School of Life and Environmental Sciences, University of Sydney, Building G08, Sydney, NSW, 2006, Australia.
Victor Chang Cardiac Research Institute, Darlinghurst, Sydney, NSW, Australia.
Sci Rep. 2021 Jul 1;11(1):13712. doi: 10.1038/s41598-021-92699-7.
We present mathematical simulations of shapes of red blood cells (RBCs) and their cytoskeleton when they are subjected to linear strain. The cell surface is described by a previously reported quartic equation in three dimensional (3D) Cartesian space. Using recently available functions in Mathematica to triangularize the surfaces we computed four types of curvature of the membrane. We also mapped changes in mesh-triangle area and curvatures as the RBCs were distorted. The highly deformable red blood cell (erythrocyte; RBC) responds to mechanically imposed shape changes with enhanced glycolytic flux and cation transport. Such morphological changes are produced experimentally by suspending the cells in a gelatin gel, which is then elongated or compressed in a custom apparatus inside an NMR spectrometer. A key observation is the extent to which the maximum and minimum Principal Curvatures are localized symmetrically in patches at the poles or equators and distributed in rings around the main axis of the strained RBC. Changes on the nanometre to micro-meter scale of curvature, suggest activation of only a subset of the intrinsic mechanosensitive cation channels, Piezo1, during experiments carried out with controlled distortions, which persist for many hours. This finding is relevant to a proposal for non-uniform distribution of Piezo1 molecules around the RBC membrane. However, if the curvature that gates Piezo1 is at a very fine length scale, then membrane tension will determine local curvature; so, curvatures as computed here (in contrast to much finer surface irregularities) may not influence Piezo1 activity. Nevertheless, our analytical methods can be extended address these new mechanistic proposals. The geometrical reorganization of the simulated cytoskeleton informs ideas about the mechanism of concerted metabolic and cation-flux responses of the RBC to mechanically imposed shape changes.
我们呈现了红细胞（RBC）在受到线性应变时的形状及其细胞骨架的数学模拟。细胞表面由三维（3D）笛卡尔空间中的先前报道的四次方方程描述。使用 Mathematica 中最近可用的函数对表面进行三角化，我们计算了膜的四种类型的曲率。我们还绘制了 RBC 变形时网格三角形面积和曲率的变化。高度可变形的红细胞（erythrocyte；RBC）通过增强糖酵解通量和阳离子转运来响应机械施加的形状变化。这种形态变化是通过将细胞悬浮在明胶凝胶中并在 NMR 光谱仪内部的定制设备中对其进行拉伸或压缩来实验产生的。一个关键观察是最大和最小主曲率在极点或赤道处的斑块中以及在应变 RBC 的主轴周围的环中对称地局部化的程度。曲率在纳米到微米尺度上的变化表明，在进行受控变形的实验中，只有一部分内在机械敏感阳离子通道 Piezo1 被激活，这种情况持续了数小时。这一发现与 Piezo1 分子在 RBC 膜周围不均匀分布的提议有关。然而，如果门控 Piezo1 的曲率处于非常精细的长度尺度，则膜张力将决定局部曲率；因此，这里计算的曲率（与更精细的表面不规则性相比）可能不会影响 Piezo1 活性。尽管如此，我们的分析方法可以扩展到解决这些新的机械学提议。模拟细胞骨架的几何重组提供了关于 RBC 对机械施加的形状变化的协同代谢和阳离子通量响应的机制的想法。
