manipulation of single molecules and cells to measure their interactions. We describe the technique, briefly reviewing the operating principles and the potential capabilities to the study of biological processes. Additional emphasis is given to the importance of fluctuations in biology and how single-molecule techniques allow access to them. We illustrate the applications by addressing experimental configurations and recent progresses in molecular and cell biology.     

Direct measurement of the mechanical properties of lipid phases in supported bilayers

Biological membranes define not only the cell boundaries but any compartment within the cell. To some extent, the functionality of membranes is related to the elastic properties of the lipid bilayer and the mechanical and hydrophobic matching with functional membrane proteins. Supported lipid bilayers (SLBs) are valid biomimetic systems for the study of membrane biophysical properties. Here, we acquired high-resolution topographic and quantitative mechanics data of phase-separated SLBs using a recent atomic force microscopy (AFM) imaging mode based on force measurements. This technique allows us to quantitatively map at high resolution the mechanical differences of lipid phases at different loading forces. We have applied this approach to evaluate the contribution of the underlying hard support in the determination of the elastic properties of SLBs and to determine the adequate indentation range for obtaining reliable elastic moduli values. At ~200 pN, elastic forces dominated the force-indentation response and the sample deformation was <20% of the bilayer thickness, at which the contribution of the support was found to be negligible. The obtained Young's modulus (E) of 19.3 MPa and 28.1 MPa allowed us to estimate the area stretch modulus (k(A)) as 106 pN/nm and 199 pN/nm and the bending stiffness (k(c)) as 18 k(B)T and 57 k(B)T for the liquid and gel phases, respectively.     

Two-chamber AFM: probing membrane proteins separating two aqueous compartments

Biological membranes compartmentalize and define physical borders of cells. They are crowded with membrane proteins that fulfill diverse crucial functions. About one-third of all genes in organisms code for, and the majority of drugs target, membrane proteins. To combine structure and function analysis of membrane proteins, we designed a two-chamber atomic force microscopy (AFM) setup that allows investigation of membranes spanned over nanowells, therefore separating two aqueous chambers. We imaged nonsupported surface layers (S layers) of Corynebacterium glutamicum at sufficient resolution to delineate a 15 A-wide protein pore. We probed the elastic and yield moduli of nonsupported membranes, giving access to the lateral interaction energy between proteins. We combined AFM and fluorescence microscopy to demonstrate the functionality of proteins in the setup by documenting proton pumping by Halobacterium salinarium purple membranes.     

Effects of oxidative stress-induced changes in the actin cytoskeletal structure on myoblast damage under compressive stress: confocal-based cell-specific finite element analysis

Muscle cells are frequently subjected to both mechanical and oxidative stresses in various physiological and pathological situations. To explore the mechanical mechanism of muscle cell damage under loading and oxidative stresses, we experimentally studied the effects of extrinsic hydrogen peroxides on the actin cytoskeletal structure in C2C12 myoblasts and presented a finite element (FE) analysis of how such changes in the actin cytoskeletal structure affected a myoblast’s capability to resist damage under compression. A confocal-based cell-specific FE model was built to parametrically study the effects of stress fiber density, fiber cross-sectional area, fiber tensile prestrain, as well as the elastic moduli of the stress fibers, actin cortex, nucleus and cytoplasm. The results showed that a decrease in the elastic moduli of both the stress fibers and actin cortex could increase the average tensile strain on the actin cortex–membrane structure and reduce the apparent cell elastic modulus. Assuming the cell would die when a certain percentage of membrane elements were strained beyond a threshold, a lower elastic modulus of actin cytoskeleton would compromise the compressive resistance of a myoblast and lead to cell death more readily. This model was used with a Weibull distribution function to successfully describe the extent of myoblasts damaged in a monolayer under compression.     

