Modeling and simulation of the cell surface

ALEJANDRO TORREZ-SÁNCHEZ; DANIEL MILLÁN; MARINO ARROYO

Barcelona

Encuentro; Joint Meeting of the Spanish Network of Excellence in Mechanobiology and the European Innovative Training Network BIOPOL; 2016

Institute for Bioengineering of Catalonia (IBEC)

Many interesting cell components exhibit much larger lateral dimensions than thickness, and hence can be well-described mathematically by surface models. Surface models have been successfully applied to describe lipid monolayers and bilayers, or the cell cortex. However previous works have mostly focused on the equilibrium behavior of these systems, or have examined problems with axisymmetry. However, many important problems in cell mechanobiology involve dynamics and general shapes. Furthermore, often mechanics closely interacts with chemistry, such as in adhesion through molecular binders or in shape generation by membrane proteins.Here we present a general theoretical framework to study the dissipative dynamics of surface models of the cell surface. Our framework is based on identifying the gradient flow structure of the problem. This requires finding appropriate dissipation and energy potentials from which thedynamics follows from a variational principle. We then realize this model in a computer code based on subdivision surfaces and on algorithms exploiting the variational structure of the dynamics. We apply our framework to the simulation of lipid bilayers, where in particular weexamine the rheology of membrane inclusions that generate intrinsic curvature in the membrane, and the cell cortex, where we study cytokinesis in asymmetric division.