Translocation-Induced Shape Transitions in Vesicles using a Neural Network-Based Solver for the Helfrich Model

Abstract

This thesis discusses our efforts to model the translocation of an enclosed lipid bilayer membrane (vesicle) through a circular pore. First, we will discuss the study of lipid bilayers, introduce the standard model for representing the energy of a membrane, and provide background on the many theoretical and experimental efforts in the field of membrane modeling. We then review the relevant theoretical and practical considerations regarding the simulation of vesicles and translocation, and implement a neural network-based solver for a scalar phase field. We will proceed to detail our efforts to characterize each constraint imposed on the vesicle throughout the translocation and model them within the context of the solver. Following this, we provide a variety of visual snapshots of the translocation process showing different classes of translocation and the resulting behavior of each. Equally important is the quantitative analysis of the energy landscape traversed by the vesicle, where we chart the induced bending energy imposed upon it by the narrow pore. Additionally, we introduce two types of external effects that modify the energy landscape and illustrate their impact on the total vesicle energy throughout its passage. We then map the results out onto the relevant parameter space to give a picture of where the thresholds between qualitatively different behaviors lie. As a final demonstration of our model’s capabilities, we estimate the time of passage of the vesicle by modeling it diffusively using the energy landscape to calculate the effect of narrower pores on the time to translocate. This model successfully demonstrates explicit phase transitions between stable vesicle states and maps out the energy landscape throughout the unstable regime under the effects of translocation.