# Anisotropic persistent random walk model simulates T-cells migration over curved landscapes

## TL;DR

This paper introduces a new model to simulate how T-cells move on curved surfaces, showing they prefer concave areas and move more efficiently there.

## Contribution

The novel anisotropic persistent random walk model captures T-cell migration behavior on curved surfaces, including directional bias and superdiffusive movement.

## Key findings

- The model accurately replicates T-cell trajectories on both flat and curved surfaces.
- T-cells exhibit a directional bias toward concave regions and superdiffusive behavior on curved surfaces.
- Anisotropic randomness in the model enhances cellular activity in concave valleys.

## Abstract

Cell migration is an important cellular process to study, as it plays a fundamental role in tissue structuring and development, while abnormal cell migration may be the cause of certain diseases. Among the known factors influencing cell migration, substrate curvature is one, with cells naturally moving towards concave areas while avoiding convex ones. The underlying causes of migration guidance by curvature remain unclear, and in particular, the way in which cell persistence is affected is still not well understood. We introduce an anisotropic persistent random walk model which includes cell heterogeneity to simulate T-cell migration across various corrugate landscapes. We compared the trajectories generated by the model with in vitro T-cells trajectories over the same topographies. The model accurately captures key features of cell trajectories on flat surfaces as well as on curved surfaces, such as a directional bias toward concave regions. The model also reveals a superdiffusive behavior on curvature, demonstrating more efficient movement compared to flat surfaces. The anisotropic randomness incorporated in the model appears as a critical feature which shapes T-cells persistence mechanisms by increasing cellular activity in the axis of concave valleys and promoting migration towards concave areas.