"A Comparison of Gene Mutation and Amplification-Driven Resistance and Their Impacts on Tumor Recurrence"
Drug sensitive cancer cells often acquire drug resistance, resulting in cancer recurrence despite an initial reduction in tumor size. Two common mechanisms for acquiring drug resistance are point mutation and gene amplification. We propose stochastic multi-type branching process models for each of these mechanisms. Using these models, we derive tumor extinction probabilities and deterministic estimates for the tumor recurrence time, that is, the time when an initially drug sensitive tumor surpasses its original size after developing resistance. For each model, we prove a law of large numbers result regarding the convergence of the stochastic recurrence time to its mean. Additionally, we prove sufficient and necessary conditions for a tumor to escape extinction under the gene amplification model, discuss behavior under biologically relevant parameters, and compare the recurrence time and tumor composition in the mutation and amplification models both analytically and using simulations.
Additional authors: Dr. Jasmine Foo - University of Minnesota; Dr. Danika Lindsay