Inspired by biological membrane shaping in the cell through means of curvature-inducing proteins, we investigate the interplay between membrane curvature and the distribution and movement of shape-inducing objects which are free to move as a consequence of the underlying shape. We initially study the self-assembly of a filament, taken as a proxy for the cross-section of a biomembrane, which is primarily driven by the chemical kinetics of attaching proteins and find that, under certain mechanical stiffness regimes of the attaching proteins, pattern formation occurs. Regions of high and low protein concentration form before spatially uniform filament shapes are obtained by means of protein adhesion and movement governed by diffusion and local curvature-seeking. However, noting that the curvature-mediated protein movement on membranes has been biologically observed to be long-range, we next study the self-assembly of embedded inclusions on a membrane as a result of the underlying geometry. We first derive an interaction law for the shape-mediated interaction of inclusions which break symmetry and find that there is a finite equilibrium distance to which the inclusions will aggregate. We derive corresponding equations of motion which describe this curvature-mediated aggregation mechanism and, using this framework, we investigate some of the properties of these self-assembled configurations, including their energy, stability, and their collective elastic behavior. Lastly, we consider the interaction energies of embedded inclusions on a periodic domain and determine that this mechanism may explain computational results of how proteins form rings to promote tubulation on cylindrical membranes.

Les objectifs de cette thèse sont de déterminer les mécanismes cellulaires et moléculaires mis en jeu lors de la co-exposition de cellules hépatiques à l'éthanol, un toxique alimentaire, et au benzo[a]pyrène (B[a]P), un important contaminant de l’environnement émis lors de combustions incomplètes. L’exposition d’hépatocytes primaires de rat pendant 8h favorise leur collaboration via l’induction d’une déplétion membranaire en cholestérol par le B[a]P, ce qui facilite l’action de l’éthanol à déstabiliser les lysosomes via la phospholipase C-1 pour entraîner la mort par apoptose. Lors d’une exposition répétée sur 96h dans les cellules WIF-B9, celles-ci provoquent une mort précoce par nécrose suivie d’une apoptose tardive via leurs métabolismes. Leur toxicité impliquerait un remodelage membranaire et un stress oxydant avec la production d’espèces réactives de l’oxygène et la variation de l’homéostasie du fer. / The aim of this work is to determine cellular and molecular mechanisms implicated in the co-exposure to ethanol, a dietary toxic substance, and benzo[a]pyrene (B[a]P), a major environmental contaminant, found during incomplete combustions. Primary rat hepatocytes exposed during 8h showed a cooperation effect between the two molecules through the depletion of membrane cholesterol by B[a]P, which promote ethanol action to destabilize lysosomes through phospholipase C-1 and facilitate apoptosis cell death. After repeated exposure during 96h of WIF-B9 cells, these two molecules provoke an early cell death by necrosis and a late apoptosis through their metabolisms. Their toxic effects implicate membrane remodeling and oxidative stress with reactive oxygen species production and modifications in iron pool.