Shape-induced memory effects on cell migration

• Applicant: Dr. Winfried Schmidt
• Subject Area: Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 563225569

Cell migration is essential for a variety of physiological and pathological processes, such as the immune system, tissue renewal, would healing, and cancer migration. Cell trajectories, which result from integration over the complex spatio-temporal dynamics of the cytoskeleton, have been shown to contain both deterministic and stochastic components. The theoretical description of such actively driven, stochastic processes traditionally relies on the Markov assumption, implying that their time-evolution is independent of their history. However, recent evidence suggests that memory effects in cell migration can profoundly influence cellular trajectories. In complex environments, cells often undergo significant deformations due to geometric constraints, yet the influence of such shape changes on long-term trajectories remains elusive. The proposed project aims to quantify the impact of shape-induced memory effects on cellular movement over extended periods of time. To this end, a numerical model will be developed which accounts for the elastic cytoskeletal response to geometry-induced deformation. Motivated by a newly identified “evasion reflex” which is triggered by an intensified cytoskeletal activity if cellular compression exceeds the size of the nucleus, the model also incorporates a temporarily increased migration speed upon a critical deformation. Numerical simulations will be combined with analytical considerations, utilizing both Generalized Langevin equations and a structured approach for the stochastic time-evolution of cell state variables. The ability of the cell to explore space will be characterized for successive, isolated cell-geometry interactions using key quantities, such as mean squared displacement, persistence time, and velocity auto-correlation functions. These observables will enable direct comparisons between simulations, analytical calculations, and available experimental cell trajectory data. Furthermore, the numerical model will allow to investigate memory effects on cell migration in complex geometries, such as arrays of circular pillars and highly compressive environments, including bottle-neck passages which are used in experiments on migrating cells. These findings will offer insights into shape-induced memory effects on cell migration but are also relevant for the application to other systems with comparable non-Markovian dynamics.

• DFG Programme: WBP Fellowship
• International Connection: France
• Host: Professor Dr. Raphael Voituriez