Quantifying topological transformation in lipid self-assemblies

Abstract

Surfactant assemblies are characterized by soft intermolecular interactions and can be deformed or topologically altered by thermal or mechanical stress of the magnitude of thermal fluctuations. In biology, the protein mediated remodeling of the lipid membrane is essential for many cellular processes such as membrane fission, fusion, formation of lipid droplets or cell lysis. Quantifying the free-energy differences between end states of formed intermediates can provide valuable insights into the potential roles and mechanisms of cellular remodeling proteins. The aim of this project was to develop and apply a versatile free-energy calculation protocol to enable the estimation of free-energy differences between meta-stable states of lipid assemblies. We propose a novel method coined ‘Density Field Thermodynamic Integration’ (DFTI) which adopts the universality and transferability of alchemical methods while simultaneously exploiting the soft excess interactions between surfactant molecules. DFTI is designed for a rapid quantification of the free energy differences between different metastable structures in soft, fluid materials. Combining thermodynamic integration, one of the most established free-energy methods with a density-based external potential, offers the possibility to outline morphologies along a reversible path connecting two meta-stable states. The same holds true for the string method adaptation used in this work, which was first used in this combination by Smirnova et al. to calculate the minimum free energy path (MFEP) for stalk formation between two apposing membranes and the influence of the presence of SNARE transmembrane domains. Both methods were tested on three example systems: the breaking of a worm-like micelle and a toroidal micelle and the formation of a stalk. In all cases DFTI and string method yielded comparable results. This work explores the usage of density field based free energy methods in its predictive power and limitations. In addition, lipid droplets, as an example for membranes as active players in biological processes, are investigated with a focus on their emergence and the role of the related protein seipin.