Mathematical Oncology

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Jacob Scott May 01, 2023

Evolutionary therapy in cancer: timescales, tools, and control

Abstract

Cancer is the uncontrolled growth of abnormal cells in the body, and it develops from a single cell to bigger masses which take control of portions of healthy tissues. Following the Darwinian evolution theory, to successfully evolve and cheat the body’s normal control, tumour cells are able to implement complex mechanisms for surviving, for instance by hiding oncogenes in small portions of DNA released outside the chromosomes, thereby relieving them of normal chromosomal constraints and enabling tumors to evolve at higher rates than normal cells. A key role in this mechanism is represented by extra chromosomal DNA (ecDNA), that then can be a major force driving tumor genomic instability. Clinical evidence shows that these genomic structures tend to form the so called ecDNA hubs, regions of the genome where ecDNA tends to cluster together. We propose a mathematical model which describes a multiple species evolutionary process, with a special focus on the mechanisms that drive the formation of ecDNA hubs. We then investigate the effects that these hubs and the interactions between different genomic species have on ecDNA copy number distribution, cells selection strength, copy number correlation and cells evolutionary trends over time. Overall, our model provides a framework for understanding the formation and behaviour of ecDNA genomic structures and may have implications for the development of new strategies for detecting and treating cancer.