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A Hybrid Model of Tumor–Stromal Interactions in Breast Cancer

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Abstract

Ductal carcinoma in situ (DCIS) is an early stage noninvasive breast cancer that originates in the epithelial lining of the milk ducts, but it can evolve into comedo DCIS and ultimately, into the most common type of breast cancer, invasive ductal carcinoma. Understanding the progression and how to effectively intervene in it presents a major scientific challenge. The extracellular matrix (ECM) surrounding a duct contains several types of cells and several types of growth factors that are known to individually affect tumor growth, but at present the complex biochemical and mechanical interactions of these stromal cells and growth factors with tumor cells is poorly understood. Here we develop a mathematical model that incorporates the cross-talk between stromal and tumor cells, which can predict how perturbations of the local biochemical and mechanical state influence tumor evolution. We focus on the EGF and TGF-β signaling pathways and show how up- or down-regulation of components in these pathways affects cell growth and proliferation. We then study a hybrid model for the interaction of cells with the tumor microenvironment (TME), in which epithelial cells (ECs) are modeled individually while the ECM is treated as a continuum, and show how these interactions affect the early development of tumors. Finally, we incorporate breakdown of the epithelium into the model and predict the early stages of tumor invasion into the stroma. Our results shed light on the interactions between growth factors, mechanical properties of the ECM, and feedback signaling loops between stromal and tumor cells, and suggest how epigenetic changes in transformed cells affect tumor progression.

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Acknowledgements

Y.J.K. was supported by a Faculty research grant from the University of Michigan–Dearborn and the faculty research fund of Konkuk University in 2012. H.G.O. was supported in part by NSF grant DMS-0517884, and NIH grant GM-29123.

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  1. Department of Mathematics, Konkuk University, Seoul, 143-701, Republic of Korea

    Yangjin Kim

  2. School of Mathematics and Digital Technology Center, University of Minnesota, Minneapolis, MN, 55455, USA

    Hans G. Othmer

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  1. Yangjin Kim
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Kim, Y., Othmer, H.G. A Hybrid Model of Tumor–Stromal Interactions in Breast Cancer. Bull Math Biol 75, 1304–1350 (2013). https://doi.org/10.1007/s11538-012-9787-0

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