Mathematical Modeling of Therapy-induced Cancer Drug Resistance: Connecting Cancer Mechanisms to Population Survival Rates

Xiaoqiang Sun,Yongzhao Shao,Jiguang Bao

doi:10.1038/srep22498

Abstract

Drug resistance significantly limits the long-term effectiveness of targeted therapeutics for cancer patients. Recent experimental studies have demonstrated that cancer cell heterogeneity and microenvironment adaptations to targeted therapy play important roles in promoting the rapid acquisition of drug resistance and in increasing cancer metastasis. The systematic development of effective therapeutics to overcome drug resistance mechanisms poses a major challenge. In this study, we used a modeling approach to connect cellular mechanisms underlying cancer drug resistance to population-level patient survival. To predict progression-free survival in cancer patients with metastatic melanoma, we developed a set of stochastic differential equations to describe the dynamics of heterogeneous cell populations while taking into account micro-environment adaptations. Clinical data on survival and circulating tumor cell DNA (ctDNA) concentrations were used to confirm the effectiveness of our model. Moreover, our model predicted distinct patterns of dose-dependent synergy when evaluating a combination of BRAF and MEK inhibitors versus a combination of BRAF and PI3K inhibitors. These predictions were consistent with the findings in previously reported studies. The impact of the drug metabolism rate on patient survival was also discussed. The proposed model might facilitate the quantitative evaluation and optimization of combination therapeutics and cancer clinical trial design.

Highlights

Drug resistance significantly limits the long-term effectiveness of targeted therapeutics for cancer patients
We modeled the secretion of drug-induced resistance factors (DIRFs) by drug-sensitive tumor cells according to Michaelis–Menten kinetics[41] as follows: Secretion d [DIRF] dt
Drug-sensitive cancer cell growth was repressed following drug administration, but it periodically rebounded during no treatment weeks

Summary

Introduction

Drug resistance significantly limits the long-term effectiveness of targeted therapeutics for cancer patients. A recent study[15] revealed a novel drug resistance mechanism in which drug-sensitive cancer cells secrete various soluble factors (e.g., IGF and HGF) into the tumor microenvironment in response to targeted therapy. These secreted factors can promote the growth, dissemination and metastasis of drug-resistant cancer cells and support the survival of drug-sensitive cells. Haeno et al.[26] developed a mathematical framework to describe pancreatic metastasis using a branching process to help understand cancer growth dynamics during metastasis and identify optimal therapeutic interventions This framework focused on genetic mutation-induced drug resistance and did not address the role of targeted therapy-induced microenvironment adaptations in drug resistance. The development of mathematical models capable of quantitatively evaluating synergism in combination drug therapy is desirable

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