In this paper we present a hybrid mathematical model of the invasion of healthy tissue by a solid tumour. In particular we consider early vascular growth, just after angiogenesis has occurred. We examine how the geometry of the growing tumour is affected by tumour cell heterogeneity caused by genetic mutations. As the tumour grows, mutations occur leading to a heterogeneous tumour cell population with some cells having a greater ability to migrate, proliferate or degrade the surrounding tissue. All of these cell properties are closely controlled by cell–cell and cell–matrix interactions and as such the physical geometry of the whole tumour will be dependent on these individual cell interactions. The hybrid model we develop focuses on four key variables implicated in the invasion process: tumour cells, host tissue (extracellular matrix), matrix-degradative enzymes and oxygen. The model is considered to be hybrid since the latter three variables are continuous (i.e. concentrations) and the tumour cells are discrete (i.e. individuals). With this hybrid model we examine how individual-based cell interactions (with one another and the matrix) can affect the tumour shape and discuss which of these interactions is perhaps most crucial in influencing the tumour's final structure.

This study addresses the role of PTEN loss in intrinsic resistance to the BRAF inhibitor PLX4720. Immunohistochemical staining of a tissue array covering all stages of melanocytic neoplasia (n = 192) revealed PTEN expression to be lost in >10% of all melanoma cases. Although PTEN expression status did not predict for sensitivity to the growth inhibitory effects of PLX4720, it was predictive for apoptosis, with only limited cell death observed in melanomas lacking PTEN expression (PTEN−). Mechanistically, PLX4720 was found to stimulate AKT signaling in the PTEN− but not the PTEN+ cell lines. Liquid chromatography multiple reaction monitoring mass spectrometry (LC-MRM) was performed to identify differences in apoptosis signaling between the two cell line groups. PLX4720 treatment significantly increased BIM expression in the PTEN+ (>14-fold) compared with the PTEN− cell lines (four-fold). A role for PTEN in the regulation of PLX4720-mediated BIM expression was confirmed by siRNA knockdown of PTEN and through reintroduction of PTEN into cells that were PTEN−. Further studies showed that siRNA knockdown of BIM significantly blunted the apoptotic response in PTEN+ melanoma cells. Dual treatment of PTEN− cells with PLX4720 and a PI3K inhibitor enhanced BIM expression at both the mRNA and protein level and increased the level of apoptosis through a mechanism involving AKT3 and the activation of FOXO3a. In conclusion, we have shown for the first time that loss of PTEN contributes to intrinsic BRAF inhibitor resistance via the suppression of BIM-mediated apoptosis. Cancer Res; 71(7); 2750–60. ©2011 AACR.