Bending elastic modulus of red blood cell membrane derived from buckling instability in micropipet aspiration tests

Label-Free Techniques for Probing Biomolecular Condensates

Biomolecular condensates play important roles in a wide array of fundamental biological processes, such as cellular compartmentalization, cellular regulation, and other biochemical reactions. Since their discovery and first observations, an extensive and expansive library of tools has been developed to investigate various aspects and properties, encompassing structural and compositional information, material properties, and their evolution throughout the life cycle from formation to eventual dissolution. This Review presents an overview of the expanded set of tools and methods that researchers use to probe the properties of biomolecular condensates across diverse scales of length, concentration, stiffness, and time. In particular, we review recent years' exciting development of label-free techniques and methodologies. We broadly organize the set of tools into 3 categories: (1) imaging-based techniques, such as transmitted-light microscopy (TLM) and Brillouin microscopy (BM), (2) force spectroscopy techniques, such as atomic force microscopy (AFM) and the optical tweezer (OT), and (3) microfluidic platforms and emerging technologies. We point out the tools' key opportunities, challenges, and future perspectives and analyze their correlative potential as well as compatibility with other techniques. Additionally, we review emerging techniques, namely, differential dynamic microscopy (DDM) and interferometric scattering microscopy (iSCAT), that have huge potential for future applications in studying biomolecular condensates. Finally, we highlight how some of these techniques can be translated for diagnostics and therapy purposes. We hope this Review serves as a useful guide for new researchers in this field and aids in advancing the development of new biophysical tools to study biomolecular condensates.

MEDUSA: A cloud-based tool for the analysis of X-ray diffuse scattering to obtain the bending modulus from oriented membrane stacks

An important mechanical property of cells is their membrane bending modulus, κ. Here, we introduce MEDUSA (MEmbrane DiffUse Scattering Analysis), a cloud-based analysis tool to determine the bending modulus, κ, from the analysis of X-ray diffuse scattering. MEDUSA uses GPU (graphics processing unit) accelerated hardware and a parallelized algorithm to run the calculations efficiently in a few seconds. MEDUSA's graphical user interface allows the user to upload 2-dimensional data collected from different sources, perform background subtraction and distortion corrections, select regions of interest, run the fitting procedure and output the fitted parameters, the membranes' bending modulus κ, and compressional modulus B.

A cell-and-plasma numerical model reveals hemodynamic stress and flow adaptation in zebrafish microvessels after morphological alteration

The development of a functional cardiovascular system ensures a sustainable oxygen, nutrient and hormone delivery system for successful embryonic development and homeostasis in adulthood. While early vessels are formed by biochemical signaling and genetic programming, the onset of blood flow provides mechanical cues that participate in vascular remodeling of the embryonic vascular system. The zebrafish is a prolific animal model for studying the quantitative relationship between blood flow and vascular morphogenesis due to a combination of favorable factors including blood flow visualization in optically transparent larvae. In this study, we have developed a cell-and-plasma blood transport model using computational fluid dynamics (CFD) to understand how red blood cell (RBC) partitioning affect lumen wall shear stress (WSS) and blood pressure in zebrafish trunk blood vascular networks with altered rheology and morphology. By performing live imaging of embryos with reduced hematocrit, we discovered that cardiac output and caudal artery flow rates were maintained. These adaptation trends were recapitulated in our CFD models, which showed reduction in network WSS via viscosity reduction in the caudal artery/vein and via pressure gradient weakening in the intersegmental vessels (ISVs). Embryos with experimentally reduced lumen diameter showed reduced cardiac output and caudal artery flow rate. Factoring in this trend into our CFD models, simulations highlighted that lumen diameter reduction increased vessel WSS but this increase was mitigated by flow reduction due to the adaptive network pressure gradient weakening. Additionally, hypothetical network CFD models with different vessel lumen diameter distribution characteristics indicated the significance of axial variation in lumen diameter and cross-sectional shape for establishing physiological WSS gradients along ISVs. In summary, our work demonstrates how both experiment-driven and hypothetical CFD modeling can be employed for the study of blood flow physiology during vascular remodeling.

Competition between deformation and free volume quantified by 3D image analysis of red blood cell

Cells in living organisms are subjected to mechanical strains caused by external forces like overcrowding, resulting in strong deformations that affect cell function. We study the interplay between deformation and crowding of red blood cells (RBCs) in dispersions of nonabsorbing rod-like viruses. We identify a sequence of configurational transitions of RBC doublets, including configurations that can only be induced by long-ranged attraction: highly fluctuating T-shaped and face-to-face configurations at low, and doublets approaching a complete spherical configuration at high, rod concentrations. Complementary simulations are used to explore different energy contributions to deformation as well as the stability of RBC doublet configurations. Our advanced analysis of 3D reconstructed confocal images of RBC doublets quantifies the depletion interaction and the resulting deformation energy. Thus, we introduce a noninvasive, high-throughput platform that is generally applicable to investigate the mechanical response of biological cells to external forces and characterize their mechanical properties.

Kinetic relaxation of giant vesicles validates diffusional softening in a binary lipid mixture

The stiffness of biological membranes determines the work required by cellular machinery to form and dismantle vesicles and other lipidic shapes. Model membrane stiffness can be determined from the equilibrium distribution of giant unilamellar vesicle surface undulations observable by phase contrast microscopy. With two or more components, lateral fluctuations of composition will couple to surface undulations depending on the curvature sensitivity of the constituent lipids. The result is a broader distribution of undulations whose complete relaxation is partially determined by lipid diffusion. In this work, kinetic analysis of the undulations of giant unilamellar vesicles made of phosphatidylcholine-phosphatidylethanolamine mixtures validates the molecular mechanism by which the membrane is made 25% softer than a single-component one. The mechanism is relevant to biological membranes, which have diverse and curvature-sensitive lipids.

