Predicting the morphology of sickle red blood cells using coarse-grained models of intracellular aligned hemoglobin polymers

Projection-based model reduction for the immersed boundary method

Fluid-structure interactions are central to many biomolecular processes, and they impose a great challenge for computational and modeling methods. In this paper, we consider the immersed boundary method (IBM) for biofluid systems, and to alleviate the computational cost, we apply reduced-order techniques to eliminate the degrees of freedom associated with the large number of fluid variables. We show how reduced models can be derived using Petrov-Galerkin projection and subspaces that maintain the incompressibility condition. More importantly, the reduced-order model (ROM) is shown to preserve the Lyapunov stability. We also address the practical issue of computing coefficient matrices in the ROM using an interpolation technique. The efficiency and robustness of the proposed formulation are examined with test examples from various applications.

Modeling Red Blood Cell Viscosity Contrast Using Inner Soft Particle Suspension

The inner viscosity of a biological red blood cell is about five times larger than the viscosity of the blood plasma. In this work, we use dissipative particles to enable the proper viscosity contrast in a mesh-based red blood cell model. Each soft particle represents a coarse-grained virtual cluster of hemoglobin proteins contained in the cytosol of the red blood cell. The particle interactions are governed by conservative and dissipative forces. The conservative forces have purely repulsive character, whereas the dissipative forces depend on the relative velocity between the particles. We design two computational experiments that mimic the classical viscometers. With these experiments we study the effects of particle suspension parameters on the inner cell viscosity and provide parameter sets that result in the correct viscosity contrast. The results are validated with both static and dynamic biological experiment, showing an improvement in the accuracy of the original model without major increase in computational complexity.

Image- and Fluorescence-Based Test Shows Oxidant-Dependent Damages in Red Blood Cells and Enables Screening of Potential Protective Molecules

An increase of oxygen saturation within blood bags and metabolic dysregulation occur during storage of red blood cells (RBCs). It leads to the gradual exhaustion of RBC antioxidant protective system and, consequently, to a deleterious state of oxidative stress that plays a major role in the apparition of the so-called storage lesions. The present study describes the use of a test (called TSOX) based on fluorescence and label-free morphology readouts to simply and quickly evaluate the oxidant and antioxidant properties of various compounds in controlled conditions. Here, TSOX was applied to RBCs treated with four antioxidants (ascorbic acid, uric acid, trolox and resveratrol) and three oxidants (AAPH, diamide and H₂O₂) at different concentrations. Two complementary readouts were chosen: first, where ROS generation was quantified using DCFH-DA fluorescent probe, and second, based on digital holographic microscopy that measures morphology alterations. All oxidants produced an increase of fluorescence, whereas H₂O₂ did not visibly impact the RBC morphology. Significant protection was observed in three out of four of the added molecules. Of note, resveratrol induced diamond-shape “Tirocytes”. The assay design was selected to be flexible, as well as compatible with high-throughput screening. In future experiments, the TSOX will serve to screen chemical libraries and probe molecules that could be added to the additive solution for RBCs storage.

Smartphone-based sickle cell disease detection and monitoring for point-of-care settings

Sickle cell disease (SCD) is a worldwide hematological disorder causing painful episodes, anemia, organ damage, stroke, and even deaths. It is more common in sub-Saharan Africa and other resource-limited countries. Conventional laboratory-based diagnostic methods for SCD are time-consuming, complex, and cannot be performed at point-of-care (POC) and home settings. Optical microscope-based classification and counting demands a significant amount of time, extensive setup, and cost along with the skilled human labor to distinguish the normal red blood cells (RBCs) from sickled cells. There is an unmet need to develop a POC and home-based test to diagnose and monitor SCD and reduce mortality in resource-limited settings. An early-stage and timely diagnosis of SCD can help in the effective management of the disease. In this article, we utilized a smartphone-based image acquisition method for capturing RBC images from the SCD patients in normoxia and hypoxia conditions. A computer algorithm is developed to differentiate RBCs from the patient's blood before and after cell sickling. Using the developed smartphone-based technique, we obtained similar percentage of sickle cells in blood samples as analyzed by conventional method (standard microscope). The developed method of testing demonstrates the potential utility of the smartphone-based test for reducing the overall cost of screening and management for SCD, thus increasing the practicality of smartphone-based screening technique for SCD in low-resource settings. Our setup does not require any special storage requirements. This is the characteristic advantage of our technique as compared to other hemoglobin-based POC diagnostic techniques.

