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Mathematical Model of Pancreatic Cancer Cell Dynamics Considering the Set of Sequential Mutations and Interaction with the Immune System

Author

Listed:
  • Alexander S. Bratus

    (Institute of Management and Digital Technologies, Russian University of Transport, 127055 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics, Lomonosov Moscow State University, 119991 Moscow, Russia)

  • Nicholas Leslie

    (School of Engineering & Physical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK)

  • Michail Chamo

    (Institute of Management and Digital Technologies, Russian University of Transport, 127055 Moscow, Russia)

  • Dmitry Grebennikov

    (Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), 119333 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics at INM RAS, 119333 Moscow, Russia
    World-Class Research Center “Digital Biodesign and Personalized Healthcare”, Sechenov First Moscow State Medical University, 119048 Moscow, Russia)

  • Rostislav Savinkov

    (Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), 119333 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics at INM RAS, 119333 Moscow, Russia
    Institute of Computer Science and Mathematical Modeling, Sechenov First Moscow State Medical University, 119048 Moscow, Russia)

  • Gennady Bocharov

    (Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS), 119333 Moscow, Russia
    Moscow Center for Fundamental and Applied Mathematics at INM RAS, 119333 Moscow, Russia
    Institute of Computer Science and Mathematical Modeling, Sechenov First Moscow State Medical University, 119048 Moscow, Russia)

  • Daniil Yurchenko

    (Institute for Sound and Vibration Research, University of Southampton, Highfield, Southampton SO17 1BJ, UK)

Abstract

Pancreatic cancer represents one of the difficult problems of contemporary medicine. The development of the illness evolves very slowly, happens in a specific place (stroma), and manifests clinically close to a final stage. Another feature of this pathology is a coexistence (symbiotic) effect between cancer cells and normal cells inside stroma. All these aspects make it difficult to understand the pathogenesis of pancreatic cancer and develop a proper therapy. The emergence of pancreatic pre-cancer and cancer cells represents a branching stochastic process engaging populations of 64 cells differing in the number of acquired mutations. In this study, we formulate and calibrate the mathematical model of pancreatic cancer using the quasispecies framework. The mathematical model incorporates the mutation matrix, fineness landscape matrix, and the death rates. Each element of the mutation matrix presents the probability of appearing as a specific mutation in the branching sequence of cells representing the accumulation of mutations. The model incorporates the cancer cell elimination by effect CD8 T cells (CTL). The down-regulation of the effector function of CTLs and exhaustion are parameterized. The symbiotic effect of coexistence of normal and cancer cells is considered. The computational predictions obtained with the model are consistent with empirical data. The modeling approach can be used to investigate other types of cancers and examine various treatment procedures.

Suggested Citation

  • Alexander S. Bratus & Nicholas Leslie & Michail Chamo & Dmitry Grebennikov & Rostislav Savinkov & Gennady Bocharov & Daniil Yurchenko, 2022. "Mathematical Model of Pancreatic Cancer Cell Dynamics Considering the Set of Sequential Mutations and Interaction with the Immune System," Mathematics, MDPI, vol. 10(19), pages 1-12, September.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3557-:d:929177
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    References listed on IDEAS

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    1. Shinichi Yachida & Siân Jones & Ivana Bozic & Tibor Antal & Rebecca Leary & Baojin Fu & Mihoko Kamiyama & Ralph H. Hruban & James R. Eshleman & Martin A. Nowak & Victor E. Velculescu & Kenneth W. Kinz, 2010. "Distant metastasis occurs late during the genetic evolution of pancreatic cancer," Nature, Nature, vol. 467(7319), pages 1114-1117, October.
    2. Faiyaz Notta & Michelle Chan-Seng-Yue & Mathieu Lemire & Yilong Li & Gavin W. Wilson & Ashton A. Connor & Robert E. Denroche & Sheng-Ben Liang & Andrew M. K. Brown & Jaeseung C. Kim & Tao Wang & Jared, 2016. "A renewed model of pancreatic cancer evolution based on genomic rearrangement patterns," Nature, Nature, vol. 538(7625), pages 378-382, October.
    3. José Luis Díaz Palencia & Julián Roa González & Saeed Ur Rahman & Antonio Naranjo Redondo, 2022. "Regularity, Asymptotic Solutions and Travelling Waves Analysis in a Porous Medium System to Model the Interaction between Invasive and Invaded Species," Mathematics, MDPI, vol. 10(7), pages 1-19, April.
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