Kymographic Imaging of the Elastic Modulus of Epithelial Cells during the Onset of Migration

Epithelial cell migration during wound repair involves a complex interplay of intracellular processes that enable motility while preserving contact among the cells. Recent evidence suggests that fluctuations of the intracellular biophysical state of cells generate traction forces at the basal side of the cells that are necessary for the cells to migrate. However, less is known about the biophysical and structural changes throughout the cells that accompany these fluctuations. Here, we utilized, to our knowledge, a novel kymographic nanoindentation method to obtain spatiotemporal measurements of the elastic moduli of living cells during migration after wounding. At the onset of migration, the elastic modulus increased near the migration front. In addition, the intensity of fluctuations in the elastic modulus changed at the migration front, and these changes were dependent upon f-actin, one of the major components of the cytoskeleton. These results demonstrate the unique biophysical changes that occur at the onset of migration as cells transition from a stationary to a migratory state.     

Fluorescence correlation spectroscopy close to a fluctuating membrane

Compartmentalization of the cytoplasm by membranes should have a strong influence on the diffusion of macromolecules inside a cell, and we have studied how this could be reflected in fluorescence correlation spectroscopy (FCS) experiments. We derived the autocorrelation function measured by FCS for fluorescent particles diffusing close to a soft membrane, and show it to be the sum of two contributions: short timescale correlations come from the diffusion of the particles (differing from free diffusion because of the presence of an obstacle), whereas long timescale correlations arise from fluctuations of the membrane itself (which create intensity fluctuations by modulating the number of detected particles). In the case of thermal fluctuations this second type of correlation depends on the elasticity of the membrane. To illustrate this calculation, we report the results of FCS experiments carried out close to a vesicle membrane. The measured autocorrelation functions display very distinctly the two expected contributions, and allow both to recover the diffusion coefficient of the fluorophore and to characterize the membrane fluctuations in term of a bending rigidity. Our results show that FCS measurements inside cells can lead to erroneous values of the diffusion coefficient if the influence of membranes is not recognized.     

The elastic deformability of closed multilayered membranes is the same as that of a bilayer membrane

The elastic behavior of closed multilayered membranes is analyzed with the assumption that the constituent layers are in close contact but are unconnected in the sense that they are free to slide by one another. The system exhibits three independent elastic deformation modes for any number of the constituent layers equal to or larger than two. These are the area expansivity of the membrane neutral surface, and the local and non-local membrane bending. The corresponding elastic moduli are expressed in terms of the elastic moduli of the constituent layers, their areas, and distances between their neutral surfaces. Closed multilayered membranes only differ from a closed bilayer membrane in that for any of their shapes some of the constituent layers are expanded and some compressed.     

Effect of membrane mechanics on charge transfer by the membrane protein prestin

Prestin was found in the membrane of outer hair cells (OHCs) located in the cochlea of the mammalian inner ear. These cells convert changes in the membrane potential into dimensional changes and (if constrained) to an active electromechanical force. The OHCs provide the ear with the mechanism of amplification and frequency selectivity that is effective up to tens of kHz. Prestin is a crucial part of the motor complex driving OHCs. Other cells transfected with prestin acquire electromechanical properties similar to those in the native cell. While the mechanism of prestin has yet to be fully understood, the charge transfer is its critical component. Here we investigate the effect of the mechanics of the surrounding membrane on electric charge transfer by prestin. We simulate changes in the membrane mechanics via the corresponding changes in the free energy of the prestin system. The free energy gradient enters a Fokker-Planck equation that describes charge transfer in our model. We analyze the effects of changes in the membrane tension and membrane elastic moduli. In the case of OHC, we simulate changes in the longitudinal and/or circumferential stiffness of the cell’s orthotropic composite membrane. In the case of cells transfected with prestin, we vary the membrane areal modulus. As a result, we show the effects of the membrane mechanics on the probabilistic characteristics of prestin-associated charge transfer for both stationary and high-frequency conditions. We compare our computational results with the available experimental data and find good agreement with the experiment.     

