Fig 1.
Two-step multiscale framework for RBC modeling.
The experimental information about the structural defects of the lipid bilayler, the cytoskeleton and their coupling via the transmembrane proteins is collected and considered as input to two-component composite CGMD model. The CGMD is then employed on a small RBC patch to compute the shear modulus (μ0), bending stiffness (kc), and network parameters (kbs), which are subsequently used as input to a whole-cell DPD model to predict the RBC shape and corresponding stress field. ‡ A schematic diagram of nanoscale knob on the membrane surface of a Pf-RBC.
Fig 2.
Schematic representation of the two-component composite CGMD model (A & C) and whole-cell DPD model (B & D) of H-RBCs and Pf-RBCs.
For the composite CGMD model, the red, blue, and grey particles represent clusters of lipid molecules, actin junctions, and actin filaments of cytoskeleton, respectively; the black and yellow particles signify band-3 complexes, of which one third (yellow ones) are connected to the spectrin network; the green patches represent the rigid knobs in the Pf-RBC membrane; the purple particles refer to the spectrin octamers. For the whole-cell DPD model, the lipid bilayer and cytoskeleton are rendered in red and grey triangular networks, respectively. Only half of the triangular network of the lipid bilayer is shown for clarity. The rigid knobs in lipid bilayer of the Pf-RBC is rendered in green, while the enhanced spectrin network of T-RBC and deficient spectrin network of S-RBC are highlighted in purple bonds and visible holes in the triangular network of the cytoskeleton. The knob density in the whole-cell DPD model is set to be lower than that in the composite CGMD model due to different levels of coarse-graining applied to these two-component models. In the whole-cell DPD model, the average size of a knob (Aknob,DPD) is around 0.04 μm2 and 0.036 μm2 for T-RBC and S-RBC, respectively, which is around 2–5 times bigger than that (Aknob,CGMD) used in the composite CGMD model. Thus, ρknob,DPD ≈ (0.2–0.5)ρknob,CGMD.
Fig 3.
Biomechanical properties obtained from two-component composite CGMD model.
(A) Shear response of the healthy and diseased RBC membranes. (B)-(D) show the vertical displacement fluctuation spectra of healthy and diseased RBC membranes as a function of wave number q. (E) Measured bilayer-cytoskeleton interaction force at different end-to-end distance between two actin junctions, dee, for healthy and defective RBCs.
Table 1.
Shear moduli of RBCs at different pathological conditions.
Fig 4.
Shape deformation and corresponding stress field of H-RBCs, T-RBCs and S-RBCs.
(A) The axial (DA) and transverse (DT) diameters of H-RBC, T-RBC, and S-RBC at stretching force Fs = 110 pN. For comparison, the stretching responses in experiments from Ref. [2] and one-component whole-cell model from Ref. [24] are shown. (B) Functional dependence of EI values of T-RBCs and S-RBCs on knob density at stretching force Fs = 110 pN. (C) Corresponding stress contours of stretched H-RBC, T-RBC (ρknob,DPD≈ 7 knobs/μm2), and S-RBC (ρknob,DPD≈ 12 knobs/μm2).
Fig 5.
Stretching responses of RBCs at stretching force Fs = 140 pN as a function of (A) tangential friction coefficient, fbs, and (B) elastic interaction coefficient, kbs.
In this figure, fbs is ranged from 0.00194 to 0.194 pN⋅μm−1s−1, and kbs from 0.46 to 46 pN/μm.
Fig 6.
(A) Stretching response and (B-C) corresponding stress field of H-RBCs and defective RBCs under different stretching force.
The black squares show experimental results from Ref. [2]. The stress contours of (B) H-RBCs and (C) defective RBCs at stretching force Fs = 0, 80, and 160 pN are shown.
Fig 7.
Variation of axial (DA) and transverse (DT) diameters of (A) H-RBCs and (B) defective RBCs at stretching force Fs = 110 pN under stretching-relaxation cycles.
Snapshots of RBC shape at time t = 0, 0.18, 0.46, 0.78, and 2.30 s are shown.