Confined filaments in soft vesicles - the case of sickle red blood cells

Abnormal shapes of red blood cells (RBC) have been associated with various diseases. Diverse RBC shapes have also been intriguing for membrane biophysics. Here we focus on sickle shaped RBC which form due to abnormal growth of semi-rigid hemoglobin (HbS) fibers confined in RBC. Using the area difference elasticity (ADE) model for RBC and worm-like chain model for the confined HbS fibers, we explore shape deformations at equilibrium using Monte-Carlo simulations. We show that while a single HbS fiber is not rigid enough to produce sickle like deformation, a fiber bundle can do so. We also consider multiple disjoint filaments and find that confinement can generate multipolar RBC shapes and can even promote helical filament conformations which have not been discussed before. We show that the same model, when applied to microtubules confined in phospholipid vesicles, predicts vesicle tubulation. In addition we reproduce the tube collapse transition and tennis racket type vesicle shapes, as reported in experiments. We conclude that with a decrease in the surface area to volume ratio, and membrane rigidity, the vesicles prefer tubulation over sickling. The highlight of this work is several important non-axisymmetric RBC and vesicle shapes, which have never been explored in simulations.

Dynamics of deformable straight and curved prolate capsules in simple shear flow

This work investigates the motion of neutrally-buoyant, slightly deformable straight and curved prolate fluid-filled capsules in unbounded simple shear flow at zero Reynolds number using direct simulations. The curved capsules serve as a model for the typical crescent-shaped sickle red blood cells in sickle cell disease (SCD). The effects of deformability and curvature on the dynamics are revealed. We show that with low deformability, straight prolate spheroidal capsules exhibit tumbling in the shear plane as their unique asymptotically stable orbit. This result contrasts with that for rigid spheroids, where infinitely many neutrally stable Jeffery orbits exist. The dynamics of curved prolate capsules are more complicated due to a combined effect of deformability and curvature. At short times, depending on the initial orientation, slightly deformable curved prolate capsules exhibit either a Jeffery-like motion such as tumbling or kayaking, or a non-Jeffery-like behavior in which the director (end-to-end vector) of the capsule crosses the shear-gradient plane back and forth. At long times, however, a Jeffery-like quasiperiodic orbit is taken regardless of the initial orientation. We further show that the average of the long-time trajectory can be well approximated using the analytical solution for Jeffery orbits with an effective orbit constant C _eff and aspect ratio ℓ _eff. These parameters are useful for characterizing the dynamics of curved capsules as a function of given deformability and curvature. As the capsule becomes more deformable or curved, C _eff decreases, indicating a shift of the orbit towards log-rolling motion, while ℓ _eff increases weakly as the degree of curvature increases but shows negligible dependency on deformability. These features are not changed substantially as the viscosity ratio between the inner and outer fluids is changed from 1 to 5. As cell deformability, cell shape, and cell-cell interactions are all pathologically altered in blood disorders such as SCD, these results will have clear implications on improving our understanding of the pathophysiology of hematologic disease.

Molecular insights into the irreversible mechanical behavior of sickle hemoglobin

Sickle cell disease is caused by the amino acid substitution of glutamic acid to valine, which leads to the polymerization of deoxygenated sickle hemoglobin (HbS) into long strands. These strands are responsible for the sickling of red blood cells (RBCs), making blood hyper-coagulable leading to an increased chance of vaso-occlusive crisis. The conformational changes in sickled RBCs traveling through narrow blood vessels in a highly viscous fluid are critical in understanding; however, there are few studies that investigate the origins of the molecular mechanical behavior of sickled RBCs. In this work, we investigate the molecular mechanical properties of HbS molecules. A mechanical model was used to estimate the directional stiffness of an HbS molecule and the results were compared to adult human hemoglobin (HbA). The comparison shows a significant difference in strength between HbS and HbA, as well as anisotropic behavior of the hemoglobin molecules. The results also indicated that the HbS molecule experienced more irreversible mechanical behavior than HbA under compression. Further, we have characterized the elastic and compressive properties of a double stranded sickle fiber using six HbS molecules, and it shows that the HbS molecules are bound to each other through strong inter-molecular forces.

