Multi-scale modeling of Snail-mediated response to hypoxia in tumor progression

TL;DR

This paper introduces a multi-scale mathematical model to understand how Snail protein influences tumor cell migration under hypoxia, linking cellular mechanisms to tumor progression through simulations and experimental validation.

Contribution

The study develops a novel multi-scale model connecting single-cell Snail dynamics to tumor-scale behavior, validated with experimental data.

Findings

Snail expression significantly affects cell migration patterns.

Hypoxia induces phenotypic changes promoting tumor invasiveness.

The model accurately predicts experimental observations of cell migration.

Abstract

Tumor cell migration within the microenvironment is a crucial aspect for cancer progression and, in this context, hypoxia has a significant role. An inadequate oxygen supply acts as an environmental stressor inducing migratory bias and phenotypic changes. In this paper, we propose a novel multi-scale mathematical model to analyze the pivotal role of Snail protein expression in the cellular responses to hypoxia. Starting from the description of single-cell dynamics driven by the Snail protein, we construct the corresponding kinetic transport equation that describes the evolution of the cell distribution. Subsequently, we employ proper scaling arguments to formally derive the equations for the statistical moments of the cell distribution, which govern the macroscopic tumor dynamics. Numerical simulations of the model are performed in various scenarios with biological relevance to provide insights into the role of the multiple tactic terms, the impact of Snail expression on cell proliferation, and the emergence of hypoxia-induced migration patterns. Moreover, quantitative comparison with experimental data shows the model's reliability in measuring the impact of Snail transcription on cell migratory potential. Through our findings, we shed light on the potential of our mathematical framework in advancing the understanding of the biological mechanisms driving tumor progression.