  We review the theoretical analyses and simulations of the interactions
between curvature-inducing proteins and biomembranes. Laterally isotropic
proteins induce spherical budding, whereas anisotropic proteins, such as
Bin/Amphiphysin/Rvs (BAR) superfamily proteins, induce tabulation. Both types
of proteins can sense the membrane curvature. We describe the theoretical
analyses of various transitions of protein binding accompanied by a change in
various properties, such as the number of buds, the radius of membrane tubes,
and the nematic order of anisotropic proteins. Moreover, we explain the
membrane-mediated interactions and protein assembly. Many types of membrane
shape transformations (spontaneous tubulation, formation of polyhedral
vesicles, polygonal tubes, periodic bumps, and network structures, etc.) have
been demonstrated by coarse-grained simulations. Furthermore, traveling waves
and Turing patterns under the coupling of reaction-diffusion dynamics and
membrane deformation are described.
