Deformation-enhanced fluctuations in the red cell skeleton with theoretical relations to elasticity, connectivity, and spectrin unfolding

Quantitative phase imaging based on holography: trends and new perspectives

In 1948, Dennis Gabor proposed the concept of holography, providing a pioneering solution to a quantitative description of the optical wavefront. After 75 years of development, holographic imaging has become a powerful tool for optical wavefront measurement and quantitative phase imaging. The emergence of this technology has given fresh energy to physics, biology, and materials science. Digital holography (DH) possesses the quantitative advantages of wide-field, non-contact, precise, and dynamic measurement capability for complex-waves. DH has unique capabilities for the propagation of optical fields by measuring light scattering with phase information. It offers quantitative visualization of the refractive index and thickness distribution of weak absorption samples, which plays a vital role in the pathophysiology of various diseases and the characterization of various materials. It provides a possibility to bridge the gap between the imaging and scattering disciplines. The propagation of wavefront is described by the complex amplitude. The complex-value in the complex-domain is reconstructed from the intensity-value measurement by camera in the real-domain. Here, we regard the process of holographic recording and reconstruction as a transformation between complex-domain and real-domain, and discuss the mathematics and physical principles of reconstruction. We review the DH in underlying principles, technical approaches, and the breadth of applications. We conclude with emerging challenges and opportunities based on combining holographic imaging with other methodologies that expand the scope and utility of holographic imaging even further. The multidisciplinary nature brings technology and application experts together in label-free cell biology, analytical chemistry, clinical sciences, wavefront sensing, and semiconductor production.

Physical mechanisms of red blood cell splenic filtration

The splenic interendothelial slits fulfill the essential function of continuously filtering red blood cells (RBCs) from the bloodstream to eliminate abnormal and aged cells. To date, the process by which 8 [Formula: see text]m RBCs pass through 0.3 [Formula: see text]m-wide slits remains enigmatic. Does the slit caliber increase during RBC passage as sometimes suggested? Here, we elucidated the mechanisms that govern the RBC retention or passage dynamics in slits by combining multiscale modeling, live imaging, and microfluidic experiments on an original device with submicron-wide physiologically calibrated slits. We observed that healthy RBCs pass through 0.28 [Formula: see text]m-wide rigid slits at 37 °C. To achieve this feat, they must meet two requirements. Geometrically, their surface area-to-volume ratio must be compatible with a shape in two tether-connected equal spheres. Mechanically, the cells with a low surface area-to-volume ratio (28% of RBCs in a 0.4 [Formula: see text]m-wide slit) must locally unfold their spectrin cytoskeleton inside the slit. In contrast, activation of the mechanosensitive PIEZO1 channel is not required. The RBC transit time through the slits follows a [Formula: see text]1 and [Formula: see text]3 power law with in-slit pressure drop and slip width, respectively. This law is similar to that of a Newtonian fluid in a two-dimensional Poiseuille flow, showing that the dynamics of RBCs is controlled by their cytoplasmic viscosity. Altogether, our results show that filtration through submicron-wide slits is possible without further slit opening. Furthermore, our approach addresses the critical need for in vitro evaluation of splenic clearance of diseased or engineered RBCs for transfusion and drug delivery.

Mechanical role of the submembrane spectrin scaffold in red blood cells and neurons

Spectrins are large, evolutionarily well-conserved proteins that form highly organized scaffolds on the inner surface of eukaryotic cells. Their organization in different cell types or cellular compartments helps cells withstand mechanical challenges with unique strategies depending on the cell type. This Review discusses our understanding of the mechanical properties of spectrins, their very distinct organization in red blood cells and neurons as two examples, and the contribution of the scaffolds they form to the mechanical properties of these cells.

A particle-based computational model to analyse remodelling of the red blood cell cytoskeleton during malaria infections

Red blood cells can withstand the harsh mechanical conditions in the vasculature only because the bending rigidity of their plasma membrane is complemented by the shear elasticity of the underlying spectrin-actin network. During an infection by the malaria parasite Plasmodium falciparum, the parasite mines host actin from the junctional complexes and establishes a system of adhesive knobs, whose main structural component is the knob-associated histidine rich protein (KAHRP) secreted by the parasite. Here we aim at a mechanistic understanding of this dramatic transformation process. We have developed a particle-based computational model for the cytoskeleton of red blood cells and simulated it with Brownian dynamics to predict the mechanical changes resulting from actin mining and KAHRP-clustering. Our simulations include the three-dimensional conformations of the semi-flexible spectrin chains, the capping of the actin protofilaments and several established binding sites for KAHRP. For the healthy red blood cell, we find that incorporation of actin protofilaments leads to two regimes in the shear response. Actin mining decreases the shear modulus, but knob formation increases it. We show that dynamical changes in KAHRP binding affinities can explain the experimentally observed relocalization of KAHRP from ankyrin to actin complexes and demonstrate good qualitative agreement with experiments by measuring pair cross-correlations both in the computer simulations and in super-resolution imaging experiments.

Malaria is one of the deadliest infectious diseases and its symptoms are related to the blood stage, when the parasite multiplies within red blood cells. In order to avoid clearance by the spleen, the parasite produces specific factors like the adhesion receptor PfEMP1 and the multifunctional protein KAHRP that lead to the formation of adhesive knobs on the surface of the red blood cells and thus increase residence time in the vasculature. We have developed a computational model for the parasite-induced remodelling of the actin-spectrin network to quantitatively predict the dynamical changes in the mechanical properties of the infected red blood cells and the spatial distribution of the different protein components of the membrane skeleton. Our simulations show that KAHRP can relocate to actin junctions due to dynamical changes in binding affinities, in good qualitative agreement with super-resolution imaging experiments. In the future, our simulation framework can be used to gain further mechanistic insight into the way malaria parasites attack the red blood cell cytoskeleton.

