"Cluster Formation in Interacting Particle Systems – Modeling and Simulation"Wehlitz, NathalieIn vitro studies of living neural cells have shown that receptors, such as ?-opioid receptors, unexpectedly form spatial clusters on the cell surface [1]. To investigate this phenomenon, a physics-based model was developed [2]. While this model successfully reproduces the pattern formation, analytical studies are challenging due to its multiscale nature. In [3], we present a simplified particle-based model for diffusion and interaction of particles, which in other contexts can also be social or biological individuals. An interaction potential can be chosen such that the particles show some collective behavior comparable to biological swarming. Using the particle-based model, we analyze the formation, motion, and fusion of clusters by means of numerical simulations. The particle-based model is given by a high-dimensional system of stochastic differential equations, making its simulation computationally intensive. An approximation via population scaling by the mean-field partial differential equation or the Dean-Kawasaki stochastic partial differential equation is desirable. It requires advanced numerical techniques based on finite-difference methods to solve these equations, as well as cluster detection algorithms such as DBSCAN to identify individual clusters. Once a model reduction is done, the results about the clustering behavior can be compared with those of the physics-based model and the experimental data. A parameter estimation will be useful to adjust our simplified model to the existing results and shed more light on the phenomenon of receptor clustering. References: [1] J. Möller, A. Isbilir, T. Sungkaworn, B. Osberg, C. Karathanasis, V. Sunkara, E. O. Grushevsky, A. Bock, P. Annibale, M. Heilemann, C. Schütte, and M. J. Lohse. Single-molecule analysis reveals agonist-specific dimer formation of ?-opioid receptors. Nature Chemical Biology, 16(9):946 – 954, 2020. [2] M. Sadeghi and F. Noé. Thermodynamics and kinetics of aggregation of flexible peripheral membrane proteins. The Journal of Physical Chemistry Letters, 12(43):10497–10504, 2021. [3] N. Wehlitz, A. Montefusco, S. Winkelmann, C. Schütte. Approximating particle-based clustering dynamics by stochastic PDEs. 2024 (in preparation). |
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