Mathematical modeling the gene mechanism of colorectal cancer and the effect of radiation exposure

Lingling Li; Yulu Hu; Xin Li; Tianhai Tian; Lingling Li; Yulu Hu; Xin Li; Tianhai Tian

doi:10.3934/mbe.2024050

Mathematical Biosciences and Engineering

2024, Volume 21, Issue 1: 1186-1202. doi: 10.3934/mbe.2024050

Previous Article Next Article

Research article Special Issues

Mathematical modeling the gene mechanism of colorectal cancer and the effect of radiation exposure

1.
School of Science, Xi'an Polytechnic University, Xi'an 710048, China
2.
School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710048, China
3.
School of Mathematics, Monash University, Melbourne Vic 3800, Australia

Received: 15 October 2023 Revised: 27 November 2023 Accepted: 30 November 2023 Published: 25 December 2023

Cancer is the result of continuous accumulation of gene mutations in normal cells. The number of mutations is different in different types of cancer and even in different patients with the same type of cancer. Therefore, studying all possible numbers of gene mutations in malignant cells is of great value for the understanding of tumorigenesis and the treatment of cancer. To this end, we applied a stochastic mathematical model considering the clonal expansion of any premalignant cells with different mutations to analyze the number of gene mutations in colorectal cancer. The age-specific colorectal cancer incidence rates from the Surveillance, Epidemiology and End Results (SEER) registry in the United States and the Life Span Study (LSS) in Nagasaki and Hiroshima, Japan are chosen to test the reasonableness of the model. Our fitting results indicate that the transformation from normal cells to malignant cells may undergo two to five driver mutations for colorectal cancer patients without radiation-exposed environment, two to four driver mutations for colorectal cancer patients with low level radiation-exposure, and two to three driver mutations for colorectal cancer patients with high level radiation-exposure. Furthermore, the net growth rate of the mutated cells with radiation-exposure was is higher than that of the mutated cells without radiation-exposure for the models with two to five driver mutations. These results suggest that radiation environment may affect the clonal expansion of cells and significantly affect the development of tumors.
- mathematical modeling,
- colorectal cancer,
- incidence rate,
- driver mutation,
- radiation exposure
Citation: Lingling Li, Yulu Hu, Xin Li, Tianhai Tian. Mathematical modeling the gene mechanism of colorectal cancer and the effect of radiation exposure[J]. Mathematical Biosciences and Engineering, 2024, 21(1): 1186-1202. doi: 10.3934/mbe.2024050

Related Papers:

Abstract

Cancer is the result of continuous accumulation of gene mutations in normal cells. The number of mutations is different in different types of cancer and even in different patients with the same type of cancer. Therefore, studying all possible numbers of gene mutations in malignant cells is of great value for the understanding of tumorigenesis and the treatment of cancer. To this end, we applied a stochastic mathematical model considering the clonal expansion of any premalignant cells with different mutations to analyze the number of gene mutations in colorectal cancer. The age-specific colorectal cancer incidence rates from the Surveillance, Epidemiology and End Results (SEER) registry in the United States and the Life Span Study (LSS) in Nagasaki and Hiroshima, Japan are chosen to test the reasonableness of the model. Our fitting results indicate that the transformation from normal cells to malignant cells may undergo two to five driver mutations for colorectal cancer patients without radiation-exposed environment, two to four driver mutations for colorectal cancer patients with low level radiation-exposure, and two to three driver mutations for colorectal cancer patients with high level radiation-exposure. Furthermore, the net growth rate of the mutated cells with radiation-exposure was is higher than that of the mutated cells without radiation-exposure for the models with two to five driver mutations. These results suggest that radiation environment may affect the clonal expansion of cells and significantly affect the development of tumors.

