(178o) Thermodynamics of Protein-Mediated Membrane Deformation – Application to Clathrin Dependent and Clathrin Independent Endocytosis

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. These proteins are implicated in membrane deformation/bending, cargo recognition and vesicle scission. While the involvement of these proteins have been established and their roles 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 atomistic to coarse-grained representations for the proteins. We describe the energetics of deformations of membranes by using the Helfrich Hamiltonian represented in two different coordinate systems: the Monge Gauge and a Curvilinear coordinate system. The Monge approach is limited to small deformations of the membrane and thermal effects are included, however it cannot describe membrane shapes in the later stages of endocytosis during which membrane overhangs are observed. Thus we also employ the surface evolution approach to describe membrane geometries by minimizing the Helfrich Hamiltonian in a curvilinear coordinate system. This approach is versatile in describing membrane geometries in both small and large deformation limits but is limited to axis-symmetric profiles of membrane. Both approaches yield membrane energies. However to explicitly calculate the role of entropy change due to membrane bud formation, we employ thermodynamic integration method in conjugation with thermodynamic cycle which is possible in Monge formalism. 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. We model curvature induced by each epsin protein as a Gaussian function centered about the position of epsin protein. Clathrin assembly induces a constant curvature onto the membrane over a range dictated by the extent of clathrin coat polymerization. Diffusion of proteins over discrete membrane grids is handled through Monte-Carlo moves. We adopt a novel strategy of integrating two different phenomenological approaches, namely, time-dependent Ginzburg?Landau (TDGL) equation for membrane dynamics with Monte Carlo (MC) for protein diffusion. This integrated multiscale approach results in a unified description of membrane dynamics at the mesoscale (~µm, ~ms), under the influence of curvature-inducing proteins at the nanoscale (~10 nm, ~100 ns). 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.