Red blood cells under flow show maximal ATP release for specific hematocrit

ATP release by red blood cells (RBCs) under shear stress (SS) plays a pivotal role in endothelial biochemical signaling cascades. The aim of this study is to investigate through numerical simulation how RBC spatiotemporal organization depends on flow and geometrical conditions to generate ATP patterns. Numerical simulations were conducted in a straight channel by considering both plasma and explicit presence of RBCs, their shape deformation and cell-cell interaction, and ATP release by RBCs. Two ATP release pathways through cell membrane are taken into account: pannexin 1 channel, sensitive to SS, and cystic fibrosis transmembrane conductance regulator, which responds to cell deformation. Several flow and hematocrit conditions are explored. The problem is solved by the lattice Boltzmann method. Application of SS to the RBC suspension triggers a nontrivial spatial RBC organization and ATP patterns. ATP localizes preferentially in the vicinity of the cell-free layer close to channel wall. Conditions for maximal ATP release per cell are identified, which depend on vessel size and hematocrit Ht. Increasing further Ht beyond optimum enhances the total ATP release but should degrade oxygen transport capacity, a compromise between an efficient ATP release and minimal blood dissipation. Moreover, ATP is boosted in capillaries, suggesting a vasomotor activity coordination throughout the resistance network.

An Active Biomechanical Model of Cell Adhesion Actuated by Intracellular Tensioning-Taxis

Cell adhesion to the extracellular matrix (ECM) is highly active and plays a crucial role in various physiological functions. The active response of cells to physicochemical cues has been universally discovered in multiple microenvironments. However, the mechanisms to rule these active behaviors of cells are still poorly understood. Here, we establish an active model to probe the biomechanical mechanisms governing cell adhesion. The framework of cells is modeled as a tensional integrity that is maintained by cytoskeletons and extracellular matrices. Active movement of the cell model is self-driven by its intrinsic tendency to intracellular tensioning, defined as tensioning-taxis in this study. Tensioning-taxis is quantified as driving potential to actuate cell adhesion, and the traction forces are solved by our proposed numerical method of local free energy adaptation. The modeling results account for the active adhesion of cells with dynamic protruding of leading edge and power-law development of mechanical properties. Furthermore, the morphogenesis of cells evolves actively depending on actin filaments alignments by a predicted mechanism of scaling and directing traction forces. The proposed model provides a quantitative way to investigate the active mechanisms of cell adhesion and holds the potential to guide studies of more complex adhesion and motion of cells coupled with multiple external cues.

The axonal actin-spectrin lattice acts as a tension buffering shock absorber

Axons span extreme distances and are subject to significant stretch deformations during limb movements or sudden head movements, especially during impacts. Yet, axon biomechanics, and its relation to the ultrastructure that allows axons to withstand mechanical stress, is poorly understood. Using a custom developed force apparatus, we demonstrate that chick dorsal root ganglion axons exhibit a tension buffering or strain-softening response, where its steady state elastic modulus decreases with increasing strain. We then explore the contributions from the various cytoskeletal components of the axon to show that the recently discovered membrane-associated actin-spectrin scaffold plays a prominent mechanical role. Finally, using a theoretical model, we argue that the actin-spectrin skeleton acts as an axonal tension buffer by reversibly unfolding repeat domains of the spectrin tetramers to release excess mechanical stress. Our results revise the current viewpoint that microtubules and their associated proteins are the only significant load-bearing elements in axons.

Deformation behaviour of stomatocyte, discocyte and echinocyte red blood cell morphologies during optical tweezers stretching

The red blood cell (RBC) deformability is a critical aspect, and assessing the cell deformation characteristics is essential for better diagnostics of healthy and deteriorating RBCs. There is a need to explore the connection between the cell deformation characteristics, cell morphology, disease states, storage lesion and cell shape-transformation conditions for better diagnostics and treatments. A numerical approach inspired from the previous research for RBC morphology predictions and for analysis of RBC deformations is proposed for the first time, to investigate the deformation characteristics of different RBC morphologies. The present study investigates the deformability characteristics of stomatocyte, discocyte and echinocyte morphologies during optical tweezers stretching and provides the opportunity to study the combined contribution of cytoskeletal spectrin network and the lipid-bilayer during RBC deformation. The proposed numerical approach predicts agreeable deformation characteristics of the healthy discocyte with the analogous experimental observations and is extended to further investigate the deformation characteristics of stomatocyte and echinocyte morphologies. In particular, the computer simulations are performed to investigate the influence of direct stretching forces on different equilibrium cell morphologies on cell spectrin link extensions and cell elongation index, along with a parametric analysis on membrane shear modulus, spectrin link extensibility, bending modulus and RBC membrane-bead contact diameter. The results agree with the experimentally observed stiffer nature of stomatocyte and echinocyte with respect to a healthy discocyte at experimentally determined membrane characteristics and suggest the preservation of relevant morphological characteristics, changes in spectrin link densities and the primary contribution of cytoskeletal spectrin network on deformation behaviour of stomatocyte, discocyte and echinocyte morphologies during optical tweezers stretching deformation. The numerical approach presented here forms the foundation for investigations into deformation characteristics and recoverability of RBCs undergoing storage lesion.

Nonlinear indentation of single human erythrocytes under application of a localized mechanical force

Despite the accepted notion that erythrocytes are uniquely deformable cells, the apparent Young's modulus values reported in the literature do not differ so much from those of other cells. We devised to measure the local deformability of living immobilized human erythrocytes at a low force, in contact-free mode, using an application of Scanning Ion Conductance Microscopy (SICM) previously developed in our laboratory. Reversible indentations were induced by forces of up to few hundreds pN. The indentation did not grow linearly with the force. The apparent Young's modulus varied from 0.2 to 1.5 kPa applying forces from 20 to 500 pN on a cell surface area of about 0.2 μm², exhibiting a progressive stiffening at increasing force. Control measurements showed that A549 cells exhibit a constant value of the apparent Young's modulus (about 2 kPa) for forces up to about 800 pN. These findings show that SICM is a suitable tool to investigate cell mechanical properties, when forces in the range of tens of pN are required, in the absence of mechanical contact between probe and sample. The nonlinear deformation of the erythrocyte has to be taken into account in modeling the complex regulation mechanism of the microvascular beds.

