Mathematical modelling of subclonal interactions in paediatric high-grade gliomas

Despite a low overall mutational burden, paediatric high-grade gliomas (pHGG) display high intra-tumour heterogeneity. Accumulating evidence suggest the presence of cellular mechanisms that maintain such high heterogeneity, possibly through interactions between subclones within a tumour. In several studies, the interplay between subclonal populations has been demonstrated to confer an overall fitness advantage to the cancer cell population as a whole. However, the mathematical and evolutionary tools to detect and quantify these interactions are continuously being developed, refined and improved. To this end, I designed and implemented a series of mathematical and computational models coupled with statistical inference on in vitro data to quantify subclonal interactions in patient-derived pHGG cell cultures. Using ordinary differential equations (ODE) and partial differential equations (PDE), I demonstrated the presence of growth interactions in 2D and 3D in vitro co-cultures. I detected both positive and negative (competition) interactions, although with great differences between 2D and 3D culture systems. Cellular automata models were also used to detect and quantify the strength of interaction that affected not just growth, but also the motility of infiltrating cells. Positive interactions that enhanced the motility of a subclone in a co-culture were detected between pairs of clones isolated from the same bulk tumour. These results demonstrated that subclonal interactions are indeed present between pHGG cells, and my computational approach quantified the magnitude and dynamics of such interactions. Additionally, the implication of heterogeneity of therapeutic response was explored using ODE and PDE models applied to co-culture assays. Indeed, interactions could affect the therapeutic sensitivity of subclones and alter the competitive landscape present between them. I also showed that my approach was suitable to model adaptive therapy in vitro model systems. An in silico exploration evaluated the applicability of adaptive treatment strategies