Modeling TGF-β in Early Stages of Cancer Tissue Dynamics

Abstract

Recent works have highlighted a double role for the Transforming Growth Factor (-): 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 - multi scale mathematical model at molecular, cellular and tissue scales. The multi scalar behaviours of the - 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 - at the single-cell level by taking into account the intracellular and extracellular balance and the autocrine and paracrine behaviour of -. Then we use the average estimates of the - 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 - 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.

Mathematical modelling of cancer invasion: The multiple roles of TGF-β pathway on tumour proliferation and cell adhesion

“…a mutated clone) moving only in a directed manner following self-adhesive and cross-adhesive cell-cell forces, as well as matrix interactions. Since TGF-β does not affect only tumour growth, but impacts also cell adhesion, 4 we model the interactions between TGF-β and integrins that influence the cell-cell and cell-matrix adhesive forces. The computational results show a range of heterogeneous invasion patterns, as a result of the opposite role of TGF-β in early and late stages of cancer.…”

Modelling Circulating Tumour Cells for Personalised Survival Prediction in Metastatic Breast Cancer

“…Mammary duct compartment. In order to describe the tissue dynamics as populations of healthy and mutated cells, we introduce a branching process based on the tissue scale model proposed in [ 2 ] where the cell populations are ρ ( ϕ , t ) and the index ϕ ∈ [0, Φ] represents the cell state which is identified with the cell phenotype.…”

“…TGF- β is among the most abundant growth factors in bone, and its role in skeletal metastases is established. It is deposited in the bone matrix by osteoblasts, released and activated during osteoclastic resorption, and it regulates bone development and remodelling [ 2 ]. Advanced cancers frequently escape growth inhibition by TGF- β , which also activates epithelial-mesenchymal transition (EMT) and invasion, promoting metastases.…”

“…In a recent work [ 2 ], we have modeled how TGF- β drives the formation of early neoplastic signature in breast and perturbs the bone remodelling process. Here, we present a multi-compartment mathematical model that aims at elucidating the effects of the TGF- β and the concomitant therapies in the three microenvironments (mammary duct, circulatory system and bone niche).…”

Osteocytes as a record of bone formation dynamics: A mathematical model of osteocyte generation in bone matrix

“…This discrete depletion models Marotti's hypothesis that osteocytes prompt the burial of osteoblasts when they become sufficiently covered with bone matrix [6,21]. In purely temporal settings, Moroz, Wimpenny et al [26,27] assume osteocytes to be generated at constant density in the matrix and removed in proportion to the level of mechanical stress, Ascolani and Liò [28] assume osteocytes to be generated in proportion to the number of osteoblasts and removed at a constant rate for one day after an explicit microfracture, and Graham, Ayati etal [29] consider a single remodelling event during which osteocytes are generated in proportion to the number of osteoblasts with a logistic rate of growth, and removed artificially at the start of the simulation to initiate the remodelling event. Several other models have included the effect of local mechanical stimuli onto bone remodelling events [30][31][32][33][34][35][36][37][38].…”