Discovering dynamics and parameters of nonlinear oscillatory and chaotic systems from partial observations

Despite rapid progress in live-imaging techniques, many complex biophysical and biochemical systems remain only partially observable, thus posing the challenge to identify valid theoretical models and estimate their parameters from an incomplete set of experimentally accessible time series. Here, we combine sensitivity methods and VoteFair popularity ranking to construct an automated hidden dynamics inference framework that can discover predictive nonlinear dynamical models for both observable and latent variables from noise-corrupted incomplete data in oscillatory and chaotic systems. After validating the framework for prototypical FitzHugh-Nagumo oscillations, we demonstrate its applicability to experimental data from squid neuron activity measurements and Belousov-Zhabotinsky (BZ) reactions, as well as to the Lorenz system in the chaotic regime.Comment: 37 pages, 18 figure

Topological braiding and virtual particles on the cell membrane

Significance Topological defects are robust particle-like structures that essentially determine the mechanics and dynamics of physical and biological matter. Examples range from vortices in quantum superfluids to the cores of spiral wave patterns in the brain. In biological systems, such defects play important roles as organizers of biochemical signaling patterns, cellular forces, and even cell death. Combining direct experimental observations with mathematical modeling and chemical perturbations, we investigated the dynamics of spiral wave defects on the surfaces of starfish egg cells. Our quantitative analysis showed that these defects exhibit complex braiding, pair creation, and annihilation dynamics, in agreement with predictions from a generic continuum theory. More broadly, these results suggest interesting parallels between information transport in living and quantum systems.</jats:p