Design of biomimetic cell-interactive substrates using hyaluronic acid hydrogels with tunable mechanical properties

Hyaluronic acid (HA) is a natural polysaccharide abundant in biological tissues with excellent potential for constructing synthetic extracellular matrix analogues. In this work, we established a simple and dependable approach to prepare hyaluronic acid-based hydrogels with controlled stiffness and cell recognition properties for use as cell-interactive substrates. This approach relied on a new procedure for the synthesis of methacrylate-modified HA macromers (HA-MA) and, on photorheometry allowing real time monitoring of gelation during photopolymerization. We showed in this way the ability to obtain gels that encompass the range of physiologically relevant elastic moduli while still maintaining the recognition properties of HA by specific cell surface receptors. These hydrogels were prepared from HA macromers having a degree of methacrylation <0.5, which allows to minimize compromising effects on the binding affinity of HA to its cell receptors due to high substitution on the one hand, and to achieve nearly 100% conversion of the methacrylate groups on the other. When the HA hydrogels were immobilized on glass substrates, it was observed that the attachment and the spreading of a variety of mammalian cells rely on CD44 and its coreceptor RHAMM. The attachment and spreading were also shown to be modulated by the elastic properties of the HA matrix. All together, these results highlight the biological potential of these HA hydrogel systems and the needs of controlling their chemical and physical properties for applications in cell culture and tissue engineering.     

Dynamic multiple-target tracing to probe spatiotemporal cartography of cell membranes

Although the highly dynamic and mosaic organization of the plasma membrane is well-recognized, depicting a resolved, global view of this organization remains challenging. We present an analytical single-particle tracking (SPT) method and tool, multiple-target tracing (MTT), that takes advantage of the high spatial resolution provided by single-fluorophore sensitivity. MTT can be used to generate dynamic maps at high densities of tracked particles, thereby providing global representation of molecular dynamics in cell membranes. Deflation by subtracting detected peaks allows detection of lower-intensity peaks. We exhaustively detected particles using MTT, with performance reaching theoretical limits, and then reconnected trajectories integrating the statistical information from past trajectories. We demonstrate the potential of this method by applying it to the epidermal growth factor receptor (EGFR) labeled with quantum dots (Qdots), in the plasma membrane of live cells. We anticipate the use of MTT to explore molecular dynamics and interactions at the cell membrane.     

Variation of frequency spectrum of the erythrocyte flickering caused by aging,osmolarity, temperature and pathological changes

Frequency spectra of the surface undulations (flickering) of erythrocyte plasma membranes are measured by direct spectral analysis of the intensity fluctuations of the light passing the cells in a phase contrast microscope. Spectra are taken as a function (1) of the temperature (2) of the viscosity and osmolarity of the outer medium (3) of the aging of cells and (4) of pathological transformations. The spectra are approximately superpositions of two Lorentzian lines. At large frequencies,f, the spectra follow f^?2. This behaviour can be interpreted in terms of cell thickness fluctuations caused by thermally excited membrane undulations provided the range of wavelengths is small. The undulations are determined by the membrane curvature elasticity while the lateral tension is negligibly small for cells of discoid shape. The technique presented allows accurate measurements of relative curvature (bending) elastic constants. The spectra of freshly drawn cells are remarkably reproducible. Aging of the cells in the medium leads to an increase in the curvature elastic constant. A decrease in osmolarity causes a reduction in the intensity and line width of the spectra and the flickering vanishes if the cell approaches a spherical shape. The effect of temperature between 10 and 40°C is astonishingly small with the exception of a sudden increase in the amplitude with increasing temperature at 35°C. The flicker spectra of a large fraction of the cells from patients suffering from cronical alcoholism exhibit a reduced line width or an increase in the curvature elastic constant.     

The Mechanical Properties of Early Drosophila Embryos Measured by High-Speed Video Microrheology

In early development, Drosophila melanogaster embryos form a syncytium, i.e., multiplying nuclei are not yet separated by cell membranes, but are interconnected by cytoskeletal polymer networks consisting of actin and microtubules. Between division cycles 9 and 13, nuclei and cytoskeleton form a two-dimensional cortical layer. To probe the mechanical properties and dynamics of this self-organizing pre-tissue, we measured shear moduli in the embryo by high-speed video microrheology. We recorded position fluctuations of injected micron-sized fluorescent beads with kHz sampling frequencies and characterized the viscoelasticity of the embryo in different locations. Thermal fluctuations dominated over nonequilibrium activity for frequencies between 0.3 and 1000 Hz. Between the nuclear layer and the yolk, the cytoplasm was homogeneous and viscously dominated, with a viscosity three orders of magnitude higher than that of water. Within the nuclear layer we found an increase of the elastic and viscous moduli consistent with an increased microtubule density. Drug-interference experiments showed that microtubules contribute to the measured viscoelasticity inside the embryo whereas actin only plays a minor role in the regions outside of the actin caps that are closely associated with the nuclei. Measurements at different stages of the nuclear division cycle showed little variation.     

