Fig 1.
Schematic of membrane-myosin interactions in RBC.
Interaction of the membrane and skeleton controls the shape of the RBC. (A) Schematic depiction of the biconcave disk shape of an RBC plasma membrane and the membrane skeleton underneath. The effect of NMIIA filaments (shown in green) is modeled by local forces applied to the plasma membrane (red and gray arrows). (B) Two distinct regions are identified in a biconcave RBC—the dimple and the rim regions. In the dimple region (blue cylinder), each RZ cross-section of the shape has a negative curvature along its arclength. In contrast, at the rim, the curvature of each RZ section is positive along the arclength. (C) The geometry of a simulated RBC in axisymmetric coordinates and the three characteristic length scales that represent the biconcave shape of the RBC. 2hmin is the minimum height at the dimple, 2hmax is the maximum height at the rim, and 2L denotes the cell’s maximum diameter. The dotted red curve shows the computational domain for our mechanical model. n is the unit normal vector to the membrane surface and as is the unit tangent vector in the direction of arclength.
Fig 2.
(A) Dimensions of healthy human RBC from the literature [73,75,78,81–83]. (B) Comparison between the proposed parametric models describing the biconcave morphology of an RBC. There is a close match between the four models for the fixed minimum height of the dimple, maximum height of the rim, and the maximum diameter (C) Discretization scheme of the parametric shape of an RBC (Eq 6) (dotted blue line) and the simulated geometry obtained from our mechanical model (Eqs 4 and 5) (solid red line). Each experimental and simulated shape is discretized into N nodes where i indicates the node index. These nodes are used to compute the total error in the simulated RBC geometry (Eq 8).
Fig 3.
Mismatch between the parametric shape of an experimentally observed RBC (Eq 6) and the shapes obtained from simulations (Eqs. S10 in S1 Text) with a uniform distribution of the pulling force density across the membrane surface. (A) RZ view of the center of an RBC from a confocal Z-stack of an RBC stained for the membrane marker glycophorin A. (B) Schematic of a biconcave RBC with a uniform distribution of the normal pulling force density (red arrows). Funiform represents the magnitude of the pulling force density. (C) Calculated error in the characteristic length scales (Eq 7), and total shape error (Eq 8) for different values of the force density. The total shape error (ϵtotal) calculated by Eq 8 is minimum for Funiform = 1.83 pN/μm2, when there is only a mismatch in the maximum height of the RBC morphology (center bar). For all three values of the applied uniform force densities, the calculated volume (V) is shown on the X-axis and is significantly different from the reported experimental data.
Fig 4.
Local force density at the RBC dimple.
A local distribution of the pulling force density at the RBC dimple results in a better agreement between the parametric shape of an RBC (Eq 6) and the shape obtained from the simulation. (A) RZ view of the center of an RBC from a confocal Z-stack of an RBC stained for the membrane marker glycophorin A. (B, upper) A schematic depicting a biconcave RBC with a local force at the dimple area (red arrows) and no force in the rim region. Fdimple represents the magnitude of the pulling force density in the dimple region. (B, lower) The applied force density at the dimple as a function of the arclength (Eq. S24 in S1 Text). (C) The simulated shape of the RBC with a local pulling force density in the dimple (solid green line) in comparison with the RBC parametric shape (dotted blue line). (C) The nonmonotonic behavior of the total error when increasing the dimple force density (Fdimple). Three different regimes can be identified based on the shape of the simulated RBC; (i) the spherical shapes where hmax = hmin for the low Fdimple (yellow area), (ii) the biconcave shapes where the dimple forms (hmax > hmin) for the mid-range of Fdimple (purple area), and (iii) the kissing shapes where hmin → 0 for large Fdimple (gray area). The shape error has the lowest value at Fdimple = 3.73 pN/μm2 (ϵtotal ~ 5.62%) when the minimum height of the dimple in the simulated geometry matches closely with the minimum height of the parametric shape. The volume of the simulated RBC at Fdimple = 3.73 pN/μm2 is about 76.78 μm3.
Fig 5.
Heterogeneous forces in the RBC dimple and rim.
