Fig 1.
Conformation of a RBC membrane modeled as a closed triangulated surface. Nm = 500.
Table 1.
Different RBC models.
Fig 2.
RBC shapes and their asphericities α which characterize the deviation from a spherical shape. The asphericity is defined as , where λ1 ≤ λ2 ≤ λ3 are the eigenvalues of the gyration tensor of a RBC and
. The corresponding RBC parameters in the order of ascending asphericity (from a stomatocytic shape to a biconcave shape) are (1) M3, κ* = 20, Y* = 43680; (2) M3, κ* = 40, Y* = 43680; (3) M2, κ* = 70, Y* = 43680; (4) M3, κ* = 70, Y* = 43680; (5) M2, κ* = 20, Y* = 8000; (6) M2, κ* = 70, Y* = 8000. The asphericity values are time-averaged over the whole simulation and the standard deviations are shown as error bars.
Fig 3.
Static scattering by a RBC with fixed orientation.
The scattering intensity I = AA* of a rigid discocyte for wave vectors q (a) parallel and (b) perpendicular to the RBC axis of rotational symmetry. h0 = 2a. Analytical solutions for a cylinder (see S3 Appendix) with different radii R and heights h are also plotted for comparison.
Fig 4.
Orientationally-averaged static scattering by a RBC.
Orientationally-averaged static scattering functions of RBCs for different parameters using the DPD method with RBC model M3. (a) Effect of surface discretization (Nm = 500 and Nm = 1000) on static scattering intensity. Model M3 with κ* = 20 and Y* = 8000. (b) Effect of bending rigidity and shear modulus on the static scattering intensity. Cells with Y* = 8000 remain biconcave, whereas those with the large value of Y* = 43680 attain a stomatocytic shape in simulations.
Fig 5.
Intermediate scattering measurements.
Intermediate scattering functions for two selected q values calculated through the orientational averaging. The curves for deformable RBCs were obtained directly from MPC simulations of a diffusing RBC (model M1 with Nm = 500, κ* = 20, and Y* = 8000). The curve for a rigid cell was obtained by the substitution of all cell snapshots in time within the trajectory for a deformable RBC with a rigid biconcave shape through matching instantaneous cell’s center of mass and orientation. Time is normalized by a characteristic relaxation time τ = ηR0/Y of a RBC. For typical values of RBC elasticity (Y = 18.9 × 10−6 N/m [31]) and plasma viscosity (η = 1.2 × 10−3 Pa⋅s [45]), τ ≈ 2.1 × 10−4 s.
Fig 6.
Effective diffusion of a RBC from MPC simulations.
The dimensionless effective diffusion coefficient of a RBC as a function of q, obtained from different methods. MPC simulation results correspond to a deformable cell represented by model M1 with Nm = 500, κ* = 20, and Y* = 8000 (black line) and to a superimposed rigid cell using the simulated trajectory of the deformable RBC (red line). The curve from HYDRO++ is for a rigid cell (blue line). The data are averaged over Navg = 2000 random q-vector orientations, see S2 Appendix.
Fig 7.
Comparison of DPD and MPC results.
The dimensionless effective diffusion coefficient Deff(q)* of a soft RBC represented by model M1 with a bending rigidity κ* = 20. Two different curves for DPD simulations correspond to different numbers Navg of random orientations of q vector used for averaging. For comparison, MPC results are also shown. In DPD, the Young’s modulus of the RBC membrane is set to Y* = 43680, whereas in MPC Y* = 8000.
Fig 8.
Effective diffusion of a RBC for various membrane properties.
The dimensionless effective diffusion coefficient Deff(q)* of RBCs with different membrane properties. The cells differ in bending rigidity κ*, Young’s modulus Y*, and spontaneous curvature. Two cells remain biconcave, whereas the other two attain a cup shape, which is reflected in the third peak at qR0 ≈ 10.