Simulations of the erythrocyte cytoskeleton at large deformation. I. Microscopic models

The dynamics of red blood cells traversing slits of mechanical heart valves under high shear

Hemolysis, including subclinical hemolysis, is a potentially severe complications of mechanical heart valves (MHVs), which leads to shortened red blood cell (RBC) lifespan and hemolytic anemia. Serious hemolysis is usually associated with structural deterioration and regurgitation. However, the shear stress in MHVs' narrow leakage slits is much lower than the shear stress threshold causing hemolysis and the mechanisms in this context remain largely unclear. This study investigated the hemolysis mechanism of RBCs in cell-size slits under high shear rates by establishing in vitro microfluidic devices and a coarse-grained molecular dynamics (CGMD) model, considering both fluid and structural effects simultaneously. Microfluidic experiments and computational simulation revealed six distinct dynamic states of RBC traversal through MHVs' microscale slits under various shear rates and slit sizes. It elucidated that RBC dynamic states were influenced by not only by fluid forces but significantly by the compressive force of slit walls. The variation of the potential energy of the cell membrane indicated its stretching, deformation, and rupture during traversal, corresponding to the six dynamic states. The maximum forces exerted on membrane by water particles and slit walls directly determined membrane rupture, serving as a critical determinant. This analysis helps in understanding the contribution of the slit walls to membrane rupture and identifying the threshold force that leads to membrane rupture. The hemolysis mechanism of traversing microscale slits is revealed to effectively explain the occurrences of hemolysis and subclinical hemolysis.

Dynamic mechanisms for membrane skeleton transitions

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

Circulating cell clusters aggravate the hemorheological abnormalities in COVID-19

Microthrombi and circulating cell clusters are common microscopic findings in patients with coronavirus disease 2019 (COVID-19) at different stages in the disease course, implying that they may function as the primary drivers in disease progression. Inspired by a recent flow imaging cytometry study of the blood samples from patients with COVID-19, we perform computational simulations to investigate the dynamics of different types of circulating cell clusters, namely white blood cell (WBC) clusters, platelet clusters, and red blood cell clusters, over a range of shear flows and quantify their impact on the viscosity of the blood. Our simulation results indicate that the increased level of fibrinogen in patients with COVID-19 can promote the formation of red blood cell clusters at relatively low shear rates, thereby elevating the blood viscosity, a mechanism that also leads to an increase in viscosity in other blood diseases, such as sickle cell disease and type 2 diabetes mellitus. We further discover that the presence of WBC clusters could also aggravate the abnormalities of local blood rheology. In particular, the extent of elevation of the local blood viscosity is enlarged as the size of the WBC clusters grows. On the other hand, the impact of platelet clusters on the local rheology is found to be negligible, which is likely due to the smaller size of the platelets. The difference in the impact of WBC and platelet clusters on local hemorheology provides a compelling explanation for the clinical finding that the number of WBC clusters is significantly correlated with thrombotic events in COVID-19 whereas platelet clusters are not. Overall, our study demonstrates that our computational models based on dissipative particle dynamics can serve as a powerful tool to conduct quantitative investigation of the mechanism causing the pathological alterations of hemorheology and explore their connections to the clinical manifestations in COVID-19.

SIMULATION OF CELL MOTION IN THE MICROCHANNEL WITH A SQUARE CAVITY

Isolating circulating tumor cells (CTCs) from the blood plays an important role in the specific treatment of tumor diseases. In this study, a dissipative particle dynamics method combined with a spring-based cell model was employed to simulate the motion of a single or two cells in the microchannel with a square cavity. For a single cell with a small diameter, it will be captured by the square cavity at an appropriate flow rate. For cells whose diameter is not small enough compared to the opening size of the square cavity, they will not be captured at any flow rate. Based on this, cells of different sizes could be successfully separated when passing through this microchannel. Through the analysis of the flow behavior of uncaptured cells, the movement of cells in microchannels is divided into four stages: “guiding,” “rapid,” “slow”, and “ascending” according to the lateral movement speed and centroid position of cells. When the CTC moves together with a red blood cell, as the flow rate decreases, it would be trapped by the microcavity, whereas the RBC is not captured. Thus, CTC can be isolated from blood samples of cancer patients. The method of predicting cell movement behavior through simulation can also provide some reference for the design of microfluidic channels.

Biomechanics of cells and subcellular components: A comprehensive review of computational models and applications

Cells are a fundamental structural, functional and biological unit for all living organisms. Up till now, considerable efforts have been made to study the responses of single cells and subcellular components to an external load, and understand the biophysics underlying cell rheology, mechanotransduction and cell functions using experimental and in silico approaches. In the last decade, computational simulation has become increasingly attractive due to its critical role in interpreting experimental data, analysing complex cellular/subcellular structures, facilitating diagnostic designs and therapeutic techniques, and developing biomimetic materials. Despite the significant progress, developing comprehensive and accurate models of living cells remains a grand challenge in the 21st century. To understand current state of the art, this review summarises and classifies the vast array of computational biomechanical models for cells. The article covers the cellular components at multi-spatial levels, that is, protein polymers, subcellular components, whole cells and the systems with scale beyond a cell. In addition to the comprehensive review of the topic, this article also provides new insights into the future prospects of developing integrated, active and high-fidelity cell models that are multiscale, multi-physics and multi-disciplinary in nature. This review will be beneficial for the researchers in modelling the biomechanics of subcellular components, cells and multiple cell systems and understanding the cell functions and biological processes from the perspective of cell mechanics.

