  In living cells, membrane morphology is regulated by various proteins. Many
membrane reshaping proteins contain a Bin/Amphiphysin/Rvs (BAR) domain, which
consists of a banana-shaped rod. The BAR domain bends the biomembrane along the
rod axis and the features of this anisotropic bending have recently been
studied. Here, we report on the role of the BAR protein rods in inducing
membrane tubulation, using large-scale coarse-grained simulations. We reveal
that a small spontaneous side curvature perpendicular to the rod can
drastically alter the tubulation dynamics at high protein density, whereas no
significant difference is obtained at low density. A percolated network is
intermediately formed depending on the side curvature. This network suppresses
tubule protrusion, leading to the slow formation of fewer tubules. Thus, the
side curvature, which is generated by protein--protein and membrane--protein
interactions, plays a significant role in tubulation dynamics. We also find
that positive surface tensions and the vesicle membrane curvature can stabilize
this network structure by suppressing the tubulation.
