Evolutionary analysis of replicator dynamics about anti-cancer combination therapy

Rujing Zhao; Xiulan Lai; Rujing Zhao; Xiulan Lai

doi:10.3934/mbe.2023030

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 1: 656-682. doi: 10.3934/mbe.2023030

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Research article

Evolutionary analysis of replicator dynamics about anti-cancer combination therapy

Rujing Zhao ¹,
Xiulan Lai ^{2
,
,}

1.
School of Mathematics, Renmin University of China, Beijing 100872, China
2.
Institute for Mathematical Sciences, Renmin University of China, Beijing 100872, China

Academic Editor: Russell Rockne

Received: 28 June 2022 Revised: 04 September 2022 Accepted: 08 September 2022 Published: 13 October 2022

The emergence and growth of drug-resistant cancer cell subpopulations during anti-cancer treatment is a major challenge for cancer therapies. Combination therapies are usually applied for overcoming drug resistance. In the present paper, we explored the evolution outcome of tumor cell populations under different combination schedules of chemotherapy and p53 vaccine, by construction of replicator dynamical model for sensitive cells, chemotherapy-resistant cells and p53 vaccine-resistant cells. The local asymptotic stability analysis of the evolutionary stable points revealed that cancer population could evolve to the population with single subpopulation, or coexistence of sensitive cells and p53 vaccine-resistant cells, or coexistence of chemotherapy-resistant cells and p53 vaccine-resistant cells under different monotherapy or combination schedules. The design of adaptive therapy schedules that maintain the subpopulations under control is also demonstrated by sequential and periodic application of combination treatment strategies based on the evolutionary velocity and evolutionary absorbing regions. Applying a new replicator dynamical model, we further explored the supportive effects of sensitive cancer cells on targeted therapy-resistant cells revealed in mice experiments. It was shown that the supportive effects of sensitive cells could drive the evolution of cell population from sensitive cells to coexistence of sensitive cells and one type of targeted therapy-resistant cells.
- drug-resistance,
- replicator dynamics,
- mathematical modeling,
- evolution,
- adaptive therapy
Citation: Rujing Zhao, Xiulan Lai. Evolutionary analysis of replicator dynamics about anti-cancer combination therapy[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 656-682. doi: 10.3934/mbe.2023030

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Abstract

The emergence and growth of drug-resistant cancer cell subpopulations during anti-cancer treatment is a major challenge for cancer therapies. Combination therapies are usually applied for overcoming drug resistance. In the present paper, we explored the evolution outcome of tumor cell populations under different combination schedules of chemotherapy and p53 vaccine, by construction of replicator dynamical model for sensitive cells, chemotherapy-resistant cells and p53 vaccine-resistant cells. The local asymptotic stability analysis of the evolutionary stable points revealed that cancer population could evolve to the population with single subpopulation, or coexistence of sensitive cells and p53 vaccine-resistant cells, or coexistence of chemotherapy-resistant cells and p53 vaccine-resistant cells under different monotherapy or combination schedules. The design of adaptive therapy schedules that maintain the subpopulations under control is also demonstrated by sequential and periodic application of combination treatment strategies based on the evolutionary velocity and evolutionary absorbing regions. Applying a new replicator dynamical model, we further explored the supportive effects of sensitive cancer cells on targeted therapy-resistant cells revealed in mice experiments. It was shown that the supportive effects of sensitive cells could drive the evolution of cell population from sensitive cells to coexistence of sensitive cells and one type of targeted therapy-resistant cells.

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