Fluctuations of coupled fluid and solid membranes with application to red blood cells

A new method for the calculation of functional and path integrals

This paper addresses a disconnect between the pivotal role of functional (path) integrals in modern theories, such as quantum mechanics and statistical thermodynamics, and the currently limited ability to perform the actual calculation. We present a new method for calculating functional integrals, based on a finite-element formulation, which solves all limitations of existing methods. This approach is far more robust, versatile, and powerful than the prevailing methods, thus allowing for more sophisticated computations and the study of problems that could not previously be tackled. Importantly, existing procedures, element libraries and shape functions, which have been developed throughout the years in the context of engineering analysis and partial differential equations, may be directly employed for this purpose.

Role of Plasma Membrane at Dielectric Relaxations and Intermembrane Interaction in Human Erythrocytes

Dielectric relaxations at 1.4 MHz (β_sp) and 9 MHz (γ1_sp) on the erythrocyte spectrin network were studied by dielectric spectroscopy using dense suspensions of erythrocytes and erythrocyte ghost membranes, subjected to extraction with up to 0.2% volume Triton-X-100. The step-wise extraction of up to 60% of membrane lipids preserved γ1_sp and gradually removed β_sp-relaxation. On increasing the concentration up to 100 mM of NaCl at either side of erythrocyte plasma membranes, the β_sp-relaxation was linearly enhanced, while the strength of γ1_sp-relaxation remained unchanged. In media with NaCl between 100 and 150 mM β_sp-relaxation became slightly inhibited, while γ1_sp-relaxation almost disappeared, possibly due to the decreased electrostatic repulsion allowing erythrocytes to come into closer contact. When these media contained, at concentrations 10-30 mg/mL dextran (MW 7 kDa), polyethylene glycol or polyvinylpyrrolidone (40 kDa), or albumin or homologous plasma with equivalent concentration of albumin, the γ1_sp-relaxation was about tenfold enhanced, while β_sp-relaxation was strengthened or preserved. The results suggest the Maxwell-Vagner accumulation of ions on the lipid bilayer as an energy source for β_sp-relaxation. While β_sp-relaxation appears sensitive to erythrocyte membrane deformability, γ1_sp-relaxation could be a sensitive marker for the inter-membrane interactions between erythrocytes.

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

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

The bending rigidity of the red blood cell cytoplasmic membrane

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

Blood bank storage of red blood cells increases RBC cytoplasmic membrane order and bending rigidity

Blood banks around the world store blood components for several weeks ensuring its availability for transfusion medicine. Red blood cells (RBCs) are known to undergo compositional changes during storage, which may impact the cells' function and eventually the recipients' health. We extracted the RBC's cytoplasmic membrane (RBCcm) to study the effect of storage on the membranes' molecular structure and bending rigidity by a combination of X-ray diffraction (XRD), X-ray diffuse scattering (XDS) and coarse grained Molecular Dynamics (MD) simulations. Blood was stored in commercial blood bags for 2 and 5 weeks, respectively and compared to freshly drawn blood. Using mass spectrometry, we measured an increase of fatty acids together with a slight shift towards shorter tail lengths. We observe an increased fraction (6%) of liquid ordered (lo) domains in the RBCcms with storage time, and an increased lipid packing in these domains, leading to an increased membrane thickness and membrane order. The size of both, lo and liquid disordered (ld) lipid domains was found to decrease with increased storage time by up to 25%. XDS experiments reveal a storage dependent increase in the RBCcm's bending modulus κ by a factor of 2.8, from 1.9 kBT to 5.3 kBT. MD simulations were conducted in the absence of proteins. The results show that the membrane composition has a small contribution to the increased bending rigidity and suggests additional protein-driven mechanisms.

