PhD thesis Defense
Alejandro Torres-Sánchez (LaCàN)
Alejandro Torres-Sánchez (Logroño, Spain) received a B.S degree in Physics from Universidad de Zaragoza (Spain) and a M.S degree in theoretical physics from Université de Cergy-Pontoise (France) in 2012. In 2015, he received a B.S degree in Mathematics from Universidad Nacional de Educación a Distancia (Spain). He started his PhD at Universitat Politècnica de Catalunya (Spain) in 2012. His research focuses on the development of theoretical and computational approaches to study the mechanics of soft-matter systems, and of lipid bilayers in particular, at multiple scales, ranging from molecular to continuum descriptions.
A theoretical and computational study of the mechanics of biomembranes at multiple scales
Lipid membranes are thin objects that form the main separation structure in cells. They have remarkable mechanical properties; while behaving as a solid shell against bending, they exhibit in-plane fluidity. These two aspects of their mechanics are not only interesting from a physical viewpoint, but are also fundamental for their biological function. Indeed, the equilibrium shapes of different organelles in the cell rely on the bending elasticity of lipid membranes. On the other hand, the in-plane fluidity of the membrane is essential in functions such as cell motility, mechano-adaptation, or for the lateral diffusion of proteins and other membrane inclusions.
In the first part of this Thesis, we investigate the relation between continuum mechanics models of lipid bilayers and their chemical composition from molecular dynamics simulations. For that, we revisit the definition of the continuous stress tensor from molecular dynamics. We propose a new approach for the computation of the stress tensor that complies with balance of linear and angular momentum, which previous definitions failed to satisfy. Our work sets the basis for future research in the connection between chemical composition, which is easily tunable from molecular dynamics simulations, and continuum mechanics theories of lipid membranes, and other systems including inhomogeneous crystals or fibrous proteins.
In the second part of the Thesis, we focus on the continuum modeling of lipid membranes. We develop a three-dimensional and non-linear theory and a simulation methodology for the mechanics of lipid membranes, which have been lacking in the field. We base our approach on a general framework for the mechanics of dissipative systems, Onsager's variational principle, and on a careful formulation of the kinematics and balance principles for fluid surfaces. For the simulation of our models, we follow a finite element approach that, however, requires of unconventional discretization methods due to the non-linear coupling between shape changes and tangent flows on fluid surfaces. Our formulation provides the basis for further investigations of the out-of-equilibrium chemo-mechanics of lipid membranes and other fluid surfaces, such as the cell cortex.