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

We present an analytical hyperelastic constitutive model of the red blood cell (erythrocyte) membrane based on recently improved characterizations of density and microscopic structure of its spectrin network from proteomics and cryo-electron tomography. The model includes distributions of both orientations and natural lengths of spectrin and updated copy numbers of proteins. By applying finite deformation to the spectrin network, we obtain the total free energy and stresses in terms of invariants of shear and area deformation. We generalize an expression of the initial shear modulus, which is independent of the number of molecular orientations within the network and also derive a simplified version of the model. We apply the model and its simplified version to analyze micropipette aspiration computationally and analytically and explore the effect of local cytoskeletal density change. We also explore the discrepancies among shear modulus values measured using different experimental techniques reported in the literature. We find that the model exhibits hardening behavior and can explain many of these discrepancies. Moreover, we find that the distribution of natural lengths plays a crucial role in the hardening behavior when the correct copy numbers of proteins are used. The initial shear modulus values we obtain using our current model (5.9-15.6 pN/μm) are close to the early estimates (6-9 pN/μm). This new, to our knowledge, constitutive model establishes a direct connection between the molecular structure of spectrin networks and constitutive laws and also defines a new picture of a much denser spectrin network than assumed in prior studies.

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

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

Modeling cell migration regulated by cell extracellular-matrix micromechanical coupling

Cell migration in fibrous extracellular matrix (ECM) is crucial to many physiological and pathological processes such as tissue regeneration, immune response, and cancer progression. During migration, individual cells can generate active pulling forces via actomyosin contraction, which are transmitted to the ECM fibers through focal adhesion complexes, remodel the ECM, and eventually propagate to and can be sensed by other cells in the system. The microstructure and physical properties of the ECM can also significantly influence cell migration, e.g., via durotaxis and contact guidance. Here, we develop a computational model for two-dimensional cell migration regulated by cell-ECM micromechanical coupling. Our model explicitly takes into account a variety of cellular-level processes, including focal adhesion formation and disassembly, active traction force generation and cell locomotion due to actin filament contraction, transmission and propagation of tensile forces in the ECM, as well as the resulting ECM remodeling. We validate our model by accurately reproducing single-cell dynamics of MCF-10A breast cancer cells migrating on collagen gels and show that the durotaxis and contact guidance effects naturally arise as a consequence of the cell-ECM micromechanical interactions considered in the model. Moreover, our model predicts strongly correlated multicellular migration dynamics, which are resulted from the ECM-mediated mechanical coupling among the migrating cell and are subsequently verified in in vitro experiments using MCF-10A cells. Our computational model provides a robust tool to investigate emergent collective dynamics of multicellular systems in complex in vivo microenvironment and can be utilized to design in vitro microenvironments to guide collective behaviors and self-organization of cells.

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.

Modeling Cell Adhesion and Extravasation in Microvascular System

The blood flow behaviors in the microvessels determine the transport modes and further affect the metastasis of circulating tumor cells (CTCs). Much biochemical and biological efforts have been made on CTC metastasis; however, precise experimental measurement and accurate theoretical prediction on its mechanical mechanism are limited. To complement these, numerical modeling of a CTC extravasation from the blood circulation, including the steps of adhesion and transmigration, is discussed in this chapter. The results demonstrate that CTCs prefer to adhere at the positive curvature of curved microvessels, which is attributed to the positive wall shear stress/gradient. Then, the effects of particulate nature of blood on CTC adhesion are investigated and are found to be significant in the microvessels. Furthermore, the presence of red blood cell (RBC) aggregates is also found to promote the CTC adhesion by providing an additional wall-directed force. Finally, a single cell passing through a narrow slit, mimicking CTC transmigration, was examined under the effects of cell deformability. It showed that the cell shape and surface area increase play a more important role than the cell elasticity in cell transit across the narrow slit.

Structural modelling of the cardiovascular system

Computational modelling of the cardiovascular system offers much promise, but represents a truly interdisciplinary challenge, requiring knowledge of physiology, mechanics of materials, fluid dynamics and biochemistry. This paper aims to provide a summary of the recent advances in cardiovascular structural modelling, including the numerical methods, main constitutive models and modelling procedures developed to represent cardiovascular structures and pathologies across a broad range of length and timescales; serving as an accessible point of reference to newcomers to the field. The class of so-called hyperelastic materials provides the theoretical foundation for the modelling of how these materials deform under load, and so an overview of these models is provided; comparing classical to application-specific phenomenological models. The physiology is split into components and pathologies of the cardiovascular system and linked back to constitutive modelling developments, identifying current state of the art in modelling procedures from both clinical and engineering sources. Models which have originally been derived for one application and scale are shown to be used for an increasing range and for similar applications. The trend for such approaches is discussed in the context of increasing availability of high performance computing resources, where in some cases computer hardware can impact the choice of modelling approach used.

Buckling of thermally fluctuating spherical shells: Parameter renormalization and thermally activated barrier crossing