Nano- and microparticles at fluid and biological interfaces

Systems with interfaces are abundant in both technological applications and biology. While a fluid interface separates two fluids, membranes separate the inside of vesicles from the outside, the interior of biological cells from the environment, and compartmentalize cells into organelles. The physical properties of interfaces are characterized by interface tension, those of membranes are characterized by bending and stretching elasticity. Amphiphilic molecules like surfactants that are added to a system with two immiscible fluids decrease the interface tension and induce a bending rigidity. Lipid bilayer membranes of vesicles can be stretched or compressed by osmotic pressure; in biological cells, also the presence of a cytoskeleton can induce membrane tension. If the thickness of the interface or the membrane is small compared with its lateral extension, both can be described using two-dimensional mathematical surfaces embedded in three-dimensional space. We review recent work on the interaction of particles with interfaces and membranes. This can be micrometer-sized particles at interfaces that stabilise emulsions or form colloidosomes, as well as typically nanometer-sized particles at membranes, such as viruses, parasites, and engineered drug delivery systems. In both cases, we first discuss the interaction of single particles with interfaces and membranes, e.g. particles in external fields, non-spherical particles, and particles at curved interfaces, followed by interface-mediated interaction between two particles, many-particle interactions, interface and membrane curvature-induced phenomena, and applications.

Hydrodynamic mobility of a solid particle near a spherical elastic membrane. II. Asymmetric motion

In this paper, we derive analytical expressions for the leading-order hydrodynamic mobility of a small solid particle undergoing motion tangential to a nearby large spherical capsule whose membrane possesses resistance toward shearing and bending. Together with the results obtained in the first part [Daddi-Moussa-Ider and Gekle, Phys. Rev. E 95, 013108 (2017)2470-004510.1103/PhysRevE.95.013108], where the axisymmetric motion perpendicular to the capsule membrane is considered, the solution of the general mobility problem is thus determined. We find that shearing resistance induces a low-frequency peak in the particle self-mobility, resulting from the membrane normal displacement in the same way, although less pronounced, to what has been observed for the axisymmetric motion. In the zero-frequency limit, the self-mobility correction near a hard sphere is recovered only if the membrane has a nonvanishing resistance toward shearing. We further compute the in-plane mean-square displacement of a nearby diffusing particle, finding that the membrane induces a long-lasting subdiffusive regime. Considering capsule motion, we find that the correction to the pair-mobility function is solely determined by membrane shearing properties. Our analytical calculations are compared and validated with fully resolved boundary integral simulations where a very good agreement is obtained.

Hydrodynamic mobility of a solid particle near a spherical elastic membrane: Axisymmetric motion

We use the image solution technique to compute the leading order frequency-dependent self-mobility function of a small solid particle moving perpendicular to the surface of a spherical capsule whose membrane possesses shearing and bending rigidities. Comparing our results with those obtained earlier for an infinitely extended planar elastic membrane, we find that membrane curvature leads to the appearance of a prominent additional peak in the mobility. This peak is attributed to the fact that the shear resistance of the curved membrane involves a contribution from surface-normal displacements, which is not the case for planar membranes. In the vanishing frequency limit, the particle self-mobility near a no-slip hard sphere is recovered only when the membrane possesses a nonvanishing resistance toward shearing. We further investigate capsule motion, finding that the pair-mobility function is solely determined by membrane shearing properties. Our analytical predictions are validated by fully resolved boundary integral simulations where a very good agreement is obtained.

Anti-erythrocyte antibodies may contribute to anaemia in Plasmodium vivax malaria by decreasing red blood cell deformability and increasing erythrophagocytosis

Background

Plasmodium vivax accounts for the majority of human malaria infections outside Africa and is being increasingly associated in fatal outcomes with anaemia as one of the major complications. One of the causes of malarial anaemia is the augmented removal of circulating non-infected red blood cells (nRBCs), an issue not yet fully understood. High levels of auto-antibodies against RBCs have been associated with severe anaemia and reduced survival of nRBCs in patients with falciparum malaria. Since there are no substantial data about the role of those antibodies in vivax malaria, this study was designed to determine whether or not auto-antibodies against erythrocytes are involved in nRBC clearance. Moreover, the possible immune mechanisms elicited by them that may be associated to induce anaemia in P. vivax infection was investigated.

Methods

Concentrations of total IgG were determined by sandwich ELISA in sera from clinically well-defined groups of P. vivax-infected patients with or without anaemia and in healthy controls never exposed to malaria, whereas the levels of specific IgG to nRBCs were determined by cell-ELISA. Erythrophagocytosis assay was used to investigate the ability of IgGs purified from each studied pooled sera in enhancing nRBC in vitro clearance by THP-1 macrophages. Defocusing microscopy was employed to measure the biomechanical modifications of individual nRBCs opsonized by IgGs purified from each group.

