Spatio-Genetic and phenotypic modelling elucidates resistance and re-sensitisation to treatment in heterogeneous melanoma

Although novel targeted therapies have significantly improved the overall survival of patients with advanced melanoma, understanding and combatting drug resistance remains a major clinical challenge. Using partial differential equations, we describe the evolution of a cellular population through time, space, and phenotype dimensions, in the presence of various drug species. We then use this framework to explore models in which resistance is attained by either mutations (irreversible) or plasticity (reversible). Numerical results suggest that punctuated evolutionary assumptions are more consistent with results obtained from murine melanoma models than gradual evolution. Furthermore, in the context of an evolving tumour cell population, sequencing the treatment, for instance applying immunotherapy before BRAF inhibitors, can increase treatment effectiveness. However, drug strategies which showed success within a spatially homogeneous tumour environment were unsuccessful under heterogeneous conditions, suggesting that spatio-environmental heterogeneity may be the greatest challenge to tumour therapies. Plastic metabolic models are additionally capable of reproducing the characteristic resistant tumour volume curves and predicting re-sensitisation to secondary waves of treatment observed in patient derived xenograft (PDX) melanomas treated with MEK and BRAF inhibitors. Nevertheless, secondary relapse due to a pre-adapted subpopulation, remaining after the first wave of treatment, results in a more rapid development of resistance. Our model provides a framework through which tumour resistance can be understood and would suggest that carefully phased treatments may be able to overcome the development of long-term resistance in melanoma.