Multiscale simulation of erythrocyte membranes

Single-cell characterization of deformation and dynamics of mesenchymal stem cells in microfluidic systems: A computational study

Understanding the homing dynamics of individual mesenchymal stem cells (MSCs) in physiologically relevant microenvironments is crucial for improving the efficacy of MSC-based therapies for therapeutic and targeting purposes. This study investigates the passive homing behavior of individual MSCs in micropores that mimic interendothelial clefts through predictive computational simulations informed by previous microfluidic experiments. Initially, we quantified the size-dependent behavior of MSCs in micropores and elucidated the underlying mechanisms. Subsequently, we analyzed the shape deformation and traversal dynamics of each MSC. In addition, we conducted a systematic investigation to understand how the mechanical properties of MSCs impact their traversal process. We considered geometric and mechanical parameters, such as reduced cell volume, cell-to-nucleus diameter ratio, and cytoskeletal prestress states. Furthermore, we quantified the changes in the MSC traversal process and identified the quantitative limits in their response to variations in micropore length. Taken together, the computational results indicate the complex dynamic behavior of individual MSCs in the confined microflow. This finding offers an objective way to evaluate the homing ability of MSCs in an interendothelial-slit-like microenvironment.

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.

A cell-resolved, Lagrangian solver for modeling red blood cell dynamics in macroscale flows

When red blood cells (RBCs) experience non-physiologically high stresses, e.g., in medical devices, they can rupture in a process called hemolysis. Directly simulating this process is computationally unaffordable given that the length scales of a medical device are several orders of magnitude larger than that of a RBC. To overcome this separation of scales, the present work introduces an affordable computational framework that accurately resolves the stress and deformation of a RBC in a spatially and temporally varying macroscale flow field such as those found in a typical medical device. The underlying idea of the present framework is to treat RBCs as one-way coupled tracers in the macroscale flow by capturing the effect of the flow on their dynamics but neglecting their effect on the flow at the macroscale. As a result, the RBC dynamics are simulated after those of the flow in a postprocessing step by receiving the fluid velocity gradient tensor measured along the RBC trajectory as the input. To resolve the fluid velocity in the immediate vicinity of the RBC as well as the motion of the membrane, we employ the boundary integral method coupled to a structural solver. The governing equations are discretized in space using spherical harmonics, yielding spectral integration accuracy. The predictions produced by this formulation are in good agreement with those obtained from simulations of spherical capsules in shear flows and optical tweezers experiments. The accuracy of the present method is evaluated using unbounded shear flow as a benchmark. Its computational cost grows proportional to p ⁵, where p is the degree of the spherical harmonic. It also exhibits a fast convergence rate that is approximately O ( p 6 ) for p ⪅ 20.

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.

Dynamics of erythrocytes in oscillatory shear flows: effects of S/V ratio

By combining a multiscale structural model of erythrocyte with a fluid-cell interaction model based on the boundary-integral method, we numerically investigate the dynamic response of erythrocytes in oscillatory shear flows (OSFs). The goal is to develop a novel experimental method to test the structural robustness of erythrocytes in transient mechanical loads with small time scales, conditions closely imitating the mechanical environment in vivo. Following the discovery of multiple response modes (wheeling, mode 1 tank treading, and mode 2 tank treading) under these conditions (Zhu & Asaro, 2019), we concentrate on deformation and stress inside RBCs driven by OSF, especially shear deformation of the membrane and the skeleton-bilayer dissociation stress, parameters that are related to mechanically induced structural remodeling such as vesiculation. Effects related to changes in surface area-to-volume (S/V) ratio are considered. Our results show that with the variation of the S/V ratio there could be significant change in terms of the occurrence of response modes even if other parameters are kept unchanged. For example, by reducing the S/V ratio of the cell, an asymmetric mode featuring a mixture of the wheeling and mode 2 tank treading responses is discovered. This mode is found to be associated with large skeleton-bilayer dissociation stress so that its potential impact on OSF-driven vesiculation should not be overlooked. By systematically examining the dependencies of skeleton deformation and skeleton-bilayer dissociation stress upon S/V, this study is critical for the development of the OSF technique in applications such as diagnosis since cell conditions are often reflected in its geometric properties.

The effect of rigid cells on blood viscosity: linking rheology and sickle cell anemia

Sickle cell anemia (SCA) is a disease that affects red blood cells (RBCs). Healthy RBCs are highly deformable objects that under flow can penetrate blood capillaries smaller than their typical size. In SCA there is an impaired deformability of some cells, which are much stiffer and with a different shape than healthy cells, and thereby affect regular blood flow. It is known that blood from patients with SCA has a higher viscosity than normal blood. However, it is unclear how the rigidity of cells is related to the viscosity of blood, in part because SCA patients are often treated with transfusions of variable amounts of normal RBCs and only a fraction of cells will be stiff. Here, we report systematic experimental measurements of the viscosity of a suspension varying the fraction of rigid particles within a suspension of healthy cells. We also perform systematic numerical simulations of a similar mixed suspension of soft RBCs, rigid particles, and their hydrodynamic interactions. Our results show that there is a rheological signature within blood viscosity to clearly identify the fraction of rigidified cells among healthy deformable cells down to a 5% volume fraction of rigidified cells. Although aggregation of RBCs is known to affect blood rheology at low shear rates, and our simulations mimic this effect via an adhesion potential, we show that such adhesion, or aggregation, is unlikely to provide a physical rationalization for the viscosity increase observed in the experiments at moderate shear rates due to rigidified cells. Through numerical simulations, we also highlight that most of the viscosity increase of the suspension is due to the rigidity of the particles rather than their sickled or spherical shape. Our results are relevant to better characterize SCA, provide useful insights relevant to rheological consequences of blood transfusions, and, more generally, extend to the rheology of mixed suspensions having particles with different rigidities, as well as offering possibilities for developments in the field of soft material composites.