Results

Anaemic patients had higher levels of total and specific anti-RBC antibodies in comparison to the non-anaemic ones. Opsonization with purified IgG from anaemic patients significantly enhanced RBCs in vitro phagocytosis by THP-1 macrophages. Auto-antibodies purified from anaemic patients decreased the nRBC dynamic membrane fluctuations suggesting a possible participation of such antibodies in the perturbation of erythrocyte flexibility and morphology integrity maintenance.

Conclusions

These findings revealed that vivax-infected patients with anaemia have increased levels of IgG auto-antibodies against nRBCs and that their deposition on the surface of non-infected erythrocytes decreases their deformability, which, in turn, may enhance nRBC clearance by phagocytes, contributing to the anaemic outcome. These data provide insights into the immune mechanisms associated with vivax malaria anaemia and may be important to the development of new therapy and vaccine strategies.

Shape of red blood cells in contact with artificial surfaces

The phenomenon of physical contact between red blood cells and artificial surfaces is considered. A fully three-dimensional mathematical model of a bilayer membrane in contact with an artificial surface is presented. Numerical results for the different geometries and adhesion intensities are found to be in agreement with experimentally observed geometries obtained by means of digital holographic microscopy.

Thermal fluctuations of vesicles and nonlinear curvature elasticity--implications for size-dependent renormalized bending rigidity and vesicle size distribution

Both closed and open biological membranes noticeably undulate at physiological temperatures. These thermal fluctuations influence a broad range of biophysical phenomena, ranging from self-assembly to adhesion. In particular, the experimentally measured thermal fluctuation spectra also provide a facile route to the assessment of mechanical and certain other physical properties of biological membranes. The theoretical assessment of thermal fluctuations, be it for closed vesicles or the simpler case of flat open lipid bilayers, is predicated upon assuming that the elastic curvature energy is a quadratic functional of the curvature tensor. However, a qualitatively correct description of several phenomena such as binding-unbinding transition, vesicle-to-bicelle transition, appearance of hats and saddles among others, appears to require consideration of constitutively nonlinear elasticity that includes fourth order curvature contributions rather than just quadratic. In particular, such nonlinear considerations are relevant in the context of large-curvature or small-sized vesicles. In this work we discuss the statistical mechanics of closed membranes (vesicles) incorporating both constitutive and geometrical nonlinearities. We derive results for the renormalized bending rigidity of small vesicles and show that significant stiffening may occur for sub-20 nm vesicle sizes. Our closed-form results may also be used to determine nonlinear curvature elasticity properties from either experimentally measured fluctuation spectra or microscopic calculations such as molecular dynamics. Finally, in the context of our results on thermal fluctuations of vesicles and nonlinear curvature elasticity, we reexamine the problem of determining the size distribution of vesicles and obtain results that reconcile well with experimental observations. However, our results are somewhat paradoxical. Specifically, the molecular dynamics predictions for the thermo-mechanical behavior of small vesicles of prior studies appear to be inconsistent with the nonlinear elastic properties that we estimate by fitting to the experimentally determined vesicle size-distribution trends and data.

Membrane-wrapping contributions to malaria parasite invasion of the human erythrocyte

The blood stage malaria parasite, the merozoite, has a small window of opportunity during which it must successfully target and invade a human erythrocyte. The process of invasion is nonetheless remarkably rapid. To date, mechanistic models of invasion have focused predominantly on the parasite actomyosin motor contribution to the energetics of entry. Here, we have conducted a numerical analysis using dimensions for an archetypal merozoite to predict the respective contributions of the host-parasite interactions to invasion, in particular the role of membrane wrapping. Our theoretical modeling demonstrates that erythrocyte membrane wrapping alone, as a function of merozoite adhesive and shape properties, is sufficient to entirely account for the first key step of the invasion process, that of merozoite reorientation to its apex and tight adhesive linkage between the two cells. Next, parasite-induced reorganization of the erythrocyte cytoskeleton and release of parasite-derived membrane can also account for a considerable energetic portion of actual invasion itself, through membrane wrapping. Thus, contrary to the prevailing dogma, wrapping by the erythrocyte combined with parasite-derived membrane release can markedly reduce the expected contributions of the merozoite actomyosin motor to invasion. We therefore propose that invasion is a balance between parasite and host cell contributions, evolved toward maximal efficient use of biophysical forces between the two cells.