Concurrent coupling of atomistic simulation and mesoscopic hydrodynamics for flows over soft multi-functional surfaces

We develop an efficient parallel multiscale method that bridges the atomistic and mesoscale regimes, from nanometers to microns and beyond, via concurrent coupling of atomistic simulation and mesoscopic dynamics. In particular, we combine an all-atom molecular dynamics (MD) description for specific atomistic details in the vicinity of the functional surface with a dissipative particle dynamics (DPD) approach that captures mesoscopic hydrodynamics in the domain away from the functional surface. In order to achieve a seamless transition in dynamic properties we endow the MD simulation with a DPD thermostat, which is validated against experimental results by modeling water at different temperatures. We then validate the MD-DPD coupling method for transient Couette and Poiseuille flows, demonstrating that the concurrent MD-DPD coupling can resolve accurately the continuum-based analytical solutions. Subsequently, we simulate shear flows over grafted polydimethylsiloxane (PDMS) surfaces (polymer brushes) for various grafting densities, and investigate the slip flow as a function of the shear stress. We verify that a "universal" power law exists for the slip length, in agreement with published results. Having validated the MD-DPD coupling method, we simulate time-dependent flows past an endothelial glycocalyx layer (EGL) in a microchannel. Coupled simulation results elucidate the dynamics of the EGL changing from an equilibrium state to a compressed state under shear by aligning the molecular structures along the shear direction. MD-DPD simulation results agree well with results of a single MD simulation, but with the former more than two orders of magnitude faster than the latter for system sizes above one micron.

Quantifying Shear-Induced Deformation and Detachment of Individual Adherent Sickle Red Blood Cells

Vaso-occlusive crisis, a common painful complication of sickle cell disease, is a complex process triggered by intercellular adhesive interactions among blood cells and the endothelium in all human organs (e.g., the oxygen-rich lung as well as hypoxic systems such as liver and kidneys). We present a combined experimental-computational study to quantify the adhesive characteristics of sickle mature erythrocytes (SMEs) and irreversibly sickled cells (ISCs) under flow conditions mimicking those in postcapillary venules. We employed an in vitro microfluidic cell adherence assay, which is coated uniformly with fibronectin. We investigated the adhesion dynamics of SMEs and ISCs in pulsatile flow under well-controlled hypoxic conditions, inferring the cell adhesion strength by increasing the flow rate (or wall shear stress (WSS)) until the onset of cell detachment. In parallel, we performed simulations of individual SMEs and ISCs under shear. We introduced two metrics to quantify the adhesion process, the cell aspect ratio (AR) as a function of WSS and its rate of change (the dynamic deformability index). We found that the AR of SMEs decreases significantly with the increase of WSS, consistent between the experiments and simulations. In contrast, the AR of ISCs remains constant in time and independent of the flow rate. The critical WSS value for detaching a single SME in oxygenated state is in the range of 3.9-5.5 Pa depending on the number of adhesion sites; the critical WSS value for ISCs is lower than that of SMEs. Our simulations show that the critical WSS value for SMEs in deoxygenated state is above 6.2 Pa (multiple adhesion sites), which is greater than their oxygenated counterparts. We investigated the effect of cell shear modulus on the detachment process; we found that for the same cell adhesion spring constant, the higher shear modulus leads to an earlier cell detachment from the functionalized surface. These findings may aid in the understanding of individual roles of sickle cell types in sickle cell disease vaso-occlusion.

