Non-affine deformation analysis and 3D packing defects: A new way to probe membrane heterogeneity in molecular simulations.

Here, we discuss a new framework developed over the last 5 years in our group to probe nanoscale membrane heterogeneity. The framework is based on the idea of characterizing lateral heterogeneity through non-affine deformation (NAD) measurements, transverse heterogeneity through three dimensional (3D) lipid packing defects, and using these approaches to formalize the seemingly trivial correlation between lateral organization and lipid packing in biological membranes. We find that measurements from NAD analysis, a prescription which is borrowed from Physics of glasses and granular material, can faithfully distinguish between liquid-ordered and disordered phases in membranes at molecular length scales and, can also be used to identify phase boundaries with high precision. Concomitantly, 3D-packing defects can not only distinguish between the two co-existing fluid phases based on their molecular scale packing (or membrane free volume), but also provide a route to connect the membrane domains to their functionality, such as exploring the molecular origins of inter-leaflet domain registration and peptide partitioning. The correlation between lateral membrane order and transverse packing presents novel molecular design-level features that can explain functions such as protein/peptide partitioning and small-molecule permeation dynamics in complex and heterogeneous membranes with high-fidelity. The framework allows us to explore the nature of lateral organization and molecular packing as a manifestation of intricate molecular interactions among a chemically rich variety of lipids and other molecules in a membrane with complex membrane composition and asymmetry across leaflets.