An analytical model describing the mechanics of erythrocyte membrane wrapping during active invasion of a plasmodium falciparum merozoite

The invasion of a merozoite into an erythrocyte by membrane wrapping is a hallmark of malaria pathogenesis. The invasion involves biomechanical interactions whereby the merozoite exerts actomyosin-based forces to push itself into and through the erythrocyte membrane while concurrently inducing biochemical damage to the erythrocyte membrane. Whereas the biochemical damage process has been investigated, the detailed mechanistic understanding of the invasion mechanics remains limited. Thus, the current study aimed to develop a mathematical model describing the mechanical factors involved in the merozoite invasion into an erythrocyte and explore the invasion mechanics. A shell theory model was developed comprising constitutive, equilibrium and governing equations of the deformable erythrocyte membrane to predict membrane mechanics during the wrapping of an entire non-deformable ellipsoidal merozoite. Predicted parameters include principal erythrocyte membrane deformations and stresses, wrapping and indentation forces, and indentation work. The numerical investigations considered two limits for the erythrocyte membrane deformation during wrapping (4% and 51% areal strain) and erythrocyte membrane phosphorylation (decrease of membrane elastic modulus from 1 to 0.5 kPa). For an intact erythrocyte, the maximum indentation force was 1 and 8.5 pN, and the indentation work was 1.92 × 10^-18 and 1.40 × 10^-17 J for 4% and 51% areal membrane strain. Phosphorylation damage in the erythrocyte membrane reduced the required indentation work by 50% to 0.97 × 10^-18 and 0.70 × 10^-17 J for 4% and 51% areal strain. The current study demonstrated the developed model's feasibility to provide new knowledge on the physical mechanisms of the merozoite invasion process that contribute to the invasion efficiency towards the discovery of new invasion-blocking anti-malaria drugs.

A mathematical model of fibrinogen-mediated erythrocyte-erythrocyte adhesion

Erythrocytes are deformable cells that undergo progressive biophysical and biochemical changes affecting the normal blood flow. Fibrinogen, one of the most abundant plasma proteins, is a primary determinant for changes in haemorheological properties, and a major independent risk factor for cardiovascular diseases. In this study, the adhesion between human erythrocytes is measured by atomic force microscopy (AFM) and its effect observed by micropipette aspiration technique, in the absence and presence of fibrinogen. These experimental data are then used in the development of a mathematical model to examine the biomedical relevant interaction between two erythrocytes. Our designed mathematical model is able to explore the erythrocyte-erythrocyte adhesion forces and changes in erythrocyte morphology. AFM erythrocyte-erythrocyte adhesion data show that the work and detachment force necessary to overcome the adhesion between two erythrocytes increase in the presence of fibrinogen. The changes in erythrocyte morphology, the strong cell-cell adhesion and the slow separation of the two cells are successfully followed in the mathematical simulation. Erythrocyte-erythrocyte adhesion forces and energies are quantified and matched with experimental data. The changes observed on erythrocyte-erythrocyte interactions may give important insights about the pathophysiological relevance of fibrinogen and erythrocyte aggregation in hindering microcirculatory blood flow.

Effect of constitutive law on the erythrocyte membrane response to large strains

Three constitutive laws, that is the Skalak, neo-Hookean and Yeoh laws, commonly employed for describing the erythrocyte membrane mechanics are theoretically analyzed and numerically investigated to assess their accuracy for capturing erythrocyte deformation characteristics and morphology. Particular emphasis is given to the nonlinear deformation regime, where it is known that the discrepancies between constitutive laws are most prominent. Hence, the experiments of optical tweezers and micropipette aspiration are considered here, for which relationships between the individual shear elastic moduli of the constitutive laws can also be established through analysis of the tension-deformation relationship. All constitutive laws were found to adequately predict the axial and transverse deformations of a red blood cell subjected to stretching with optical tweezers for a constant shear elastic modulus value. As opposed to Skalak law, the neo-Hookean and Yeoh laws replicated the erythrocyte membrane folding, that has been experimentally observed, with the trade-off of sustaining significant area variations. For the micropipette aspiration, the suction pressure-aspiration length relationship could be excellently predicted for a fixed shear elastic modulus value only when Yeoh law was considered. Importantly, the neo-Hookean and Yeoh laws reproduced the membrane wrinkling at suction pressures close to those experimentally measured. None of the constitutive laws suffered from membrane area compressibility in the micropipette aspiration case.

Dynamic response of red blood cells in health and disease

The viscoelastic response of the red blood cells (RBCs) affected by hematological disorders become severely impaired by the altered biophysical and morphological properties. These include traits like reduced deformability, increased membrane viscosity, and change in cell shape, causing substantial changes in the overall hemodynamics. RBCs, by virtue of their highly elastic membrane and low bending rigidity, exhibit complex dynamics when exposed to cyclic, transient forces in the microcirculation. Here, we employ mesoscopic numerical simulations based on the dissipative particle dynamics (DPD) framework to explore the dynamics of healthy, schizont stage malaria-infected and type 2 diabetes mellitus affected RBCs subjected to external time-dependent loads. The paper focuses on the imposition and cessation of external forcing on the cells of two different typologies, saw-tooth cyclic wave loading and sudden loads in the form of creep and relaxation phenomena. The effects of varying the rate of stress and the applied stress magnitude were investigated. Our simulations disclosed unique shape transitions of the hysteresis curves at varied loading rates. A careful analysis reveals a critical threshold of half cycle time of the from wherein the deformation of all cells observed, healthy or otherwise, falls under the nearly reversible deformation regime displaying minimal energy dissipation. Finally, we also examined the individual effects of the different constitutive and geometric characteristics attributed to the pathological cells and observed interesting recovery dynamics of spherocytes and cells having high shear moduli. The distinguished deformation behaviour of healthy and diseased cells could establish external force as a valuable initial biomarker.

Structural and mechanical properties of the red blood cell’s cytoplasmic membrane seen through the lens of biophysics

Red blood cells (RBCs) are the most abundant cell type in the human body and critical suppliers of oxygen. The cells are characterized by a simple structure with no internal organelles. Their two-layered outer shell is composed of a cytoplasmic membrane (RBC_cm) tethered to a spectrin cytoskeleton allowing the cell to be both flexible yet resistant against shear stress. These mechanical properties are intrinsically linked to the molecular composition and organization of their shell. The cytoplasmic membrane is expected to dominate the elastic behavior on small, nanometer length scales, which are most relevant for cellular processes that take place between the fibrils of the cytoskeleton. Several pathologies have been linked to structural and compositional changes within the RBC_cm and the cell’s mechanical properties. We review current findings in terms of RBC lipidomics, lipid organization and elastic properties with a focus on biophysical techniques, such as X-ray and neutron scattering, and Molecular Dynamics simulations, and their biological relevance. In our current understanding, the RBC_cm’s structure is patchy, with nanometer sized liquid ordered and disordered lipid, and peptide domains. At the same time, it is surprisingly soft, with bending rigidities κ of 2–4 k_BT. This is in strong contrast to the current belief that a high concentration of cholesterol results in stiff membranes. This extreme softness is likely the result of an interaction between polyunsaturated lipids and cholesterol, which may also occur in other biological membranes. There is strong evidence in the literature that there is no length scale dependence of κ of whole RBCs.