We study the influence of thermal fluctuations on the buckling behavior of thin elastic capsules with spherical rest shape. Above a critical uniform pressure, an elastic capsule becomes mechanically unstable and spontaneously buckles into a shape with an axisymmetric dimple. Thermal fluctuations affect the buckling instability by two mechanisms. On the one hand, thermal fluctuations can renormalize the capsule's elastic properties and its pressure because of anharmonic couplings between normal displacement modes of different wavelengths. This effectively lowers its critical buckling pressure [Košmrlj and Nelson, Phys. Rev. X 7, 011002 (2017)2160-330810.1103/PhysRevX.7.011002]. On the other hand, buckled shapes are energetically favorable already at pressures below the classical buckling pressure. At these pressures, however, buckling requires to overcome an energy barrier, which only vanishes at the critical buckling pressure. In the presence of thermal fluctuations, the capsule can spontaneously overcome an energy barrier of the order of the thermal energy by thermal activation already at pressures below the critical buckling pressure. We revisit parameter renormalization by thermal fluctuations and formulate a buckling criterion based on scale-dependent renormalized parameters to obtain a temperature-dependent critical buckling pressure. Then we quantify the pressure-dependent energy barrier for buckling below the critical buckling pressure using numerical energy minimization and analytical arguments. This allows us to obtain the temperature-dependent critical pressure for buckling by thermal activation over this energy barrier. Remarkably, both parameter renormalization and thermal activation lead to the same parameter dependence of the critical buckling pressure on temperature, capsule radius and thickness, and Young's modulus. Finally, we study the combined effect of parameter renormalization and thermal activation by using renormalized parameters for the energy barrier in thermal activation to obtain our final result for the temperature-dependent critical pressure, which is significantly below the results if only parameter renormalization or only thermal activation is considered.

An Enhanced Spring-Particle Model for Red Blood Cell Structural Mechanics: Application to the Stomatocyte–Discocyte–Echinocyte Transformation

Red blood cells (RBCs) are the most abundant cellular element suspended in blood. Together with the usual biconcave-shaped RBCs, i.e., discocytes, unusual-shaped RBCs are also observed under physiological and experimental conditions, e.g., stomatocytes and echinocytes. Stomatocytes and echinocytes are formed from discocytes and in addition can revert back to being discocytes; this shape change is known as the stomatocyte–discocyte–echinocyte (SDE) transformation. To-date, limited research has been conducted on the numerical prediction of the full SDE transformation. Spring-particle RBC (SP-RBC) models are commonly used to numerically predict RBC mechanics and rheology. However, these models are incapable of predicting the full SDE transformation because the typically employed bending model always leads to numerical instability with severely deformed shapes. In this work, an enhanced SP-RBC model is proposed in order to extend the capability of this model type and so that the full SDE transformation can be reproduced. This is achieved through the leveraging of an advanced bending model. Transformed vesicle and RBC shapes are predicted for a range of reduced volume and reduced membrane area difference (MAD), and very good agreement is obtained in the comparison of predicted shapes with experimental observations. Through these predictions, vesicle and SDE transformation phase diagrams are developed and, importantly, in the SDE case, shape boundaries are proposed for the first time relating RBC shape categories to RBC reduced volume and reduced MAD.

Nuclear mechanical resilience but not stiffness is modulated by αII-spectrin

Spectrins are multi-domain, elastic proteins that provide elasticity to the plasma membrane of erythrocytes and select nucleated cells. Spectrins have also been found in the nucleus of non-erythrocytes, but their function remains to be uncovered. It has been hypothesized that a spring-like spectrin network exists within the lamina nucleoskeleton, however, experiments testing a spectrin network׳s mechanical impact on the nucleus are lacking. Here, we knock-down levels of nuclear αII-spectrin with the goal of disrupting this nucleoskeletal spectrin network. We mechanically test live cells with intranuclear particle tracking and compression assays to probe changes in nuclear mechanics with decreases in αII-spectrin. We show no changes in chromatin mechanics or in the stiffness of nuclei under compression. However, we do observe a reduction in the ability of nuclei with decreased αII-spectrin to recover after compression. These results establish spectrin as a nucleoskeletal component that specifically contributes to elastic recovery after compression.

Effects of flowing RBCs on adhesion of a circulating tumor cell in microvessels

Adhesion of circulating tumor cells (CTCs) to the microvessel wall largely depends on the blood hydrodynamic conditions, one of which is the blood viscosity. Since blood is a non-Newtonian fluid, whose viscosity increases with hematocrit, in the microvessels at low shear rate. In this study, the effects of hematocrit, vessel size, flow rate and red blood cell (RBC) aggregation on adhesion of a CTC in the microvessels were numerically investigated using dissipative particle dynamics. The membrane of cells was represented by a spring-based network connected by elastic springs to characterize its deformation. RBC aggregation was modeled by a Morse potential function based on depletion-mediated assumption, and the adhesion of the CTC to the vessel wall was achieved by the interactions between receptors and ligands at the CTC and those at the endothelial cells forming the vessel wall. The results demonstrated that in the microvessel of [Formula: see text] diameter, the CTC has an increasing probability of adhesion with the hematocrit due to a growing wall-directed force, resulting in a larger number of receptor-ligand bonds formed on the cell surface. However, with the increase in microvessel size, an enhanced lift force at higher hematocrit detaches the initial adherent CTC quickly. If the microvessel is comparable to the CTC in diameter, CTC adhesion is independent of Hct. In addition, the velocity of CTC is larger than the average blood flow velocity in smaller microvessels and the relative velocity of CTC decreases with the increase in microvessel size. An increased blood flow resistance in the presence of CTC was also found. Moreover, it was found that the large deformation induced by high flow rate and the presence of aggregation promote the adhesion of CTC.

Stiffening of Red Blood Cells Induced by Cytoskeleton Disorders: A Joint Theory-Experiment Study

The functions and elasticities of the cell are largely related to the structures of the cytoskeletons underlying the lipid bilayer. Among various cell types, the red blood cell (RBC) possesses a relatively simple cytoskeletal structure. Underneath the membrane, the RBC cytoskeleton takes the form of a two-dimensional triangular network, consisting of nodes of actins (and other proteins) and edges of spectrins. Recent experiments focusing on the malaria-infected RBCs (iRBCs) show that there is a correlation between the elongation of spectrins in the cytoskeletal network and the stiffening of the iRBCs. Here we rationalize the correlation between these two observations by combining the wormlike chain model for single spectrins and the effective medium theory for the network elasticity. We specifically focus on how the disorders in the cytoskeletal network affect its macroscopic elasticity. Analytical and numerical solutions from our model reveal that the stiffness of the membrane increases with increasing end-to-end distances of spectrins, but has a nonmonotonic dependence on the variance of the end-to-end distance distributions. These predictions are verified quantitatively by our atomic force microscopy and micropipette aspiration measurements of iRBCs. The model may, from a molecular level, provide guidelines for future identification of new treatment methods for RBC-related diseases, such as malaria infection.

