3D dynamical simulations of the fully nonlinear mechanics of biomembranes

ALEJANDRO TORREZ-SÁNCHEZ; DANIEL MILLÁN; MARINO ARROYO

Madrid

Congreso; 9th European Solid Mechanics Conference (ESMC2015); 2015

Madrid Institute for Advanced Studies of Materials

Lipid bilayers are quasi-two-dimensional systems composed of two monolayers of lipid molecules. Due to the special properties of this kind of molecular arrangement, lipid bilayers (1) behave as elastic sheets and (2) exhibit in-plane fluidity. These two features are essential for many cellular functions. Membrane elasticity allows the formation of cell organelles with very different shapes, ranging from spherical vesicles to thin tubes, and regulate the dynamics of cell deformation. Interfacial fluidity allows the lateral motion of inclusions such as membrane proteins or the transport of lipids from different cells through membrane tubes. Furthermore, the coupling between out-plane deformations and in-plane fluidity results in special visco-elastic properties of the lipid fluid. Thus, biomembranes present unique mechanical properties that must be carefully considered for a full understanding of cell mechanics. However, the 3D fully nonlinear dynamics of bilayers accounting for its elastic and fluid character, and possibly its interactions with chemical agents, has been barely studied. In this work we describe biomembranes as 3D deformable surfaces and consider both their elastic and hydrodynamical properties. We also study the coupling with chemistry, such as lipid composition or the presence of scaffolding proteins, and the interaction with cytoskeletal filaments. To obtain the membrane dynamics, we follow an integrated variational approach, which allows incorporating different dissipative processes consistently. For the discretization of the biomembrane we use subdivision surfaces, which lead to smooth surface parametrizations required to handle the higher order partial differential equations involved.