The bending rigidity of the red blood cell cytoplasmic membrane

An important mechanical property of cells is the membrane bending modulus, κ. In the case of red blood cells (RBCs) there is a composite membrane consisting of a cytoplasmic membrane and an underlying spectrin network. Literature values of κ are puzzling, as they are reported over a wide range, from 5 kBT to 230 kBT. To disentangle the contribution of the cytoplasmic membrane from the spectrin network, we investigated the bending of red blood cell cytoplasmic membranes (RBCcm) in the absence of spectrin and adenosine triphosphate (ATP). We used a combination of X-ray diffuse scattering (XDS), neutron spin-echo (NSE) spectrometry and Molecular Dynamics (MD) simulations. Our results indicate values of κ of order 4 kBT to 6 kBT, relatively small compared to literature values for most single component lipid bilayers. We suggest two ways this relative softness might confer biological advantage.

Non-Invasive Dynamic Reperfusion of Microvessels In Vivo Controlled by Optical Tweezers

Distributive shock is considered to be a condition of microvascular hypoperfusion, which can be fatal in severe cases. However, traditional therapeutic methods to restore the macro blood flow are difficult to accurately control the blood perfusion of microvessels, and the currently developed manipulation techniques are inevitably incompatible with biological systems. In our approach, infrared optical tweezers are used to dynamically control the microvascular reperfusion within subdermal capillaries in the pinna of mice. Furthermore, we estimate the effect of different optical trap positions on reperfusion at branch and investigate the effect of the laser power on reperfusion. The results demonstrate the ability of optical tweezers to control microvascular reperfusion. This strategy allows near-noninvasive reperfusion of the microvascular hypoperfusion in vivo. Hence, our work is expected to provide unprecedented insights into the treatment of distributive shock.

Morphological Characteristics, Hemoglobin Content, and Membrane Mechanical Properties of Red Blood Cell Delivery Systems

Red blood cell (RBC)-based systems are under extensive development as platforms for the delivery of various biomedical agents. While the importance of the membrane biochemical characteristics in relation to circulation kinetics of RBC delivery systems has been recognized, the membrane mechanical properties of such carriers have not been extensively studied. Using optical methods in conjunction with image analysis and mechanical modeling, we have quantified the morphological and membrane mechanical characteristics of RBC-derived microparticles containing the near-infrared cargo indocyanine green (ICG). We find that these particles have a significantly lower surface area, volume, and deformability as compared to normal RBCs. The residual hemoglobin has a spatially distorted distribution in the particles. The membrane bending modulus of the particles is about twofold higher as compared to normal RBCs and exhibits greater resistance to flow. The induced increase in the viscous characteristics of the membrane is dominant over the elastic and entropic effects of ICG. Our results suggest that changes to the membrane mechanical properties are a result of impaired membrane-cytoskeleton attachment in these particles. We provide a mechanistic explanation to suggest that the compromised membrane-cytoskeleton attachment and altered membrane compositional and structural asymmetry induce curvature changes to the membrane, resulting in mechanical remodeling of the membrane. These findings highlight the importance of membrane mechanical properties as an important criterion in the design and engineering of future generations of RBC-based delivery systems to achieve prolonged circulation.

A new membrane formulation for modelling the flow of stomatocyte, discocyte, and echinocyte red blood cells

In this work, a numerical model that enables simulation of the deformation and flow behaviour of differently aged Red Blood Cells (RBCs) is developed. Such cells change shape and decrease in deformability as they age, thus impacting their ability to pass through the narrow capillaries in the body. While the body filters unviable cells from the blood naturally, cell aging poses key challenges for blood stored for transfusions. Therefore, understanding the influence RBC morphology and deformability have on their flow is vital. While several existing models represent young Discocyte RBC shapes well, a limited number of numerical models are developed to model aged RBC morphologies like Stomatocytes and Echinocytes. The existing models are also limited to shear and stretching simulations. Flow characteristics of these morphologies are yet to be investigated. This paper aims to develop a new membrane formulation for the numerical modelling of Stomatocyte, Discocytes and Echinocyte RBC morphologies to investigate their deformation and flow behaviour. The model used represents blood plasma using the Lattice Boltzmann Method (LBM) and the RBC membrane using the discrete element method (DEM). The membrane and the plasma are coupled by the Immersed Boundary Method (IBM). Previous LBM-IBM-DEM formulations represent RBC membrane response based on forces generated from changes in the local area, local length, local bending, and cell volume. In this new model, two new force terms are added: the local area difference force and the local curvature force, which are specially incorporated to model the flow and deformation behaviour of Stomatocytes and Echinocytes. To verify the developed model, the deformation behaviour of the three types of RBC morphologies are compared to well-characterised stretching and shear experiments. The flow modelling capabilities of the method are then demonstrated by modelling the flow of each cell through a narrow capillary. The developed model is found to be as accurate as benchmark Smoothed Particle Hydrodynamics (SPH) approaches while being significantly more computationally efficient.

Technologies for measuring red blood cell deformability

Human red blood cells (RBCs) are approximately 8 μm in diameter, but must repeatedly deform through capillaries as small as 2 μm in order to deliver oxygen to all parts of the body. The loss of this capability is associated with the pathology of many diseases, and is therefore a potential biomarker for disease status and treatment efficacy. Measuring RBC deformability is a difficult problem because of the minute forces (∼pN) that must be exerted on these cells, as well as the requirements for throughput and multiplexing. The development of technologies for measuring RBC deformability date back to the 1960s with the development of micropipette aspiration, ektacytometry, and the cell transit analyzer. In the past 10 years, significant progress has been made using microfluidics by leveraging the ability to precisely control fluid flow through microstructures at the size scale of individual RBCs. These technologies have now surpassed traditional methods in terms of sensitivity, throughput, consistency, and ease of use. As a result, these efforts are beginning to move beyond feasibility studies and into applications to enable biomedical discoveries. In this review, we provide an overview of both traditional and microfluidic techniques for measuring RBC deformability. We discuss the capabilities of each technique and compare their sensitivity, throughput, and robustness in measuring bulk and single-cell RBC deformability. Finally, we discuss how these tools could be used to measure changes in RBC deformability in the context of various applications including pathologies caused by malaria and hemoglobinopathies, as well as degradation during storage in blood bags prior to blood transfusions.