Modeling of band-3 protein diffusion in the normal and defective red blood cell membrane

We employ a two-component red blood cell (RBC) membrane model to simulate lateral diffusion of band-3 proteins in the normal RBC and in the RBC with defective membrane proteins. The defects reduce the connectivity between the lipid bilayer and the membrane skeleton (vertical connectivity), or the connectivity of the membrane skeleton itself (horizontal connectivity), and are associated with the blood disorders of hereditary spherocytosis (HS) and hereditary elliptocytosis (HE) respectively. Initially, we demonstrate that the cytoskeleton limits band-3 lateral mobility by measuring the band-3 macroscopic diffusion coefficients in the normal RBC membrane and in a lipid bilayer without the cytoskeleton. Then, we study band-3 diffusion in the defective RBC membrane and quantify the relation between band-3 diffusion coefficients and percentage of protein defects in HE RBCs. In addition, we illustrate that at low spectrin network connectivity (horizontal connectivity) band-3 subdiffusion can be approximated as anomalous diffusion, while at high horizontal connectivity band-3 diffusion is characterized as confined diffusion. Our simulations show that the band-3 anomalous diffusion exponent depends on the percentage of protein defects in the membrane cytoskeleton. We also confirm that the introduction of attraction between the lipid bilayer and the spectrin network reduces band-3 diffusion, but we show that this reduction is lower than predicted by the percolation theory. Furthermore, we predict that the attractive force between the spectrin filament and the lipid bilayer is at least 20 times smaller than the binding forces at band-3 and glycophorin C, the two major membrane binding sites. Finally, we explore diffusion of band-3 particles in the RBC membrane with defects related to vertical connectivity. We demonstrate that in this case band-3 diffusion can be approximated as confined diffusion for all attraction levels between the spectrin network and the lipid bilayer. By comparing the diffusion coefficients measured in horizontal vs. vertical defects, we conclude that band-3 mobility is primarily controlled by the horizontal connectivity.

Numerical simulation of a single cell passing through a narrow slit

The narrow slit between endothelial cells that line the microvessel wall is the principal pathway for tumor cell extravasation to the surrounding tissue. To understand this crucial step for tumor hematogenous metastasis, we used dissipative particle dynamics method to investigate an individual cell passing through a narrow slit numerically. The cell membrane was simulated by a spring-based network model which can separate the internal cytoplasm and surrounding fluid. The effects of the cell elasticity, cell shape, nucleus and slit size on the cell transmigration through the slit were investigated. Under a fixed driving force, the cell with higher elasticity can be elongated more and pass faster through the slit. When the slit width decreases to 2/3 of the cell diameter, the spherical cell becomes jammed despite reducing its elasticity modulus by 10 times. However, transforming the cell from a spherical to ellipsoidal shape and increasing the cell surface area by merely 9.3 % can enable the cell to pass through the narrow slit. Therefore, the cell shape and surface area increase play a more important role than the cell elasticity in cell passing through the narrow slit. In addition, the simulation results indicate that the cell migration velocity decreases during entrance but increases during exit of the slit, which is qualitatively in agreement with the experimental observation.

Modeling cytoadhesion of Plasmodium falciparum-infected erythrocytes and leukocytes-common principles and distinctive features

Cytoadhesion of Plasmodium falciparum‐infected erythrocytes to the microvascular endothelial lining shares striking similarities to cytoadhesion of leukocytes. In both cases, adhesins are presented in structures that raise them above the cell surface. Another similarity is the enhancement of adhesion under physical force (catch bonding). Here, we review recent advances in our understanding of the molecular and biophysical mechanisms underlying cytoadherence in both cellular systems. We describe how imaging, flow chamber experiments, single‐molecule measurements, and computational modeling have been used to decipher the relevant processes. We conclude that although the parasite seems to induce processes that resemble the cytoadherence of leukocytes, the mechanics of erythrocytes is such that the resulting behavior in shear flow is fundamentally different.

Computation of the effective mechanical response of biological networks accounting for large configuration changes

The asymptotic homogenization technique is involved to derive the effective elastic response of biological membranes viewed as repetitive beam networks. Thereby, a systematic methodology is established, allowing the prediction of the overall mechanical properties of biological membranes in the nonlinear regime, reflecting the influence of the geometrical and mechanical micro-parameters of the network structure on the overall response of the equivalent continuum. Biomembranes networks are classified based on nodal connectivity, so that we analyze in this work 3, 4 and 6-connectivity networks, which are representative of most biological networks. The individual filaments of the network are described as undulated beams prone to entropic elasticity, with tensile moduli determined from their persistence length. The effective micropolar continuum evaluated as a continuum substitute of the biological network has a kinematics reflecting the discrete network deformation modes, involving a nodal displacement and a microrotation. The statics involves the classical Cauchy stress and internal moments encapsulated into couple stresses, which develop internal work in duality to microcurvatures reflecting local network undulations. The relative ratio of the characteristic bending length of the effective micropolar continuum to the unit cell size determines the relevant choice of the equivalent medium. In most cases, the Cauchy continuum is sufficient to model biomembranes. The peptidoglycan network may exhibit a re-entrant hexagonal configuration due to thermal or pressure fluctuations, for which micropolar effects become important. The homogenized responses are in good agreement with FE simulations performed over the whole network. The predictive nature of the employed homogenization technique allows the identification of a strain energy density of a hyperelastic model, for the purpose of performing structural calculations of the shape evolutions of biomembranes.

