Mechanics of Constriction during Cell Division: A Variational Approach

Abstract

During symmetric division cells undergo large constriction deformations at a stable midcell site. Using a variational approach, we investigate the mechanical route for symmetric constriction by computing the bending energy of deformed vesicles with rotational symmetry. Forces required for constriction are explicitly computed at constant area and constant volume, and their values are found to be determined by cell size and bending modulus. For cell-sized vesicles, considering typical bending modulus of k = 10kBT, we calculate constriction forces in the range 0.1 - 1pN. The instability of symmetrical constriction is shown and quantified with a characteristic coefficient of the order of - 50kBT, thus evidencing that cells need a robust mechanism to stabilize constriction at midcell.