Critical role of spectrin in hearing development and deafness

Inner ear hair cells (HCs) detect sound through the deflection of mechanosensory stereocilia. Stereocilia are inserted into the cuticular plate of HCs by parallel actin rootlets, where they convert sound-induced mechanical vibrations into electrical signals. The molecules that support these rootlets and enable them to withstand constant mechanical stresses underpin our ability to hear. However, the structures of these molecules have remained unknown. We hypothesized that αII- and βII-spectrin subunits fulfill this role, and investigated their structural organization in rodent HCs. Using super-resolution fluorescence imaging, we found that spectrin formed ring-like structures around the base of stereocilia rootlets. These spectrin rings were associated with the hearing ability of mice. Further, HC-specific, βII-spectrin knockout mice displayed profound deafness. Overall, our work has identified and characterized structures of spectrin that play a crucial role in mammalian hearing development.

Modified cells as potential ocular drug delivery systems

Drug delivery to ocular targets is problematic, especially in retinal disease treatment. Therefore, targeted drug delivery, prolonged drug action, and minimally invasive treatments are needed. In this review, we describe cell technologies for drug delivery. These technologies are based on genetic engineering and nongenetic-based approaches for cell modification. In principle, cell technologies enable targeted delivery, long drug action, and minimally invasive administration, but they have only been sparsely studied for ocular drug delivery. Herein, these technologies are discussed in the ocular context.

Erythrocyte Aging, Protection via Vesiculation: An Analysis Methodology via Oscillatory Flow

We demonstrate that erythrocyte deformations, specifically of a type as occur in splenic flow (Zhu et al., 2017), and of the type that promote vesiculation can be caused by simple, yet tailored, oscillatory shear flow. We show that such oscillatory shear flow provides an ideal environment to explore a wide variety of metabolic and biochemical effects that promote erythrocyte vesiculation. Deformation details, typical of splenic flow, such as in-folding and implications for membrane/skeleton interaction are demonstrated and quantitatively analyzed. We introduce a theoretical, essentially analytical, vesiculation model that directly couples to our more complex numerical, multilevel, model that clearly delineates various fundamental elements, i.e., sub-processes, that are involved and mediate the vesiculation process. This analytical model highlights particulary important vesiculation precursors such as areas of membrane/skeleton disruptions that trigger the vesiculation process. We demonstrate, using flow cytometry, that the deformations we experimentally induce on cells, and numerically simulate, do not induce lethal forms of cell damage but do induce vesiculation as theoretically forecasted. This, we demonstrate, provides a direct link to cell membrane/skeletal damage such as is associated with metabolic and aging damage. An additional noteworthy feature of this approach is the avoidance of artificial devices, e.g., micro-fluidic chambers, in which deformations and their time scales are often unrepresentative of physiological processes such as splenic flow.

Do Skeletal Dynamics Mediate Sugar Uptake and Transport in Human Erythrocytes?

We explore, herein, the hypothesis that transport of molecules or ions into erythrocytes may be affected and directly stimulated by the dynamics of the spectrin/actin skeleton. Skeleton/actin motions are driven by thermal fluctuations that may be influenced by ATP hydrolysis as well as by structural alterations of the junctional complexes that connect the skeleton to the cell's lipid membrane. Specifically, we focus on the uptake of glucose into erythrocytes via glucose transporter 1 and on the kinetics of glucose disassociation at the endofacial side of glucose transporter 1. We argue that glucose disassociation is affected by both hydrodynamic forces induced by the actin/spectrin skeleton and by probable contact of the swinging 37-nm-long F-actin protofilament with glucose, an effect we dub the "stickball effect." Our hypothesis and results are interpreted within the framework of the kinetic measurements and compartmental kinetic models of Carruthers and co-workers; these experimental results and models describe glucose disassociation as the "slow step" (i.e., rate-limiting step) in the uptake process. Our hypothesis is further supported by direct simulations of skeleton-enhanced transport using our molecular-based models for the actin/spectrin skeleton as well as by experimental measurements of glucose uptake into cells subject to shear deformations, which demonstrate the hydrodynamic effects of advection. Our simulations have, in fact, previously demonstrated enhanced skeletal dynamics in cells in shear deformations, as they occur naturally within the skeleton, which is an effect also supported by experimental observations.

Single Molecule Studies of the Diffusion of Band 3 in Sickle Cell Erythrocytes

Sickle cell disease (SCD) is caused by an inherited mutation in hemoglobin that leads to sickle hemoglobin (HbS) polymerization and premature HbS denaturation. Previous publications have shown that HbS denaturation is followed by binding of denatured HbS (a.k.a. hemichromes) to band 3, the consequent clustering of band 3 in the plane of the erythrocyte membrane that in turn promotes binding of autologous antibodies to the clustered band 3, and removal of the antibody-coated erythrocytes from circulation. Although each step of the above process has been individually demonstrated, the fraction of band 3 that is altered by association with denatured HbS has never been determined. For this purpose, we evaluated the lateral diffusion of band 3 in normal cells, reversibly sickled cells (RSC), irreversibly sickled cells (ISC), and hemoglobin SC erythrocytes (HbSC) in order to estimate the fraction of band 3 that was diffusing more slowly due to hemichrome-induced clustering. We labeled fewer than ten band 3 molecules per intact erythrocyte with a quantum dot to avoid perturbing membrane structure and we then monitored band 3 lateral diffusion by single particle tracking. We report here that the size of the slowly diffusing population of band 3 increases in the sequence: normal cells<HbSC<RSC<ISC. We also demonstrate that the size of the compartment in which band 3 is free to diffuse decreases roughly in the same order, with band 3 diffusing in two compartments of sizes 35 and 71 nm in normal cells, but only a single compartment in HbSC cells (58 nm), RSC (45 nm) and ISC (36 nm). These data suggest that the mobility of band 3 is increasingly constrained during SCD progression, suggesting a global impact of the mutated hemoglobin on erythrocyte membrane properties.

