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

Giulia Chiari, Martina Conte, Marcello Delitala
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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.
肿瘤进展过程中蜗牛介导的缺氧反应的多尺度建模
肿瘤细胞在微环境中的迁移是癌症进展的一个重要方面,在这方面,缺氧具有重要作用。氧气供应不足是诱发迁移偏倚和表型变化的环境应激源。在本文中,我们提出了一个新颖的多尺度数学模型来分析蜗牛蛋白表达在细胞对低氧反应中的关键作用。从描述蜗牛蛋白驱动的单细胞动力学开始,我们构建了描述细胞分布演化的相应动力学传输方程。此外,与实验数据的定量比较表明,该模型在测量蜗牛转录对细胞迁移潜力的影响方面非常可靠。通过我们的发现,我们揭示了数学框架在推进对肿瘤进展生物机制的理解方面的潜力。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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