Fluctuations of red blood cell membranes: The role of the cytoskeleton

We theoretically investigate the membrane fluctuations of red blood cells with focus laid on the role of the cytoskeleton, viewing the system as a membrane coupled to a sparse spring network. This model is exactly solvable and enables us to examine the coupling strength dependence of the membrane undulation. We find that the coupling modifies the fluctuation spectrum at wavelengths longer than the mesh size of the network, while leaving the fluid-like behavior of the membrane intact at shorter wavelengths. The fluctuation spectra can be markedly different, depending on not only the relative amplitude of the bilayer bending energy with respect to the cytoskeleton deformation energy but also the bilayer-cytoskelton coupling strength.

Inability to maintain GSH pool in G6PD-deficient red cells causes futile AMPK activation and irreversible metabolic disturbance

AIMS

Glucose 6-phosphate dehydrogenase (G6PD) is essential for maintenance of nicotinamide dinucleotide hydrogen phosphate (NADPH) levels and redox homeostasis. A number of drugs, such as antimalarial drugs, act to induce reactive oxygen species and hemolytic crisis in G6PD-deficient patients. We used diamide (DIA) to mimic drug-induced oxidative stress and studied how these drugs affect cellular metabolism using a metabolomic approach.

RESULTS

There are a few differences in metabolome between red blood cells (RBCs) from normal and G6PD-deficient individuals. DIA causes modest changes in normal RBC metabolism. In contrast, there are significant changes in various biochemical pathways, namely glutathione (GSH) metabolism, purine metabolism, and glycolysis, in G6PD-deficient cells. GSH depletion is concomitant with a shift in energy metabolism. Adenosine monophosphate (AMP) and adenosine diphosphate (ADP) accumulation activates AMP protein kinase (AMPK) and increases entry of glucose into glycolysis. However, inhibition of pyruvate kinase (PK) reduces the efficacy of energy production. Metabolic changes and protein oxidation occurs to a greater extent in G6PD-deficient RBCs than in normal cells, leading to severe irreversible loss of deformability of the former.

INNOVATION AND CONCLUSION

Normal and G6PD-deficient RBCs differ in their responses to oxidants. Normal cells have adequate NADPH regeneration for maintenance of GSH pool. In contrast, G6PD-deficient cells are unable to regenerate enough NADPH under a stressful situation, and switch to biosynthetic pathway for GSH supply. Rapid GSH exhaustion causes energy crisis and futile AMPK activation. Our findings suggest that drug-induced oxidative stress differentially affects metabolism and metabolite signaling in normal and G6PD-deficient cells. It also provides an insight into the pathophysiology of acute hemolytic anemia in G6PD-deficient patients.

Hydrodynamic lift of vesicles and red blood cells in flow--from Fåhræus & Lindqvist to microfluidic cell sorting

Hydrodynamic lift forces acting on cells and particles in fluid flow receive ongoing attention from medicine, mathematics, physics and engineering. The early findings of Fåhræus & Lindqvist on the viscosity change of blood with the diameter of capillaries motivated extensive studies both experimentally and theoretically to illuminate the underlying physics. We review this historical development that led to the discovery of the inertial and non-inertial lift forces and elucidate the origins of these forces that are still not entirely clear. Exploiting microfluidic techniques induced a tremendous amount of new insights especially into the more complex interactions between the flow field and deformable objects like vesicles or red blood cells. We trace the way from the investigation of single cell dynamics to the recent developments of microfluidic techniques for particle and cell sorting using hydrodynamic forces. Such continuous and label-free on-chip cell sorting devices promise to revolutionize medical analyses for personalized point-of-care diagnosis. We present the state-of-the-art of different hydrodynamic lift-based techniques and discuss their advantages and limitations.

Physics of cell adhesion: some lessons from cell-mimetic systems

Cell adhesion is a paradigm of the ubiquitous interplay of cell signalling, modulation of material properties and biological functions of cells. It is controlled by competition of short range attractive forces, medium range repellant forces and the elastic stresses associated with local and global deformation of the composite cell envelopes. We review the basic physical rules governing the physics of cell adhesion learned by studying cell-mimetic systems and demonstrate the importance of these rules in the context of cellular systems. We review how adhesion induced micro-domains couple to the intracellular actin and microtubule networks allowing cells to generate strong forces with a minimum of attractive cell adhesion molecules (CAMs) and to manipulate other cells through filopodia over micrometer distances. The adhesion strength can be adapted to external force fluctuations within seconds by varying the density of attractive and repellant CAMs through exocytosis and endocytosis or protease-mediated dismantling of the CAM-cytoskeleton link. Adhesion domains form local end global biochemical reaction centres enabling the control of enzymes. Actin-microtubule crosstalk at adhesion foci facilitates the mechanical stabilization of polarized cell shapes. Axon growth in tissue is guided by attractive and repulsive clues controlled by antagonistic signalling pathways.

