Assembly of Membrane-deforming Objects in Tubular and Vesicular Membranes: Theory and Simulations

Abstract

Biological membranes are selective soft barriers that compartmentalize internal structure of a cell into organelles and separate them as a whole from the external environment. Due to their innate feature of being able to undergo constant reshaping, cellular membranes spatially attain diverse shapes ranging from simple spherical vesicles to more peculiar structures like the interconnected network of tubes found in the endoplasmic reticulum. Membranes are not only composed of lipids, but also host an enormous number of inclusions like proteins. Recent studies of biological membranes have revealed that such inclusions play a key role in diverse biological processes through either sensing or inducing perturbations to the membrane shape. In this dissertation, we studied the interplay between the shape of membrane and the spatial organization of attached curvature inducing objects using mathematical tools and numerical simulations in highly curved spherical and cylindrical geometries. First, we investigated the interaction between inclusions of different shapes embedded in/adhered to tubular membranes. Our combined theoretical analysis and numerical simulation results evinced that tubular membranes, in contrast to their planar counterpart, transmit an attractive force between inclusions, stemming from their closed and curved geometry. We then elucidated that collective interaction between proteins results in the formation of line-like and ring-like clusters, depending on the their intrinsic shape (Chapters 2–4). We further showed how curvature sensing crescent-like proteins in high densities can constrict tubular membranes and facilitate their splitting, demonstrating that both the curvature-sensing and curvature-inducing property of proteins are two sides of the same coin. Moreover, we used our simulation results to explain how mitochondorial machinery triggers, facilitates and drives membrane fission in its tubular network to avoid entanglements (Chapter 3). Next, we examined the interaction of spherical proteins adhered to closed vesicles. Our simulation results – supported by recent experimental evidence – revealed membrane curvature as a common physical origin for interactions between any membrane deforming objects, from nanometre-sized proteins to micrometre-sized particles (Chapter 5). Our further simulations unraveled how introducing curvature variation on the surface of a closed vesicle can be exploited by inanimate particles to regulate their pattern formation (Chapter 6). Finally, through theoretical calculations,we analyzed the interplay between the shape of a cell and the rearrangement of attached microtubules (Chapter 7). Our results particularly suggested that the commonly reported parallel structure and bundling of microtubules can be induced by membrane mediated interactions.