Modeling TGF-β in early stages of cancer tissue dynamics.

Recent works have highlighted a double role for the Transforming Growth Factor β (TGF-β): it inhibits cancer in healthy cells and potentiates tumor progression during late stage of tumorigenicity, respectively; therefore it has been termed the "Jekyll and Hyde" of cancer or, alternatively, an "excellent servant but a bad master". It remains unclear how this molecule could have the two opposite behaviours. In this work, we propose a TGF-β multi scale mathematical model at molecular, cellular and tissue scales. The multi scalar behaviours of the TGF-β are described by three coupled models built up together which can approximatively be related to distinct microscopic, mesoscopic, and macroscopic scales, respectively. We first model the dynamics of TGF-β at the single-cell level by taking into account the intracellular and extracellular balance and the autocrine and paracrine behaviour of TGF-β. Then we use the average estimates of the TGF-β from the first model to understand its dynamics in a model of duct breast tissue. Although the cellular model and the tissue model describe phenomena at different time scales, their cumulative dynamics explain the changes in the role of TGF-β in the progression from healthy to pre-tumoral to cancer. We estimate various parameters by using available gene expression datasets. Despite the fact that our model does not describe an explicit tissue geometry, it provides quantitative inference on the stage and progression of breast cancer tissue invasion that could be compared with epidemiological data in literature. Finally in the last model, we investigated the invasion of breast cancer cells in the bone niches and the subsequent disregulation of bone remodeling processes. The bone model provides an effective description of the bone dynamics in healthy and early stages cancer conditions and offers an evolutionary ecological perspective of the dynamics of the competition between cancer and healthy cells.