A mathematical model of chromosome recombination-induced drug resistance in cancer therapy

Hongli Yang; Jinzhi Lei; Hongli Yang; Jinzhi Lei

doi:10.3934/mbe.2019356

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 6: 7098-7111. doi: 10.3934/mbe.2019356

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A mathematical model of chromosome recombination-induced drug resistance in cancer therapy

Hongli Yang ¹,
Jinzhi Lei ^{2
,
,}

1.
School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021,China
2.
Zhou Pei-Yuan Center for Applied Mathematics, MOE Key Laboratory of Bioinformatics, Tsinghua University, Beijing 100084, China

Received: 01 April 2019 Accepted: 17 July 2019 Published: 05 August 2019

Cytotoxic chemotherapeutics are common treatment methods of many cancers, and patients are often dosed at maximum tolerated dose (MTD), which is trying to eliminate cancer cells as much as possible. However, highly doses chemotherapy may induce unexpected gene mutations or DNA recombinations, which in turn result in unpredictable outcomes and drug resistance. In this study, we focus on the occurrence of DNA recombinations, and present a mathematical model for the influence of genomic disorder due to chemotherapy, and investigate how it may lead to drug resistance. We show that there is an optimal dose so that the tumor cells number is minimum at the steady state, which suggests the existence of an optimal dose of chemotherapy below the MTD. Model simulations show that when the dose is either low or high, the tumor cancer cells number may maintain a higher level steady state, or even sustained oscillations when the dose is too high, which are clinically inappropriate. Our results provide a theoretical study on the dose control of chemotherapy in cancer therapy.
- delay differential equation,
- genomic disorder,
- non-clonal chromosome aberrations,
- chemotherapy,
- drug resistance
Citation: Hongli Yang, Jinzhi Lei. A mathematical model of chromosome recombination-induced drug resistance in cancer therapy[J]. Mathematical Biosciences and Engineering, 2019, 16(6): 7098-7111. doi: 10.3934/mbe.2019356

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Abstract

Cytotoxic chemotherapeutics are common treatment methods of many cancers, and patients are often dosed at maximum tolerated dose (MTD), which is trying to eliminate cancer cells as much as possible. However, highly doses chemotherapy may induce unexpected gene mutations or DNA recombinations, which in turn result in unpredictable outcomes and drug resistance. In this study, we focus on the occurrence of DNA recombinations, and present a mathematical model for the influence of genomic disorder due to chemotherapy, and investigate how it may lead to drug resistance. We show that there is an optimal dose so that the tumor cells number is minimum at the steady state, which suggests the existence of an optimal dose of chemotherapy below the MTD. Model simulations show that when the dose is either low or high, the tumor cancer cells number may maintain a higher level steady state, or even sustained oscillations when the dose is too high, which are clinically inappropriate. Our results provide a theoretical study on the dose control of chemotherapy in cancer therapy.

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