Kalender

Adjoint polynomials of convex polytopes have recently received attention from the field of particle physics, and the question has been raised whether they admit determinantal representations. In this talk we define the notion of adjoint polynomials/hypersurfaces and characterize them through their degree and a simple vanishing condition. Through this vanishing condition we derive a certificate for the existence of singularities on the adjoint hypersurface. We then survey the classical theory on determinantal representations. We prove that the adjoint curve of a polygon always has a natural symmetric determinantal representation that certifies hyperbolicity. For three-dimensional polytopes we show that if the adjoint is smooth, then a determinantal representation exists. The methods to find these representations are computationally viable. There are also some negative results for higher dimensions. The presented results are based on joint work with Mario Kummer and Dmitrii Pavlov (both TU Dresden) and with Julian Weigert (MPI-MIS Leipzig).

Cell division is a process fundamental to life. After the genetic material is duplicated, mitosis is concluded by cytokinesis. This highly conserved process starts with the ingression of a cleavage furrow between the two daughter cells. The central spindle transforms into the intercellular bridge, an extremely dense microtubule bundle connecting the dividing cells, which later is cut when the cells abscise by an ESCRT-dependent process. While the main players that execute the ingression of the cleavage furrow, the formation of the midbody in the intercellular bridge and finally the abscission of the dividing cells have long been identified, the temporal progression and nanoscale organization of molecules acting during cytokinesis remain only rudimentarily understood. This is due to the relatively fast process of furrow ingression and its three-dimensional nature, which is difficult to study at high spatiotemporal resolution, especially below the diffraction limit of light. In this seminar, I will present a spatiotemporal atlas of cytokinesis, based on the combination of fast volumetric imaging using lattice light-sheet microscopy and super-resolution expansion microscopy (ExM). Computational modelling of cytokinesis based on the septin and microtubule cytoskeleton as markers allows the correlation and registration of multiple cytokinetic factors along a pseudotime axis. Our ExM-based workflow unlocks the midbody dark zone for visualization and provides three-dimensional and contextual information with high resolution, thus offering unprecedented insights into mammalian cytokinesis and an assay to further explore its perturbation.

Neuronal microtubule-associated protein tau can protect the microtubule surface, maintaining microtubule stability. In neurodegenerative diseases termed tauopathies, tau forms cyto-toxic aggregates presumably as a consequence of tau delocalization from microtubules, accompanied by an increase in cytoplasm-localized tau and microtubule destabilization. The underlying mechanisms, however, remain unclear. Here, we show that decline of adenosine triphosphate (ATP), related to aging and neurodegeneration, leads to tau delocalization from microtubules and microtubule disintegration. Combining reconstitution experiments with molecular modeling, we show that ATP stabilizes tau molecules on the microtubule surface through electrostatic interactions. We propose that pathological decline of ATP can destabilize microtubule-tau interactions and lead to an increase of cytoplasmic tau, providing a plausible functional link between ATP homeostasis and tauopathies.