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.

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.

How the spleen reshapes and retains young and old red blood cells: A computational investigation

The spleen, the largest secondary lymphoid organ in humans, not only fulfils a broad range of immune functions, but also plays an important role in red blood cell’s (RBC) life cycle. Although much progress has been made to elucidate the critical biological processes involved in the maturation of young RBCs (reticulocytes) as well as removal of senescent RBCs in the spleen, the underlying mechanisms driving these processes are still obscure. Herein, we perform a computational study to simulate the passage of RBCs through interendothelial slits (IES) in the spleen at different stages of their lifespan and investigate the role of the spleen in facilitating the maturation of reticulocytes and in clearing the senescent RBCs. Our simulations reveal that at the beginning of the RBC life cycle, intracellular non-deformable particles in reticulocytes can be biomechanically expelled from the cell upon passage through IES, an insightful explanation of why this peculiar “pitting” process is spleen-specific. Our results also show that immature RBCs shed surface area by releasing vesicles after crossing IES and progressively acquire the biconcave shape of mature RBCs. These findings likely explain why RBCs from splenectomized patients are significantly larger than those from nonsplenectomized subjects. Finally, we show that at the end of their life span, senescent RBCs are not only retained by IES due to reduced deformability but also become susceptible to mechanical lysis under shear stress. This finding supports the recent hypothesis that transformation into a hemolyzed ghost is a prerequisite for phagocytosis of senescent RBCs. Altogether, our computational investigation illustrates critical biological processes in the spleen that cannot be observed in vivo or in vitro and offer insights into the role of the spleen in the RBC physiology.

The spleen, the largest secondary lymphoid organ in humans, not only fulfils a broad range of immune functions, but also plays an important role in red blood cell (RBC) life cycle. In this study, we perform a computational study to simulate the passage of RBCs through interendothelial slits (IES) in the spleen at different stages of their lifespan, a critical biological process that cannot be observed in humans. Our simulation results illustrate a specific role of spleen in shaping young RBCs, which points to a probable missing step in current in vitro RBC culture protocols that fail to generate a majority of typical biconcave RBCs. Our results also reveal that intra-splenic mechanical constraints likely contribute to the final clearance and elimination of aged RBCs. Altogether, we demonstrate that our computational model can provide mechanistic rationales for experimental studies, offer insights into the role of the spleen in the RBC physiology and help the optimization of in vitro RBC culture techniques.

Red Blood Cells: Tethering, Vesiculation, and Disease in Micro-Vascular Flow

The red blood cell has become implicated in the progression of a range of diseases; mechanisms by which red cells are involved appear to include the transport of inflammatory species via red cell-derived vesicles. We review this role of RBCs in diseases such as diabetes mellitus, sickle cell anemia, polycythemia vera, central retinal vein occlusion, Gaucher disease, atherosclerosis, and myeloproliferative neoplasms. We propose a possibly unifying, and novel, paradigm for the inducement of RBC vesiculation during vascular flow of red cells adhered to the vascular endothelium as well as to the red pulp of the spleen. Indeed, we review the evidence for this hypothesis that links physiological conditions favoring both vesiculation and enhanced RBC adhesion and demonstrate the veracity of this hypothesis by way of a specific example occurring in splenic flow which we argue has various renderings in a wide range of vascular flows, in particular microvascular flows. We provide a mechanistic basis for membrane loss and the formation of lysed red blood cells in the spleen that may mediate their turnover. Our detailed explanation for this example also makes clear what features of red cell deformability are involved in the vesiculation process and hence require quantification and a new form of quantitative indexing.

Tethering, evagination, and vesiculation via cell-cell interactions in microvascular flow

Vesiculation is a ubiquitous process undergone by most cell types and serves a variety of vital cell functions; vesiculation from erythrocytes, in particular, is a well-known example and constitutes a self-protection mechanism against premature clearance, inter alia. Herein, we explore a paradigm that red blood cell derived vesicles may form within the microvascular, in intense shear flow, where cells become adhered to either other cells or the extracellular matrix, by forming tethers or an evagination. Adherence may be enhanced, or caused, by diseased states or chemical anomalies as are discussed herein. The mechanisms for such processes are detailed via numerical simulations that are patterned directly from video-recorded cell microflow within the splenic venous sinus (MacDonald et al. 1987), as included, e.g., as Supplementary Material. The mechanisms uncovered highlight the necessity of accounting for remodeling of the erythrocyte's membrane skeleton and, specifically, for the time scales associated with that process that is an integral part of cell deformation. In this way, the analysis provides pointed, and vital, insights into the notion of what the, often used phrase, cell deformability actually entails in a more holistic manner. The analysis also details what data are required to make further quantitative descriptions possible and suggests experimental pathways for acquiring such.

