Project
AA1-18
Synchronization and Geometric Structures of Stochastic Biochemical Oscillators
Project Heads
Maximilian Engel, Felix Höfling, Stefanie Winkelmann
Project Members
Arthur Straube
Project Duration
01.01.2023 − 31.12.2025
Located at
ZIB
Description
The project developed mathematical frameworks for multi-scale dynamics in deterministic and stochastic dynamical systems, motivated by chemical pH oscillations in vesicle-confined urea–urease reactions. By combining model reduction with geometric singular perturbation theory, it derived accurate, low-dimensional descriptions explaining the emergence, timing, and stability of oscillations through underlying fast–slow dynamics and membrane transport asymmetries. Extending these methods to stochastic reaction networks, revealed synchronization effects induced by common noise. The project further contributed to the analysis of bifurcation scenarios, in particular, under bounded noise, and linked them to nano-science experiments.
External Website
Website at ZIB.
Related Publications
- D. Boniface, A. V. Straube, and P. Tierno. Photocatalytic magnetic microgyroscopes with activity-tunable precessional dynamics. Nano Letters, 24(47):14950–14956, 2024.
- E. Cereceda-López, M. Ostinato, A. Ortiz-Ambriz, A. Straube, M. Palassini, P. Tierno. Excluded volume induces buckling in optically driven colloidal rings. Physical Review Research, 6(1), 2024.
- R. Chemnitz, M. Engel, and G. Olicón-Méndez. Random attractors on countable state spaces. Electronic Journal of Probability, 30:1–25, 2025.
- M. Engel and G. Olicón-Méndez. A singular perturbation analysis for the Brusselator. J. Differential Equations, 457:113866, 2026.
- M. Engel, G. Olicón-Méndez, N. Wehlitz, and S. Winkelmann. Synchronization and random attractors in reaction jump processes. Journal of Dynamics and Differential Equations, 37(2):1207–1242, 2025.
- M. C. Eser, E. S. Medeiros, M. Riza, and M. Engel. Dynamic link switching induces stable synchronized states in sparse networks, 2026. arXiv:2507.08007
- F. Höfling and A. V. Straube. Langevin equations and a geometric integration scheme for the overdamped limit of rotational Brownian motion of axisymmetric particles. Physical Review Research, 7(4):043034, 2025.
- M. N. Kourov, A. E. Samoilova, and A. Straube. Dynamics of a chain of interacting magnetic particles in a one-dimensional periodic energy landscape. Bulletin of the Russian Academy of Sciences: Physics, 89(7):1086–1092, 2025.
- A. V. Straube and F. Höfling. Depinning transition of self-propelled particles. Physical Review E, 110(6):L062601, 2024.
- A. V. Straube and F. Höfling. Memory effects in colloidal motion under confinement and driving. Journal of Physics A: Mathematical and Theoretical, 57(29):295003, 2024.
- A. V. Straube, S. Winkelmann, F. Höfling. Accurate reduced models for the pH oscillations in the urea-urease reaction confined to giant lipid vesicles. J. Phys. Chem. B 127, 2023.
- A. V. Straube, S. Winkelmann, C. Schütte, F. Höfling. Stochastic pH oscillations in a model of the urea–urease reaction confined to lipid vesicles. J. Phys. Chem. Lett. 12, 2021.
- A. V. Straube, G. Olicón-Méndez, S. Winkelmann, F. Höfling, and M. Engel. Unfolding the geometric structure and multiple timescales of the urea-urease pH oscillator, 2025. Journal of Nonlinear Science, under review. arXiv:2508.07275
Related Pictures