Erythrocyte membrane model with explicit description of the lipid bilayer and the spectrin network

The membrane of the red blood cell (RBC) consists of spectrin tetramers connected at actin junctional complexes, forming a two-dimensional (2D) sixfold triangular network anchored to the lipid bilayer. Better understanding of the erythrocyte mechanics in hereditary blood disorders such as spherocytosis, elliptocytosis, and especially, sickle cell disease requires the development of a detailed membrane model. In this study, we introduce a mesoscale implicit-solvent coarse-grained molecular dynamics (CGMD) model of the erythrocyte membrane that explicitly describes the phospholipid bilayer and the cytoskeleton, by extending a previously developed two-component RBC membrane model. We show that the proposed model represents RBC membrane with the appropriate bending stiffness and shear modulus. The timescale and self-consistency of the model are established by comparing our results with experimentally measured viscosity and thermal fluctuations of the RBC membrane. Furthermore, we measure the pressure exerted by the cytoskeleton on the lipid bilayer. We find that defects at the anchoring points of the cytoskeleton to the lipid bilayer (as in spherocytes) cause a reduction in the pressure compared with an intact membrane, whereas defects in the dimer-dimer association of a spectrin filament (as in elliptocytes) cause an even larger decrease in the pressure. We conjecture that this finding may explain why the experimentally measured diffusion coefficients of band-3 proteins are higher in elliptocytes than in spherocytes, and higher than in normal RBCs. Finally, we study the effects that possible attractive forces between the spectrin filaments and the lipid bilayer have on the pressure applied on the lipid bilayer by the filaments. We discover that the attractive forces cause an increase in the pressure as they diminish the effect of membrane protein defects. As this finding contradicts with experimental results, we conclude that the attractive forces are moderate and do not impose a complete attachment of the filaments to the lipid bilayer.

Multi-scale biological and physical modelling of the tumour micro-environment

Paced by advances in high performance computing, and algorithms for multi-physics and multi-scale simulation, a number of groups have recently established numerical models of flowing blood systems, where cell-scale interactions are explicitly resolved. To be biologically representative, these models account for some or all of: (1) fluid dynamics of the carrier flow, (2) structural dynamics of the cells and vessel walls, (3) interaction and transport biochemistry, and, (4) methods for scaling to physiologically representative numbers of cells. In this article, our interest is the modelling of the tumour micro-environment. We review the broader area of cell-scale resolving blood flow modelling, while focusing on the particular interactions of tumour cells and white blood cells, known to play an important role in metastasis.

Deformability-based circulating tumor cell separation with conical-shaped microfilters: Concept, optimization, and design criteria

Circulating tumor cells (CTCs) separation technology has made positive impacts on cancer science in many aspects. The ability of detecting and separating CTCs can play a key role in early cancer detection and treatment. In recent years, there has been growing interest in using deformability-based CTC separation microfilters due to their simplicity and low cost. Most of the previous studies in this area are mainly based on experimental work. Although experimental research provides useful insights in designing CTC separation devices, there is still a lack of design guidelines based on fundamental understandings of the cell separation process in the filters. While experimental efforts face challenges, especially microfabrication difficulties, we adopt numerical simulation here to study conical-shaped microfilters using deformability difference between CTCs and blood cells for the separation process. We use the liquid drop model for modeling a CTC passing through such microfilters. The accuracy of the model in predicting the pressure signature of the system is validated by comparing it with previous experiments. Pressure-deformability analysis of the cell going through the channel is then carried out in detail in order to better understand how a CTC behaves throughout the filtration process. Different system design criteria such as system throughput and unclogging of the system are discussed. Specifically, pressure behavior under different system throughput is analyzed. Regarding the unclogging issue, we define pressure ratio as a key parameter representing the ability to overcome clogging in such CTC separation devices and investigate the effect of conical angle on the optimum pressure ratio. Finally, the effect of unclogging applied pressure on the system performance is examined. Our study provides detailed understandings of the cell separation process and its characteristics, which can be used for developing more efficient CTC separation devices.

Multiple stiffening effects of nanoscale knobs on human red blood cells infected with Plasmodium falciparum malaria parasite

Our coarse-grained molecular dynamics (CGMD) simulations show that the deposition of nanoscale knobs, rather than spectrin network remodeling, is the primary cause of the dramatically increased stiffness of the Plasmodium falciparum (Pf)-infected red blood cell (RBC) membranes. Our analyses further reveal that the knobs stiffen the RBC membrane in a unique manner by simultaneously harnessing composite strengthening, strain hardening, and knob density-dependent vertical coupling effects. In addition to providing a fundamental understanding of the stiffening mechanism of Pf-infected RBCs, our simulation results suggest potential targets for antimalarial therapies.

