(457a) The Use of Free Energy Methods to Study Morphological Transitions in Vesicles and Cells Induced By Membrane Remodeling Proteins

We investigate the interplay between cell membrane curvature induced at the atomic scale, due to specialized peripheral membrane proteins, and the resulting membrane morphologies, of varying complexity, observed at the mesoscale. The biological membrane, in our approach, is represented by a dynamically triangulated surface while the proteins are modeled as curvature fields on the membrane, that are either isotropic or anisotropic. In order to compare with experiments, we have focused on the ENTH domain containing EPSIN  whose curvature field is modeled as isotropic, and on the BAR,  Exo70  and ESCRT family proteins whose curvature fields are determined to be anisotropic, both in experiments and in molecular simulations.  Thermal undulations in the membrane and cooperativity in the curvature fields, due to the stabilization of a nematic phase, collectively drive the membrane into different morphological states (buds, tubules, etc.) that resemble those in cellular experiments in vivo and vesicle experiments  in vitro. These complex shapes are emergent  in our phenomenological model, that extends the Helfrich Hamiltonian to include the role of anisotropic elasticity and orientational order.

We determine the relative stability of the above mentioned shapes based on the free energy of these membrane configurations, determined using the methods of Thermodynamic Integration (TI) and Bennett Acceptance (BA).  Based on the absolute free energy computed using TI and the relative free energies computed using BA, we predict  the critical protein density and critical protein induced curvature required for tubulation of invaginations and exvaginations in spherical membranes.  Results are shown for the case of Exo70 protein and N-BAR domains and also compared against those determined from experiments.

The membrane model has been extended to study how a functionalized nanocarrier binds to a  fluctuating membrane surface mediated by multivalent receptor-ligand interactions.  Our studies show that thermal undulations tend to enhance the multivalency of binding, leading to a stronger binding affinity, when the free energy change due to a bond formation is large compared to thermal energy. Further, formation of multiple bonds leads to considerable membrane deformation around the binding sites, which we hypothesize to be  a precursor to activation of the various protein machineries  behind the internalization of nanocarrier  by cells. 

[1] N. Ramakrishnan, P. B. Sunil Kumar and Ravi Radhakrishnan, Physics Reports (article in review)