Synergistic Integration of Laboratory and Numerical Approaches in Studies of the Biomechanics of Diseased Red Blood Cells

In red blood cell (RBC) disorders, such as sickle cell disease, hereditary spherocytosis, and diabetes, alterations to the size and shape of RBCs due to either mutations of RBC proteins or changes to the extracellular environment, lead to compromised cell deformability, impaired cell stability, and increased propensity to aggregate. Numerous laboratory approaches have been implemented to elucidate the pathogenesis of RBC disorders. Concurrently, computational RBC models have been developed to simulate the dynamics of RBCs under physiological and pathological conditions. In this work, we review recent laboratory and computational studies of disordered RBCs. Distinguished from previous reviews, we emphasize how experimental techniques and computational modeling can be synergically integrated to improve the understanding of the pathophysiology of hematological disorders.

Local Hematocrit Fluctuation Induced by Malaria-Infected Red Blood Cells and Its Effect on Microflow

We investigate numerically the microscale blood flow in which red blood cells (RBCs) are partially infected by Plasmodium falciparum, the malaria parasite. The infected RBCs are modeled as more rigid cells with less deformability than healthy ones. Our study illustrates that, in a 10 μm microvessel in low-hematocrit conditions (18% and 27%), the Plasmodium falciparum-infected red blood cells (Pf-IRBCs) and healthy ones first form a train of cells. Because of the slow moving of the Pf-IRBCs, the local hematocrit (H_ct) near the Pf-IRBCs is then increased, to approximately 40% or even higher values. This increase of the local hematocrit is temporary and is kept for a longer length of time because of the long RBC train formed in 27%-H_ct condition. Similar hematocrit elevation at the downstream region with 45%-H_ct in the same 10 μm microvessel is also observed with the cells randomly located. In 20 μm microvessels with 45%-H_ct, the Pf-IRBCs slow down the velocity of the healthy red blood cells (HRBCs) around them and then locally elevate the volume fraction and result in the accumulation of the RBCs at the center of the vessels, thus leaving a thicker cell free layer (CFL) near the vessel wall than normal. Variation of wall shear stress (WSS) is caused by the fluctuation of local H_ct and the distance between the wall and the RBCs. Moreover, in high-hematocrit condition (45%), malaria-infected cells have a tendency to migrate to the edge of the aggregates which is due to the uninterrupted hydrodynamic interaction between the HRBCs and Pf-IRBC. Our results suggest that the existence of Pf-IRBCs is a nonnegligible factor for the fluctuation of hematocrit and WSS and also contributes to the increase of CFL of pathological blood flow in microvessels. The numerical approach presented has the potential to be utilized to RBC disorders and other hematologic diseases.

Computational Biomechanics of Human Red Blood Cells in Hematological Disorders

We review recent advances in multiscale modeling of the biomechanical characteristics of red blood cells (RBCs) in hematological diseases, and their relevance to the structure and dynamics of defective RBCs. We highlight examples of successful simulations of blood disorders including malaria and other hereditary disorders, such as sickle-cell anemia, spherocytosis, and elliptocytosis.

Mesoscopic Adaptive Resolution Scheme toward Understanding of Interactions between Sickle Cell Fibers

Understanding of intracellular polymerization of sickle hemoglobin (HbS) and subsequent interaction with the membrane of a red blood cell (RBC) is important to predict the altered morphologies and mechanical properties of sickle RBCs in sickle cell anemia. However, modeling the integrated processes of HbS nucleation, polymerization, HbS fiber interaction, and subsequent distortion of RBCs is challenging as they occur at multispatial scales, ranging from nanometers to micrometers. To make progress toward simulating the integrated processes, we propose a hybrid HbS fiber model, which couples fine-grained and coarse-grained HbS fiber models through a mesoscopic adaptive resolution scheme (MARS). To this end, we apply a microscopic model to capture the dynamic process of polymerization of HbS fibers, while maintaining the mechanical properties of polymerized HbS fibers by the mesoscopic model, thus providing a means of bridging the subcellular and cellular phenomena in sickle cell disease. At the subcellular level, this model can simulate HbS polymerization with preexisting HbS nuclei. At the cellular level, if combined with RBC models, the generated HbS fibers could be applied to study the morphologies and membrane stiffening of sickle RBCs. One important feature of the MARS is that it can be easily employed in other particle-based multiscale simulations where a dynamic coarse-graining and force-blending method is required. As demonstrations, we first apply the hybrid HbS fiber model to simulate the interactions of two growing fibers and find that their final configurations depend on the orientation and interaction distance between two fibers, in good agreement with experimental observations. We also model the formation of fiber bundles and domains so that we explore the mechanism that causes fiber branching.

