Approximating particle-based clustering dynamics by SPDEs
A talk in the SPDEvent series by
Nathalie Wehlitz from Zuse Institute Berlin
| Abstract: | Receptors on cell surfaces exhibit intriguing clustering behavior, as revealed by in vitro studies [1]. The behavior is reproduced by a physics-based model [2], which is challenging to analyze due to its complexity. In [3], we propose a simplified particle-based model for diffusion and pairwise interaction of a finite number of particles. Using numerical simulation and cluster detection methods, we analyze the formation, motion, and fusion of clusters over time. To reduce the computational costs, a mean field approximation via a stochastic partial differential equation (SPDE), known as the Dean-Kawasaki equation, is introduced. We provide a concrete simulation scheme to regularize this highly singular SPDE using finite differences for spatial discretization. Comparing the models based on clustering behavior, we find that the Dean-Kawasaki equation offers a convincing approximation to the particle-based dynamics. Additionally, a Markov jump process for the cluster number evolution is introduced, which serves both for model comparison and as a standalone reduced model. {[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 $\mu$-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) |