Non-genetic engineering of cells for drug delivery and cell-based therapy

Cell-based therapy is a promising modality to address many unmet medical needs. In addition to genetic engineering, material-based, biochemical, and physical science-based approaches have emerged as novel approaches to modify cells. Non-genetic engineering of cells has been applied in delivering therapeutics to tissues, homing of cells to the bone marrow or inflammatory tissues, cancer imaging, immunotherapy, and remotely controlling cellular functions. This new strategy has unique advantages in disease therapy and is complementary to existing gene-based cell engineering approaches. A better understanding of cellular systems and different engineering methods will allow us to better exploit engineered cells in biomedicine. Here, we review non-genetic cell engineering techniques and applications of engineered cells, discuss the pros and cons of different methods, and provide our perspectives on future research directions.

Biomechanical properties of red blood cells in health and disease towards microfluidics

Red blood cells (RBCs) possess a unique capacity for undergoing cellular deformation to navigate across various human microcirculation vessels, enabling them to pass through capillaries that are smaller than their diameter and to carry out their role as gas carriers between blood and tissues. Since there is growing evidence that red blood cell deformability is impaired in some pathological conditions, measurement of RBC deformability has been the focus of numerous studies over the past decades. Nevertheless, reports on healthy and pathological RBCs are currently limited and, in many cases, are not expressed in terms of well-defined cell membrane parameters such as elasticity and viscosity. Hence, it is often difficult to integrate these results into the basic understanding of RBC behaviour, as well as into clinical applications. The aim of this review is to summarize currently available reports on RBC deformability and to highlight its association with various human diseases such as hereditary disorders (e.g., spherocytosis, elliptocytosis, ovalocytosis, and stomatocytosis), metabolic disorders (e.g., diabetes, hypercholesterolemia, obesity), adenosine triphosphate-induced membrane changes, oxidative stress, and paroxysmal nocturnal hemoglobinuria. Microfluidic techniques have been identified as the key to develop state-of-the-art dynamic experimental models for elucidating the significance of RBC membrane alterations in pathological conditions and the role that such alterations play in the microvasculature flow dynamics.

Structural and mechanical heterogeneity of the erythrocyte membrane reveals hallmarks of membrane stability

The erythrocyte membrane, a metabolically regulated active structure that comprises lipid molecules, junctional complexes, and the spectrin network, enables the cell to undergo large passive deformations when passing through the microvascular system. Here we use atomic force microscopy (AFM) imaging and quantitative mechanical mapping at nanometer resolution to correlate structure and mechanics of key components of the erythrocyte membrane, crucial for cell integrity and function. Our data reveal structural and mechanical heterogeneity modulated by the metabolic state at unprecedented nanometer resolution. ATP-depletion, reducing skeletal junction phosphorylation in RBC cells, leads to membrane stiffening. Analysis of ghosts and shear-force opened erythrocytes show that, in the absence of cytosolic kinases, spectrin phosphorylation results in membrane stiffening at the extracellular face and a reduced junction remodeling in response to loading forces. Topography and mechanical mapping of single components at the cytoplasmic face reveal that, surprisingly, spectrin phosphorylation by ATP softens individual filaments. Our findings suggest that, besides the mechanical signature of each component, the RBC membrane mechanics is regulated by the metabolic state and the assembly of its structural elements.

Cytoskeletal strains in modeled optohydrodynamically stressed healthy and diseased biological cells

Controlled external chemomechanical stimuli have been shown to influence cellular and tissue regeneration/degeneration, especially with regards to distinct disease sequelae or health maintenance. Recently, a unique three-dimensional stress state was mathematically derived to describe the experimental stresses applied to isolated living cells suspended in an optohydrodynamic trap (optical tweezers combined with microfluidics). These formulae were previously developed in two and three dimensions from the fundamental equations describing creeping flows past a suspended sphere. The objective of the current study is to determine the full-field cellular strain response due to the applied three-dimensional stress environment through a multiphysics computational simulation. In this investigation, the multiscale cytoskeletal structures are modeled as homogeneous, isotropic, and linearly elastic. The resulting computational biophysics can be directly compared with experimental strain measurements, other modeling interpretations of cellular mechanics including the liquid drop theory, and biokinetic models of biomolecule dynamics. The described multiphysics computational framework will facilitate more realistic cytoskeletal model interpretations, whose intracellular structures can be distinctly defined, including the cellular membrane substructures, nucleus, and organelles.

Pf155/RESA protein influences the dynamic microcirculatory behavior of ring-stage Plasmodium falciparum infected red blood cells

Proteins exported by Plasmodium falciparum to the red blood cell (RBC) membrane modify the structural properties of the parasitized RBC (Pf-RBC). Although quasi-static single cell assays show reduced ring-stage Pf-RBCs deformability, the parameters influencing their microcirculatory behavior remain unexplored. Here, we study the dynamic properties of ring-stage Pf-RBCs and the role of the parasite protein Pf155/Ring-Infected Erythrocyte Surface Antigen (RESA). Diffraction phase microscopy revealed RESA-driven decreased Pf-RBCs membrane fluctuations. Microfluidic experiments showed a RESA-dependent reduction in the Pf-RBCs transit velocity, which was potentiated at febrile temperature. In a microspheres filtration system, incubation at febrile temperature impaired traversal of RESA-expressing Pf-RBCs. These results show that RESA influences ring-stage Pf-RBCs microcirculation, an effect that is fever-enhanced. This is the first identification of a parasite factor influencing the dynamic circulation of young asexual Pf-RBCs in physiologically relevant conditions, offering novel possibilities for interventions to reduce parasite survival and pathogenesis in its human host.

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.