References

[1]	H. Sung, J. Ferlay, R. L. Siegel, M. Laversanne, I. Soerjomataram, A. Jemal, et al., Global cancer statistics 2020: globocan estimates of incidence and mortality worldwide for 36 cancers in 185 countries, CA-Cancer J. Clin., 71 (2021), 209–249. https://doi.org/10.3322/caac.21660 doi: 10.3322/caac.21660
[2]	K. L. Newcomer, L. D. Porter, A delayed path to diagnosis: Findings from young-onset colorectal cancer patients and survivors, J. Clin. Oncol., 39 (2021), 5. https://doi.org/10.1200/JCO.2021.39.3_suppl.5 doi: 10.1200/JCO.2021.39.3_suppl.5
[3]	H. J. Li, D. Boakye, X. C. Chen, M. Hoffmeister, H. Brenner, Association of body mass index with risk of early-onset colorectal cancer: Systematic review and meta-analysis, Am. J. Gastroenterol., 116 (2021), 2173–2183. https://doi.org/10.14309/ajg.0000000000001393 doi: 10.14309/ajg.0000000000001393
[4]	W. Liu, Y. Deng, Z. Li, Y. Chen, X. Zhu, X. Tan, et al., Cancer evo-dev: a theory of inflammation-induced oncogenesis, Front. Immunol., 12 (2021), 768098. https://doi.org/10.3389/fimmu.2021.768098 doi: 10.3389/fimmu.2021.768098
[5]	R. R. Huxley, A. Ansary-Moghaddam, P. Clifton, S. Czernichow, C. L. Parr, M. Woodward, The impact of dietary and lifestyle risk factors on risk of colorectal cancer: a quantitative overview of the epidemiological evidence, Int. J. Cancer, 125 (2009), 171–180. https://doi.org/10.1002/ijc.24343 doi: 10.1002/ijc.24343
[6]	J. P. Thakkar, B. J. McCarthy, J. L. Villano, Age-specific cancer incidence rates increase through the oldest age groups, Am. J. Med. Sci., 348 (2014), 65–70. https://doi.org/10.1097/maj.0000000000000281 doi: 10.1097/maj.0000000000000281
[7]	S. Jones, W. D. Chen, G. Parmigiani, F. Diehl, N. Beerenwinkel, T. Antal, et al., Comparative lesion sequencing provides insights into tumor evolution, PNAS, 105 (2008), 4283–4288. https://doi.org/10.1073/pnas.0712345105 doi: 10.1073/pnas.0712345105
[8]	L. A. Loeb, Mutator phenotype may be required for multistage carcinogenesis, Cancer Res., 51 (1991), 3075–3079.
[9]	B. Vogelstein, K. W. Kinzler, Cancer genes and the pathways they control, Nat. Med., 10 (2004), 789–799. https://doi.org/10.1038/nm1087 doi: 10.1038/nm1087
[10]	S. Guo, Y. Ye, X. Liu, Y. Gong, M. Xu, L. Song, et al., Intra-tumor heterogeneity of colorectal cancer necessitates the multi-regional sequencing for comprehensive mutational profiling, Cancer Manag. Res., 13 (2021), 9209–9223. https://doi.org/10.2147/cmar.s327596 doi: 10.2147/cmar.s327596
[11]	Y. Kamal, G. Idos, Incidental young-onset adenomas: sporadic findings or harbingers of increased colon cancer risk, Curr. Treat. Options Gastroenterol., 20 (2022), 122–132. https://doi.org/10.1007/S11938-022-00375-0 doi: 10.1007/S11938-022-00375-0
[12]	V. Wunderlich, Early references to the mutational origin of cancer, Int. J. Epidemiol., 36 (2007), 246–247. https://doi.org/10.1093/ije/dyl272 doi: 10.1093/ije/dyl272
[13]	P. Armitage, R. Doll, The age distribution of cancer and a multi-stage theory of carcinogenesis, Br. J. Cancer, 8 (1954), 1–12. https://doi.org/10.1038/bjc.1954.1 doi: 10.1038/bjc.1954.1
[14]	A. G. Knudson, Mutation and cancer: statistical study of retinoblastoma, PNAS, 68 (1971), 820–823. https://doi.org/10.1073/pnas.68.4.820 doi: 10.1073/pnas.68.4.820