OpenRBC: A Fast Simulator of Red Blood Cells at Protein Resolution

We present OpenRBC, a coarse-grained molecular dynamics code, which is capable of performing an unprecedented in silico experiment-simulating an entire mammal red blood cell lipid bilayer and cytoskeleton as modeled by multiple millions of mesoscopic particles-using a single shared memory commodity workstation. To achieve this, we invented an adaptive spatial-searching algorithm to accelerate the computation of short-range pairwise interactions in an extremely sparse three-dimensional space. The algorithm is based on a Voronoi partitioning of the point cloud of coarse-grained particles, and is continuously updated over the course of the simulation. The algorithm enables the construction of the key spatial searching data structure in our code, i.e., a lattice-free cell list, with a time and space cost linearly proportional to the number of particles in the system. The position and the shape of the cells also adapt automatically to the local density and curvature. The code implements OpenMP parallelization and scales to hundreds of hardware threads. It outperforms a legacy simulator by almost an order of magnitude in time-to-solution and >40 times in problem size, thus providing, to our knowledge, a new platform for probing the biomechanics of red blood cells.

Biomechanics and biorheology of red blood cells in sickle cell anemia

Sickle cell anemia (SCA) is an inherited blood disorder that causes painful crises due to vaso-occlusion of small blood vessels. The primary cause of the clinical phenotype of SCA is the intracellular polymerization of sickle hemoglobin resulting in sickling of red blood cells (RBCs) in deoxygenated conditions. In this review, we discuss the biomechanical and biorheological characteristics of sickle RBCs and sickle blood as well as their implications toward a better understanding of the pathophysiology and pathogenesis of SCA. Additionally, we highlight the adhesive heterogeneity of RBCs in SCA and their specific contribution to vaso-occlusive crisis.

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.

Shape control of lipid bilayer membranes by confined actin bundles

In living cells, lipid membranes and biopolymers determine each other's conformation in a delicate force balance. Cellular polymers such as actin filaments are strongly confined by the plasma membrane in cell protrusions such as lamellipodia and filopodia. Conversely, protrusion formation is facilitated by actin-driven membrane deformation and these protrusions are maintained by dense actin networks or bundles of actin filaments. Here we investigate the mechanical interplay between actin bundles and lipid bilayer membranes by reconstituting a minimal model system based on cell-sized liposomes with encapsulated actin filaments bundled by fascin. To address the competition between the deformability of the membrane and the enclosed actin bundles, we tune the bundle stiffness (through the fascin-to-actin molar ratio) and the membrane rigidity (through protein decoration). Using confocal microscopy and quantitative image analysis, we show that actin bundles deform the liposomes into a rich set of morphologies. For liposomes having a small membrane bending rigidity, the actin bundles tend to generate finger-like membrane protrusions that resemble cellular filopodia. Stiffer bundles formed at high crosslink density stay straight in the liposome body, whereas softer bundles formed at low crosslink density are bent and kinked. When the membrane has a large bending rigidity, membrane protrusions are suppressed. In this case, membrane enclosure forces the actin bundles to organize into cortical rings, to minimize the energy cost associated with filament bending. Our results highlight the importance of taking into account mechanical interactions between the actin cytoskeleton and the membrane to understand cell shape control.

