Mathematical models of intercellular signaling in breast cancer

The development and regulation of healthy and cancerous breast tissue is guided by communication between cells. Diverse signals are exchanged between cancer cells and non-cancerous cells of the tumor microenvironment (TME), influencing all stages of tumor progression. Mathematical models are essential for understanding how this complex network determines cancer progression and the effectiveness of treatment.

We reviewed the current dynamical mathematical models of intercellular signaling in breast cancer, examining models with cancer cells only, fibroblasts, endothelial cells, macrophages and the immune system as whole. We categorized the goals and complexity of these models, to highlight how they can explain many features of cancer emergence and progression.

We found that dynamical models of intercellular signaling can elucidate tissue-level dysregulation in cancer by explaining: i) maintenance of non-heritable intratumor phenotypic heterogeneity, ii) transitions between tumor dormancy and accelerated invasive growth, iii) stromal support of tumor vascularization and growth factor enrichment and iv) suppression of immune infiltration and cancer surveillance. These models also provide a framework to propose novel TME-targeting treatment strategies. However, most models were focused on a highly selected and small set of signaling interactions between a few cell types, and their translational applicability were severely limited by the availability of tumor-specific data for personalized model calibration.

Mathematical models of breast cancer have many challenges and opportunities to incorporate signaling. The four key challenges are: 1) finding ways to treat signaling networks as a context-dependent language that incorporates non-linear and non-additive responses, 2) identifying the key cell phenotypes that signals control and understanding the feedbacks between signals and phenotype that determine the progression of cancer, (3) estimating parameters of specific patient tumors early in treatment, 4) linking models with novel data collection methods that have single cell and spatial resolution. As our approaches advance, it is our hope that dynamical mathematical models of inter-cellular signaling can play a central role in identifying and testing new treatment strategies as well as forecasting impacts of disease treatment.