[15]	E. G. Luebeck, S. H. Moolgavkar, Multistage carcinogenesis and the incidence of colorectal cancer, PNAS, 99 (2002), 15095–19100. https://doi.org/10.1073/pnas.222118199 doi: 10.1073/pnas.222118199
[16]	R. Meza, J. Jeon, S. H. Moolgavkar, E. G. Luebeck, Age-specific incidence of cancer: phases, transitions, and biological implications, PNAS, 105 (2008), 16284–16289. https://doi.org/10.1073/pnas.0801151105 doi: 10.1073/pnas.0801151105
[17]	E. G. Luebeck, K. Curtius, J. Jeon, W. D. Hazelton, Impact of tumor progression on cancer incidence curves, Cancer Res., 73 (2013), 1086–1096. https://doi.org/10.1158/0008-5472.can-12-2198 doi: 10.1158/0008-5472.can-12-2198
[18]	B. M. Lang, J. Kuipers, B. Misselwitz, N. Beerenwinkel, Predicting colorectal cancer risk from adenoma detection via a two-type branching process model, PLoS Comput. Biol., 16 (2020), e1007552. https://doi.org/10.1371/journal.pcbi.1007552 doi: 10.1371/journal.pcbi.1007552
[19]	C. Paterson, H. Clevers, I. Bozic, Mathematical model of colorectal cancer initiation, PNAS, 117 (2020), 20681–20688. https://doi.org/10.1073/pnas.2003771117 doi: 10.1073/pnas.2003771117
[20]	A. Niida, K. Mimori, T. Shibata, S. Miyano, Modeling colorectal cancer evolution, J Hum Genet, 66 (2021), 869–878. https://doi.org/10.1038/s10038-021-00930-0 doi: 10.1038/s10038-021-00930-0
[21]	M. S. Lawrence, P. Stojanov, C. H. Mermel, J. T. Robinson, L. A. Garraway, T. R. Golub, et al., Discovery and saturation analysis of cancer genes across 21 tumour types, Nature, 505 (2014), 495–501. https://doi.org/10.1038/nature12912 doi: 10.1038/nature12912
[22]	J. L. Bos, E. R. Fearon, S. R. Hamilton, V. M. Verlaande, J. H. Van-Boom, A. J. Van-der, et al., Prevalence of ras gene-mutations in human colorectal cancers, Nature, 327 (1987), 293–297. https://doi.org/10.1038/327293a0 doi: 10.1038/327293a0
[23]	E. J. Grant, A. Brenner, H. Sugiyama, R. Sakata, A. Sadakane, M. Utada, et al., Solid cancer incidence among the life span study of atomic bomb survivors: 1958–2009, Radiat. Res., 187 (2017), 513–537. https://doi.org/10.1667/RR14492.1 doi: 10.1667/RR14492.1
[24]	S. H. Moolgavkar, A. Dewanji, D. J. Venzon, A stochastic two-stage model for cancer risk assessment. I. The hazard function and the probability of tumor, Risk Anal., 8 (1988), 383–392. https://doi.org/10.1111/j.1539-6924.1988.tb00502.x doi: 10.1111/j.1539-6924.1988.tb00502.x
[25]	C. J. Portier, A. Kopp-Schneider, C. D. Sherman, Calculating tumor incidence rates in stochastic models of carcinogenesis, Math. Biosci., 135 (1996), 129–146. https://doi.org/10.1016/0025-5564(96)00011-9 doi: 10.1016/0025-5564(96)00011-9
[26]	L. Li, T. Tian, X. Zhang, Mutation mechanisms of human breast cancer, J. Comput. Biol., 25 (2018), 396–404. https://doi.org/10.1089/cmb.2017.0111 doi: 10.1089/cmb.2017.0111
[27]	K. S. Crump, R. P. Subramaniam, C. B. Van-Landingham, A numerical solution to the nonhomogeneous two-stage MVK model of cancer, Risk Anal., 25 (2005), 921–926. https://doi.org/10.1111/j.1539-6924.2005.00651.x doi: 10.1111/j.1539-6924.2005.00651.x
[28]	H. Fakir, W. Y. Tan, L. Hlatky, P. Hahnfeldt, R. K. Sachs, Stochastic population dynamic effects for lung cancer progression, Radiat. Res., 172 (2009), 383–393. https://doi.org/10.1667/rr1621.1 doi: 10.1667/rr1621.1