Theoretical Bases for the Role of Red Blood Cell Shape in the Regulation of Its Volume

The red blood cell (RBC) membrane contains a mechanosensitive cation channel Piezo1 that is involved in RBC volume homeostasis. In a recent model of the mechanism of its action it was proposed that Piezo1 cation permeability responds to changes of the RBC shape. The aim here is to review in a descriptive manner different previous studies of RBC behavior that formed the basis for this proposal. These studies include the interpretation of RBC and vesicle shapes based on the minimization of membrane bending energy, the analyses of various consequences of compositional and structural features of RBC membrane, in particular of its membrane skeleton and its integral membrane proteins, and the modeling of the establishment of RBC volume. The proposed model of Piezo1 action is critically evaluated, and a perspective presented for solving some remaining experimental and theoretical problems. Part of the discussion is devoted to the usefulness of theoretical modeling in studies of the behavior of cell systems in general.

Non-uniform distribution of myosin-mediated forces governs red blood cell membrane curvature through tension modulation

The biconcave disk shape of the mammalian red blood cell (RBC) is unique to the RBC and is vital for its circulatory function. Due to the absence of a transcellular cytoskeleton, RBC shape is determined by the membrane skeleton, a network of actin filaments cross-linked by spectrin and attached to membrane proteins. While the physical properties of a uniformly distributed actin network interacting with the lipid bilayer membrane have been assumed to control RBC shape, recent experiments reveal that RBC biconcave shape also depends on the contractile activity of nonmuscle myosin IIA (NMIIA) motor proteins. Here, we use the classical Helfrich-Canham model for the RBC membrane to test the role of heterogeneous force distributions along the membrane and mimic the contractile activity of sparsely distributed NMIIA filaments. By incorporating this additional contribution to the Helfrich-Canham energy, we find that the RBC biconcave shape depends on the ratio of forces per unit volume in the dimple and rim regions of the RBC. Experimental measurements of NMIIA densities at the dimple and rim validate our prediction that (a) membrane forces must be non-uniform along the RBC membrane and (b) the force density must be larger in the dimple than the rim to produce the observed membrane curvatures. Furthermore, we predict that RBC membrane tension and the orientation of the applied forces play important roles in regulating this force-shape landscape. Our findings of heterogeneous force distributions on the plasma membrane for RBC shape maintenance may also have implications for shape maintenance in different cell types.

The spectrin-actin network of the membrane skeleton plays an important role in controlling specialized cell membrane morphology. In the paradigmatic red blood cell (RBC), where actin filaments are present exclusively in the membrane skeleton, recent experiments reveal that nonmuscle myosin IIA (NMIIA) motor contractility maintains the RBC biconcave disk shape. In this study, we have identified criteria for micron-scale distributions of NMIIA forces at the membrane required to maintain the biconcave disk shape of an RBC in the resting condition. Supported by experimental measurements of RBC NMIIA distribution, we showed that a heterogeneous force distribution with a larger force density at the dimple is able to capture the experimentally observed biconcave morphology of an RBC with better accuracy compared to previous models that did not consider the heterogeneity in the force distribution. Furthermore, we showed that the biconcave geometry of the RBC is closely regulated by the effective membrane tension and the direction of applied forces on the membrane. These findings can be generalized to any force-mediated membrane shape, providing insight into the role of actomyosin forces in prescribing and maintaining the morphology of different cell types.

Modelling of Red Blood Cell Morphological and Deformability Changes during In-Vitro Storage

Storage lesion is a critical issue facing transfusion treatments, and it adversely affects the quality and viability of stored red blood cells (RBCs). RBC deformability is a key indicator of cell health. Deformability measurements of each RBC unit are a key challenge in transfusion medicine research and clinical haematology. In this paper, a numerical study, inspired from the previous research for RBC deformability and morphology predictions, is conducted for the first time, to investigate the deformability and morphology characteristics of RBCs undergoing storage lesion. This study investigates the evolution of the cell shape factor, elongation index and membrane spicule details, where applicable, of discocyte, echinocyte I, echinocyte II, echinocyte III and sphero-echinocyte morphologies during 42 days of in-vitro storage at 4 °C in saline-adenine-glucose-mannitol (SAGM). Computer simulations were performed to investigate the influence of storage lesion-induced membrane structural defects on cell deformability and its recoverability during optical tweezers stretching deformations. The predicted morphology and deformability indicate decreasing quality and viability of stored RBCs undergoing storage lesion. The loss of membrane structural integrity due to the storage lesion further degrades the cell deformability and recoverability during mechanical deformations. This numerical approach provides a potential framework to study the RBC deformation characteristics under varying pathophysiological conditions for better diagnostics and treatments.

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.

