Curvature instability of an active gel growing on a wavy membrane

Kristiana Mihali; Dennis Wörthmüller; Pierre Sens

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arXiv · 2510.17701

Curvature instability of an active gel growing on a wavy membrane

Kristiana Mihali·Dennis Wörthmüller·Pierre Sens

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Abstract

Cell shape changes are largely controlled by the actin cytoskeleton, a dynamic filament network beneath the plasma membrane. Several cell types can form extended free-standing protrusions not supported by an extracellular substrate or matrix, and regulated by proteins that modulate cytoskeletal dynamics in a way sensitive to the curvature of the cell membrane. We develop a theoretical model for the mechanics of a free-standing viscous actin network growing on a corrugated membrane. The model couples the dynamics of the viscous active gel with membrane deformation and the recruitment of curvature-sensitive actin nucleators. We show that an actin layer polymerising uniformly on the membrane always exerts a stabilising effect that reduces membrane deformation. However, curvature-sensitive actin nucleator proteins can render the membrane linearly unstable, depending on the interplay between membrane and actin dynamics, giving rise to spontaneous membrane deformation which could initiate extended free-standing cellular protrusion.

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Kristiana Mihali, Dennis Wörthmüller, Pierre Sens. 2025-10-20. Curvature instability of an active gel growing on a wavy membrane. https://arxiv.org/abs/2510.17701

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