[29]	R. R. Mercer, M. L. Russell, V. L. Roggli, J. D. Crapo, Cell number and distribution in human and rat airways, Am. J. Respir. Cell Mol. Biol., 10 (1995), 613–624. https://doi.org/10.1165/ajrcmb.10.6.8003339 doi: 10.1165/ajrcmb.10.6.8003339
[30]	C. Tomasetti, J. Poling, N. J. Roberts, N. R. London, M. E. Pittman, M. C. Haffner, et al., Cell division rates decrease with age, providing a potential explanation for the age-dependent deceleration in cancer incidence, PNAS, 116 (2019), 20482–20488. https://doi.org/10.1073/pnas.1905722116 doi: 10.1073/pnas.1905722116
[31]	C. Simonetto, U. Mansmann, J. C. Kaiser, Shape-specific characterization of colorectal adenoma growth and transition to cancer with stochastic cell-based models, PLoS Comput. Biol., 19 (2023), e1010831. https://doi.org/10.1371/journal.pcbi.1010831 doi: 10.1371/journal.pcbi.1010831
[32]	D. Peér, S. Ogawa, O. Elhanani, Tumor heterogeneity, Cancer Cell, 39 (2021), 1015–1017. https://doi.org/10.1016/j.ccell.2021.07.009 doi: 10.1016/j.ccell.2021.07.009
[33]	B. Vogelstein, N. Papadopoulos, V. E. Velculescu, S. Zhou, L. A. Diaz, K. W. Kinzler, Cancer genome landscapes, Science, 339 (2013), 1546–1558. https://doi.org/10.1126/science.1235122 doi: 10.1126/science.1235122
[34]	C. Tomasetti, B. Vogelstein, Cancer etiology. Variation in cancer risk among tissues can be explained by the number of stem cell divisions, Science, 347 (2015), 78–81. https://doi.org/10.1126/science.1260825 doi: 10.1126/science.1260825
[35]	C. S. Potten, C. Booth, D. Hargreaves, The small intestine as a model for evaluating adult tissue stem cell drug targets, Cell Prolif., 36 (2003), 115–129. https://doi.org/10.1046/j.1365-2184.2003.00264.x doi: 10.1046/j.1365-2184.2003.00264.x
[36]	F. Michor, Y. Iwasa, M. A. Nowak, Dynamics of cancer progression, Nat. Rev. Cancer, 4 (2004), 197–205.
[37]	C. J. Kaiser, R. Meckbach, P. Jacob, Genomic instability and radiation risk in molecular pathways to colon cancer, PLoS One, 9 (2014), e111024. https://doi.org/10.1371/journal.pone.0111024 doi: 10.1371/journal.pone.0111024
[38]	L. Li, X. Zhang, T. Tian, Mathematical modelling the pathway of genomic instability in lung cancer, Sci. Rep., 9 (2019), 14136. https://doi.org/10.1038/s41598-019-50500-w doi: 10.1038/s41598-019-50500-w
[39]	D. Fernandez-Antoran, G. Piedrafita, K. Murai, S. H. Ong, A. Herms, C. Frezza, et al., Outcompeting p53-mutant cells in the normal esophagus by redox manipulation, Cell Stem Cell, 25 (2019), 329–341. https://doi.org/10.1016/j.stem.2019.06.011 doi: 10.1016/j.stem.2019.06.011
[40]	N. Nori, A hypothesis: radiation carcinogenesis may result from tissue injuries and subsequent recovery processes which can act as tumor promoters and lead to an earlier onset of cancer, Br. J. Radiol., 93 (2020), 20190843. https://doi.org/10.1259/bjr.20190843 doi: 10.1259/bjr.20190843
[41]	M. Eidemüller, J. Becker, J. C. Kaiser, A. Ulanowski, A. I. Apostoaei, F. O. Hoffman, Concepts of association between cancer and ionizing radiation: accounting for specific biological mechanisms, Radiat. Environ. Biophys., 62 (2023), 1–15. https://doi.org/10.1007/s00411-022-01012-1 doi: 10.1007/s00411-022-01012-1

Reader Comments

Your name:*

Email:*
© 2024 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)