Impact of Resistance on Therapeutic Design: A Moran Model of Cancer Growth

by Mason Lacy & Adrianne Jenner 

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Cancers often develop resistance to standard treatments, such as chemotherapy. Understanding how the appearance of resistant cells impacts the effectiveness of treatment is an important area of study. In this work, we use a Moran model to investigate the impact of resistance on two styles of treatment administration: single high-dose injections (or maximum tolerated dose) and sustained low-dose treatments.

Experimentalists have been developing devices, such as hydrogels, that can be loaded with drug and injected close to the tumour. These devices then release the treatment slowly over time, giving a sustained (often low) dose of the therapy. Using a Moran model capturing a population of sensitive and resistant cells, we were able to show that maximum tolerated dosages are still the most effective protocols in the presence of an aggressive, resistant-prone tumour. We showed how even when the Moran model was calibrated to capture experimental data for treatment of breast cancer, the same result holds.

Caption: Schematic depicting tumour evolution over time and the fixation of a resistant clone following therapy. As a cancer grows, it is subjected to various pressures which can cause mutations to arise. Some clones may contain mutations that may be more adept at coping with treatment or provide a fitness advantage to those cells, such as faster proliferation rates, and we denote these as driver mutations. After treatment, often cells with driver mutations conferring resistance and/or fitness advantages will expand in number. In some cases, this can result in a tumour that is no longer as genetically complex. Most importantly, these tumours are often no-longer sensitive to the original therapy (Color figure online)