Phase segregation in bio-inspired multi-component vesicles encompassing double tail phospholipid species

Our aim is to investigate the phase segregation and the structure of multi-component bio-inspired phospholipid vesicles via dissipative particle dynamics. The chemical distinction in the phospholipid species arises due to different head and tail group moieties, and molecular stiffness of the hydrocarbon tails. The individual amphiphilic phospholipid molecular species are represented by a hydrophilic head group and two hydrophobic tails. The distinct chemical nature of the moieties is modeled effectively via soft repulsive interaction parameters, and the molecular rigidity is tuned via suitable three-body potential constants. We demonstrate the formation of a stable hybrid vesicle through the self-assembly of the amphiphilic phospholipid molecules in the presence of a hydrophilic solvent. We investigate and characterize the phase segregation and the structure of the binary vesicles for different phospholipid mixtures. Our results demonstrate macroscopic phase separation for phospholipid mixtures composed of species with different hydrocarbon tail groups. We also investigate the relationship between the phase segregation and thermodynamic variables such as interfacial line tension and surface tension, and obtain correspondence between existing theory and experiments, and our simulation results. We report variations in the molecular chain stiffness to have negligible contributions to the phase segregation in the mixed bilayer, and to demonstrate shape transformations of the hybrid vesicle. Our results can be used to design novel bio-inspired hybrid vehicles for potential applications in biomedicine, sensing, imaging and sustainability.

Haemolysis and abnormal haemorheology in sickle cell anaemia

Although pulmonary hypertension, leg ulcers, priapism, stroke and glomerulopathy in sickle cell anaemia (SCA) result from the adverse effects of chronic haemolysis on vascular function (haemolytic phenotype), osteonecrosis, acute chest syndrome and painful vaso-occlusive crises are caused by abnormal vascular cell adhesion and increased blood viscosity (viscosity-vaso-occlusion phenotype). However, this model with two sub-phenotypes does not take into account the haemorheological dimension. We tested the relationships between the biological parameters reflecting the haemolytic rate (haemolytic component) and red blood cell (RBC) rheological characteristics in 97 adults with SCA. No significant difference in the proportion of patients with low or high haemolytic component in the low and high blood viscosity groups was observed. The RBC elongation index (i.e. deformability) was negatively correlated with the haemolytic component. The RBC aggregates strength (i.e. RBC aggregates robustness) was negatively correlated with RBC elongation index. Sickle RBCs with high density had lower elongation index and higher aggregates strength. In conclusion, (i) the 'haemolytic' phenotype is characterized by decreased RBC deformability and increased RBC aggregates strength and (ii) the viscosity-vaso-occlusive phenotype is characterized by increased RBC deformability but not always by increased blood viscosity. α-thalassaemia modulates the haemorheological properties but other factors seem to be involved.

Multiscale modeling of blood flow: from single cells to blood rheology

Mesoscale simulations of blood flow, where the red blood cells are described as deformable closed shells with a membrane characterized by bending rigidity and stretching elasticity, have made much progress in recent years to predict the flow behavior of blood cells and other components in various flows. To numerically investigate blood flow and blood-related processes in complex geometries, a highly efficient simulation technique for the plasma and solutes is essential. In this review, we focus on the behavior of single and several cells in shear and microcapillary flows, the shear-thinning behavior of blood and its relation to the blood cell structure and interactions, margination of white blood cells and platelets, and modeling hematologic diseases and disorders. Comparisons of the simulation predictions with existing experimental results are made whenever possible, and generally very satisfactory agreement is obtained.

Effect of chain chirality on the self-assembly of sickle hemoglobin

We present simulation results on the self-assembly behavior of sickle hemoglobin (HbS). A coarse-grained HbS model, which contains hydrophilic and hydrophobic particles explicitly, is constructed to match the structural properties and physical description of HbS. The hydrophobic interactions are shown to be necessary with chirality being the main driver for the formation of HbS fibers. In the absence of chain chirality, only small self-assembled aggregates are observed whereas self-assembled elongated steplike bundle microstructures appear when we include chain chirality. We also investigate the effect of confinement on self-assembly, and find that elongated fibers-similar to open-space ones-can be obtained in hard confinement domains but cannot be formed within compliant red blood cell (RBC) domains under the same assumptions. We show, however, that by placing explicitly HbS fibers inside the RBCs and subjecting them to linear elongation and bending, we obtain different types of sickle-shaped RBCs as observed in sickle cell anemia.

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.