A coarse-grained red blood cell membrane model to study stomatocyte-discocyte-echinocyte morphologies

An improved red blood cell (RBC) membrane model is developed based on the bilayer coupling model (BCM) to accurately predict the complete sequence of stomatocyte-discocyte-echinocyte (SDE) transformation of a RBC. The coarse-grained (CG)-RBC membrane model is proposed to predict the minimum energy configuration of the RBC from the competition between lipid-bilayer bending resistance and cytoskeletal shear resistance under given reference constraints. In addition to the conventional membrane surface area, cell volume and bilayer-leaflet-area-difference constraints, a new constraint: total-membrane-curvature is proposed in the model to better predict RBC shapes in agreement with experimental observations. A quantitative evaluation of several cellular measurements including length, thickness and shape factor, is performed for the first time, between CG-RBC model predicted and three-dimensional (3D) confocal microscopy imaging generated RBC shapes at equivalent reference constraints. The validated CG-RBC membrane model is then employed to investigate the effect of reduced cell volume and elastic length scale on SDE transformation, to evaluate the RBC deformability during SDE transformation, and to identify the most probable RBC cytoskeletal reference state. The CG-RBC membrane model can predict the SDE shape behaviour under diverse shape-transforming scenarios, in-vitro RBC storage, microvascular circulation and flow through microfluidic devices.

Effects of membrane reference state on shape memory of a red blood cell

By using a three-dimensional continuum model, we simulate the shape memory of a red blood cell after the remove of external forces. The purpose of this study is to illustrate the effect of membrane reference state on cell behavior during the recovery process. The reference state of an elastic element is the geometry with zero stress. Since the cell membrane is composed of cytoskeleton and lipid bilayer, both the reference states of cytoskeleton (RSC) and lipid bilayer (RSL) are considered. Results show that a non-spherical RSC can result in shape memory. The energy barrier due to non-spherical RSC is determined by the ratio of the equator length to the meridian length of the RSC. Thus different RSCs can have similar energy barrier and leading to identical recovery response. A series of simulations of more intermediate RSCs show that the recovery time scale is inversely proportional to the energy barrier. Comparing to spherical RSL, a spheroid RSL contributes to the energy barrier and recovery time. Furthermore, we observe a folding recovery due to the biconcave RSL which is different from the tank treading recovery. These results may motivate novel numerical and experimental studies to determine the exact RSC and RSL.

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.

Modeling Membrane Curvature Generation due to Membrane⁻Protein Interactions

To alter and adjust the shape of the plasma membrane, cells harness various mechanisms of curvature generation. Many of these curvature generation mechanisms rely on the interactions between peripheral membrane proteins, integral membrane proteins, and lipids in the bilayer membrane. Mathematical and computational modeling of membrane curvature generation has provided great insights into the physics underlying these processes. However, one of the challenges in modeling these processes is identifying the suitable constitutive relationships that describe the membrane free energy including protein distribution and curvature generation capability. Here, we review some of the commonly used continuum elastic membrane models that have been developed for this purpose and discuss their applications. Finally, we address some fundamental challenges that future theoretical methods need to overcome to push the boundaries of current model applications.

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.

Investigation of red blood cell mechanical properties using AFM indentation and coarse-grained particle method

Background

Red blood cells (RBCs) deform significantly and repeatedly when passing through narrow capillaries and delivering dioxygen throughout the body. Deformability of RBCs is a key characteristic, largely governed by the mechanical properties of the cell membrane. This study investigated RBC mechanical properties using atomic force microscopy (AFM) with the aim to develop a coarse-grained particle method model to study for the first time RBC indentation in both 2D and 3D. This new model has the potential to be applied to further investigate the local deformability of RBCs, with accurate control over adhesion, probe geometry and position of applied force.

Results

The model considers the linear stretch capacity of the cytoskeleton, bending resistance and areal incompressibility of the bilayer, and volumetric incompressibility of the internal fluid. The model’s performance was validated against force–deformation experiments performed on RBCs under spherical AFM indentation. The model was then used to investigate the mechanisms which absorbed energy through the indentation stroke, and the impact of varying stiffness coefficients on the measured deformability. This study found the membrane’s bending stiffness was most influential in controlling RBC physical behaviour for indentations of up to 200 nm.

Conclusions

As the bilayer provides bending resistance, this infers that structural changes within the bilayer are responsible for the deformability changes experienced by deteriorating RBCs. The numerical model presented here established a foundation for future investigations into changes within the membrane that cause differences in stiffness between healthy and deteriorating RBCs, which have already been measured experimentally with AFM.

Electronic supplementary material

The online version of this article (10.1186/s12938-017-0429-5) contains supplementary material, which is available to authorized users.

Prospects for Human Erythrocyte Skeleton-Bilayer Dissociation during Splenic Flow

Prospects of vesiculation occurring during splenic flow of erythrocytes are addressed via model simulations of RBC flow through the venous slits of the human spleen. Our model is multiscale and contains a thermally activated rate-dependent description of the entropic elasticity of the RBC spectrin cytoskeleton, including domain unfolding/refolding. Our model also includes detail of the skeleton attachment to the fluidlike lipid bilayer membrane, including a specific accounting for the expansion/contraction of the skeleton that may occur via anchor protein diffusive motion, that is, band 3 and glycophorin, through the membrane. This ability allows us to follow the change in anchor density and thereby the strength of the skeleton/membrane attachment. We define a negative pressure between the skeleton/membrane connection that promotes separation; critical levels for this are estimated using published data on the work of adhesion of this connection. By following the maximum range of negative pressure, along with the observed slight decrease in skeletal density, we conclude that there must be biochemical influences that probably include binding of degraded hemoglobin, among other things, that significantly reduce effective attachment density. These findings are consistent with reported trends in vesiculation that are believed to occur in cases of various hereditary anemias and during blood storage. Our findings also suggest pathways for further study of erythrocyte vesiculation that point to the criticality of understanding the biochemical phenomena involved with cytoskeleton/membrane attachment.

