From confinement to remodeling: modeling topotaxis-driven cell migration in obstacles networks

Several physiological and pathological processes, such as development, wound healing, and cancer invasion, depend on cell migration through fibrous extracellular matrix (ECM). In such contexts, topographical features of the ECM, including fiber alignment and pore size, strongly bias migration, a phenomenon known as topotaxis. To explore this guidance mechanism in a controlled theoretical setting, we present a minimal particle-based model of single-cell motility in two-dimensional environments abstracted as networks of elongated obstacles. This abstraction captures key geometric and topographical constraints of fibrous microenvironments while remaining computationally tractable. Our framework integrates chemotactic bias, stochastic polarity dynamics, steric repulsion from obstacles, escape strategies from mechanical trapping, and minimal remodeling of the obstacles network. Adaptive polarity perturbations mimic active cellular responses such as invadopodial protrusion or random reorientation, while a displacement-based criterion detects trapping events. Heterogeneity is incorporated by assigning variable repulsion strengths to obstacles, and remodeling is implemented by allowing local displacements induced by cell-obstacle contact. Simulation results show that active remodeling of obstacles consistently enhances migration efficiency and target acquisition, whereas escape strategies alone provide only partial improvement, and heterogeneity introduces directional variability. At long timescales, trajectories converge toward effective diffusion, but intermediate dynamics display nontrivial deviations due to confinement and obstacle interactions, highlighting a topotaxis-driven component of motility. Overall, this work positions cell migration within the theoretical context of obstacles networks, providing mechanistic insight into how confinement, anomalous transport, and remodeling interact to shape directional migration. While simplified to two dimensions and lacking entanglement effects characteristic of real three-dimensional ECMs, the model offers a tractable and extensible framework for future studies, including the incorporation of cell deformations or more realistic ECM architectures.