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 special apparatus inside an NMR spectrometer. However, direct mathematical predictions of the shapes of the morphed cells have not been reported before. We used recently available functions in Mathematica to triangularize and then compute four types of curvature. The RBCs were described by a previously presented quartic equation in three dimensional (3D) Cartesian space. A key finding was the extent to which the maximum and minimum Principal Curvatures were localized symmetrically in patches at the poles or equators and distributed in rings around the main axis of the strained RBC. The simulations, on the nano-metre 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 that persist for many hours. This view is consistent with a recent proposal for non-uniform distribution of Piezo1 molecules around the RBC membrane. On the other hand, if the curvature that gates Piezo1 is at a much finer length scale, then membrane tension will determine local curvature and micron scale curvature as described here will be less likely to influence Piezo1 activity.
The geometrical reorganization of the simulated cytoskeleton helps understanding of the concerted metabolic and cation-flux responses of the RBC to mechanically imposed shape changes.