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

Abstract

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.

Figure 1

(A) Schematic of the human RBC membrane. The blue sphere represents a lipid particle and the red sphere signifies an actin junctional complex. The gray sphere represents a spectrin particle and the black sphere represents a glycophorin particle. The yellow and green circles correspond to a band-3 complex connected to the spectrin network and a mobile band-3 complex, respectively. A mesoscale detailed membrane model. (B) Top view of the initial configuration. (C) Side view of the initial configuration. (D) Side view of the equilibrium configuration. “A” type particles represent actin junctional complexes; “B” type particles represent spectrin particles; “C” type particles represent glycophorin particles; “D” type particles represent a band-3 complex that are connected to the spectrin network (“immobile” band-3); “E” type particles represent band-3 complex that are not connected to the network (“mobile” band-3); and “F” type particles represent lipid particles. To see this figure in color, go online.

Figure 2

The interaction potentials employed in the membrane model. The blue curve represents the pairwise potential between lipid particles. The green curve represents the spring potential between spectrin particles. The red curve represents the spring potential between actin and spectrin particles. The black curve represents the repulsive L-J potential between the lipid and spectrin particles. To see this figure in color, go online.

Figure 3

(A) Thermally equilibrated membrane of N = 29,567 particles at a reference time, representing a membrane with dimension of ∼ 0.8 × 0.8 μm. The tiles with different colors are used to differentiate the positions of the particles at a reference time. (B) After 1 × 10⁶ time steps, the particles are mixed because of diffusion, demonstrating the fluidic behavior of the membrane model. (C) Linear time dependence of the mean square displacement (MSD) of the proposed membrane model. (D) Radial distribution function of the 2D fluid membrane embedded in three dimensions. To see this figure in color, go online.

Figure 4

Vertical displacement fluctuation spectrum of membrane model as a function of the dimensionless quantity $q\sigma /\pi$, where q is the wave number and σ is the unit length corresponding to ∼ 4.45 nm. To see this figure in color, go online.

Figure 5

(A) Thermally equilibrated fluid membrane at a temperature of k_BT/ε = 0.22. (B) Sheared thermally equilibrated membrane at engineering shear strain of 1. (C) Shear stress-strain response of the membrane at two different strain rates. The red curve represents the response of the “bare” spectrin network. The blue and green curves signify the shear stress obtained at the strain rates of 0.001σ/t_s and 0.01σ/t_s, respectively. The purple curve represents the shear stress measured from the “bare” spectrin network plus the 8μN/m attributed to viscosity. To see this figure in color, go online.

Figure 6

(A) Power spectral density (PSD) corresponding to thermal fluctuations of the membrane model. The data marked as red circles are generated from the average displacement of the particles belonging to a triangular compartment of the lipid bilayer. The data marked as blue squares are generated from a particle positioned in the middle of a spectrin filament. f_c represents the thermal fluctuation frequency of the cytoskeleton; and f_l represents the thermal fluctuation frequency of the lipid bilayer. Inset: equilibrium state of the proposed RBC membrane model. (B) PSD corresponding to thermal fluctuations of a particle positioned in the middle of a spectrin filament in the “bare” cytoskeleton. Inset: equilibrium state of “bare” cytoskeleton. To see this figure in color, go online.

Figure 7

The pressure distribution exerted by the spectrin filaments on the lipid bilayer with attraction parameters (A) n = 0; (B) n = 0.05; (C) n = 0.1; and (D) n = 0.2. d_ee is the end-to-end distance of the spectrin filaments. The blue curve represents the pressure distribution measured from the membrane model. The purple curve represents the pressure distribution obtained from the analytical estimation for a normal membrane (56). The red curve represents the pressure distribution applied on the membrane with ankyrin protein defects. The black curve represents the pressure distribution obtained analytically for a membrane with ankyrin protein defects (56). The green curve represents the pressure distribution measured from the membrane with spectrin protein defects. To see this figure in color, go online.