Numerical Study of Particle Margination in a Square Channel Flow with Red Blood Cells

Red blood cells flow near the axis in a small vessel, known as axial accumulation. This causes a region called the cell-free layer, which does not contain red blood cells near the wall. Then, small particles such as platelets come out to the cell-free layer. This phenomenon is called platelet margination. In this study, related to this phenomenon, direct numerical simulations were conducted using the immersed boundary method. The effects of the shear rate, channel size, and hematocrit value were investigated on the pressure-driven flow in a straight tube with a square cross-section. The simulation results indicated that the margination rate, which is the ratio of the distance traveled in the flow direction to the margination distance in the wall direction, is independent of the shear rate. The effect of the channel size on platelet margination was found to be well scaled by introducing a dimensionless parameter, which included the shear rate and effective area of the particle movement. It was also found that the margination rate varied nonlinearly with the tube hematocrit. This was due to the volume exclusion effect of red blood cells, which facilitated or hindered the motion of particles depending on the hematocrit. The relationship between the stable position of the particles near the corner and the width of the cell-free layer was also found. Furthermore, velocity fluctuations normalized by wall shear rate in a cross-section collapsed to one curve in the presented simulations. This indicates that the lateral force acting on the particles increases linearly with the shear rate.

Scale-invariance in miniature coarse-grained red blood cells by fluctuation analysis

To accurately represent the morphological and elastic properties of a human red blood cell, Fu et al. [Fu et al., Lennard-Jones type pair-potential method for coarse-grained lipid bilayer membrane simulations in LAMMPS, 2017, 210, 193-203] recently developed a coarse-grained molecular dynamics model with particular detail in the membrane. However, such a model accrues an extremely high computational cost for whole-cell simulation when assuming an appropriate length scaling - that of the bilayer thickness. To date, the model has only simulated "miniature" cells in order to circumvent this, with the a priori assumption that these miniaturised cells correctly represent their full-sized counterparts. The present work assesses the validity of this approach, by testing the scale invariance of the model through simulating cells of various diameters; first qualitatively in their shape evolution, then quantitatively by measuring their bending rigidity through fluctuation analysis. Cells of diameter of at least 0.5 μm were able to form the characteristic biconcave shape of human red blood cells, though smaller cells instead equilibrated to bowl-shaped stomatocytes. Thermal fluctuation analysis showed the bending rigidity to be constant over all cell sizes tested, and consistent between measurements on the whole-cell and on a planar section of bilayer. This is as expected from the theory on both counts. Therefore, we confirm that the evaluated model is a good representation of a full-size RBC when the model diameter is ≥0.5 μm, in terms of the morphological and mechanical properties investigated.

The effect of stiffened diabetic red blood cells on wall shear stress in a reconstructed 3D microaneurysm

Blood flow within the vasculature of the retina has been found to influence the progression of diabetic retinopathy. In this research cell resolved blood flow simulations are used to study the pulsatile flow of whole blood through a segmented retinal microaneurysm. Images were collected using adaptive optics optical coherence tomography of the retina of a patient with diabetic retinopathy, and a sidewall (sacciform) microaneurysm was segmented from the volumetric data. The original microaneurysm neck width was varied to produce two additional aneurysm geometries in order to probe the influence of neck width on the transport of red blood cells and platelets into the aneurysm. Red blood cell membrane stiffness was also increased to resolve the impact of rigid red blood cells, as a result of diabetes, in blood flow. Wall shear stress and wall shear stress gradients were calculated throughout the aneurysm domains, and the quantification of the influence of the red blood cells is presented. Average wall shear stress and wall shear stress gradients increased due to the increase of red blood cell membrane stiffness. Stiffened red blood cells were also found to induce higher local wall shear stress and wall shear stress gradients as they passed through the leading and draining parental vessels. Stiffened red blood cells were found to penetrate the aneurysm sac more than healthy red blood cells, as well as decreasing the margination of platelets to the vessel walls of the parental vessel, which caused a decrease in platelet penetration into the aneurysm sac.

Normalization of Blood Viscosity According to the Hematocrit and the Shear Rate

The rheological properties of blood depend highly on the properties of its red blood cells: concentration, membrane elasticity, and aggregation. These properties affect the viscosity of blood as well as its shear thinning behavior. Using an experimental analysis of the interface advancement of blood in a microchannel, we determine the viscosity of different samples of blood. In this work, we present two methods that successfully normalize the viscosity of blood for a single and for different donors, first according to the concentration of erythrocytes and second according to the shear rate. The proposed methodology is able to predict the health conditions of the blood samples by introducing a non-dimensional coefficient that accounts for the response to shear rate of the different donors blood samples. By means of these normalization methods, we were able to determine the differences between the red blood cells of the samples and define a range where healthy blood samples can be described by a single behavior.

Microfluidics Approach to the Mechanical Properties of Red Blood Cell Membrane and Their Effect on Blood Rheology

In this article, we describe the general features of red blood cell membranes and their effect on blood flow and blood rheology. We first present a basic description of membranes and move forward to red blood cell membranes’ characteristics and modeling. We later review the specific properties of red blood cells, presenting recent numerical and experimental microfluidics studies that elucidate the effect of the elastic properties of the red blood cell membrane on blood flow and hemorheology. Finally, we describe specific hemorheological pathologies directly related to the mechanical properties of red blood cells and their effect on microcirculation, reviewing microfluidic applications for the diagnosis and treatment of these diseases.

Flow driven vesicle unbinding under mechanosensitive adhesion

Ligand receptor based adhesion is the primary mode of interaction of cellular blood constituents with the endothelium. These adhered entities also experience shear flow imposed by the blood which may lead to their detachment due to the viscous lift forces. Here, we have studied the role of the ligand-receptor bond kinetics in the detachment of an adhered vesicle (a simplified cell model) under shear flow. Using boundary integral formulation we performed numerical simulation of a two dimensional vesicle under shear flow for different values of applied shear rates and time scale of bond kinetics. We observe that the vesicle demonstrates three steady state configurations - adhered, pinned and detached for fast enough ligand-receptor kinetics (akin to Lennard-Jones adhesion). However, for slow bond kinetics the pinned state is not observed. We present scaling laws for the critical shear rates corresponding to the transitions among these three states. These results can help with identifying the processes of cell adhesion/detachment in the blood stream, prevalent features during the immune response and cancer metastasis.

Erythrocyte sedimentation: Effect of aggregation energy on gel structure during collapse

The erythrocyte (or red blood cell) sedimentation rate (ESR) is commonly interpreted as a measure of cell aggregation and as a biomarker of inflammation. It is well known that an increase of fibrinogen concentration, an aggregation-inducing protein for erythrocytes, leads to an increase of the sedimentation rate of erythrocytes, which is generally explained through the formation and faster settling of large disjoint aggregates. However, many aspects of erythrocyte sedimentation conform well with the collapse of a particle gel rather than with the sedimentation of disjoint aggregates. Using experiments and cell-level numerical simulations, we systematically investigate the dependence of ESR on fibrinogen concentration and its relation to the microstructure of the gel-like erythrocyte suspension. We show that for physiological aggregation interactions, an increase in the attraction strength between cells results in a cell network with larger void spaces. This geometrical change in the network structure occurs due to anisotropic shape and deformability of erythrocytes and leads to an increased gel permeability and faster sedimentation. Our results provide a comprehensive relation between the ESR and the cell-level structure of erythrocyte suspensions and support the gel hypothesis in the interpretation of blood sedimentation.