Theory and algorithms to compute Helfrich bending forces: a review

Cell membranes are vital to shield a cell's interior from the environment. At the same time they determine to a large extent the cell's mechanical resistance to external forces. In recent years there has been considerable interest in the accurate computational modeling of such membranes, driven mainly by the amazing variety of shapes that red blood cells and model systems such as vesicles can assume in external flows. Given that the typical height of a membrane is only a few nanometers while the surface of the cell extends over many micrometers, physical modeling approaches mostly consider the interface as a two-dimensional elastic continuum. Here we review recent modeling efforts focusing on one of the computationally most intricate components, namely the membrane's bending resistance. We start with a short background on the most widely used bending model due to Helfrich. While the Helfrich bending energy by itself is an extremely simple model equation, the computation of the resulting forces is far from trivial. At the heart of these difficulties lies the fact that the forces involve second order derivatives of the local surface curvature which by itself is the second derivative of the membrane geometry. We systematically derive and compare the different routes to obtain bending forces from the Helfrich energy, namely the variational approach and the thin-shell theory. While both routes lead to mathematically identical expressions, so-called linear bending models are shown to reproduce only the leading order term while higher orders differ. The main part of the review contains a description of various computational strategies which we classify into three categories: the force, the strong and the weak formulation. We finally give some examples for the application of these strategies in actual simulations.

Multiscale modeling methods in biomechanics

More and more frequently, computational biomechanics deals with problems where the portion of physical reality to be modeled spans over such a large range of spatial and temporal dimensions, that it is impossible to represent it as a single space-time continuum. We are forced to consider multiple space-time continua, each representing the phenomenon of interest at a characteristic space-time scale. Multiscale models describe a complex process across multiple scales, and account for how quantities transform as we move from one scale to another. This review offers a set of definitions for this emerging field, and provides a brief summary of the most recent developments on multiscale modeling in biomechanics. Of all possible perspectives, we chose that of the modeling intent, which vastly affect the nature and the structure of each research activity. To the purpose we organized all papers reviewed in three categories: 'causal confirmation,' where multiscale models are used as materializations of the causation theories; 'predictive accuracy,' where multiscale modeling is aimed to improve the predictive accuracy; and 'determination of effect,' where multiscale modeling is used to model how a change at one scale manifests in an effect at another radically different space-time scale. Consistent with how the volume of computational biomechanics research is distributed across application targets, we extensively reviewed papers targeting the musculoskeletal and the cardiovascular systems, and covered only a few exemplary papers targeting other organ systems. The review shows a research subdomain still in its infancy, where causal confirmation papers remain the most common. WIREs Syst Biol Med 2017, 9:e1375. doi: 10.1002/wsbm.1375 For further resources related to this article, please visit the WIREs website.

Effects of stiffness and volume on the transit time of an erythrocyte through a slit

By using a fully coupled fluid-cell interaction model, we numerically simulate the dynamic process of a red blood cell passing through a slit driven by an incoming flow. The model is achieved by combining a multiscale model of the composite cell membrane with a boundary element fluid dynamics model based on the Stokes flow assumption. Our concentration is on the correlation between the transit time (the time it takes to finish the whole translocation process) and different conditions (flow speed, cell orientation, cell stiffness, cell volume, etc.) that are involved. According to the numerical prediction (with some exceptions), the transit time rises as the cell is stiffened. It is also highly sensitive to volume increase inside the cell. In general, even slightly swollen cells (i.e., the internal volume is increased while the surface area of the cell kept unchanged) travel dramatically slower through the slit. For these cells, there is also an increased chance of blockage.

MD/DPD Multiscale Framework for Predicting Morphology and Stresses of Red Blood Cells in Health and Disease

Healthy red blood cells (RBCs) have remarkable deformability, squeezing through narrow capillaries as small as 3 microns in diameter without any damage. However, in many hematological disorders the spectrin network and lipid bilayer of diseased RBCs may be significantly altered, leading to impaired functionality including loss of deformability. We employ a two-component whole-cell multiscale model to quantify the biomechanical characteristics of the healthy and diseased RBCs, including Plasmodium falciparum-infected RBCs (Pf-RBCs) and defective RBCs in hereditary disorders, such as spherocytosis and elliptocytosis. In particular, we develop a two-step multiscale framework based on coarse-grained molecular dynamics (CGMD) and dissipative particle dynamics (DPD) to predict the static and dynamic responses of RBCs subject to tensile forcing, using experimental information only on the structural defects in the lipid bilayer, cytoskeleton, and their interaction. We first employ CGMD on a small RBC patch to compute the shear modulus, bending stiffness, and network parameters, which are subsequently used as input to a whole-cell DPD model to predict the RBC shape and corresponding stress field. For Pf-RBCs at trophozoite and schizont stages, the presence of cytoadherent knobs elevates the shear response in the lipid bilayer and stiffens the RBC membrane. For RBCs in spherocytosis and elliptocytosis, the bilayer-cytoskeleton interaction is weakened, resulting in substantial increase of the tensile stress in the lipid bilayer. Furthermore, we investigate the transient behavior of stretching deformation and shape relaxation of the normal and defective RBCs. Different from the normal RBCs possessing high elasticity, our simulations reveal that the defective RBCs respond irreversibly, i.e., they lose their ability to recover the normal biconcave shape in successive loading cycles of stretching and relaxation. Our findings provide fundamental insights into the microstructure and biomechanics of RBCs, and demonstrate that the two-step multiscale framework presented here can be used effectively for in silico studies of hematological disorders based on first principles and patient-specific experimental input at the protein level.

