Dresden 2026 – scientific programme
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BP: Fachverband Biologische Physik
BP 7: Poster Session I
BP 7.47: Poster
Monday, March 9, 2026, 15:00–17:00, P5
Topologically invariant coordinates for dynamic epithelia undergoing morphogenesis — •Paweł Korzeb1, Marko Popović1,4, and Frank Jülicher1,2,3 — 1Max Planck Institute for Physics of Complex Systems, Dresden, Germany — 2Center for Systems Biology, Dresden, Germany — 3Cluster of Excellence Physics of life, Technische Universität Dresden, Dresden, Germany — 4Rudjer Bošković Institute, Zagreb, Croatia
Epithelia are two-dimensional tissues, sheets of tightly connected cells that form many structures in organs. Such tissues acquire their shape and function through morphogenesis, a process that involves changes in both their geometry and cellular network topology. A key question in morphogenesis is to understand how cellular processes, such as cell division or T1 transitions, contribute to tissue morphology by changing its geometry and topology. For a curved epithelium, this problem can be formulated in a continuous covariant description on the tissue surface. In this work, we propose two sets of topologically invariant coordinates, describing cellular networks, obtained by embedding a graph representation of the network into R2 using only its connectivity, without the need to take into account the underlying tissue geometry. We construct these embeddings using the spectrum of the graph Laplacian and a spring-meshwork representation. Local changes of these topologically invariant coordinates allow us to identify the cellular processes occurring during tissue development. This formalism provides a framework to investigate the coupled evolution of epithelial geometry and topology.
Keywords: morphogenesis; networks; topology; geometry