On the different models describing the equilibrium shape of an erythrocyte (original) (raw)
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On different models describing the equilibrium shape of erythrocyte
2015
Red blood cells (erythrocytes) fall to one of the most important families of cells in all vertebrate organisms. The study of the equilibrium shapes of this kind of cells is of particular importance for the understanding of their physical, chemical and mechanical properties. In the present work, several well-known and widely acknowledged models describing the equilibrium shapes of the red blood cells are analysed. For each of the regarded models we make a comparison between the shapes of the meridional contours predicted by it and the known experimental data. The obtained results can be used to choose a suitable model for the analytical study of the interactions between individual erythrocytes or between them and the walls of blood vessels, for the diagnosis of diseases associated with a change of the equilibrium shape of the cells or for the experimental study of the red blood cells by light scattering methods.
Formation of the three-dimensional geometry of the red blood cell membrane
ANZIAM J., 2014
Red blood cells (RBCs) are nonnucleated liquid capsules, enclosed in deformable viscoelastic membranes with complex three dimensional geometrical structures. Generally, RBC membranes are highly incompressible and resistant to areal changes. However, RBC membranes show a planar shear deformation and out of plane bending deformation. The behaviour of RBCs in blood vessels is investigated using numerical models. All the characteristics of RBC membranes should be addressed to develop a more accurate and stable model. This article presents an effective methodology to model the three dimensional geometry of the RBC membrane with the aid of commercial software COMSOL Multiphysics 4.2a and Fortran programming. Initially, a mesh is generated for a sphere using the COMSOL Multiphysics software to represent the RBC membrane. The elastic energy of the membrane is considered to determine a stable membrane shape. Then, the actual biconcave shape of the membrane is obtained based on the principle of virtual work, when the total energy is minimised. The geometry of the RBC membrane could be used with meshfree particle methods to simulate motion and deformation of RBCs in micro-capillaries.
Normal red blood cells’ shape stabilized by membrane’s in-plane ordering
Scientific Reports
Red blood cells (RBCs) are present in almost all vertebrates and their main function is to transport oxygen to the body tissues. RBCs’ shape plays a significant role in their functionality. In almost all mammals in normal conditions, RBCs adopt a disk-like (discocyte) shape, which optimizes their flow properties in vessels and capillaries. Experimentally measured values of the reduced volume (v) of stable discocyte shapes range in a relatively broad window between v ~ 0.58 and 0.8. However, these observations are not supported by existing theoretical membrane-shape models, which predict that discocytic RBC shape is stable only in a very narrow interval of v values, ranging between v ~ 0.59 and 0.65. In this study, we demonstrate that this interval is broadened if a membrane’s in-plane ordering is taken into account. We model RBC structures by using a hybrid Helfrich-Landau mesoscopic approach. We show that an extrinsic (deviatoric) curvature free energy term stabilizes the RBC disco...
General coarse-grained red blood cell models: I. Mechanics
2009
We present a rigorous procedure to derive coarse-grained red blood cell (RBC) models, which lead to accurate mechanical properties of realistic RBCs. Based on a semi-analytic theory linear and nonlinear elastic properties of the RBC membrane can be matched with those obtained in optical tweezers stretching experiments. In addition, we develop a nearly stress-free model which avoids a number of pitfalls of existing RBC models, such as non-biconcave equilibrium shape and dependence of RBC mechanical properties on the triangulation quality. The proposed RBC model is suitable for use in many existing numerical methods, such as Lattice Boltzmann, Multiparticle Collision Dynamics, Immersed Boundary, etc.
Journal of Theoretical Biology, 1976
Mathematical modeling was used to test two assumptions regarding red cell shape. The assumptions are that the elastic moduli of the red cell membrane are uniformly distributed throughout the membrane shell and that the biconcave shape results primarily from minlltion of strain energy when this uniform shell is partially deflated. This strain energy is assumed to arise from bending (involving surface area strain) and shear (involving superlicial tensile strain). The mathematical delineation demonstrated that it was impossible to produce a smooth symmetrical biconcave shape by minimizing shear energy in a partially deflated shell. It was possible to generate a symmetrical biconcave shape by minimizing bending energy; the shape was, however, thicker along the axis of symmetry than the measured red cell shape. A combination of bending and shear in the ratio of 6 to 1 produced a shape which matched the measured shape of a red cell to better than lx, a deviation of the order of the thickness of the red cell membrane. The success of the mathematical model provides very strong evidence for the uniform shell-minimum bending energy hypothesis as the primary determinant of the discoid red cell shape.