During its asexual development within the red blood cell (RBC), Plasmodium falciparum (Pf), the most virulent human malaria parasite, exports proteins that modify the host RBC membrane. The attendant increase in cell stiffness and cytoadherence leads to sequestration of infected RBCs in microvasculature, which enables the parasite to evade the spleen, and leads to organ dysfunction in severe cases of malaria. Despite progress in understanding malaria pathogenesis, the molecular mechanisms responsible for the dramatic loss of deformability of Pf-infected RBCs have remained elusive. By recourse to a coarse-grained (CG) model that captures the molecular structures of Pf-infected RBC membrane, here we show that nanoscale surface protrusions, known as “knobs,” introduce multiple stiffening mechanisms through composite strengthening, strain hardening, and knob density-dependent vertical coupling. On one hand, the knobs act as structural strengtheners for the spectrin network; on the other, the presence of knobs results in strain inhomogeneity in the spectrin network with elevated shear strain in the knob-free regions, which, given its strain-hardening property, effectively stiffens the network. From the trophozoite to the schizont stage that ensues within 24–48 h of parasite invasion into the RBC, the rise in the knob density results in the increased number of vertical constraints between the spectrin network and the lipid bilayer, which further stiffens the membrane. The shear moduli of Pf-infected RBCs predicted by the CG model at different stages of parasite maturation are in agreement with experimental results. In addition to providing a fundamental understanding of the stiffening mechanisms of Pf-infected RBCs, our simulation results suggest potential targets for antimalarial therapies.

The spatial-temporal characteristics of type I collagen-based extracellular matrix

Type I collagen abounds in mammalian extracellular matrix (ECM) and is crucial to many biophysical processes. While previous studies have mostly focused on bulk averaged properties, here we provide a comprehensive and quantitative spatial-temporal characterization of the microstructure of type I collagen-based ECM as the gelation temperature varies. The structural characteristics including the density and nematic correlation functions are obtained by analyzing confocal images of collagen gels prepared at a wide range of gelation temperatures (from 16 °C to 36 °C). As temperature increases, the gel microstructure varies from a "bundled" network with strong orientational correlation between the fibers to an isotropic homogeneous network with no significant orientational correlation, as manifested by the decaying of length scales in the correlation functions. We develop a kinetic Monte-Carlo collagen growth model to better understand how ECM microstructure depends on various environmental or kinetic factors. We show that the nucleation rate, growth rate, and an effective hydrodynamic alignment of collagen fibers fully determines the spatiotemporal fluctuations of the density and orientational order of collagen gel microstructure. Also the temperature dependence of the growth rate and nucleation rate follow the prediction of classical nucleation theory.

Erythrocyte stiffness during morphological remodeling induced by carbon ion radiation

The adverse effect induced by carbon ion radiation (CIR) is still an unavoidable hazard to the treatment object. Thus, evaluation of its adverse effects on the body is a critical problem with respect to radiation therapy. We aimed to investigate the change between the configuration and mechanical properties of erythrocytes induced by radiation and found differences in both the configuration and the mechanical properties with involving in morphological remodeling process. Syrian hamsters were subjected to whole-body irradiation with carbon ion beams (1, 2, 4, and 6 Gy) or X-rays (2, 4, 6, and 12 Gy) for 3, 14 and 28 days. Erythrocytes in peripheral blood and bone marrow were collected for cytomorphological analysis. The mechanical properties of the erythrocytes were determined using atomic force microscopy, and the expression of the cytoskeletal protein spectrin-α1 was analyzed via western blotting. The results showed that dynamic changes were evident in erythrocytes exposed to different doses of carbon ion beams compared with X-rays and the control (0 Gy). The magnitude of impairment of the cell number and cellular morphology manifested the subtle variation according to the irradiation dose. In particular, the differences in the size, shape and mechanical properties of the erythrocytes were well exhibited. Furthermore, immunoblot data showed that the expression of the cytoskeletal protein spectrin-α1 was changed after irradiation, and there was a common pattern among its substantive characteristics in the irradiated group. Based on these findings, the present study concluded that CIR could induce a change in mechanical properties during morphological remodeling of erythrocytes. According to the unique characteristics of the biomechanical categories, we deduce that changes in cytomorphology and mechanical properties can be measured to evaluate the adverse effects generated by tumor radiotherapy. Additionally, for the first time, the current study provides a new strategy for enhancing the assessment of the curative effects and safety of clinical radiotherapy, as well as reducing adverse effects.

The effects of 3D channel geometry on CTC passing pressure--towards deformability-based cancer cell separation

Various lab on a chip devices have been developed recently to detect and separate circulating tumour cells (CTCs) for early stage cancer detection. Because CTCs are extremely rare in the blood, next generation CTC microfilters aim at significant improvement in both efficiency and throughput. CTC microfilters based on cell deformability seem to be a promising direction. In the present research, we study a CTC passing event through a micro-filtering channel with various 3D geometries. The pressure signatures for different types of cells passing through different channels are characterized numerically. Specifically, five kinds of cross-sections, circular, square, triangular and two kinds of rectangular channels with aspect ratios of 2 and 5, are studied in this work. The total pressures for cells passing through the channels are calculated and reveal different behaviour from what is predicted by the static surface tension model. Among all five cross-sections studied, the circular cross-section features the highest critical pressure and thus is most suitable for high efficiency CTC separation. The square filtering channel provides the second largest critical pressure, and the triangular cross-section provides the least critical pressure among these three cross-sections. All these three cross-sections are better than the rectangular channels with aspect ratios of 2 and 5. For the rectangular channel, a high aspect ratio channel may lead to cell splitting at high speed, which will result in a periodic pressure signature. Our findings will provide valuable information for the design of next generation CTC microfilters.

Tensegrity, cellular biophysics, and the mechanics of living systems

The recent convergence between physics and biology has led many physicists to enter the fields of cell and developmental biology. One of the most exciting areas of interest has been the emerging field of mechanobiology that centers on how cells control their mechanical properties, and how physical forces regulate cellular biochemical responses, a process that is known as mechanotransduction. In this article, we review the central role that tensegrity (tensional integrity) architecture, which depends on tensile prestress for its mechanical stability, plays in biology. We describe how tensional prestress is a critical governor of cell mechanics and function, and how use of tensegrity by cells contributes to mechanotransduction. Theoretical tensegrity models are also described that predict both quantitative and qualitative behaviors of living cells, and these theoretical descriptions are placed in context of other physical models of the cell. In addition, we describe how tensegrity is used at multiple size scales in the hierarchy of life—from individual molecules to whole living organisms—to both stabilize three-dimensional form and to channel forces from the macroscale to the nanoscale, thereby facilitating mechanochemical conversion at the molecular level.

