Formal model of the interplay between TGF-β1 and MMP-9 and their dynamics in hepatocellular carcinoma

Transforming growth factor beta1 (TGF-beta 1) and matrix metalloproteinase-9 (MMP-9) have been associated with migration and invasion in hepatocellular carcinoma (HCC). Recent studies have suggested a positive feedback loop between TGF-beta 1 and MMP-9 mediated by the PI3K signaling pathway that confers acquired invasion and metastasis in HCC via induction of the epithelial-mesenchymal transition (EMT), which grows into invasive carcinoma. But the potential molecular mechanism of this loop on HCC has not been clarified yet. Therefore, this study is designed to explore the association between the two entities and their key determinants such as NF kappa B, TIMP-1, and hepatic stellate cells (HSCs). Hence, a qualitative modeling framework is implemented that predict the role of biological regulatory network (BRN) during recovery and HCC metastasis. Qualitative modeling predicts discrete trajectories, stable states, and cycles that highlight the paths leading to disease recovery and homeostasis, respectively. The deadlock stable state (1, 1, 1, 1, 1) predicts high expression of all the entities in the BRN, resulting in the progression of HCC. The qualitative model predicts 30 cycles representing significant paths leading to recovery and homeostasis and amongst these the most significant discrete cycle was selected based on the highest betweenness centralities of the discrete states. We further verified our model with network modeling and simulation analysis based on petri net modeling approach. The BRN dynamics were analyzed over time. The results implied that over the course of disease condition or homeostasis, the biological entities are activated in a variable manner. Taken together, our findings suggest that the TGF-beta 1 and the MMP-9 feedback loop is critical in tumor progression, as it may aid in the development of treatment strategies that are designed to target both TGF-beta and MMP-9.