Dynamic and rheological properties of soft biological cell suspensions

Quantifying dynamic and rheological properties of suspensions of soft biological particles such as vesicles, capsules, and red blood cells (RBCs) is fundamentally important in computational biology and biomedical engineering. In this review, recent studies on dynamic and rheological behavior of soft biological cell suspensions by computer simulations are presented, considering both unbounded and confined shear flow. Furthermore, the hemodynamic and hemorheological characteristics of RBCs in diseases such as malaria and sickle cell anemia are highlighted.

Deformation and internal stress in a red blood cell as it is driven through a slit by an incoming flow

To understand the deformation and internal stress of a red blood cell when it is pushed through a slit by an incoming flow, we conduct a numerical investigation by combining a fluid-cell interaction model based on boundary-integral equations with a multiscale structural model of the cell membrane that takes into account the detailed molecular architecture of this biological system. Our results confirm the existence of cell 'infolding', during which part of the membrane is inwardly bent to form a concave region. The time histories and distributions of area deformation, shear deformation, and contact pressure during and after the translocation are examined. Most interestingly, it is found that in the recovery phase after the translocation significant dissociation pressure may develop between the cytoskeleton and the lipid bilayer. The magnitude of this pressure is closely related to the locations of the dimple elements during the transit. Large dissociation pressure in certain cases suggests the possibility of mechanically induced structural remodeling and structural damage such as vesiculation. With quantitative knowledge about the stability of intra-protein, inter-protein and protein-to-lipid linkages under dynamic loads, it will be possible to achieve numerical prediction of these processes.

Continuum modeling of deformation and aggregation of red blood cells

In order to gain better understanding for rheology of an isolated red blood cell (RBC) and a group of multiple RBCs, new continuum models for describing mechanical properties of cellular structures of an RBC and inter-cellular interactions among multiple RBCs are developed. The viscous property of an RBC membrane, which characterizes dynamic behaviors of an RBC under stress loading and unloading processes, is determined using a generalized Maxwell model. The present model is capable of predicting stress relaxation and stress-strain hysteresis, of which prediction is not possible using the commonly used Kelvin-Voigt model. Nonlinear elasticity of an RBC is determined using the Yeoh hyperelastic material model in a framework of continuum mechanics using finite-element approximation. A novel method to model inter-cellular interactions among multiple adjacent RBCs is also developed. Unlike the previous modeling approaches for aggregation of RBCs, where interaction energy for aggregation is curve-fitted using a Morse-type potential function, the interaction energy is analytically determined. The present aggregation model, therefore, allows us to predict various effects of physical parameters such as the osmotic pressure, the thickness of a glycocalyx layer, the penetration depth, and the permittivity, on the depletion and electrostatic energy among RBCs. Simulations for elongation and recovery deformation of an RBC and for aggregation of multiple RBCs are conducted to evaluate the efficacy of the present continuum modeling methods.

A simple model to understand the effect of membrane shear elasticity and stress-free shape on the motion of red blood cells in shear flow

An analytical model was proposed by Keller and Skalak in 1982 to understand the motion of red blood cells in shear flow. The cell was described as a fluid ellipsoid of fixed shape. This model was extended in 2007 to introduce shear elasticity of the red blood cell membrane. Here, this model is further extended to take into account that the cell discoid shape physiologically observed is not a stress-free shape. The model shows that spheroid stress-free shapes allow us to fit the experimental data with the values of shear elasticity typical to that found with micropipette and optical tweezer experiments. In the range of moderate shear rates (for which RBCs keep their discoid shape) this model enables us to quantitatively determine (i) an effective cell viscosity, which combines membrane and hemoglobin viscosities and (ii) an effective shear modulus of the membrane that combines the shear modulus and the stress-free shape. This model can also be used to determine RBC mechanical parameters not only in the tanktreading regime when cells are suspended in medium of high viscosity but also in the tumbling regime characteristic of cells suspended in media of low viscosity. In this regime, a transition is predicted between a rigid-like tumbling motion and a fluid-like tumbling motion above a critical shear rate, which is directly related to the mechanical parameters of the cell.

A novel strain energy relationship for red blood cell membrane skeleton based on spectrin stiffness and its application to micropipette deformation

Red blood cell (RBC) membrane skeleton is a closed two-dimensional elastic network of spectrin tetramers with nodes formed by short actin filaments. Its three-dimensional shape conforms to the shape of the bilayer, to which it is connected through vertical linkages to integral membrane proteins. Numerous methods have been devised over the years to predict the response of the RBC membrane to applied forces and determine the corresponding increase in the skeleton elastic energy arising either directly from continuum descriptions of its deformation, or seeking to relate the macroscopic behavior of the membrane to its molecular constituents. In the current work, we present a novel continuum formulation rooted in the molecular structure of the membrane and apply it to analyze model deformations similar to those that occur during aspiration of RBCs into micropipettes. The microscopic elastic properties of the skeleton are derived by treating spectrin tetramers as simple linear springs. For a given local deformation of the skeleton, we determine the average bond energy and define the corresponding strain energy function and stress-strain relationships. The lateral redistribution of the skeleton is determined variationally to correspond to the minimum of its total energy. The predicted dependence of the length of the aspirated tongue on the aspiration pressure is shown to describe the experimentally observed system behavior in a quantitative manner by taking into account in addition to the skeleton energy an energy of attraction between RBC membrane and the micropipette surface.