Many-body contact repulsion of deformable disks

We use a spring-and-plaquette network model to analyze the repulsion between elastic disks in contact. By studying various 2D geometries, we find that as disks approach the incompressibility limit the many-body effects become dominant and the disk-disk interaction is not pairwise additive. Upon compression, the disks undergo a transition from the localized to the distributed deformation regime accompanied by a steep increase of energy consistent with the onset of a hard core. These results shed new light on the structures formed by deformable objects such as soft nanocolloids.

How malaria parasites reduce the deformability of infected red blood cells

The pathogenesis of malaria is largely due to stiffening of the infected red blood cells (RBCs). Contemporary understanding ascribes the loss of RBC deformability to a 10-fold increase in membrane stiffness caused by extra cross-linking in the spectrin network. Local measurements by micropipette aspiration, however, have reported only an increase of ∼3-fold in the shear modulus. We believe the discrepancy stems from the rigid parasite particles inside infected cells, and have carried out numerical simulations to demonstrate this mechanism. The cell membrane is represented by a set of discrete particles connected by linearly elastic springs. The cytosol is modeled as a homogeneous Newtonian fluid, and discretized by particles as in standard smoothed particle hydrodynamics. The malaria parasite is modeled as an aggregate of particles constrained to rigid-body motion. We simulate RBC stretching tests by optical tweezers in three dimensions. The results demonstrate that the presence of a sizeable parasite greatly reduces the ability of RBCs to deform under stretching. With the solid inclusion, the observed loss of deformability can be predicted quantitatively using the local membrane elasticity measured by micropipettes.

Tank-treading of swollen erythrocytes in shear flows

In this paper, we investigate computationally the oscillatory tank-treading motion of healthy swollen human erythrocytes (owing to lower than physiological plasma osmolarity) in shear flows with capillary number Ca=O(1) and small to moderate viscosity ratios 0.01≤λ≤2.75. Swollen cells show similar shear flow dynamics with normal cells but with significantly higher inclination and tank-treading speed owing to the higher cell thickness. For a given viscosity ratio, as the flow rate increases, the steady-state erythrocyte length L (in the shear plane) increases logarithmically while its depth W (normal to the shear plane) decreases logarithmically; increase of the viscosity ratio results in lower cell deformation. The erythrocyte width S, which exists in the shear plane, is practically invariant in time, flow rate, and viscosity ratio and corresponds to a real cell thickness of about 2.5 μm at physiological osmolarity (300 mO) and 3.4 μm at an osmolarity of 217 mO. The erythrocyte inclination decreases as the flow rate increases or as the surrounding fluid viscosity decreases, owing to the increased inner rotational flow which tends to align the cell toward the flow direction. The ektacytometry deformation of swollen cells increases logarithmically with the shear stress but with a slower slope than that for normal cells owing mainly to the higher orientation of the more swollen cells. As the cell swelling increases, the tank-treading period decreases owing to the higher thickness of the actual cell which overcomes the opposite action of the reduced shape-memory effects (i.e., the more spherical-like erythrocyte's reference shape of shearing resistance). The local area incompressibility tensions from the lipid bilayer increase with the cell swelling and cause a higher cytoskeleton prestress; this increased prestress results in smaller, but still measurable, local area changes on the spectrin skeleton of the more swollen erythrocytes. Our work provides insight on the effects of clinical syndromes and biophysical processes associated with lowered plasma osmolarity (and thus higher cell swelling) such as inappropriate antidiuretic hormone secretion and diuretic therapy.

Multiscale models of thrombogenesis

To restrict the loss of blood follow from the rupture of blood vessels, the human body rapidly forms a clot consisting of platelets and fibrin. However, to prevent pathological clotting within vessels as a result of vessel damage, the response must be regulated. Clots forming within vessels (thrombi) can restrict the flow of blood causing damage to tissues in the flow field. Additionally, fragments dissociating from the primary thrombus (emboli) may lodge and clog vessels in the brain (causing ischemic stroke) or lungs (resulting in pulmonary embolism). Pathologies related to the obstruction of blood flow through the vasculature are the major cause of mortality in the United States. Venous thromboembolic disease alone accounts for 900,000 hospitalizations and 300,000 deaths per year and the incidence will increase as the population ages (Wakefield et al. J Vasc Surg 2009, 49:1620-1623). Thus, understanding the interplay between the many processes involved in thrombus development is of significant biomedical value. In this article, we first review computational models of important subprocesses of hemostasis/thrombosis including coagulation reactions, platelet activation, and fibrin assembly, respectively. We then describe several multiscale models integrating these subprocesses to simulate temporal and spatial development of thrombi. The development of validated computational models and predictive simulations will enable one to explore how the variation of multiple hemostatic factors affects thrombotic risk providing an important new tool for thrombosis research.

