Membrane-mediated interactions induce spontaneous filament bundling

The plasma membrane and cytoskeleton of living cells are closely coupled dynamical systems. Internal cytoskeletal elements such as actin filaments and microtubules continually exert forces on the membrane, resulting in the formation of membrane protrusions. In this paper we investigate the interplay between the shape of a cell distorted by pushing and pulling forces generated by microtubules and the resulting rearrangement of the microtubule network. From analytical calculations, we find that two microtubules that deform the vesicle can both attract or repel each other, depending on their angular separations and the direction of the imposed forces. We also show how the existence of attractive interactions between multiple microtubules can be deduced analytically, and further explore general interactions through Monte Carlo simulations. Our results suggest that the commonly reported parallel structures of microtubules in both biological and artificial systems can be a natural consequence of membrane mediated interactions.