Dynamics of Chemotactic Particles in Heterogeneous Environments

Chemotaxis guides cellular movement in response to chemical gradients, yet the link between microscopic movement strategies and macroscopic dynamics remains unclear. This study examines two chemotactic models: a gradient-sensing model (KS Model) and a local-sensing model (IM Model). To analyze the emergent macroscopic behavior, we derive governing equations for both models using a master equation formulation and a Fokker-Planck approximation. Numerical simulations are performed in both one-dimensional and two-dimensional environments to examine how environmental heterogeneity affects chemotactic dynamics. The effects are quantified by evaluating key metrics such as escape time and relaxation time. Results show that increasing chemotaxis strength prolongs escape time, while relaxation time behaves differently: it initially decreases in the KS model but increases at high chemotaxis levels, whereas in the IM model, it grows exponentially, indicating prolonged trapping. Environmental obstacles further amplify these effects, particularly in the KS model, where strong chemotaxis leads to long-tailed relaxation time distributions.