Two-component coarse-grained molecular-dynamics model for the human erythrocyte membrane

We present a two-component coarse-grained molecular-dynamics model for simulating the erythrocyte membrane. The proposed model possesses the key feature of combing the lipid bilayer and the erythrocyte cytoskeleton, thus showing both the fluidic behavior of the lipid bilayer and the elastic properties of the erythrocyte cytoskeleton. In this model, three types of coarse-grained particles are introduced to represent clusters of lipid molecules, actin junctions, and band-3 complexes, respectively. The proposed model facilitates simulations that span large length scales (approximately micrometers) and timescales (approximately milliseconds). By tuning the interaction potential parameters, we were able to control the diffusivity and bending rigidity of the membrane model. We studied the membrane under shearing and found that at a low shear strain rate, the developed shear stress was due mainly to the spectrin network, whereas the viscosity of the lipid bilayer contributed to the resulting shear stress at higher strain rates. In addition, we investigated the effects of a reduced spectrin network connectivity on the shear modulus of the membrane.

Contractile network models for adherent cells

Cells sense the geometry and stiffness of their adhesive environment by active contractility. For strong adhesion to flat substrates, two-dimensional contractile network models can be used to understand how force is distributed throughout the cell. Here we compare the shape and force distribution for different variants of such network models. In contrast to Hookean networks, cable networks reflect the asymmetric response of biopolymers to tension versus compression. For passive networks, contractility is modeled by a reduced resting length of the mechanical links. In actively contracting networks, a constant force couple is introduced into each link in order to model contraction by molecular motors. If combined with fixed adhesion sites, all network models lead to invaginated cell shapes, but only actively contracting cable networks lead to the circular arc morphology typical for strongly adhering cells. In this case, shape and force distribution are determined by local rather than global determinants and thus are suited to endow the cell with a robust sense of its environment. We also discuss nonlinear and adaptive linker mechanics as well as the relation to tissue shape.

Red blood cell dynamics: from cell deformation to ATP release

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

Membrane compartmentalization in Southeast Asian ovalocytosis red blood cells

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

Equivalent mechanical properties of biological membranes from lattice homogenization

The goal of this manuscript is to set up a novel methodology for the calculation of the effective mechanical properties of biological membranes viewed as repetitive networks of elastic filaments, based on the discrete asymptotic homogenization method. We will show that for some lattice configurations, flexional effects due to internal structure mechanisms at the unit cell scale lead to additional flexional effects at the continuum scale, accounted for by an internal length associated to a micropolar behavior. Thereby, a systematic methodology is established, allowing the prediction of the overall mechanical properties of biological membranes for a given network topology, as closed form expressions of the geometrical and mechanical micro-parameters. The peptidoglycan and the erythrocyte have been analyzed using this methodology, and their effective moduli are calculated and recorded versus the geometrical and mechanical lattice parameters. A classification of lattices with respect to the choice of the equivalent continuum model is proposed: The Cauchy continuum and a micropolar continuum are adopted as two possible effective medium, for a given beam model. The relative ratio of the characteristic length of the micropolar continuum to the unit cell size determines the relevant choice of the equivalent medium. In most cases, the Cauchy continuum is sufficient to model membranes in most of their configurations. The peptidoglycan network may exhibit a re-entrant hexagonal lattice, for which micropolar effects become important. This is attested by the characteristic length becoming larger than the beam length for such configurations. The homogenized moduli give accurate results for both membranes, as revealed by comparison with experimental measurements or simulation results from the literature at the network scale. A first insight into the nonlinear mechanical behavior of the hexagonal and triangular networks is lastly investigated using a perturbative method.

Tank-treading of erythrocytes in strong shear flows via a nonstiff cytoskeleton-based continuum computational modeling

We develop a computationally efficient cytoskeleton-based continuum erythrocyte algorithm. The cytoskeleton is modeled as a two-dimensional elastic solid with comparable shearing and area-dilatation resistance that follows a material law (Skalak, R., A. Tozeren, R. P. Zarda, and S. Chien. 1973. Strain energy function of red blood cell membranes. Biophys. J. 13:245-264). Our modeling enforces the global area-incompressibility of the spectrin skeleton (being enclosed beneath the lipid bilayer in the erythrocyte membrane) via a nonstiff, and thus efficient, adaptive prestress procedure which accounts for the (locally) isotropic stress imposed by the lipid bilayer on the cytoskeleton. In addition, we investigate the dynamics of healthy human erythrocytes in strong shear flows with capillary number Ca =O(1) and small-to-moderate viscosity ratios 0.001 ≤ λ ≤ 1.5. These conditions correspond to a wide range of surrounding medium viscosities (4-600 mPa s) and shear flow rates (0.02-440 s(-1)), and match those used in ektacytometry systems. Our computational results on the cell deformability and tank-treading frequency are compared with ektacytometry findings. The tank-treading period is shown to be inversely proportional to the shear rate and to increase linearly with the ratio of the cytoplasm viscosity to that of the suspending medium. Our modeling also predicts that the cytoskeleton undergoes measurable local area dilatation and compression during the tank-treading of the cells.

Combined simulation and experimental study of large deformation of red blood cells in microfluidic systems

We investigate the biophysical characteristics of healthy human red blood cells (RBCs) traversing microfluidic channels with cross-sectional areas as small as 2.7 × 3 μm. We combine single RBC optical tweezers and flow experiments with corresponding simulations based on dissipative particle dynamics (DPD), and upon validation of the DPD model, predictive simulations and companion experiments are performed in order to quantify cell deformation and pressure-velocity relationships for different channel sizes and physiologically relevant temperatures. We discuss conditions associated with the shape transitions of RBCs along with the relative effects of membrane and cytosol viscosity, plasma environments, and geometry on flow through microfluidic systems at physiological temperatures. In particular, we identify a cross-sectional area threshold below which the RBC membrane properties begin to dominate its flow behavior at room temperature; at physiological temperatures this effect is less profound.

Nanomechanics of multiple units in the erythrocyte membrane skeletal network

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