Mechanistic modelling of treatment resistance in cancer

Summary

Despite advances in targeted medicine, most patients with advanced cancer will experience drug resistance, treatment failure and, ultimately, disease recurrence. This drug resistance, long thought to result from genetic heterogeneity and Darwinian evolution, is increasingly understood as the result of non-genetic evolutionary adaptations to therapy. Recent experimental studies identifies the importance of reversible drug-tolerant phenotypes in driving drug resistance to anti-cancer therapy. This phenotypic adaptation is modulated by a number of complex physiological factors, including the current state of the tumour population and microenvironment, as well as the life history of the parental cell. As systems-level experiments of the complex interactions driving treatment resistance are currently intractable, mathematical models are integral to our understanding of how therapeutic selection pressure shapes the epigenetic evolution of malignant tumours. The proposed research will advance the development of mathematical models to understand the reversible epigenetic resistance observed experimentally.

Many of the existing mathematical models of intra-tumour dynamics extensively use the theoretical framework of evolutionary game theory. There, treatment-driven evolution is typically modelled as a multi-species replicator equation describing clonal dynamics over fixed genetic landscapes. In these models, tumour dynamics are entirely determined by clonal frequency and pre-determined sensitivity to therapy. However, these evolutionary games are incompatible with the continuous phenotypic adaptation to therapy that is increasingly observed in experiments. Thus, the proposed research will develop a mathematical framework to characterise this continuous adaptation and techniques to calibrate the resulting mathematical models to appropriate data.

Potential areas for further investigation are:

1) In a population of genetically identical non-small cell lung cancer cells, a reversible drug-tolerant phenotype expands during anti-cancer targeted therapies and drives tumour rebound during treatment. Existing mathematical model consider this evolutionary adaptation by using a phenomelogical models that enforce discrete “sensitive” and “resistance” states. Here, we could consider the more biologically realisitc case of continuous or stochastic phenotypic adaptation and the extension of this model to understand cooperation during in vitro experiments.

2) Roughly 50% of melanoma cases harbour an activating mutation in the Mitogen Activated Protein Kinase (MAPK) pathway that drives tumour growth. Inhibitors targeting this pathway represented a breakthrough in the treatment of melanoma with over 65% of patients showing clinical benefit during continuous treatment. However, treatment resistance inevitably develops and leads to disease progression. Recent experimental evidence suggests that including period of no treatment -so called drug holidays- can delay the onset of treatment resistance. Here, we could develop mathematical models to understand the evolutionary dynamics leading to development of resistance to MAPK inhibitors.

3) Drug resistance results from changes at the cellular scale. However, the results of this resistance, namely treatment failure and tumour growth, are only observed at a much larger scale. Bridging the in vitro experimental results with clinical scale measurements requires a deep understanding of biological mechanisms and multi-scale models. Here, we could investigate modelling techniques to bridge the inherent multi-scale nature of treatment resistance and the generation of clinically relevant virtual populations.

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