Spectrin-ankyrin interaction mechanics: A key force balance factor in the red blood cell membrane skeleton

As major components of red blood cell (RBC) cytoskeleton, spectrin and F-actin form a network that covers the entire cytoplasmic surface of the plasma membrane. The cross-linked two layered structure, called the membrane skeleton, keeps the structural integrity of RBC under drastically changing mechanical environment during circulation. We performed force spectroscopy experiments on the atomic force microscope (AFM) as a means to clarify the mechanical characteristics of spectrin-ankyrin interaction, a key factor in the force balance of the RBC cytoskeletal structure. An AFM tip was functionalized with ANK1-62k and used to probe spectrin crosslinked to mica surface. A force spectroscopy study gave a mean unbinding force of ~30 pN under our experimental conditions. Two energy barriers were identified in the unbinding process. The result was related to the well-known flexibility of spectrin tetramer and participation of ankyrin 1-spectrin interaction in the overall balance of membrane skeleton dynamics.

Elastic behavior of a red blood cell with the membrane's nonuniform natural state: equilibrium shape, motion transition under shear flow, and elongation during tank-treading motion

Direct numerical simulations of the mechanics of a single red blood cell (RBC) were performed by considering the nonuniform natural state of the elastic membrane. A RBC was modeled as an incompressible viscous fluid encapsulated by an elastic membrane. The in-plane shear and area dilatation deformations of the membrane were modeled by Skalak constitutive equation, while out-of-plane bending deformation was formulated by the spring model. The natural state of the membrane with respect to in-plane shear deformation was modeled as a sphere ([Formula: see text]), biconcave disk shape ([Formula: see text]) and their intermediate shapes ([Formula: see text]) with the nonuniformity parameter [Formula: see text], while the natural state with respect to out-of-plane bending deformation was modeled as a flat plane. According to the numerical simulations, at an experimentally measured in-plane shear modulus of [Formula: see text] and an out-of-plane bending rigidity of [Formula: see text] of the cell membrane, the following results were obtained. (i) The RBC shape at equilibrium was biconcave discoid for [Formula: see text] and cupped otherwise; (ii) the experimentally measured fluid shear stress at the transition between tumbling and tank-treading motions under shear flow was reproduced for [Formula: see text]; (iii) the elongation deformation of the RBC during tank-treading motion from the simulation was consistent with that from in vitro experiments, irrespective of the [Formula: see text] value. Based on our RBC modeling, the three phenomena (i), (ii), and (iii) were mechanically consistent for [Formula: see text]. The condition [Formula: see text] precludes a biconcave discoid shape at equilibrium (i); however, it gives appropriate fluid shear stress at the motion transition under shear flow (ii), suggesting that a combined effect of [Formula: see text] and the natural state with respect to out-of-plane bending deformation is necessary for understanding details of the RBC mechanics at equilibrium. Our numerical results demonstrate that moderate nonuniformity in a membrane's natural state with respect to in-plane shear deformation plays a key role in RBC mechanics.

Lipid bilayer and cytoskeletal interactions in a red blood cell

We study the biomechanical interactions between the lipid bilayer and the cytoskeleton in a red blood cell (RBC) by developing a general framework for mesoscopic simulations. We treated the lipid bilayer and the cytoskeleton as two distinct components and developed a unique whole-cell model of the RBC, using dissipative particle dynamics (DPD). The model is validated by comparing the predicted results with measurements from four different and independent experiments. First, we simulated the micropipette aspiration and quantified the cytoskeletal deformation. Second, we studied the membrane fluctuations of healthy RBCs and RBCs parasitized to different intraerythrocytic stages by the malaria-inducing parasite Plasmodium falciparum. Third, we subjected the RBC to shear flow and investigated the dependence of its tank-treading frequency on shear rate. Finally, we simulated the bilayer-cytoskeletal detachment in channel flow to quantify the strength of such interactions when the corresponding bonds break. Taken together, these experiments and corresponding systematic DPD simulations probe the governing constitutive response of the cytoskeleton, elastic stiffness, viscous friction, and strength of bilayer-cytoskeletal interactions as well as membrane viscosities. Hence, the DPD simulations and comparisons with available independent experiments serve as validation of the unique two-component model and lead to useful insights into the biomechanical interactions between the lipid bilayer and the cytoskeleton of the RBC. Furthermore, they provide a basis for further studies to probe cell mechanistic processes in health and disease in a manner that guides the design and interpretation of experiments and to develop simulations of phenomena that cannot be studied systematically by experiments alone.

Continuum- and particle-based modeling of shapes and dynamics of red blood cells in health and disease

We review recent advances in multiscale modeling of the mechanics of healthy and diseased red blood cells (RBCs), and blood flow in the microcirculation. We cover the traditional continuum-based methods but also particle-based methods used to model both the RBCs and the blood plasma. We highlight examples of successful simulations of blood flow including malaria and sickle cell anemia.

