# Kinetic models with non-local sensing determining cell polarization and speed according to independent cues

## TL;DR

This paper develops a kinetic model for cell movement that incorporates non-local sensing cues influencing both direction and speed, analyzing how environmental factors affect cell polarization and motility.

## Contribution

It introduces a novel velocity-jump process model with double bias based on non-local environmental cues, linking microscopic sensing to macroscopic cell behavior.

## Key findings

- The model captures how external cues influence cell polarization.
- Analysis of cell size and sensing mechanisms on population dynamics.
- Comparison between kinetic and macroscopic models validates the approach.

## Abstract

Cells move by run and tumble, a kind of dynamics in which the cell alternates runs over straight lines and re-orientations. This erratic motion may be influenced by external factors, like chemicals, nutrients, the extra-cellular matrix, in the sense that the cell measures the external field and elaborates the signal eventually adapting its dynamics. We propose a kinetic transport equation implementing a velocity-jump process in which the transition probability takes into account a double bias, which acts, respectively, on the choice of the direction of motion and of the speed. The double bias depends on two different non-local sensing cues coming from the external environment. We analyze how the size of the cell and the way of sensing the environment with respect to the variation of the external fields affect the cell population dynamics by recovering an appropriate macroscopic limit and directly integrating the kinetic transport equation. A comparison between the solutions of the transport equation and of the proper macroscopic limit is also performed.