A Theoretical Basis for Nanodomains

We review the current theories of nanodomain, or "raft," formation. We emphasize that the idea that they are co-exisiting Lo and Ld phases is fraught with difficulties, as is the closely related idea that they are due to critical fluctuations. We then review an alternate theory that the plasma membrane is a two-dimensional microemulsion, and that the mechanism that drives to zero the line tension between Lo and Ld phases is the coupling of height and composition fluctuations. The theory yields rafts of SM and cholesterol in the outer leaf and POPS and POPC in the inner leaf. The "sea" between rafts consists of POPC in the outer leaf and POPE and cholesterol in the inner leaf. The characteristic size of the domain structures is tens of nanometers.

Rapid propagation of membrane tension at retinal bipolar neuron presynaptic terminals

Many cellular activities, such as cell migration, cell division, phagocytosis, and exo-endocytosis, generate and are regulated by membrane tension gradients. Membrane tension gradients drive membrane flows, but there is controversy over how rapidly plasma membrane flow can relax tension gradients. Here, we show that membrane tension can propagate rapidly or slowly, spanning orders of magnitude in speed, depending on the cell type. In a neuronal terminal specialized for rapid synaptic vesicle turnover, membrane tension equilibrates within seconds. By contrast, membrane tension does not propagate in neuroendocrine adrenal chromaffin cells secreting catecholamines. Stimulation of exocytosis causes a rapid, global decrease in the synaptic terminal membrane tension, which recovers slowly due to endocytosis. Thus, membrane flow and tension equilibration may be adapted to distinct membrane recycling requirements.

Red blood cell shape transitions and dynamics in time-dependent capillary flows

The dynamics of single red blood cells (RBCs) determine microvascular blood flow by adapting their shape to the flow conditions in the narrow vessels. In this study, we explore the dynamics and shape transitions of RBCs on the cellular scale under confined and unsteady flow conditions using a combination of microfluidic experiments and numerical simulations. Tracking RBCs in a comoving frame in time-dependent flows reveals that the mean transition time from the symmetric croissant to the off-centered, nonsymmetric slipper shape is significantly faster than the opposite shape transition, which exhibits pronounced cell rotations. Complementary simulations indicate that these dynamics depend on the orientation of the RBC membrane in the channel during the time-dependent flow. Moreover, we show how the tank-treading movement of slipper-shaped RBCs in combination with the narrow channel leads to oscillations of the cell's center of mass. The frequency of these oscillations depends on the cell velocity, the viscosity of the surrounding fluid, and the cytosol viscosity. These results provide a potential framework to identify and study pathological changes in RBC properties.

Membrane tension

The cell membrane serves as a barrier that restricts the rate of exchange of diffusible molecules. Tension in the membrane regulates many crucial cell functions involving shape changes and motility, cell signaling, endocytosis, and mechanosensation. Tension reflects the forces contributed by the lipid bilayer, the cytoskeleton, and the extracellular matrix. With a fluid-like bilayer model, membrane tension is presumed uniform and hence propagated instantaneously. In this review, we discuss techniques to measure the mean membrane tension and how to resolve the stresses in different components and consider the role of bilayer heterogeneity.

Mechanical activation of spike fosters SARS-CoV-2 viral infection

The outbreak of SARS-CoV-2 (SARS2) has caused a global COVID-19 pandemic. The spike protein of SARS2 (SARS2-S) recognizes host receptors, including ACE2, to initiate viral entry in a complex biomechanical environment. Here, we reveal that tensile force, generated by bending of the host cell membrane, strengthens spike recognition of ACE2 and accelerates the detachment of spike's S1 subunit from the S2 subunit to rapidly prime the viral fusion machinery. Mechanistically, such mechano-activation is fulfilled by force-induced opening and rotation of spike's receptor-binding domain to prolong the bond lifetime of spike/ACE2 binding, up to 4 times longer than that of SARS-S binding with ACE2 under 10 pN force application, and subsequently by force-accelerated S1/S2 detachment which is up to ~10³ times faster than that in the no-force condition. Interestingly, the SARS2-S D614G mutant, a more infectious variant, shows 3-time stronger force-dependent ACE2 binding and 35-time faster force-induced S1/S2 detachment. We also reveal that an anti-S1/S2 non-RBD-blocking antibody that was derived from convalescent COVID-19 patients with potent neutralizing capability can reduce S1/S2 detachment by 3 × 10⁶ times under force. Our study sheds light on the mechano-chemistry of spike activation and on developing a non-RBD-blocking but S1/S2-locking therapeutic strategy to prevent SARS2 invasion.

Osmotic Vesicle Collapse of Sealed Inside-Out Membrane Vesicles From Red Blood Cells

The preparation of plasma membrane vesicles from a large variety of cells has contributed a wealth of information on the identity and vectorial properties of membrane transporters and enzymes. Vesicles from red blood cell (RBC) membranes are generated in media of extremely low tonicity. For functional studies, it is required to suspend the vesicles in higher tonicity media in order to bring the concentrations of the substrates of transporters and enzymes under investigation within the physiological ranges. We investigated the effects of hypertonic transitions on the vesicle morphology using transmission electron microscopy. The results show that hypertonic transitions cause an irreversible osmotic collapse of sealed membrane vesicles. Awareness of the collapsed condition of vesicles during functional studies is critical for the proper interpretation of experimental results.

Effect of cell geometry in the evaluation of erythrocyte viscoelastic properties

The red blood cell membrane-cytoskeleton is a complex structure mainly responsible for giving the cell rigidity and shape. It also provides the erythrocyte with the ability to pass through narrow capillaries of the vertebrate blood circulatory system. Although the red blood cell viscoelastic properties have been extensively studied, reported experimental data differ by up to three orders of magnitude. This could be attributed to the natural cell variability, to the different techniques employed, and also to the models used for the cell response, which are highly dependent on cell geometry. Here, we use two methodologies based on optical tweezers to investigate the viscoelastic behavior of healthy human red blood cells, one applying small cell deformations (microrheology) and another imposing large deformations (tether extraction). We also establish a defocusing microscopy-based method to characterize the cell geometry and thus the erythrocyte form factor, an essential parameter that allows comparisons among the viscoelastic properties at different conditions. Moreover, for small deformations, a soft glassy rheology model is used to discuss the results, while for large deformations two surface shear moduli and one surface viscosity are determined, together with the surface tension and bending modulus of the erythrocyte membrane lipid component. We also show that F-actin is not detected in tethers, although the erythrocyte membrane has physical properties like those of other adherent cells, known to have tethers containing F-actin inside. Altogether, our results show good agreement with the reported literature and we argue that, to properly compare the viscoelastic properties of red blood cells in different situations, the task of cell geometry characterization must be accomplished. This may be especially important when the influence of agents, like the malaria parasite, induces changes in both the geometry and chemical constituents of the erythrocyte membrane. Together, the new methodologies and procedures used in this study would allow the erythrocyte community to better explore the mechanical behavior of red blood cells and may be useful to characterize erythrocyte viscoelasticity changes in several blood diseases.