Analysis of the mobilities of band 3 populations associated with ankyrin protein and junctional complexes in intact murine erythrocytes

Current models of the erythrocyte membrane depict three populations of band 3: (i) a population tethered to spectrin via ankyrin, (ii) a fraction attached to the spectrin-actin junctional complex via adducin, and (iii) a freely diffusing population. Because many studies of band 3 diffusion also distinguish three populations of the polypeptide, it has been speculated that the three populations envisioned in membrane models correspond to the three fractions observed in diffusion analyses. To test this hypothesis, we characterized band 3 diffusion by single-particle tracking in wild-type and ankyrin- and adducin-deficient erythrocytes. We report that ∼40% of total band 3 in wild-type murine erythrocytes is attached to ankyrin, whereas ∼33% is immobilized by adducin, and ∼27% is not attached to any cytoskeletal anchor. More detailed analyses reveal that mobilities of individual ankyrin- and adducin-tethered band 3 molecules are heterogeneous, varying by nearly 2 orders of magnitude and that there is considerable overlap in diffusion coefficients for adducin and ankyrin-tethered populations. Taken together, the data suggest that although the ankyrin- and adducin-immobilized band 3 can be monitored separately, significant heterogeneity still exists within each population, suggesting that structural and compositional properties likely vary considerably within each band 3 complex.

Red blood cell dynamics: from cell deformation to ATP release

The mechanisms of red blood cell (RBC) deformation under both static and dynamic, i.e., flow, conditions have been studied extensively since the mid 1960s. Deformation-induced biochemical reactions and possible signaling in RBCs, however, were proposed only fifteen years ago. Therefore, the fundamental relationship between RBC deformation and cellular signaling dynamics i.e., mechanotransduction, remains incompletely understood. Quantitative understanding of the mechanotransductive pathways in RBCs requires integrative studies of physical models of RBC deformation and cellular biochemical reactions. In this article we review the physical models of RBC deformation, spanning from continuum membrane mechanics to cellular skeleton dynamics under both static and flow conditions, and elaborate the mechanistic links involved in deformation-induced ATP release.

Membrane compartmentalization in Southeast Asian ovalocytosis red blood cells

Red blood cells (RBCs) from individuals with Southeast Asian ovalocytosis (SAO) contain a mutant band 3 protein that causes the formation of unique linear oligomers in the RBC membrane. We used single-particle tracking to measure the lateral diffusion of individual glycophorin C (GPC), band 3, and CD58 proteins in membranes of intact SAO RBCs and normal RBCs (nRBCs). GPC, an integral protein that binds with high affinity to the RBC membrane skeleton, showed oscillatory motion within confinement areas that were smaller in SAO RBCs than in nRBCs. The additional confinement in SAO RBCs could be due to membrane stiffening associated with the SAO phenotype. Band 3 in both SAO RBCs and nRBCs also showed confined motion over short times (ms) and distances (nm), and the area of confinement was smaller in SAO RBCs than in nRBCs. These data presumably reflect the constraints imposed by band 3 oligomerization. Similarly, the glycosylphosphatidylinositol-linked protein CD58 showed loosely confined diffusion in nRBCs and a substantially higher degree of confinement in SAO RBCs. Restricted protein mobility could contribute to the altered adherence of parasite-infected RBCs to vascular endothelium that is thought to protect individuals with SAO from severe manifestations of malaria.

Axisymmetric Optical-Trap Measurement of Red Blood Cell Membrane Elasticity

The elastic properties of the cell membrane play a crucial role in determining the equilibrium shape of the cell, as well as its response to the external forces it experiences in its physiological environment. Red blood cells are a favored system for studying membrane properties because of their simple structure: a lipid bilayer coupled to a membrane cytoskeleton and no cytoplasmic cytoskeleton. An optical trap is used to stretch a red blood cell, fixed to a glass surface, along its symmetry axis by pulling on a micron-sized latex bead that is bound at the center of the exposed cell dimple. The system, at equilibrium, shows Hookean behavior with a spring constant of 1.5×10−6 N/m over a 1–2 μm range of extension. This choice of simple experimental geometry preserves the axial symmetry of the native cell throughout the stretch, probes membrane deformations in the small-extension regime, and facilitates theoretical analysis. The axisymmetry makes the experiment amenable to simulation using a simple model that makes no a priori assumption on the relative importance of shear and bending in membrane deformations. We use an iterative relaxation algorithm to solve for the geometrical configuration of the membrane at mechanical equilibrium for a range of applied forces. We obtain estimates for the out-of-plane membrane bending modulus B≈1×10−19 Nm and an upper limit to the in-plane shear modulus H<2×10−6 N/m. The partial agreement of these results with other published values may serve to highlight the dependence of the cell’s resistance to deformation on the scale and geometry of the deformation.

Spectrin mutations that cause spinocerebellar ataxia type 5 impair axonal transport and induce neurodegeneration in Drosophila

How spectrin mutations caused Purkinje cell death becomes clearer following studies that examined the effect of expressing mutant SCA5 in the fly eye. Mutant spectrin causes deficits in synapse formation at the neuromuscular junction and disrupts vesicular trafficking.

Spinocerebellar ataxia type 5 (SCA5) is an autosomal dominant neurodegenerative disorder caused by mutations in the SPBTN2 gene encoding β-III–spectrin. To investigate the molecular basis of SCA5, we established a series of transgenic Drosophila models that express human β-III–spectrin or fly β-spectrin proteins containing SCA5 mutations. Expression of the SCA5 mutant spectrin in the eye causes a progressive neurodegenerative phenotype, and expression in larval neurons results in posterior paralysis, reduced synaptic terminal growth, and axonal transport deficits. These phenotypes are genetically enhanced by both dynein and dynactin loss-of-function mutations. In summary, we demonstrate that SCA5 mutant spectrin causes adult-onset neurodegeneration in the fly eye and disrupts fundamental intracellular transport processes that are likely to contribute to this progressive neurodegenerative disease.

Analysis of the kinetics of band 3 diffusion in human erythroblasts during assembly of the erythrocyte membrane skeleton

During definitive erythropoiesis, erythroid precursors undergo differentiation through multiple nucleated states to an enucleated reticulocyte, which loses its residual RNA/organelles to become a mature erythrocyte. Over the course of these transformations, continuous changes in membrane proteins occur, including shifts in protein abundance, rates of expression, isoform prominence, states of phosphorylation, and stability. In an effort to understand when assembly of membrane proteins into an architecture characteristic of the mature erythrocyte occurs, we quantitated the lateral diffusion of the most abundant membrane protein, band 3 (AE1), during each stage of erythropoiesis using single particle tracking. Analysis of the lateral trajectories of individual band 3 molecules revealed a gradual reduction in mobility of the anion transporter as erythroblasts differentiated. Evidence for this progressive immobilization included a gradual decline in diffusion coefficients as determined at a video acquisition rate of 120 frames/s and a decrease in the percentage of compartment sizes >100 nm. Because complete acquisition of the properties of band 3 seen in mature erythrocytes is not observed until circulating erythrocytes are formed, we suggest that membrane maturation involves a gradual and cooperative assembly process that is not triggered by the synthesis of any single protein.

