  Biological membranes constitute boundaries of cells and cell organelles.
Physico-chemical mechanisms at the atomic scale are dictated by protein-lipid
interaction strength, lipid composition, lipid distribution in the vicinity of
the protein, shape and amino acid composition of the protein, and its amino
acid contents. The specificity of molecular interactions together with the
cooperativity of multiple proteins induce and stabilize complex membrane shapes
at the mesoscale. These shapes span a wide spectrum ranging from the spherical
plasma membrane to the complex cisternae of the Golgi apparatus. Mapping the
relation between the protein-induced deformations at the molecular scale and
the resulting mesoscale morphologies is key to bridging cellular experiments
across the various length scales. In this review, we focus on the theoretical
and computational methods used to understand the phenomenology underlying
protein-driven membrane remodeling. The suite of methods discussed here can be
tailored to applications in specific cellular settings such as endocytosis
during cargo trafficking and tubulation of filopodial structures in migrating
cells, which makes these methods a powerful complement to experimental studies.