On the Role of Curved Membrane Nanodomains, and Passive and Active Skeleton Forces in the Determination of Cell Shape and Membrane Budding

Biological membranes are composed of isotropic and anisotropic curved nanodomains. Anisotropic membrane components, such as Bin/Amphiphysin/Rvs (BAR) superfamily protein domains, could trigger/facilitate the growth of membrane tubular protrusions, while isotropic curved nanodomains may induce undulated (necklace-like) membrane protrusions. We review the role of isotropic and anisotropic membrane nanodomains in stability of tubular and undulated membrane structures generated or stabilized by cyto- or membrane-skeleton. We also describe the theory of spontaneous self-assembly of isotropic curved membrane nanodomains and derive the critical concentration above which the spontaneous necklace-like membrane protrusion growth is favorable. We show that the actin cytoskeleton growth inside the vesicle or cell can change its equilibrium shape, induce higher degree of segregation of membrane nanodomains or even alter the average orientation angle of anisotropic nanodomains such as BAR domains. These effects may indicate whether the actin cytoskeleton role is only to stabilize membrane protrusions or to generate them by stretching the vesicle membrane. Furthermore, we demonstrate that by taking into account the in-plane orientational ordering of anisotropic membrane nanodomains, direct interactions between them and the extrinsic (deviatoric) curvature elasticity, it is possible to explain the experimentally observed stability of oblate (discocyte) shapes of red blood cells in a broad interval of cell reduced volume. Finally, we present results of numerical calculations and Monte-Carlo simulations which indicate that the active forces of membrane skeleton and cytoskeleton applied to plasma membrane may considerably influence cell shape and membrane budding.

Spicule movement on RBCs during echinocyte formation and possible segregation in the RBC membrane

We use phase contrast microscopy of red blood cells to observe the transition between the initial discocyte shape and a spiculated echinocyte form. During the early stages of this change, spicules can move across the surface of the cell; individual spicules can also split apart into pairs. One possible explanation of this behaviour is that the membrane forms large scale domains in association with the spicules. The spicules are formed initially at the rim of the cell and then move at speeds of up to 3 μm/min towards the centre of the disc. Spicule formation that was reversed and then allowed to proceed a second time resulted in spicules at reproducible places, a shape memory effect that implies that the cytoskeleton contributes towards stopping the spicule movement. The splitting of the spicules produces a well-defined shape change with an increase in membrane curvature associated with formation of the daughter pair of spicules; the total boundary length around the spicules also increases. Following the model in which the spicules are associated with lipid domains, these observations suggest an experimental procedure that could potentially be applied to the calculation of the line tension of lipid domains in living cells.

A system for the high-throughput measurement of the shear modulus distribution of human red blood cells

Reduced deformability of red blood cells (RBCs) can affect the hemodynamics of the microcirculation and reduce oxygen transport efficiency. It is also well known that reduced RBC deformability is a signature of various physical disorders, including sepsis, and that the primary determinant of RBC deformability is the membrane shear modulus. To measure the distribution of an individual's RBC shear modulus with high throughput, we a) developed a high-fidelity computational model of RBCs in confined microchannels to inform design decisions; b) created a novel experimental system combining microfluidic flow, imaging, and image analysis; and c) performed automated comparisons between measured quantities and numerical predictions to extract quantitative measures of the RBC shear modulus for each of thousands of cells. We applied our computational simulation platform to construct the appropriate deformability figure(s) of merit to quantify RBC stiffness based on an experimentally measured, steady-state cell shape in flow through a microchannel. In particular, we determined a shape parameter based on the second moment of the cell shape that is sensitive to the changes in the membrane stiffness and cell size. We then conducted microfluidic experiments and developed custom automated image processing codes to identify and track the position and shape of individual RBCs within micro-constrictions. The fabricated microchannels include a square cross-section imaging region (7 by 7 μm) and we applied order 10 kPa pressure differences to induce order 10 mm s^-1 cell velocities. The combination of modeling, microfluidics, and imaging enables, for the first time, quantitative measurement of the shear moduli of thousands of RBCs in human blood samples. We demonstrate the high-throughput features by sensitive quantification of the changes in the distribution of RBC stiffness with aging. This combined measurement and computational platform is ultimately intended to diagnose blood cell disorders in patients.

Deformation Response of Catenated DNA Networks in a Planar Elongational Field

A kinetoplast is a complex catenated DNA network that bears resemblance to a two-dimensional polymeric system. In this work, we use single-molecule experiments to study the transient and steady-state deformation of kinetoplasts in a planar elongational field. We demonstrate that kinetoplasts deform in a stagewise manner and undergo transient deformation at large strains, due to conformational rearrangements from an intermediate metastable state. Kinetoplasts in an elongational field achieve a steady-state deformation that depends on strain rate, akin to the deformation of linear polymers. We do not observe an abrupt transition between the nondeformed and deformed states of a kinetoplast, in contrast to the coil-stretch transition for a linear polymer.

Stochastic bond dynamics facilitates alignment of malaria parasite at erythrocyte membrane upon invasion

Malaria parasites invade healthy red blood cells (RBCs) during the blood stage of the disease. Even though parasites initially adhere to RBCs with a random orientation, they need to align their apex toward the membrane in order to start the invasion process. Using hydrodynamic simulations of a RBC and parasite, where both interact through discrete stochastic bonds, we show that parasite alignment is governed by the combination of RBC membrane deformability and dynamics of adhesion bonds. The stochastic nature of bond-based interactions facilitates a diffusive-like re-orientation of the parasite at the RBC membrane, while RBC deformation aids in the establishment of apex-membrane contact through partial parasite wrapping by the membrane. This bond-based model for parasite adhesion quantitatively captures alignment times measured experimentally and demonstrates that alignment times increase drastically with increasing rigidity of the RBC membrane. Our results suggest that the alignment process is mediated simply by passive parasite adhesion.

