Spatio-Genetic and Phenotypic Modelling Elucidates Resistance and Re-Sensitisation to Treatment in Heterogeneous Melanoma

Abstract

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.

Computational Model of Heterogeneity in Melanoma: Designing Therapies and Predicting Outcomes

“…Spatial fluxes occur when cells move in space. As in previous models of the spatial evolution of cancer [3,1],…”

“…Using a novel framework (given in eq. ( 1) of the main text ) for higherdimensional mathematical modelling of population dynamics in cancer [1], we are here able to represent the dynamics of the population in time, space, and approximated gene expression levels. The approach results in partial differential equations in a number of dimensions equal to the spatial dimension plus the gene expression dimensions.…”

“…As in several previous models of cancer invasion [5,3,6,1], we assume that the cancer cell population invades the stroma by degrading the ECNE to make space for invading cells. Hence, there is a chemically-mediated degradation, with the rate vector δv = The chemical species, themselves, diffuse with a rate vector Dm .…”

“…The non-genetic nature of adaptive resistance in melanoma is first suggested by the reversibility of this process: resistant tumors can re-sensitize upon a drug holiday [Das Thakur et al(2013), Sun et al(2014)]. Coexistence of sensitive and resistant cells with anti-correlated fitness in treated and untreated conditions can also explain apparent tumour re-sensitization in the absence of drug by positive selection of sensitive cells and negative selection of resistant cells, without the need for transitions between different cell states [Hodgkinson et al(2019)].…”

Integrative Models for TGF-β Signaling and Extracellular Matrix

“…We have recently introduced a new approach to cope with this variability while remaining in a continuous framework that is convenient for simulation and analysis. This approach uses mesoscopic PDEs over temporal, spatial, and structural dimensions [Hodgkinson et al, 2018, Hodgkinson et al, 2019.…”