Lipid bilayer and cytoskeletal interactions in a red blood cell

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

Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering

Red blood cells (RBCs) present unique reversible shape deformability, essential for both function and survival, resulting notably in cell membrane fluctuations (CMF). These CMF have been subject of many studies in order to obtain a better understanding of these remarkable biomechanical membrane properties altered in some pathological states including blood diseases. In particular the discussion over the thermal or metabolic origin of the CMF has led in the past to a large number of investigations and modeling. However, the origin of the CMF is still debated. In this article, we present an analysis of the CMF of RBCs by combining digital holographic microscopy (DHM) with an orthogonal subspace decomposition of the imaging data. These subspace components can be reliably identified and quantified as the eigenmode basis of CMF that minimizes the deformation energy of the RBC structure. By fitting the observed fluctuation modes with a theoretical dynamic model, we find that the CMF are mainly governed by the bending elasticity of the membrane and that shear and tension elasticities have only a marginal influence on the membrane fluctations of the discocyte RBC. Further, our experiments show that the role of ATP as a driving force of CMF is questionable. ATP, however, seems to be required to maintain the unique biomechanical properties of the RBC membrane that lead to thermally excited CMF.

Artificial Spectrin Shells Reconstituted on Giant Vesicles

In the experimental approach to a synthetic minimal cell, the membrane compartment is a main component. Lipid vesicles represent the natural host for the artificial reconstruction of a cytomimetic membrane skeleton able to support mechanical function. Using the membrane component of human erythroid cells, we have reconstructed a membrane shell composed of a spectrin skeleton and fed by ATP. The structural and mechanical analysis reveals this spectrin skeleton as topological network supporting mechanical rigidity. Such an artificial shell would define a membrane compartment mechanically stable under physiological conditions.

Effect of hydroperoxides on red blood cell membrane mechanical properties

We investigate the effect of oxidative stress on red blood cell membrane mechanical properties in vitro using detailed analysis of the membrane thermal fluctuation spectrum. Two different oxidants, the cytosol-soluble hydrogen peroxide and the membrane-soluble cumene hydroperoxide, are used, and their effects on the membrane bending elastic modulus, surface tension, strength of confinement due to the membrane skeleton, and 2D shear elastic modulus are measured. We find that both oxidants alter significantly the membrane elastic properties, but their effects differ qualitatively and quantitatively. While hydrogen peroxide mainly affects the elasticity of the membrane protein skeleton (increasing the membrane shear modulus), cumene hydroperoxide has an impact on both membrane skeleton and lipid bilayer mechanical properties, as can be seen from the increased values of the shear and bending elastic moduli. The biologically important implication of these results is that the effects of oxidative stress on the biophysical properties, and hence the physiological functions, of the cell membrane depend on the nature of the oxidative agent. Thermal fluctuation spectroscopy provides a means of characterizing these different effects, potentially in a clinical milieu.

On the mechanical stabilization of filopodia

We studied force-induced elongation of filopodia by coupling magnetic tweezers to the tip through the bacterial coat protein invasin, which couples the force generator to the actin bundles (through myosin X), thus impeding the growth of the actin plus end. Single force pulses (15-30 s) with amplitudes between 20 and 600 pN and staircase-like force scenarios (amplitudes, ∼50 pN; step widths, 30 s) were applied. In both cases, the responses consist of a fast viscoelastic deflection followed by a linear flow regime. The deflections are reversible after switching off the forces, suggesting a mechanical memory. The elongation velocity exhibits an exponential distribution (half-width <v(1/2)>, ∼0.02 μm s(-1)) and did not increase systematically with the force amplitudes. We estimate the bending modulus (0.4 × 10(-23) J m) and the number of actin filaments (∼10) by analyzing filopodium bending fluctuations. Sequestering of intracellular Ca(2+) by BAPTA caused a strong reduction in the amplitude of elongation, whereas latrunculin A resulted in loss of the elastic response. We attribute the force-independent velocity to the elongation of actin bundles enabled by the force-induced actin membrane uncoupling and the reversibility by the treadmilling mechanism and an elastic response.