The applied force densities at the RBC dimple and rim regions regulate the shape error. (A, upper) Schematic of a biconcave RBC with a large force density (red arrows) at the dimple and a small force density (gray arrows) at the rim region. Schematic is overlaid on an RZ view of the center of an RBC from a confocal Z-stack of an RBC stained for the membrane marker glycophorin A. (A, lower) The applied force density along the membrane as a function of the arclength (Eq. S24 in S1 Text). (B) Heat map shows the calculated shape error (Eq 8) for a range of the force densities at the dimple (Fdimple) and rim (Frim) regions. We stopped the simulations when the height at the dimple tends to zero (hmin→ 0). The marked point X shows the case that has the lowest value of the error in the heat map at Fdimple = 4.05 pN/μm2 and Frim = 0.28 pN/μm2 (ϵtotal ~ 4.1%) with V = 85.61 μm3. A comparison between the parametric shape of an RBC (dotted blue line) and the shape obtained from the simulation at point X (dashed red line) is shown in the lower panel. (C) The shape error as a function of force density at the dimple (Fdimple) for five different values of the applied force density at the rim region. The dotted purple line shows a discontinuous transition in the shape error with increasing the dimple force density for Frim = 2 pN/μm2. Similar to Fig 4B, independent of the value of Frim, the total error is a nonmonotonic function of the dimple force density (Fdimple).
Fig 6.
Experimental measurement of NMII puncta.
The RBC dimple has a higher average NMIIA puncta density than the RBC rim. (A) Maximum intensity projections of super-resolution Airyscan confocal Z stacks of individual human RBCs immunostained with an antibody to NMIIA motor domain (grey scale, top row), together with merged images (second row) of NMIIA (green) and rhodamine phalloidin for F-actin (red). (B) Schematic illustrating volume segmentation of RBCs and NMIIA puncta distribution. Optical section of a super-resolution Airyscan confocal Z-stack of human RBC immunostained with an antibody to the motor domain of NMIIA (green) and rhodamine-phalloidin for F-actin (orange). The top left image shows a perspective view of the optical section. Top right and bottom left images show YZ and XZ slices, respectively, of the RBC from planes perpendicular to this optical section. The bottom right image shows an XY view of the optical section. The blue cylinder represents the region identified as the dimple region. The rest of the RBC is identified as the rim region. Note, the myosin puncta near the RBC membrane are difficult to visualize in these merged images due to the bright F-actin staining. (C) The percent of total RBC volume occupied by the dimple region. Mean ± S.D. = 7.37 ± 1.79. (D) The percent of total NMIIA puncta in the dimple region. Mean ± S.D. = 9.11 ± 3.30. (E) The RBC dimple region has a ~25% higher density of NMIIA puncta than whole RBCs (Total) (p = 0.0051) or the rim region (p = 0.0023) by Tukey’s multiple comparisons test. Mean ± S.D.: Total = 1.73 ± 0.562; Dimple = 2.15 ± 0.888; Rim = 1.70 ± 0.556. (F) Ratio of dimple and rim region NMIIA puncta densities for each RBC. Mean ± S.D. = 1.29 ± 0.452. (C-F) n = 55 RBCs from 3 individual donors.
Fig 7.
The role of effective tension.
Effective membrane tension is a key parameter in regulating the RBC biconcave shape in addition to applied forces in the dimple and rim regions. (A-C) Heat maps show the total error in the shape of the simulated RBCs for (A) low tension (tension = 10−4 pN/nm), (B) intermediate tension (tension = 10−3 pN/nm), and (C) high tension (tension = 10−2 pN/nm). In each heat map, the point with the minimum error is marked with X. Also, for each marked point, the volume of the simulated RBC (V) is calculated using Eq. S13b in S1 Text, and the shape (solid yellow line) is shown in comparison with the reference parametric shape (dotted blue line). At intermediate tension, the shape error has the lowest value when Fratio = 1.27 consistent with our experimental results in Fig 6. (D-F) The calculated shape error (Eq 8) as a function of the dimple force density (Fdimple) for different values of the force density at the rim region and the membrane tension.
Fig 8.
The role of tension and angle of applied forces.
Effective membrane tension and the angle of applied forces in the RBC dimple and rim regions work together to maintain the biconcave shape of an RBC. (A) Schematic of a biconcave RBC with a non-uniform distribution of force density across the dimple and rim regions. In both regions, the forces per unit area are applied with angle ϕ with respect to the tangent vector (as). (B-D) The shape error and the RBC shapes obtained from simulation for different angles of the applied forces (ϕ) for (B) tensionless membrane, (C) low tension (tension = 10−4 pN/nm), and (D) intermediate tension (tension = 10−3 pN/nm). For all values of the membrane tension, as the angle of forces deviates from normal (ϕ = 900) to tangential orientation (ϕ = 0), the simulated shapes flatten and the shape error increases.