  Curvature-inducing proteins containing a Bin/Amphiphysin/Rvs domain often
have intrinsically disordered domains. Recent experiments have shown that these
disordered chains enhance curvature sensing and generation. Here, we report on
the modification of protein-membrane interactions by disordered chains using
meshless membrane simulations. The protein and bound membrane are modeled
together as a chiral crescent protein rod with two excluded-volume chains. As
the chain length increases, the repulsion between them reduces the cluster size
of the proteins. It induces spindle-shaped vesicles and a transition between
arc-shaped and circular protein assemblies in a disk-shaped vesicle. For flat
membranes, an intermediate chain length induces many tubules owing to the
repulsion between the protein assemblies, whereas longer chains promote
perpendicular elongation of tubules. Moreover, protein rods with zero rod
curvature and sufficiently long chains stabilize the spherical buds. For
proteins with a negative rod curvature, an intermediate chain length induces a
rugged membrane with branched protein assemblies, whereas longer chains induce
the formation of tubules with periodic concave-ring structures.