Curling and local shape changes of red blood cell membranes driven by cytoskeletal reorganization

Human red blood cells (RBCs) lack the actin-myosin-microtubule cytoskeleton that is responsible for shape changes in other cells. Nevertheless, they can display highly dynamic local deformations in response to external perturbations, such as those that occur during the process of apical alignment preceding merozoite invasion in malaria. Moreover, after lysis in divalent cation-free media, the isolated membranes of ruptured ghosts show spontaneous inside-out curling motions at the free edges of the lytic hole, leading to inside-out vesiculation. The molecular mechanisms that drive these rapid shape changes are unknown. Here, we propose a molecular model in which the spectrin filaments of the RBC cortical cytoskeleton control the sign and dynamics of membrane curvature depending on whether the ends of the filaments are free or anchored to the bilayer. Computer simulations of the model reveal that curling, as experimentally observed, can be obtained either by an overall excess of weakly-bound filaments throughout the cell, or by the flux of such filaments toward the curling edges. Divalent cations have been shown to arrest the curling process, and Ca2+ ions have also been implicated in local membrane deformations during merozoite invasion. These effects can be replicated in our model by attributing the divalent cation effects to increased filament-membrane binding. This process converts the curl-inducing loose filaments into fully bound filaments that arrest curling. The same basic mechanism can be shown to account for Ca2+-induced local and dynamic membrane deformations in intact RBCs. The implications of these results in terms of RBC membrane dynamics under physiological, pathological, and experimental conditions is discussed.

One-particle-thick, solvent-free, coarse-grained model for biological and biomimetic fluid membranes

Biological membranes are involved in numerous intriguing biophysical and biological cellular phenomena of different length scales, ranging from nanoscale raft formation, vesiculation, to microscale shape transformations. With extended length and time scales as compared to atomistic simulations, solvent-free coarse-grained membrane models have been exploited in mesoscopic membrane simulations. In this study, we present a one-particle-thick fluid membrane model, where each particle represents a cluster of lipid molecules. The model features an anisotropic interparticle pair potential with the interaction strength weighed by the relative particle orientations. With the anisotropic pair potential, particles can robustly self-assemble into fluid membranes with experimentally relevant bending rigidity. Despite its simple mathematical form, the model is highly tunable. Three potential parameters separately and effectively control diffusivity, bending rigidity, and spontaneous curvature of the model membrane. As demonstrated by selected examples, our model can naturally simulate dynamics of phase separation in multicomponent membranes and the topological change of fluid vesicles.

Metabolic remodeling of the human red blood cell membrane

The remarkable deformability of the human red blood cell (RBC) results from the coupled dynamic response of the phospholipid bilayer and the spectrin molecular network. Here we present quantitative connections between spectrin morphology and membrane fluctuations of human RBCs by using dynamic full-field laser interferometry techniques. We present conclusive evidence that the presence of adenosine 5'-triphosphate (ATP) facilitates non-equilibrium dynamic fluctuations in the RBC membrane that are highly correlated with the biconcave shape of RBCs. Spatial analysis of the fluctuations reveals that these non-equilibrium membrane vibrations are enhanced at the scale of spectrin mesh size. Our results indicate that the dynamic remodeling of the coupled membranes powered by ATP results in non-equilibrium membrane fluctuations manifesting from both metabolic and thermal energies and also maintains the biconcave shape of RBCs.

ATP-dependent mechanics of red blood cells

Red blood cells are amazingly deformable structures able to recover their initial shape even after large deformations as when passing through tight blood capillaries. The reason for this exceptional property is found in the composition of the membrane and the membrane-cytoskeleton interaction. We investigate the mechanics and the dynamics of RBCs by a unique noninvasive technique, using weak optical tweezers to measure membrane fluctuation amplitudes with mus temporal and sub nm spatial resolution. This enhanced edge detection method allows to span over >4 orders of magnitude in frequency. Hence, we can simultaneously measure red blood cell membrane mechanical properties such as bending modulus kappa = 2.8 +/- 0.3 x 10(-19)J = 67.6 +/- 7.2 k(B)T, tension sigma = 6.5 +/- 2.1 x 10(-7)N/m, and an effective viscosity eta(eff) = 81 +/- 3.7 x 10(-3) Pa s that suggests unknown dissipative processes. We furthermore show that cell mechanics highly depends on the membrane-spectrin interaction mediated by the phosphorylation of the interconnection protein 4.1R. Inhibition and activation of this phosphorylation significantly affects tension and effective viscosity. Our results show that on short time scales (slower than 100 ms) the membrane fluctuates as in thermodynamic equilibrium. At time scales longer than 100 ms, the equilibrium description breaks down and fluctuation amplitudes are higher by 40% than predicted by the membrane equilibrium theory. Possible explanations for this discrepancy are influences of the spectrin that is not included in the membrane theory or nonequilibrium fluctuations that can be accounted for by defining a nonthermal effective energy of up to E(eff) = 1.4 +/- 0.1 k(B)T, that corresponds to an actively increased effective temperature.

