Noncommutative Geometry Seminar

The plasma membranes of neurons are liquid crystalline aggregates that not only insulate the cells, but further play an essential role in their functioning. In particular, through fusion of spherical bilayer lipid structures (or vesicles) with the membranes, neurotransmitters are released into the extracellular space, which activate receptor proteins and thereby enable neuronal communication. Subsequently, the membrane forms new vesicles to maintain a quasi-equilibrium, i.e. a critical number for synaptic transmission. These processes show astonishing similarities with models in string theory. Membrane fusion is one of the most fundamental processes in life that occurs when two separate lipid membranes merge into a single continuous bilayer. It has recently been suggested that fusion is ultimately triggered by a membrane destabilization through extremal membrane curvature. The hereby induced stress promotes the formation of a hemifusion intermediate, opening of the fusion pore and finally convergence towards a 2-dimensional lipid bilayer surface of mean zero curvature. This process is significantly governed by proteins located at the surface of vesicles and membranes. Proteins also play a key role in vesicle formation, particularly by inducing perturbations that change the orientation of the membrane locally. A number of experimental and theoretical investigations have shed light on different aspects of this process, however less attention has been paid to its multi-scale dynamics and geometrical aspects that contain non-trivial singularities. The aim of this talk is to familiarize the audience with the mathematical foundations of possible strategies to address this question.