| In eukaryotic cells, the internalization of extracellular cargo into the cytoplasm via the endocytosis machinery is an important regulatory process required for a large number of essential cellular functions, including nutrient uptake, cell-cell communication, and modulation of cell-membrane composition. Endocytosis is orchestrated by a variety of proteins implicated in membrane deformation, cargo recognition and vesicle scission. While the involvement and roles of these proteins in membrane deformation, cargo recognition, and vesicle scission have been identified, current conceptual understanding falls short of a mechanistic description of the cooperativity and the bioenergetics of the underlying vesicle nucleation event which we address here using theoretical models based on an elastic continuum representation for the membrane and coarse-grained representations for the proteins. We describe the energetics of deformations of membranes by solving the Helfrich Hamiltonian by two different formalisms: Monge formalism and surface of evolution formalism. The Monge approach is limited to small deformations of the membrane and thermal effects are included while the surface of evolution approach is versatile in describing membrane geometries in both small and large deformation limits but is limited to axis-symmetric profiles of membrane. To explicitly calculate the role of entropy change due to membrane bud formation, we employ thermodynamic integration method in conjugation with thermodynamic cycle. In our model, curvature inducing proteins and protein assembly like epsin and clathrin coat affect the membrane Hamiltonian by changing the preferred mean curvature of the membrane. This integrated multiscale approach results in a unified description of membrane behavior at the mesoscale, under the influence of curvature-inducing proteins at the nanoscale. Using this toolkit of the methods, we demonstrate the role of the endocytic protein assembly in driving membrane vesiculation and further quantify the energetics of the underlying process. |
