Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

Alexander Sergeevich Bratus
* ORCID logo ,
Nicholas R. Leslie
ORCID logo ,
Michail Ruslanovich Chamo
,
Dmitry Sergeevich Grebennikov
ORCID logo ,
Rostislav Sergeevich Savinkov
,
Gennady Alexeevich Bocharov
ORCID logo ,
Daniil Vadimovich Yurchenko
ORCID logo
Version 1 : Received: 30 August 2022 / Approved: 1 September 2022 / Online: 1 September 2022 (10:52:10 CEST)

A peer-reviewed article of this Preprint also exists.

Bratus, A.S.; Leslie, N.; Chamo, M.; Grebennikov, D.; Savinkov, R.; Bocharov, G.; Yurchenko, D. Mathematical Model of Pancreatic Cancer Cell Dynamics Considering the Set of Sequential Mutations and Interaction with the Immune System. Mathematics 2022, 10, 3557. Bratus, A.S.; Leslie, N.; Chamo, M.; Grebennikov, D.; Savinkov, R.; Bocharov, G.; Yurchenko, D. Mathematical Model of Pancreatic Cancer Cell Dynamics Considering the Set of Sequential Mutations and Interaction with the Immune System. Mathematics 2022, 10, 3557.

Abstract

Pancreatic cancer represents one of the difficult problems of contemporary medicine. The development illness evolves very slowly, takes place in special sake (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 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 modelling approach can be used to investigate other types of cancers and examine various treatment procedures.

Keywords

Pancreatic cancer; cancer evolution; tumour microenvironment; mathematical model; open quasispecies model

Subject

Computer Science and Mathematics, Applied Mathematics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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