Systematic coarse-graining of spectrin-level red blood cell models

We present a rigorous procedure to derive coarse-grained red blood cell (RBC) models, which yield accurate mechanical response. Based on a semi-analytic theory the linear and nonlinear elastic properties of healthy and infected RBCs in malaria can be matched with those obtained in optical tweezers stretching experiments. The present analysis predicts correctly the membrane Young's modulus in contrast to about 50% error in predictions by previous models. In addition, we develop a stress-free model which avoids a number of pitfalls of existing RBC models, such as non-smooth or poorly controlled equilibrium shape and dependence of the mechanical properties on the initial triangulation quality. Here we employ dissipative particle dynamics for the implementation but the proposed model is general and suitable for use in many existing continuum and particle-based numerical methods.

Nanomechanics of multiple units in the erythrocyte membrane skeletal network

Erythrocytes undergo deformations when they transport O₂ and CO₂ across the membrane, yet the 3D nanomechanics of the skeletal network remains poorly understood. Expanding from our previous single isolated unit, we now simulate networks consisting of 1–10 concentric rings of repeating units in equibiaxial deformation. The networks are organized with (1) a 3D model for a single unit, (2) a wrap-around mode between Sp and actin protofilament in the intra-unit interaction, and (3) a random inter-unit connectivity. These assumptions permit efficient five-degrees-of-freedom (5DOF) simulations when up to 30 pN of radial forces are applied to the boundary spectrin (Sp) and the center and other units are analyzed. As 6 Sp balance their tensions, hexagonal units become irregular. While actin protofilaments remain tangent to the network, their yaw (Φ) angles change drastically with addition of neighboring units or an Sp unfolding. It is anticipated that during deformation, transmembrane complexes associated with the network move laterally through the lipid bilayer and increase the diffusion of molecules across the membrane. When protofilament/Sp sweeps under the lipid bilayer, they mix up the submembrane concentration gradient. Thus, the nanomechanics of actin protofilaments and Sp may enhance the transport of molecules during erythrocyte deformation.

Multiscale simulation of erythrocyte membranes

To quantitatively predict the mechanical response and mechanically induced remodeling of red blood cells, we developed a multiscale method to correlate distributions of internal stress with overall cell deformation. This method consists of three models at different length scales: in the complete cell level the membrane is modeled as two distinct layers of continuum shells using finite element method (Level III), in which the skeleton-bilayer interactions are depicted as a slide in the lateral (i.e., in-plane) direction (caused by the mobility of the skeleton-bilayer pinning points) and a normal contact force; the constitutive laws of the inner layer (the protein skeleton) are obtained from a molecular-based model (Level II); the mechanical properties of the spectrin (Sp, a key component of the skeleton), including its folding/unfolding reactions, are obtained with a stress-strain model (Level I). Model verification is achieved through comparisons with existing numerical and experimental studies in terms of the resting shape of the cell as well as cell deformations induced by micropipettes and optical tweezers. Detailed distributions of the interaction force between the lipid bilayer and the skeleton that may cause their dissociation and lead to phenomena such as vesiculation are predicted. Specifically, our model predicts correlation between the occurrence of Sp unfolding and increase in the mechanical load upon individual skeleton-bilayer pinning points. Finally a simulation of the necking process after skeleton-bilayer dissociation, a precursor of vesiculation, is conducted.

Flickering analysis of erythrocyte mechanical properties: dependence on oxygenation level, cell shape, and hydration level

Erythrocytes (red blood cells) play an essential role in the respiratory functions of vertebrates, carrying oxygen from lungs to tissues and CO(2) from tissues to lungs. They are mechanically very soft, enabling circulation through small capillaries. The small thermally induced displacements of the membrane provide an important tool in the investigation of the mechanics of the cell membrane. However, despite numerous studies, uncertainties in the interpretation of the data, and in the values derived for the main parameters of cell mechanics, have rendered past conclusions from the fluctuation approach somewhat controversial. Here we revisit the experimental method and theoretical analysis of fluctuations, to adapt them to the case of cell contour fluctuations, which are readily observable experimentally. This enables direct measurements of membrane tension, of bending modulus, and of the viscosity of the cell cytoplasm. Of the various factors that influence the mechanical properties of the cell, we focus here on: 1), the level of oxygenation, as monitored by Raman spectrometry; 2), cell shape; and 3), the concentration of hemoglobin. The results show that, contrary to previous reports, there is no significant difference in cell tension and bending modulus between oxygenated and deoxygenated states, in line with the softness requirement for optimal circulatory flow in both states. On the other hand, tension and bending moduli of discocyte- and spherocyte-shaped cells differ markedly, in both the oxygenated and deoxygenated states. The tension in spherocytes is much higher, consistent with recent theoretical models that describe the transitions between red blood cell shapes as a function of membrane tension. Cell cytoplasmic viscosity is strongly influenced by the hydration state. The implications of these results to circulatory flow dynamics in physiological and pathological conditions are discussed.

