Thesis title: Phase Field Modelling of Intramembrane Cavitation in Lipid Bilayers
Biological membranes are complex structures essential for life. Among the various aspects that characterize them, the mechanism of adhesion, mainly defined by electrostatic forces and protein interactions, is crucial for several reasons. It defines the basis of communication between cells and the environment, playing an important role in tissue development. It maintains the cell’s structural integrity, is involved in tissue engineering applications, and enables the deformation of cell membranes for endocytosis, which is important for improving drug delivery systems. However, the interaction between the two layers of the lipid membrane is rarely considered. Understanding this interaction could be crucial for advancing applications such as industrial processes that utilize phase transitions for heat dissipation, improving medical treatments, and gaining deeper insights into embolism formation in plants. In this Thesis, I propose a Phase-Field model, based on the Canham-Helfrich elasticity theory for a fluid lipid membrane, that accounts for adhesion and thermal fluctuations. Phase-field models exploit auxiliary continuous fields to define interfaces as diffuse rather than sharp. This makes them particularly well-suited for numerically solving interface problems in dynamic contexts. After initially validating the model by simulating vesicle adhesion to surfaces, I apply it to the case of the two lipid leaflets, attempting to separate them by exerting an external pressure, which results in the formation of an interlayer bubble. I also show that thermal noise is an important factor as it leads to cavity formation at lower pressures than in fluid bulk, matching measurements previously obtained from molecular dynamics (MD) simulations, which are limited to small membrane sizes and short times due to high computational costs. This continuous model overcomes those limitations and also provides information on the contribution of bending energy to the activation energy needed to separate the layers, which is particularly significant near the cavitation pressure. The mesoscale modeling developed in this Thesis opens the way to a multi-scale understanding of the cavitation process from the atomistic scale of the bilayer to the macroscopic hydrodynamics of nucleated bubbles.