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

被引:0
作者
Bratus, Alexander S. [1 ,2 ]
Leslie, Nicholas [3 ]
Chamo, Michail [1 ]
Grebennikov, Dmitry [4 ,5 ,6 ]
Savinkov, Rostislav [4 ,5 ,7 ]
Bocharov, Gennady [4 ,5 ,7 ]
Yurchenko, Daniil [8 ]
机构
[1] Russian Univ Transport, Inst Management & Digital Technol, Moscow 127055, Russia
[2] Lomonosov Moscow State Univ, Moscow Ctr Fundamental & Appl Math, Moscow 119991, Russia
[3] Heriot Watt Univ, Sch Engn & Phys Sci, Edinburgh EH14 4AS, Midlothian, Scotland
[4] Russian Acad Sci, Marchuk Inst Numer Math, RAS, INM, Moscow 119333, Russia
[5] RAS, Moscow Ctr Fundamental & Appl Math, INM, Moscow 119333, Russia
[6] Sechenov First Moscow State Med Univ, World Class Res Ctr Digital Biodesign & Personali, Moscow 119048, Russia
[7] Sechenov First Moscow State Med Univ, Inst Comp Sci & Math Modeling, Moscow 119048, Russia
[8] Univ Southampton, Inst Sound & Vibrat Res, Southampton SO17 1BJ, Hants, England
关键词
pancreatic cancer; cancer evolution; tumor microenvironment; mathematical model; open quasispecies model; EVOLUTION; GROWTH;
D O I
10.3390/math10193557
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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.
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页数:12
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  • [1] Pancreatic stellate cells-role in pancreas cancer
    Bachem, Max G.
    Zhou, Shaoxia
    Buck, Karin
    Schneiderhan, Wilhelm
    Siech, Marco
    [J]. LANGENBECKS ARCHIVES OF SURGERY, 2008, 393 (06) : 891 - 900
  • [2] A dynamical motif comprising the interactions between antigens and CD8 T cells may underlie the outcomes of viral infections
    Baral, Subhasish
    Antia, Rustom
    Dixit, Narendra M.
    [J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2019, 116 (35) : 17393 - 17398
  • [3] Modelling the dynamics of LCMV infection in mice: Conventional and exhaustive CTL responses
    Bocharov, GA
    [J]. JOURNAL OF THEORETICAL BIOLOGY, 1998, 192 (03) : 283 - 308
  • [4] On Diffusive Stability of Eigen's Quasispecies Model
    Bratus, Alexander S.
    Hu, Chin-Kun
    Safro, Mikhail V.
    Novozhilov, Artem S.
    [J]. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2016, 22 (01) : 1 - 14
  • [5] The immune contexture and Immunoscore in cancer prognosis and therapeutic efficacy
    Bruni, Daniela
    Angell, Helen K.
    Galon, Jerome
    [J]. NATURE REVIEWS CANCER, 2020, 20 (11) : 662 - 680
  • [6] Regularity, Asymptotic Solutions and Travelling Waves Analysis in a Porous Medium System to Model the Interaction between Invasive and Invaded Species
    Diaz Palencia, Jose Luis
    Roa Gonzalez, Julian
    Rahman, Saeed Ur
    Redondo, Antonio Naranjo
    [J]. MATHEMATICS, 2022, 10 (07)
  • [7] The role of stroma in pancreatic cancer: diagnostic and therapeutic implications
    Erkan, Mert
    Hausmann, Simone
    Michalski, Christoph W.
    Fingerle, Alexander A.
    Dobritz, Martin
    Kleeff, Joerg
    Friess, Helmut
    [J]. NATURE REVIEWS GASTROENTEROLOGY & HEPATOLOGY, 2012, 9 (08) : 454 - 467
  • [8] CD8+ cytotoxic T lymphocytes in cancer immunotherapy: A review
    Farhood, Bagher
    Najafi, Masoud
    Mortezaee, Keywan
    [J]. JOURNAL OF CELLULAR PHYSIOLOGY, 2019, 234 (06) : 8509 - 8521
  • [9] Inhibition of transforming growth factor β signaling reduces pancreatic adenocarcinoma growth and invasiveness
    Gaspar, Nicholas J.
    Li, Lingyun
    Kapoun, Ann M.
    Medicherla, Satyanarayana
    Reddy, Mamatha
    Li, Georgia
    O'Young, Gilbert
    Quon, Diana
    Henson, Margaret
    Damm, Deborah L.
    Muiru, Gladys T.
    Murphy, Alison
    Higgins, Linda S.
    Chakravarty, Sarvajit
    Wong, Darren H.
    [J]. MOLECULAR PHARMACOLOGY, 2007, 72 (01) : 152 - 161
  • [10] The pancreatic cancer genome revisited
    Hayashi, Akimasa
    Hong, Jungeui
    Iacobuzio-Donahue, Christine A.
    [J]. NATURE REVIEWS GASTROENTEROLOGY & HEPATOLOGY, 2021, 18 (07) : 469 - 481