Seminar on the Theory of Complex Systems  Winter Term 2019/2020

Caveolae are small, 60-80 nm, flask-like structures formed, abundantly, on the plasma membranes of mammalian cells by membrane proteins, caveolins, cytosolic proteins and cavins. Caveolae are remarkably uniform in their shapes and dimensions and can cover up to 50% of the membrane surface. Whereas caveolae have been suggested to participate in different processes of intracellular trafficking, the most prominent proposed role of these structures is to serve as a membrane reservoir, which buffers the changes of membrane tension in response to cell swelling or stretching. The mechanism of the latter phenomenon is closely related to the interplay between the caveolae organization on the plasma membrane and the membrane tension. Our study addresses, theoretically, this interplay and its possible consequences for the caveolar function. We analyze the membrane-mediated and tension dependent interaction between caveolae, and model the related formation of the caveolae superstructures described as caveolar oligomers or rosettes. We show that self-assembly and stabilization of such caveolar oligomers are driven by low membrane tensions and can serve as a mechanism of buffering the tension variations. We analyze the formation of caveolar doublets, triplets, quadruplets and pentaplets, compare their oligomerization energies and kinetic stability. We demonstrate that the numerically recovered morphologies of these caveolar oligomers are in a close agreement with experimental observations predict the probability of formation of each kind of oligomers and estimate their relative contributions to the tension buffering.

Looking for some fresh bathroom tiles? Why don't you try regular 7-gons this time, it looks really cool! Only requirement: You'd need to live in hyperbolic space of constant negative curvature. To see how this would be like, let me take you onto a journey into hyperbolic space through recent breakthrough experiments in circuit quantum electrodynamics, where such tilings are realized with superconducting resonators and photons are tricked into believing that space is hyperbolic. I will show how these finite lattice geometries can be mapped onto quantum field theories in continuous negatively curved space. We use this as a computational tool to quantitatively reproduce ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincare disk, and show how conformal symmetry emerges for large lattices. This sets the stage for studying interactions and disorder on hyperbolic graphs, and to resolve fundamental open problems at the interface of interacting many-body systems, quantum field theory in curved space, and quantum gravity using tabletop experiments.

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