Shapes of red blood cells: Comparison of 3D confocal images with the bilayer-couple model
Cellular and Molecular Bioengineering, 2008
Cells and organelles are shaped by the chemical and physical forces that bend cell membranes. The human red blood cell (RBC) is a model system for studying how such forces determine cell morphology. It is thought that RBCs, which are typically biconcave discoids, take the shape that minimizes their membrane-bending energies, subject to the constraints of fixed area and volume. However, recently it has been hypothesized that shear elasticity arising from the membraneassociated cytoskeleton (MS) is necessary to account for shapes of real RBCs, especially ones with highly curved features such as echinocytes. In this work we tested this hypothesis by following RBC shape changes using spherical harmonic series expansions of theoretical cell surfaces and those estimated from 3D confocal microscopy images of live cells. We found (i) quantitative agreement between shapes obtained from the theoretical model including the MS and real cells, (ii) that weakening the MS, by using urea (which denatures spectrin), leads to the theoretically predicted gradual decrease in spicule number of echinocytes, (iii) that the theory predicts that the MS is essential for stabilizing the discocyte morphology against changes in lipid composition, and that without it, the shape would default to the elliptocyte (a biconcave ellipsoid), (iv) that we were able to induce RBCs to adopt the predicted elliptocyte morphology by treating healthy discocytes with urea. The latter observation is consistent with the known connection between the blood disease hereditary elliptocytosis and spectrin mutations that weaken the cell cortex. We conclude that while the discocyte, in absence of shear, is indeed a minimum energy shape, its stabilization in healthy RBCs requires the MS, and that elliptocytosis can be explained based on purely mechanical considerations.
A Multiscale Red Blood Cell Model with Accurate Mechanics, Rheology, and Dynamics
Biophysical Journal, 2010
Red blood cells (RBCs) have highly deformable viscoelastic membranes exhibiting complex rheological response and rich hydrodynamic behavior governed by special elastic and bending properties and by the external/internal fluid and membrane viscosities. We present a multiscale RBC model that is able to predict RBC mechanics, rheology, and dynamics in agreement with experiments. Based on an analytic theory, the modeled membrane properties can be uniquely related to the experimentally established RBC macroscopic properties without any adjustment of parameters. The RBC linear and nonlinear elastic deformations match those obtained in optical-tweezers experiments. The rheological properties of the membrane are compared with those obtained in optical magnetic twisting cytometry, membrane thermal fluctuations, and creep followed by cell recovery. The dynamics of RBCs in shear and Poiseuille flows is tested against experiments and theoretical predictions, and the applicability of the latter is discussed. Our findings clearly indicate that a purely elastic model for the membrane cannot accurately represent the RBC's rheological properties and its dynamics, and therefore accurate modeling of a viscoelastic membrane is necessary.
Biophysical journal, 2009
Erythrocytes (red blood cells) play an essential role in the respiratory functions of vertebrates, carrying oxygen from lungs to tissues and CO 2 from tissues to lungs. They are mechanically very soft, enabling circulation through small capillaries. The small thermally induced displacements of the membrane provide an important tool in the investigation of the mechanics of the cell membrane. However, despite numerous studies, uncertainties in the interpretation of the data, and in the values derived for the main parameters of cell mechanics, have rendered past conclusions from the fluctuation approach somewhat controversial. Here we revisit the experimental method and theoretical analysis of fluctuations, to adapt them to the case of cell contour fluctuations, which are readily observable experimentally. This enables direct measurements of membrane tension, of bending modulus, and of the viscosity of the cell cytoplasm. Of the various factors that influence the mechanical properties of the cell, we focus here on: 1), the level of oxygenation, as monitored by Raman spectrometry; 2), cell shape; and 3), the concentration of hemoglobin. The results show that, contrary to previous reports, there is no significant difference in cell tension and bending modulus between oxygenated and deoxygenated states, in line with the softness requirement for optimal circulatory flow in both states. On the other hand, tension and bending moduli of discocyte-and spherocyteshaped cells differ markedly, in both the oxygenated and deoxygenated states. The tension in spherocytes is much higher, consistent with recent theoretical models that describe the transitions between red blood cell shapes as a function of membrane tension. Cell cytoplasmic viscosity is strongly influenced by the hydration state. The implications of these results to circulatory flow dynamics in physiological and pathological conditions are discussed.
A low-dimensional model for the red blood cell
Soft Matter, 2010
The red blood cell (RBC) is an important determinant of the rheological properties of blood because of its predominant number density, special mechanical properties and dynamics. Here, we develop a new low-dimensional RBC model based on dissipative particle dynamics (DPD). The model is constructed as a closed-torus-like ring of 10 colloidal particles connected by wormlike chain springs combined with bending resistance. Each colloidal particle is represented by a single DPD particle with a repulsive core. The model is able to capture the essential mechanical properties of RBCs, and allows for economical exploration of the rheology of RBC suspensions. Specifically, we find that the linear and non-linear elastic deformations of healthy and malaria-infected cells match those obtained in optical tweezers experiments. Through simulations of some key features of blood flow in vessels, i.e., the cell-free layer (CFL), the Fahraeus effect and the Fahraeus-Lindqvist effect, we verify that the new model captures the essential shear flow properties of real blood, except for capillaries of sizes comparable to the cell diameter. Finally, we investigate the influence of a geometrical constriction in the flow on the enhancement of the downstream CFL. Our results are in agreement with recent experiments.