ATP-dependent mechanics of red blood cells

Red blood cells are amazingly deformable structures able to recover their initial shape even after large deformations as when passing through tight blood capillaries. The reason for this exceptional property is found in the composition of the membrane and the membrane-cytoskeleton interaction. We investigate the mechanics and the dynamics of RBCs by a unique noninvasive technique, using weak optical tweezers to measure membrane fluctuation amplitudes with mus temporal and sub nm spatial resolution. This enhanced edge detection method allows to span over >4 orders of magnitude in frequency. Hence, we can simultaneously measure red blood cell membrane mechanical properties such as bending modulus kappa = 2.8 +/- 0.3 x 10(-19)J = 67.6 +/- 7.2 k(B)T, tension sigma = 6.5 +/- 2.1 x 10(-7)N/m, and an effective viscosity eta(eff) = 81 +/- 3.7 x 10(-3) Pa s that suggests unknown dissipative processes. We furthermore show that cell mechanics highly depends on the membrane-spectrin interaction mediated by the phosphorylation of the interconnection protein 4.1R. Inhibition and activation of this phosphorylation significantly affects tension and effective viscosity. Our results show that on short time scales (slower than 100 ms) the membrane fluctuates as in thermodynamic equilibrium. At time scales longer than 100 ms, the equilibrium description breaks down and fluctuation amplitudes are higher by 40% than predicted by the membrane equilibrium theory. Possible explanations for this discrepancy are influences of the spectrin that is not included in the membrane theory or nonequilibrium fluctuations that can be accounted for by defining a nonthermal effective energy of up to E(eff) = 1.4 +/- 0.1 k(B)T, that corresponds to an actively increased effective temperature.

Imaging of the diffusion of single band 3 molecules on normal and mutant erythrocytes

Membrane-spanning proteins may interact with a variety of other integral and peripheral membrane proteins via a diversity of protein-protein interactions. Not surprisingly, defects or mutations in any one of these interacting components can impact the physical and biological properties on the entire complex. Here we use quantum dots to image the diffusion of individual band 3 molecules in the plasma membranes of intact human erythrocytes from healthy volunteers and patients with defects in one of their membrane components, leading to well-known red cell pathologies (hereditary spherocytosis, hereditary elliptocytosis, hereditary hydrocytosis, Southeast Asian ovalocytosis, and hereditary pyropoikilocytosis). After characterizing the motile properties of the major subpopulations of band 3 in intact normal erythrocytes, we demonstrate that the properties of these subpopulations of band 3 change significantly in diseased cells, as evidenced by changes in the microscopic and macroscopic diffusion coefficients of band 3 and in the compartment sizes in which the different band 3 populations can diffuse. Because the above membrane abnormalities largely arise from defects in other membrane components (eg, spectrin, ankyrin), these data suggest that single particle tracking of band 3 might constitute a useful tool for characterizing the general structural integrity of the human erythrocyte membrane.

Hereditary spherocytosis

Hereditary spherocytosis is a common inherited disorder that is characterised by anaemia, jaundice, and splenomegaly. It is reported worldwide and is the most common inherited anaemia in individuals of northern European ancestry. Clinical severity is variable with most patients having a well-compensated haemolytic anaemia. Some individuals are asymptomatic, whereas others have severe haemolytic anaemia requiring erythrocyte transfusion. The primary lesion in hereditary spherocytosis is loss of membrane surface area, leading to reduced deformability due to defects in the membrane proteins ankyrin, band 3, beta spectrin, alpha spectrin, or protein 4.2. Many isolated mutations have been identified in the genes encoding these membrane proteins; common hereditary spherocytosis-associated mutations have not been identified. Abnormal spherocytes are trapped and destroyed in the spleen and this is the main cause of haemolysis in this disorder. Common complications are cholelithiasis, haemolytic episodes, and aplastic crises. Splenectomy is curative but should be undertaken only after careful assessment of the risks and benefits.

Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum

Parasitization by malaria-inducing Plasmodium falciparum leads to structural, biochemical, and mechanical modifications to the host red blood cells (RBCs). To study these modifications, we investigate two intrinsic indicators: the refractive index and membrane fluctuations in P. falciparum-invaded human RBCs (Pf-RBCs). We report experimental connections between these intrinsic indicators and pathological states. By employing two noninvasive optical techniques, tomographic phase microscopy and diffraction phase microscopy, we extract three-dimensional maps of refractive index and nanoscale cell membrane fluctuations in isolated RBCs. Our systematic experiments cover all intraerythrocytic stages of parasite development under physiological and febrile temperatures. These findings offer potential, and sufficiently general, avenues for identifying, through cell membrane dynamics, pathological states that cause or accompany human diseases.

The nonlinear mechanical response of the red blood cell

We measure the dynamical mechanical properties of human red blood cells. A single cell response is measured with optical tweezers. We investigate both the stress relaxation following a fast deformation and the effect of varying the strain rate. We find a power-law decay of the stress as a function of time, down to a plateau stress, and a power-law increase of the cell's elasticity as a function of the strain rate. Interestingly, the exponents of these quantities violate the linear superposition principle, indicating a nonlinear response. We propose that this is due to the breaking of a fraction of the crosslinks during the deformation process. The soft glassy rheology model accounts for the relation between the exponents we observe experimentally. This picture is consistent with recent models of bond remodeling in the red blood cell's molecular structure. Our results imply that the blood cell's mechanical behavior depends critically on the deformation process.

Sticky chain model for shear response of red blood cells

A sticky chain model has been proposed to describe the unfolding of spectrin network under applied mechanical loads. With the model, the response of a red blood cell (RBC) under static and cyclic shear loading has been predicted, which agrees qualitatively with relevant experimental results.

An image-processing technique for measuring the dynamic movement of cell membranes

An automated method has been developed to measure and compare the dynamic movement of cell membranes. Using the red blood cell as a common example the method locates the edge of the cell, with sub-pixel precision at multiple points on the periphery. This method is a different implementation to a technique used for giant unilamellar vesicles and addresses issues relating specifically to biological cells, in particular relating to finding a local minima, calculating equi-spaced measuring points for arbitrary shapes and using the perpendicular direction to the edge for position measurement. Parameters have been defined to characterise the cell's membrane behaviour and the analysis program allows the automatic compilation of multiple tests under varying conditions, and statistical comparison of identical populations of cells.

