Constitutive Model of Erythrocyte Membranes with Distributions of Spectrin Orientations and Lengths

Dynamic mechanisms for membrane skeleton transitions

The plasma membrane and the underlying skeleton form a protective barrier for eukaryotic cells. The molecules forming this complex composite material constantly rearrange under mechanical stress to confer this protective capacity. One of those molecules, spectrin, is ubiquitous in the membrane skeleton and primarily located proximal to the inner leaflet of the plasma membrane and engages in protein-lipid interactions via a set of membrane-anchoring domains. Spectrin is linked by short actin filaments and its conformation varies in different types of cells. In this work, we developed a generalized network model for the membrane skeleton integrated with myosin contractility and membrane mechanics to investigate the response of the spectrin meshwork to mechanical loading. We observed that the force generated by membrane bending is important to maintain a smooth skeletal structure. This suggests that the membrane is not just supported by the skeleton, but has an active contribution to the stability of the cell structure. We found that spectrin and myosin turnover are necessary for the transition between stress and rest states in the skeleton. Our model reveals that the actin-spectrin meshwork dynamics are balanced by the membrane forces with area constraint and volume restriction promoting the stability of the membrane skeleton. Furthermore, we showed that cell attachment to the substrate promotes shape stabilization. Thus, our proposed model gives insight into the shared mechanisms of the membrane skeleton associated with myosin and membrane that can be tested in different types of cells.

Energy Dissipation in the Human Red Cell Membrane

The membrane of the human red cell consists of a lipid bilayer and a so-called membrane skeleton attached on the cytoplasmic side of the bilayer. Upon the deformation of red cells, energy is dissipated in their cytoplasm and their membrane. As to the membrane, three contributions can be distinguished: (i) A two-dimensional shear deformation with the membrane viscosity as the frictional parameter; (ii) A motion of the membrane skeleton relative to the bilayer; (iii) A relative motion of the two monolayers of the bilayer. The frictional parameter in contributions (ii) and (iii) is a frictional coefficient specific for the respective contribution. This perspective describes the history up to recent advances in the knowledge of these contributions. It reviews the mechanisms of energy dissipation on a molecular scale and suggests new ones, particularly for the first contribution. It proposes a parametric fitting expected to shed light on the discrepant values found for the membrane viscosity by different experimental approaches. It proposes strategies that could allow the determination of the frictional coefficients pertaining to the second and the third contribution. It highlights the consequences characteristic times have on the state of the red cell membrane in circulation as well as on the adaptation of computer models to the red cell history in an in vitro experiment.

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.

Nanoscale Dynamics of Actin Filaments in the Red Blood Cell Membrane Skeleton

Red blood cell (RBC) shape and deformability are supported by a planar network of short actin filament (F-actin) nodes (∼37 nm length, 15–18 subunits) interconnected by long spectrin strands at the inner surface of the plasma membrane. Spectrin-F-actin network structure underlies quantitative modeling of forces controlling RBC shape, membrane curvature, and deformation, yet the nanoscale organization and dynamics of the F-actin nodes in situ are not well understood. We examined F-actin distribution and dynamics in RBCs using fluorescent-phalloidin labeling of F-actin imaged by multiple microscopy modalities. Total internal reflection fluorescence and Zeiss Airyscan confocal microscopy demonstrate that F-actin is concentrated in multiple brightly stained F-actin foci ∼200–300 nm apart interspersed with dimmer F-actin staining regions. Single molecule stochastic optical reconstruction microscopy imaging of Alexa 647-phalloidin-labeled F-actin and computational analysis also indicates an irregular, nonrandom distribution of F-actin nodes. Treatment of RBCs with latrunculin A and cytochalasin D indicates that F-actin foci distribution depends on actin polymerization, while live cell imaging reveals dynamic local motions of F-actin foci, with lateral movements, appearance and disappearance. Regulation of F-actin node distribution and dynamics via actin assembly/disassembly pathways and/or via local extension and retraction of spectrin strands may provide a new mechanism to control spectrin-F-actin network connectivity, RBC shape, and membrane deformability.

Development of Mechanical Stability in Late-Stage Embryonic Erythroid Cells: Insights From Fluorescence Imaged Micro-Deformation Studies

The combined use of fluorescence labeling and micro-manipulation of red blood cells has proven to be a powerful tool for understanding and characterizing fundamental mechanisms underlying the mechanical behavior of cells. Here we used this approach to study the development of the membrane-associated cytoskeleton (MAS) in primary embryonic erythroid cells. Erythropoiesis comes in two forms in the mammalian embryo, primitive and definitive, characterized by intra- and extra-vascular maturation, respectively. Primitive erythroid precursors in the murine embryo first begin to circulate at embryonic day (E) 8.25 and mature as a semi-synchronous cohort before enucleating between E12.5 and E16.5. Previously, we determined that the major components of the MAS become localized to the membrane between E10.5 and E12.5, and that this localization is associated with an increase in membrane mechanical stability over this same period. The change in mechanical stability was reflected in the creation of MAS-free regions of the membrane at the tips of the projections formed when cells were aspirated into micropipettes. The tendency to form MAS-free regions decreases as primitive erythroid cells continue to mature through E14.5, at least 2 days after all detectable cytoskeletal components are localized to the membrane, indicating continued strengthening of membrane cohesion after membrane localization of cytoskeletal components. Here we demonstrate that the formation of MAS-free regions is the result of a mechanical failure within the MAS, and not the detachment of membrane bilayer from the MAS. Once a "hole" is formed in the MAS, the skeletal network contracts laterally along the aspirated projection to form the MAS-free region. In protein 4.1-null primitive erythroid cells, the tendency to form MAS-free regions is markedly enhanced. Of note, similar MAS-free regions were observed in maturing erythroid cells from human marrow, indicating that similar processes occur in definitive erythroid cells. We conclude that localization of cytoskeletal components to the cell membrane of mammalian erythroid cells during maturation is insufficient by itself to produce a mature MAS, but that subsequent processes are additionally required to strengthen intraskeletal interactions.

Nonlinear large deformation of a spherical red blood cell induced by ultrasonic standing wave

A computational model is developed to investigate the nonlinear static deformation of a spherical (osmotically swollen) red blood cell (RBC) induced by ultrasonic standing wave. The ultrasonic standing wave can generate steady acoustic radiation stress to deform the cell, and in turn, the deformed cell reshapes the acoustic field. This is a real-time coupling problem between the acoustic field and the mechanical field. In the computational model, the acoustic radiation stress acting on the RBC membrane is modeled by adopting the nonviscous momentum flux theory. The RBC membrane is modeled as a hyperelastic shell considering the in-plane elasticity, bending elasticity, and surface tension of the membrane. The volume conservation constraint of the membrane sealing fluid is applied to ensure the osmotic balance of the membrane. To address this real-time coupling problem, the computational model is implemented by a finite element method algorithm. The numerical results are compared with the existing theoretical model and experimental data, and the strain hardening trend of the experimental data is successfully predicted, which verifies the accuracy and effectiveness of the computational model. The computational model can accurately extract the mechanical properties of cells from acoustic deformation experiments, which is helpful for the diagnosis of some human diseases.