The cell membrane is a structure in which the actomyosin cortex lines inside of a plasma membrane via the ERM protein family. The actomyosin cortex forms network structures of actomyosin filaments that control cell membrane stiffness and shape [1]. The localization and contraction of myosin in the actomyosin cortex [2] causes some ERM ruptures [3], resulting in a localized decrease in cell membrane stiffness, followed by the protrusion of the plasma membrane according to detachment of the cortex. Although the development and size of membrane protrusions are thought to be determined by mechanical balances between the plasma membrane and actomyosin cortex, including filaments and plasma membrane tension, ERM rupture, myosin localization and contraction, and intermolecular electrochemical repulsion, much is unknown for hierarchical mechanisms between protein and cellular scales.

Although there have been several mathematical models for cell dynamics including interactions between the plasma membrane and actin cytoskeleton (e.g., [4, 5]) there is no model to address the membrane protrusion including both the dynamics of protein and membrane in a cellular scale size.

We propose a mechanical model of the cell membrane including the dynamics of the actomyosin cortex and plasma membrane deformation, which is inspired by a mesoscopic cell model [6] and extended to deal with the membrane protrusion in the cellular scale. Actomyosin and ERM are modeled as line elements consisting of multiple nodes, and the plasma membrane is modeled as a mesh capsule consisting of triangular elements. Actomyosin filaments are placed as a network in the plasma membrane and connected via ERM filaments to represent the actomyosin cortex.

In a validation for a cell tensile test, the present results showed qualitatively good agreement with the corresponding experiments [7]. Also, to model the membrane protrusion, we imposed tensile loads and ERM ruptures on a part of the membrane surface. We confirmed that the tensile loads become nonlinearly smaller with increasing the ERM rupture area, where the load level is comparable to a load by actin polymerization considering an actual size of protrusion.

References

[1]    Kelkar M., et al., Curr. Opin. Cell Biol., 2020:66, 69-78.

[2]    Asante-Asamani E., et al., PLoS. One., 2022:17, e0265380.

[3]    Welf ES, et al., Dev. Cell., 2020:55, 723-736.

[4]    Strychalski W., Front. Phys., 2021:9, 775465.

[5]    Kim MC, et al., Sci Rep., 2022:12, 1231.

[6]    Lykov K., et al., PLoS Comput. Biol., 2017:13, e1005726.

[7]    Ujihara Y., Ann. Biomed. Eng., 2010:38, 1530-1538.