A Novel Technique of Quantifying Flexural Stiffness of Rod-Like Structures

In cellular and molecular biomechanics, extensional stiffness of rod-like structures such as leukocyte microvilli can be easily measured with many techniques, but not many techniques are available for measuring their flexural stiffness. In this paper, we report a novel technique of measuring the flexural stiffness of rod-like structures. This technique is based on image deconvolution and, as an example, it was used for determining the flexural stiffness of neutrophil microvilli. The probes we used were 40-nm-diameter fluorescent beads, which were bound to the tips of neutrophil microvilli by anti-L-selectin antibody. The fluorescent images of the bead, which was positioned at the center of the cell bottom, were acquired with high magnification and long exposure time (3 s). Using a Gaussian function as the point spread function of our imaging system, we established a convolution equation based on Boltzmann's law, which yields an analytical expression that relates the bead image profile to the flexural stiffness of the microvillus. The flexural stiffness was then obtained by the least squares regression. On average, the flexural stiffness was determined to be 7 pN/mum for single neutrophil microvilli. With the resolution of our imaging system, this technique can be used for measuring any flexural stiffness smaller than 34 pN/mum and it has great potential in single molecule biomechanics.

Unique elastic properties of the spectrin tetramer as revealed by multiscale coarse-grained modeling

The force-extension profile of tetrameric spectrin is determined by using multiscale computer simulation. Fluctuation results of atomistic simulations of double spectrin repeat units (DSRU) are used to systematically build a coarse-grained (CG) model for the tetrameric form of spectrin. It is found that the spectrin tetramer can be modeled as a soft polymer with a unique flat force-extension profile over the range of biologically important lengths. It is also concluded that in the cytoskeletal network of the red blood cell the tetramer is in an "overcompressed" state. These findings are in contrast to the commonly used models of spectrin tetramer elasticity, namely the "entropic spring" polymer models. From these results, it is concluded that stable intact helical linker regions are needed to maintain the soft elasticity of the spectrin tetramer.

Spectrin folding versus unfolding reactions and RBC membrane stiffness

Spectrin (Sp), a key component of the erythrocyte membrane, is routinely stretched to near its fully folded contour length during cell deformations. Such dynamic loading may induce domain unfolding as suggested by recent experiments. Herein we develop a model to describe the folding/unfolding of spectrin during equilibrium or nonequilibrium extensions. In both cases, our model indicates that there exists a critical extension beyond which unfolding occurs. We further deploy this model, together with a three-dimensional model of the junctional complex in the erythrocyte membrane, to explore the effect of Sp unfolding on the membrane's mechanical properties, and on the thermal fluctuation of membrane-attached beads. At large deformations our results show a distinctive strain-induced unstiffening behavior, manifested in the slow decrease of the shear modulus, and accompanied by an increase in bead fluctuation. Bead fluctuation is also found to be influenced by mode switching, a phenomenon predicted by our three-dimensional model. The amount of stiffness reduction, however, is modest compared with that reported in experiments. A possible explanation for the discrepancy is the occurrence of spectrin head-to-head disassociation which is also included within our modeling framework and used to analyze bead motion as observed via experiment.

Fluctuations of coupled fluid and solid membranes with application to red blood cells

The fluctuation spectra and the intermembrane interaction of two membranes at a fixed average distance are investigated. Each membrane can either be a fluid or a solid membrane, and in isolation, its fluctuations are described by a bare or a wave-vector-dependent bending modulus, respectively. The membranes interact via their excluded-volume interaction; the average distance is maintained by an external, homogeneous pressure. For strong coupling, the fluctuations can be described by a single, effective membrane that combines the elastic properties. For weak coupling, the fluctuations of the individual, noninteracting membranes are recovered. The case of a composite membrane consisting of one fluid and one solid membrane can serve as a microscopic model for the plasma membrane and cytoskeleton of the red blood cell. We find that, despite the complex microstructure of bilayers and cytoskeletons in a real cell, the fluctuations with wavelengths lambda greater, similar 400 nm are well described by the fluctuations of a single, polymerized membrane (provided that there are no inhomogeneities of the microstructure). The model is applied to the fluctuation data of discocytes ("normal" red blood cells), a stomatocyte, and an echinocyte. The elastic parameters of the membrane and an effective temperature that quantifies active, metabolically driven fluctuations are extracted from the experiments.

Forced unfolding of proteins within cells

To identify cytoskeletal proteins that change conformation or assembly within stressed cells, in situ labeling of sterically shielded cysteines with fluorophores was analyzed by fluorescence imaging, quantitative mass spectrometry, and sequential two-dye labeling. Within red blood cells, shotgun labeling showed that shielded cysteines in the two isoforms of the cytoskeletal protein spectrin were increasingly labeled as a function of shear stress and time, indicative of forced unfolding of specific domains. Within mesenchymal stem cells-as a prototypical adherent cell-nonmuscle myosin IIA and vimentin are just two of the cytoskeletal proteins identified that show differential labeling in tensed versus drug-relaxed cells. Cysteine labeling of proteins within live cells can thus be used to fluorescently map out sites of molecular-scale deformation, and the results also suggest means to colocalize signaling events such as phosphorylation with forced unfolding.

Probing cellular mechanical responses to stimuli using ballistic intracellular nanorheology

We describe a new method to measure the local and global micromechanical properties of the cytoplasm of single living cells in their physiological milieu and subjected to external stimuli. By tracking spontaneous, Brownian movements of individual nanoparticles of diameter>or=100 nm distributed within the cell with high spatial and temporal resolutions, the local viscoelastic properties of the intracellular milieu can be measured in different locations within the cell. The amplitude and the time-dependence of the mean-squared displacement of each nanoparticle directly reflect the elasticity and the viscosity of the cytoplasm in the vicinity of the nanoparticle. In our previous versions of particle tracking, we delivered nanoparticles via microinjection, which limited the number of cells amenable to measurement, rendering our technique incompatible with high-throughput experiments. Here we introduce ballistic injection to effectively deliver a large number of nanoparticles to a large number of cells simultaneously. When coupled with multiple particle tracking, this new method-ballistic intracellular nanorheology (BIN)-makes it now possible to probe the viscoelastic properties of cells in high-throughput experiments, which require large quantities of injected cells for seeding in various conditions. For instance, BIN allows us to probe an ensemble of cells embedded deeply inside a three-dimensional extracellular matrix or as a monolayer of cells subjected to shear flows.