A Comparison of Mutation and Amplification-Driven Resistance Mechanisms and Their Impacts on Tumor Recurrence

TL;DR

This paper models and compares how mutation and gene amplification mechanisms influence tumor recurrence, revealing their distinct impacts on recurrence time, tumor heterogeneity, and resistance levels using stochastic and analytical methods.

Contribution

It provides a mathematical comparison of mutation and amplification-driven resistance, deriving recurrence probabilities and times, and analyzing their effects on tumor dynamics and heterogeneity.

Findings

Amplification-driven recurrence depends linearly on the number of amplification events.

Recurrence time ratios are influenced by the frequency of mutation vs. amplification events.

Higher drug concentrations lead to less heterogeneous, more aggressive recurrent tumors.

Abstract

Tumor recurrence, driven by the evolution of drug resistance is a major barrier to therapeutic success in cancer. Resistance is often caused by genetic alterations such as point mutation, which refers to the modification of a single genomic base pair, or gene amplification, which refers to the duplication of a region of DNA that contains a gene. Here we investigate the dependence of tumor recurrence dynamics on these mechanisms of resistance, using stochastic multi-type branching process models. We derive tumor extinction probabilities and deterministic estimates for the tumor recurrence time, defined as the time when an initially drug sensitive tumor surpasses its original size after developing resistance. For models of amplification-driven and mutation-driven resistance, we prove law of large numbers results regarding the convergence of the stochastic recurrence times to their 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. In comparing these mechanisms, we find that the ratio between recurrence times driven by amplification vs. mutation depends linearly on the number of amplification events required to acquire the same degree of resistance as a mutation event, and we find that the relative frequency of amplification and mutation events plays a key role in determining the mechanism under which recurrence is more rapid. In the amplification-driven resistance model, we also observe that increasing drug concentration leads to a stronger initial reduction in tumor burden, but that the eventual recurrent tumor population is less heterogeneous, more aggressive, and harbors higher levels of drug-resistance.