Dual shape recovery of red blood cells flowing out of a microfluidic constriction

Micropipette aspiration, optical tweezers, rheometry, or ecktacytometry have been used to study the shape recovery of healthy human Red Blood Cells (RBCs) and measure associated relaxation times of the order of 100-300 ms. These measurements are in good agreement with the Kelvin-Voigt model, which describes the cell as a visco-elastic material, predicting that its relaxation time only depends on cell intrinsic properties. However, such mechanical solicitation techniques are far from being relevant regarding RBC solicitation in vivo. In this paper, we report for the first time the existence of two different behaviors of the RBC shape recovery while flowing out of a microfluidic constricted channel. The calculation of the viscous stress corresponding to the frontier between the two recovery modes confirms that the RBC resistance to shear μ is the elastic property dominating the transition between the two recovery behaviors. We also quantified associated recovery times τ r and report values as low as 4 ms-which is almost two decades smaller than the typical RBC relaxation time-at high viscosity and flow velocity of the carrier fluid. Although we cannot talk about relaxation time because the cell is never at rest, we believe that the measured shape recovery time arises from the coupling of the cell intrinsic deformability and the hydrodynamic stress. Depending on the flow conditions, the cell mechanics becomes dominant and drives the shape recovery process, allowing the measurement of recovery times of the same order of magnitude than relaxation times previously published. Finally, we demonstrated that the measurement of the shape recovery time can be used to distinguish Plasmodium falciparum (causing malaria) infected RBCs from healthy RBCs.

Model Plasma Membrane Exhibits a Microemulsion in Both Leaves Providing a Foundation for "Rafts"

We consider a model lipid plasma membrane, one that describes the outer leaf as consisting of sphingomyelin, phosphatidylcholine, and cholesterol and the inner leaf of phosphatidylethanolamine, phosphatidylserine, phosphatidylcholine, and cholesterol. Their relative compositions are taken from experiment; the cholesterol freely interchanges between leaves. Fluctuations in local composition are coupled to fluctuations in the local membrane curvature, as in the Leibler-Andelman mechanism. Structure factors of components in both leaves display a peak at nonzero wavevector. This indicates that the disordered fluid membrane is characterized by structure of the corresponding wavelength. The scale is given by membrane properties: its bending modulus and its surface tension, which arises from the membrane's connections to the cytoskeleton. From measurements on the plasma membrane, this scale is on the order of 100 nm. We find that the membrane can be divided into two different kinds of domains that differ not only in their composition but also in their curvature. The first domain in the outer, exoplasmic leaf is rich in cholesterol and sphingomyelin, whereas the inner, cytoplasmic leaf is rich in phosphatidylserine and phosphatidylcholine. The second kind of domain is rich in phosphatidylcholine in the outer leaf and in cholesterol and phosphatidylethanolamine in the inner leaf. The theory provides a tenable basis for the origin of structure in the plasma membrane and an illuminating picture of the organization of lipids therein.

Estimation of membrane bending modulus of stiffness tuned human red blood cells from micropore filtration studies

Human red blood cells (RBCs) need to deform in order to pass through capillaries in human vasculature with diameter smaller than that of the RBC. An altered RBC cell membrane stiffness (CMS), thereby, is likely to have consequences on their flow rate. RBC CMS is known to be affected by several commonly encountered disease conditions. This study was carried out to investigate whether an increase in RBC CMS, to the extent seen in such commonly encountered medical conditions, affects the RBC flow rate through channels with diameters comparable to that of the RBC. To do this, we use RBCs extracted from a healthy individual with no known medical conditions and treated with various concentrations of Bovine Serum Albumin (BSA). We study their flow through polycarbonate membranes with pores of diameter 5μm and 8μm which are smaller than and comparable to the RBC diameter respectively. The studies are carried out at constant hematocrit and volumetric flow rate. We find that when the diameter of the capillary is smaller than that of the RBC, the flow rate of the RBCs is lowered as the concentration of BSA is increased while the reverse is true when the diameter is comparable to that of the RBC. We confirm that this is a consequence of altered CMS of the RBCs from their reorientation dynamics in an Optical Tweezer. We find that a treatment with 0.50mg/ml BSA mimics the situation for RBCs extracted from a healthy individual while concentrations higher than 0.50mg/ml elevate the RBC CMS across a range expected for individuals with a condition of hyperglycemia. Using a simple theoretical model of the RBC deformation process at the entry of a narrow channel, we extract the RBC membrane bending modulus from their flow rate.

Normal red blood cells' shape stabilized by membrane's in-plane ordering

Red blood cells (RBCs) are present in almost all vertebrates and their main function is to transport oxygen to the body tissues. RBCs' shape plays a significant role in their functionality. In almost all mammals in normal conditions, RBCs adopt a disk-like (discocyte) shape, which optimizes their flow properties in vessels and capillaries. Experimentally measured values of the reduced volume (v) of stable discocyte shapes range in a relatively broad window between v ~ 0.58 and 0.8. However, these observations are not supported by existing theoretical membrane-shape models, which predict that discocytic RBC shape is stable only in a very narrow interval of v values, ranging between v ~ 0.59 and 0.65. In this study, we demonstrate that this interval is broadened if a membrane's in-plane ordering is taken into account. We model RBC structures by using a hybrid Helfrich-Landau mesoscopic approach. We show that an extrinsic (deviatoric) curvature free energy term stabilizes the RBC discocyte shapes. In particular, we show on symmetry grounds that the role of extrinsic curvature is anomalously increased just below the nematic in-plane order-disorder phase transition temperature.

Controlled reversible buckling of polydopamine spherical microcapsules: revealing the hidden rich phenomena of post-buckling of spherical polymeric shells

Under external pressure compression, various kinds of artificial microcapsules can undergo buckling induced deformation and catastrophic rupturing failure, which needs to be understood for their diverse practical applications. For this, many theories and numerical simulations have recently emerged, leading to some intriguing but often debatable predictions and scaling laws. However, experimental testing of these predictions is very limited, due to challenges in realizing prescribed buckling pathways and in situ monitoring of the buckling procedure. Herein, we report the buckling behaviors of well-defined spherical polydopamine (PDA) capsules with tunable sizes and homogeneous nanoscale shells. Simple but controlled solvent evaporation was implemented inside a home-made optical chamber to induce buckling of PDA capsules by following a prescribed pathway toward targeted shapes that are only dictated by the inherent material properties of the capsules. In addition, the buckling speed was slowed down to the timescale of minutes, which can prevent buckling from being trapped at some metastable intermediate states as well as facilitating in situ optical monitoring of the whole buckling procedure in slow motion. In this way, several classic buckling behaviors were clearly observed, including the sudden appearance of spinodal-like dimples above critical pressures, transition of the indentation rim from the axisymmetric to polygonal shape, and evolution of multi-indented buckling into single indented buckling following Ostwald ripening. These observations are qualitatively comparable with recent predictions from numerical results. Furthermore, some novel buckling phenomena have been reported for the first time, which might stimulate further theories and numerical simulations.

