Scaling properties of centering forces

Abstract

Motivated by the centering of microtubule asters in cells, we study the general properties of three types of centering forces: bulk pulling forces, surface (cortical) pulling forces, and pushing forces. We evidence unexpected scaling laws between the net force on the aster and its position for different modes of centering, and also address how the effective centering stiffness depends on the cell size. Importantly, we find that both scaling laws and effective stiffness depend on the spatial dimensions, and thus that 1D and 2D ansatz usually considered could misguide the interpretation of experimental results. We also show how scaling laws depend on the cell shape. While some hold for any convex cell, others strongly depend on the shape. By deriving these scaling laws for any spatial dimension, we generalize these results beyond the biological perspective. This analysis provides a broad framework to understand shape sensing mechanisms.