Physical model for the width distribution of axons

The distribution of widths of axons was recently investigated, and was found to have a distinct peak at an optimized value. The optimized axon width at the peak may arise from the conflicting demands of minimizing energy consumption and assuring signal transmission reliability. The distribution around this optimized value is found to have a distinct non-Gaussian shape, with an exponential "tail". We propose here a mechanical model whereby this distribution arises from the interplay between the elastic energy of the membrane surrounding the axon core, the osmotic pressure induced by the neurofilaments inside the axon bulk, and active processes that remodel the microtubules and neurofilaments inside the axon. The axon's radius of curvature can be determined by the cell's control of the osmotic pressure difference across the membrane, the membrane tension or by changing the composition of the different components of the membrane. We find that the osmotic pressure, determined by the neurofilaments, seems to be the dominant control parameter.

Diffusion in a fluid membrane with a flexible cortical cytoskeleton

We calculate the influence of a flexible network of long-chain proteins, which is anchored to a fluid membrane, on protein diffusion in this membrane. This is a model for the cortical cytoskeleton and the lipid bilayer of the red blood cell, which we apply to predict the influence of the cytoskeleton on the diffusion coefficient of a mobile band 3 protein. Using the pressure field that the cytoskeleton exerts on the membrane, from the steric repulsion between the diffusing protein and the cytoskeletal filaments, we define a potential landscape for the diffusion within the bilayer. We study the changes to the diffusion coefficient on removal of one type of anchor proteins, e.g., in several hemolytic anemias, as well as for isotropic and anisotropic stretching of the cytoskeleton. We predict an overall increase of the diffusion for a smaller number of anchor proteins and increased diffusion for anisotropic stretching in the direction of the stretch, because of the decrease in the spatial frequency as well as in the height of the potential barriers.

Polarizability of shelled particles of arbitrary shape in lossy media with an application to hematic cells

We show that within the dipole approximation the complex polarizability of shelled particles of arbitrary shape can be written as the volume of the particle times a weighted average of the electric field in the particle, with weights determined by the differences in permittivities between the shells and the external, possibly lossy media. To calculate the electric field we use an adaptive-mesh finite-element method which is very effective in handling the irregular domains, material inhomogeneities, and complex boundary conditions usually found in biophysical applications. After extensive tests with exactly solvable models, we apply the method to four types of hematic cells: platelets, T-lymphocytes, erythrocytes, and stomatocytes. Realistic shapes of erythrocytes and stomatocytes are generated by a parametrization in terms of Jacobi elliptic functions. Our results show, for example, that if the average polarizability is the main concern, a confocal ellipsoid may be used as a model for a normal erythrocyte, but not for a stomatocyte. A comparison with experimental electrorotation data shows quantitatively the effect of an accurate geometry in the derivation of electrical cell parameters from fittings of theoretical models to the experimental data.

Membrane fluctuations near a plane rigid surface

We use analytical calculations and Monte Carlo simulations to determine the thermal fluctuation spectrum of a membrane patch of a few tens of nanometer in size, whose corners are located at a fixed distance d above a plane rigid surface. Our analysis shows that the surface influence on the bilayer fluctuations can be effectively described in terms of a uniform confining potential that grows quadratically with the height of the membrane h relative to the surface: V=(1/2)gammah2. The strength gamma of the harmonic confining potential vanishes when the corners of the membrane patch are placed directly on the surface (d=0), and achieves its maximum value when d is of the order of a few nanometers. However, even at maximum strength, the confinement effect is quite small and has a noticeable impact only on the amplitude of the largest bending mode.