Self-Assembly and Biogenesis of the Cellular Membrane are Dictated by Membrane Stretch and Composition

The cell plasma membrane is a highly dynamic organelle governing a wide range of cellular activities including ion transport, secretion, cell division, growth, and development. The fundamental process involved in the addition of new membranes to pre-existing plasma membranes, however, is unclear. Here, we report, using biophysical, morphological, biochemical, and molecular dynamic simulations, the selective incorporation of proteins and lipids from the cytosol into the cell plasma membrane dictated by membrane stretch and composition. Stretching of the cell membrane as a consequence of volume increase following incubation in a hypotonic solution and results in the incorporation of cytosolic proteins and lipids into the existing plasma membrane. Molecular dynamic simulations further confirm that increased membrane stretch results in the rapid insertion of lipids into the existing plasma membrane. Similarly, depletion of cholesterol from the cell plasma membrane selectively alters the incorporation of lipids into the membrane.

Giant Vesicles and Their Use in Assays for Assessing Membrane Phase State, Curvature, Mechanics, and Electrical Properties

Giant unilamellar vesicles represent a promising and extremely useful model biomembrane system for systematic measurements of mechanical, thermodynamic, electrical, and rheological properties of lipid bilayers as a function of membrane composition, surrounding media, and temperature. The most important advantage of giant vesicles over other model membrane systems is that the membrane responses to external factors such as ions, (macro)molecules, hydrodynamic flows, or electromagnetic fields can be directly observed under the microscope. Here, we briefly review approaches for giant vesicle preparation and describe several assays used for deducing the membrane phase state and measuring a number of material properties, with further emphasis on membrane reshaping and curvature.

Cholesterol-Dependent Bending Energy Is Important in Cholesterol Distribution of the Plasma Membrane

We consider the plasma membrane that contains a cholesterol molar fraction of 0.4 and ask how that cholesterol is distributed between the two leaves. Because of the rapid flip-flop of cholesterol between leaves, we assume that its distribution is determined by the equality of its chemical potentials in the two leaves. When we consider only the contributions of entropy and interactions to the cholesterol chemical potential in our model system, we find, not surprisingly, that the cholesterol is mostly in the outer leaf because of the strong attraction between cholesterol and sphingomyelin (SM), which is predominantly in that leaf. We find 72% there. We then include the contribution from the bending energy in each leaf that must be overcome to join the leaves in a flat bilayer. The product of bending modulus and spontaneous curvature is obtained from simulation. We find that the addition of cholesterol to the outer leaf reduces the spontaneous curvature, which is initially positive, until it passes through zero when the molar fraction of cholesterol in the outer leaf is 0.28. Additional cholesterol is driven toward the inner leaf by the sphingomyelin phosphatidylcholine mixture. This is resisted by the bending energy contribution to the inner leaf. We find, again by simulation, that the addition of cholesterol monotonically increases the magnitude of the spontaneous curvature of the inner leaf, which is negative. This increases its bending energy. We conclude that, as a result of these competing effects, the percentage of cholesterol in the outer leaf is reduced to ∼63 ± 6%.

Mechanical characterization of HIV-1 with a solid-state nanopore sensor

Enveloped viruses fuse with cells to transfer their genetic materials and infect the host cell. Fusion requires deformation of both viral and cellular membranes. Since the rigidity of viral membrane is a key factor in their infectivity, studying the rigidity of viral particles is of great significance in understating viral infection. In this paper, a nanopore is used as a single molecule sensor to characterize the deformation of pseudo-type human immunodeficiency virus type 1 at sub-micron scale. Non-infective immature viruses were found to be more rigid than infective mature viruses. In addition, the effects of cholesterol and membrane proteins on the mechanical properties of mature viruses were investigated by chemically modifying the membranes. Furthermore, the deformability of single virus particles was analyzed through a recapturing technique, where the same virus was analyzed twice. The findings demonstrate the ability of nanopore resistive pulse sensing to characterize the deformation of a single virus as opposed to average ensemble measurements.

Equilibrium Modeling of the Mechanics and Structure of the Cancer Glycocalyx

The glycocalyx is a thick coat of proteins and carbohydrates on the outer surface of all eukaryotic cells. Overproduction of large, flexible or rod-like biopolymers, including hyaluronic acid and mucins, in the glycocalyx strongly correlates with the aggression of many cancer types. However, theoretical frameworks to predict the effects of these changes on cancer cell adhesion and other biophysical processes remain limited. Here, we propose a detailed modeling framework for the glycocalyx incorporating important physical effects of biopolymer flexibility, excluded volume, counterion mobility, and coupled membrane deformations. Because mucin and hyaluronic biopolymers are proposed to extend and rigidify depending on the extent of their decoration with side chains, we propose and consider two limiting cases for the structural elements of the glycocalyx: stiff beams and flexible chains. Simulations predict the mechanical response of the glycocalyx to compressive loads, which are imposed on cells residing in the highly confined spaces of the solid tumor or invaded tissues. Notably, the shape of the mechanical response transitions from hyperbolic to sigmoidal for more rod-like glycocalyx elements. These mechanical responses, along with the corresponding equilibrium protein organizations and membrane topographies, are summarized to aid in hypothesis generation and the evaluation of future experimental measurements. Overall, the modeling framework developed provides a theoretical basis for understanding the physical biology of the glycocalyx in human health.

Glycan-decorated protocells: novel features for rebuilding cellular processes

In synthetic biology approaches, lipid vesicles are widely used as protocell models. While many compounds have been encapsulated in vesicles (e.g. DNA, cytoskeleton and enzymes), the incorporation of glycocalyx components in the lipid bilayer has attracted much less attention so far. In recent years, glycoconjugates have been integrated in the membrane of giant unilamellar vesicles (GUVs). These minimal membrane systems have largely contributed to shed light on the molecular mechanisms of cellular processes. In this review, we first introduce several preparation and biophysical characterization methods of GUVs. Then, we highlight specific applications of protocells investigating glycolipid-mediated endocytosis of toxins, viruses and bacteria. In addition, we delineate how prototissues have been assembled from glycan-decorated protocells by using lectin-mediated cross-linking of opposed glycoreceptors (e.g. glycolipids and glycopeptides). In future applications, glycan-decorated protocells might be useful for investigating cell-cell interactions (e.g. adhesion and communication). We also speculate about the implication of lectin-glycoreceptor interactions in membrane fusion processes.