Shaping membrane vesicles by tuning the activity of confined active polymer chains

Semi-flexible polymers, such as actin filaments, can deform the shape of membrane when confined in a membrane vesicle, playing an important role in biological processes. Here, we use dynamic Monte Carlo simulations to study an active polymer chain confined in a membrane vesicle. For flexible polymer chains, the membrane shape is governed by the competition between membrane bending rigidity and polymer activity. Stiff membrane is unaffected by small active forces, but moderate forces cause the polymer to alternate between stretched and disordered configurations, increasing the asphericity of both the polymer and the vesicle. For semi-flexible polymer chains, their stiffness can significantly impact both the vesicle and polymer shapes. We identify distinct classes of configurations that emerge as a function of polymer stiffness, membrane bending rigidity, and polymer activity. A weak polymer activity can cause the polymer to align along its contour, effectively increasing its stiffness. However, a moderate polymer activity softens the polymer chain. For membranes with low bending rigidities κ, large-scale deformations, such as wormlike or tadpole-shaped vesicles, appear at a weak polymer activity and high polymer stiffness. In the wormlike configuration, the polymer chain adopts a hairpin configuration to minimize the polymer bending energy. As the polymer stiffness increases, a tadpole-like vesicle forms, with part of the polymer deforming the membrane into a protrusion while the rest remaining confined in a bud-like structure. For stiffer membranes, we observe oblate vesicles containing toroidal polymer chains, resulting from the high cost of membrane bending energy. A moderate polymer activity causes the softening of the polymer chain, leading to a nearly spherical vesicle with slight shape fluctuation. We further characterize the order parameter of toroidal polymer chains in oblate vesicles and reveal that a slight increase in polymer activity leads to a more ordered helical structure of polymer chains.