Optical measurement of biomechanical properties of individual erythrocytes from a sickle cell patient

Sickle cell disease (SCD) is characterized by the abnormal deformation of red blood cells (RBCs) in the deoxygenated condition, as their elongated shape leads to compromised circulation. The pathophysiology of SCD is influenced by both the biomechanical properties of RBCs and their hemodynamic properties in the microvasculature. A major challenge in the study of SCD involves accurate characterization of the biomechanical properties of individual RBCs with minimum sample perturbation. Here we report the biomechanical properties of individual RBCs from a SCD patient using a non-invasive laser interferometric technique. We optically measure the dynamic membrane fluctuations of RBCs. The measurements are analyzed with a previously validated membrane model to retrieve key mechanical properties of the cells: bending modulus; shear modulus; area expansion modulus; and cytoplasmic viscosity. We find that high cytoplasmic viscosity at ambient oxygen concentration is principally responsible for the significantly decreased dynamic membrane fluctuations in RBCs with SCD, and that the mechanical properties of the membrane cortex of irreversibly sickled cells (ISCs) are different from those of the other types of RBCs in SCD.

Stress-free state of the red blood cell membrane and the deformation of its skeleton

The response of a red blood cell (RBC) to deformation depends on its membrane, a composite of a lipid bilayer and a skeleton, which is a closed, two-dimensional network of spectrin tetramers as its bonds. The deformation of the skeleton and its lateral redistribution are studied in terms of the RBC resting state for a fixed geometry of the RBC, partially aspirated into a micropipette. The geometry of the RBC skeleton in its initial state is taken to be either two concentric circles, a references biconcave shape or a sphere. It is assumed that in its initial state the skeleton is distributed laterally in a homogeneous manner with its bonds either unstressed, presenting its stress-free state, or prestressed. The lateral distribution was calculated using a variational calculation. It was assumed that the spectrin tetramer bonds exhibit a linear elasticity. The results showed a significant effect of the initial skeleton geometry on its lateral distribution in the deformed state. The proposed model is used to analyze the measurements of skeleton extension ratios by the method of applying two modes of RBC micropipette aspiration.

Three-dimensional numerical simulation of vesicle dynamics using a front-tracking method

Three-dimensional numerical simulation using the front-tracking method is presented on the dynamics of a vesicle in a linear shear flow. The focus here is to elucidate the parametric dependence and the self-similarity of the vesicle dynamics, quantification of vesicle deformation, and the analysis of shape dynamics. A detailed comparison of the numerical results is made with various theoretical models and experiments. It is found that the applicability of the theoretical models is limited despite some general agreement with the simulations and experiments. The deviations between the perturbative results and the simulation results occur even in the absence of thermal noise. Specifically, we find that the vesicle dynamics does not follow a self-similar behavior in a two-parameter phase space, as proposed in a theoretical model. Rather, the dynamics is governed by three controlling parameters, namely, the excess area, viscosity ratio, and dimensionless shear rate. Additionally, we find that a linear scaling of the tank-treading angle, as proposed in the theoretical model, is possible only for nearly spherical vesicles. The breakdown of the scaling occurs at higher values of the excess area even in the absence of thermal noise. We find that the vesicle deformation saturates at large shear rates, and the asymptotic deformation matches well with a theoretical prediction for nearly spherical vesicles. The dependence of the critical viscosity ratio associated with the onset of unsteady dynamics on the vesicle excess area is in excellent agreement with the experimental observation. We show that near the transition between the tank-treading and tumbling dynamics, both the vacillating-breathing-like motion characterized by a smooth ellipsoidal shape and the trembling-like motion characterized by a highly deformed shape are possible. For the trembling-like motion, the shape is highly three-dimensional with concavities and lobes, and the vesicle deforms more in the vorticity direction than in the shear plane. A Fourier spectral analysis of the vesicle shape shows the presence of the odd harmonics and higher order modes beyond fourth order.

Host cell deformability is linked to transmission in the human malaria parasite Plasmodium falciparum

Gametocyte maturation in Plasmodium falciparum is a critical step in the transmission of malaria. While the majority of parasites proliferate asexually in red blood cells, a small fraction of parasites undergo sexual conversion and mature over 2 weeks to become competent for transmission to a mosquito vector. Immature gametocytes sequester in deep tissues while mature stages must be able to circulate, pass the spleen and present themselves to the mosquito vector in order to complete transmission. Sequestration of asexual red blood cell stage parasites has been investigated in great detail. These studies have demonstrated that induction of cytoadherence properties through specific receptor-ligand interactions coincides with a significant increase in host cell stiffness. In contrast, the adherence and biophysical properties of gametocyte-infected red blood cells have not been studied systematically. Utilizing a transgenic line for 3D live imaging, in vitro capillary assays and 3D finite element whole cell modelling, we studied the role of cellular deformability in determining the circulatory characteristics of gametocytes. Our analysis shows that the red blood cell deformability of immature gametocytes displays an overall decrease followed by rapid restoration in mature gametocytes. Intriguingly, simulations suggest that along with deformability variations, the morphological changes of the parasite may play an important role in tissue distribution in vivo. Taken together, we present a model, which suggests that mature but not immature gametocytes circulate in the peripheral blood for uptake in the mosquito blood meal and transmission to another human host thus ensuring long-term survival of the parasite.