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During breast cancer progression, there is typically increased collagen deposition resulting in elevated extracellular matrix rigidity. This results in changes to cell-matrix adhesion and cell migration, impacting processes such as the epithelial-mesenchymal transition (EMT) and metastasis. We aim to investigate the roles of cell-matrix adhesion and cell migration on breast tumor growth and progression by studying the impacts of different types of extracellular matrices and their rigidities. We embedded MCF7 spheroids within three-dimensional (3D) collagen matrices and agarose matrices. MCF7 cells adhere to collagen but not agarose. Contrasting the results between these two matrices allows us to infer the role of cell-matrix adhesion. We found that MCF7 spheroids exhibited the fastest growth rate when embedded in a collagen matrix with a rigidity of 5.1 kPa (0.5 mg/mL collagen), whereas, for the agarose matrix, the rigidity for the fastest growth rate is 15 kPa (1.0% agarose) instead. This discrepancy is attributable to the presence of cell adhesion molecules in the collagen matrix, which initiates collagen matrix remodeling and facilitates cell migration from the tumor through the EMT. As breast tumors do not adhere to agarose matrices, it is suitable to simulate the cell-cell interactions during the early stage of breast tumor growth. We conducted further analysis to characterize the stresses exerted by the expanding spheroid on the agarose matrix. We identified two distinct MCF7 cell populations, namely, those that are non-dividing and those that are dividing, which exerted low and high expansion stresses on the agarose matrix, respectively. We confirmed this using Western blot which showed the upregulation of proliferating cell nuclear antigen, a proliferation marker, in spheroids grown in the 1.0% agarose (≈13 kPa). By treating the embedded MCF7 spheroids with an inhibitor or activator of myosin contractility, we showed that the optimum spheroids’ growth can be increased or decreased, respectively. This finding suggests that tumor growth in the early stage, where cell-cell interaction is more prominent, is determined by actomyosin tension, which alters cell rounding pressure during cell division. However, when breast tumors begin generating collagen into the surrounding matrix, collagen remodeling triggers EMT to promote cell migration and invasion, ultimately leading to metastasis.

Reduction of the rapid delayed rectifier potassium current (IKr) via drug binding to the human Ether-à-go-go-Related Gene (hERG) channel is a well recognised mechanism that can contribute to an increased risk of Torsades de Pointes. Mathematical models have been created to replicate the effects of channel blockers, such as reducing the ionic conductance of the channel. Here, we study the impact of including state-dependent drug binding in a mathematical model of hERG when translating hERG inhibition to action potential changes. We show that the difference in action potential predictions when modelling drug binding of hERG using a state-dependent model versus a conductance scaling model depends not only on the properties of the drug and whether the experiment achieves steady state, but also on the experimental protocols. Furthermore, through exploring the model parameter space, we demonstrate that the state-dependent model and the conductance scaling model generally predict different action potential prolongations and are not interchangeable, while at high binding and unbinding rates, the conductance scaling model tends to predict shorter action potential prolongations. Finally, we observe that the difference in simulated action potentials between the models is determined by the binding and unbinding rate, rather than the trapping mechanism. This study demonstrates the importance of modelling drug binding and highlights the need for improved understanding of drug trapping which can have implications for the uses in drug safety assessment.