Mathematical Model of Pancreatic Cancer Cell Dynamics Considering the Set of Sequential Mutations and Interaction with the Immune System
Abstract
:1. Introduction
- The process of formation of precancerous and cancerous cells represents a successive chain of mutations over a relatively long period of time (10 to 20 years). During this time, the disease often causes very limited noticeable symptoms, and the cancer has often already spread at the time of diagnosis, with the most common sites of metastasis being the liver, lung, and peritoneum [3].
Framework for Quasispecies Dynamics
- (a)
- is a smooth function ;
- (b)
- ;
- (c)
- If , then ;
- (d)
- Function has only one maximum at the point , .
2. Development of the Cancer Mutations
3. Model Calibration for Cancer and Precancerous Cell Dynamics
4. Computational Experiments
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
PDAC | Pancreatic ductal adenocarcinoma |
CTL | effector CD8+ T lymphocyte |
ODE | ordinary differential equation |
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Mutation Type | Doubling Time (Days) | Mortality |
---|---|---|
K (KRAS) | 200 | |
P (TP53) | 800 | |
C (CDKN2A) | 800 | |
S (SMAD4) | 900 | |
140 | ||
180 | ||
180 | ||
750 | ||
600 | ||
600 | ||
120 | ||
120 | ||
120 | ||
500 | ||
100 |
Cell type | K | P | C | S | ||||
Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
Cell Type | ||||||||
Number | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
Mutation type, i | K | P | C | S | ||||
Symbiosis, | 4 | 1 | 1 | 2 | 20 | 24 | 24 | |
Mutation type, i | ||||||||
Symbiosis, | 33 | 32 | 32 | 20 | 20 | 20 | 36 | 20 |
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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. https://doi.org/10.3390/math10193557
Bratus AS, 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(19):3557. https://doi.org/10.3390/math10193557
Chicago/Turabian StyleBratus, Alexander S., Nicholas Leslie, Michail Chamo, Dmitry Grebennikov, Rostislav Savinkov, Gennady Bocharov, and Daniil Yurchenko. 2022. "Mathematical Model of Pancreatic Cancer Cell Dynamics Considering the Set of Sequential Mutations and Interaction with the Immune System" Mathematics 10, no. 19: 3557. https://doi.org/10.3390/math10193557