Measuring optical and mechanical properties of a living cell with defocusing microscopy

Defocusing microscopy (DM) is a recently developed technique that allows quantitative analysis of membrane surface dynamics of living cells using a simple bright-field optical microscope. According to DM, the contrast of defocused images is proportional to cell surface curvature. Although, until now, this technique was used mainly to determine size and amount of membrane shape fluctuations, such as ruffles and small random membrane fluctuations, in macrophages, its applications on cell biology extend beyond that. We show how DM can be used to measure optical and mechanical properties of a living macrophage, such as cell refractive index n, membrane bending modulus K(c), and effective cell viscosity eta for membrane-actin meshwork relaxation. Experimental data collected from defocused images of bone marrow-derived macrophages were used to evaluate these parameters. The obtained values, averaged over several different macrophages, are n = (1.384 +/- 0.015), K(c) approximately 3.2 x 10(-19) J, and eta approximately 459 Pa.s. We also estimate the amplitude of the small fluctuations to be of the order of 3 nm, which is around the step size of a polymerizing actin filament.     

Local rheology of human neutrophils investigated using atomic force microscopy

During the immune response, neutrophils display localized mechanical events by interacting with their environment through the micro-vascular transit, trans-endothelial, and trans-epithelial migration. Nano-mechanical studies of human neutrophils on localized nano-domains could provide the essential information for understanding their immune responsive functions. Using the Atomic Force Microscopy (AFM)-based micro-rheology, we have investigated rheological properties of the adherent human neutrophils on local nano-domains. We have applied the modified Hertz model to obtain the viscoelastic moduli from the relatively thick body regions of the neutrophils. In addition, by using more advanced models to account for the substrate effects, we have successfully characterized the rheological properties of the thin leading and tail regions as well. We found a regional difference in the mechanical compliances of the adherent neutrophils. The central regions of neutrophils were significantly stiffer (1,548 ± 871 Pa) than the regions closer to the leading edge (686 ± 801 Pa), while the leading edge and the tail (494 ± 537 Pa) regions were mechanically indistinguishable. The frequency-dependent elastic and viscous moduli also display a similar regional difference. Over the studied frequency range (100 to 300 Hz), the complex viscoelastic moduli display the partial rubber plateau behavior where the elastic moduli are greater than the viscous moduli for a given frequency. The non-disparaging viscous modulus indicates that the neutrophils display a viscoelastic dynamic behavior rather than a perfect elastic behavior like polymer gels. In addition, we found no regional difference in the structural damping coefficient between the leading edge and the cell body. Thus, we conclude that despite the lower loss and storage moduli, the leading edges of the human neutrophils display partially elastic properties similar to the cell body. These results suggest that the lower elastic moduli in the leading edges are more favorable for the elastic fluctuation of actin filaments, which supports the polymerization of the actin filaments leading to the active protrusion during the immune response.     

A Multiscale Red Blood Cell Model with Accurate Mechanics, Rheology, and Dynamics

Red blood cells (RBCs) have highly deformable viscoelastic membranes exhibiting complex rheological response and rich hydrodynamic behavior governed by special elastic and bending properties and by the external/internal fluid and membrane viscosities. We present a multiscale RBC model that is able to predict RBC mechanics, rheology, and dynamics in agreement with experiments. Based on an analytic theory, the modeled membrane properties can be uniquely related to the experimentally established RBC macroscopic properties without any adjustment of parameters. The RBC linear and nonlinear elastic deformations match those obtained in optical-tweezers experiments. The rheological properties of the membrane are compared with those obtained in optical magnetic twisting cytometry, membrane thermal fluctuations, and creep followed by cell recovery. The dynamics of RBCs in shear and Poiseuille flows is tested against experiments and theoretical predictions, and the applicability of the latter is discussed. Our findings clearly indicate that a purely elastic model for the membrane cannot accurately represent the RBC's rheological properties and its dynamics, and therefore accurate modeling of a viscoelastic membrane is necessary.