MODELING OCCURRENCE AND GROWTH OF CANCERS IN THE COLLECTIVE INTERACTION OF LIVE TISSUE CELLS EXCHANGING CHEMICAL AND MECHANICAL SIGNALS
DOI:
Keywords:
mathematical modeling, carcinoma, circadian rhythms, gene regulation, complex systemsAbstract
In this paper, we propose a chemo-mechanical model of cancer tumor occurrence and development in a quasi-two-dimensional epithelial tissue. The model includes the individual dynamics of each cell which depends on the change of its shape and volume, location in tissue, intercalation and ability to divide. We have introduced two series of cells, normal and cancer ones, which differ in the set of chemical and mechanical parameters. In this paper it is assumed that cancer cells arise from a local failure of spatial synchronization of circadian rhythms. The circadian pattern formation is produced due to transcription/translation processes inside epithelial cells and the exchange of chemical signals between cells. In order to calibrate the complex system parameters we have used a large number of microphotographs representing the morphology of both normal and cancer cells. Both deterministic and stochastic descriptions of the system have been applied. Numerical study of evolutionary dynamics of the model has shown different protein patterns, some of which can provoke tumor occurrence. Variations in the system parameters have allowed reproducing different types of carcinomas including both invasive and non-invasive types. The model we developed can be used for a detailed study of the influence of targeting drugs on tumor cells.
References
- Bratsun D.A., Merkuriev D.V., Zakharov A.P., Pismen L.M. Multiscale modeling of tumor growth induced by circadian rhythm disruption in epithelial tissue // J. Biol. Phys. - 2016. - Vol. 42, No 1. - P. 107-132.
- Zaharov A.P., Bracun D.A. Sinhronizacii cirkadiannyh ritmov v masstabah gena, kletki i vsego organizma // Komp’uternye issledovania i modelirovanie. - 2013. - T. 5, No 2. - S. 255-270.
- Bracun D.A., Zaharov A.P., Pis’men L.M. Mnogourovnevoe matematiceskoe modelirovanie vozniknovenia i rosta opuholi v tkani epitelia // Komp’uternye issledovania i modelirovanie. - 2014. - T. 6, No 4. - S. 585-604.
- Bracun D.A., Zaharov A.P. Matematiceskoe modelirovanie rakovyh obrazovanij pri kollektivnom vzaimodejstvii kletok epitelia // Vest. Perm. gos. gum.-ped. un-ta. Ser. No 2: Fiziko- matematiceskie i estestvennye nauki. - 2014. - Vyp. 1. - S. 20-34.
- Bratsun D., Volfson D., Hasty J., Tsimring L. Delay-induced stochastic oscillations in gene regulation // PNAS. - 2005. - Vol. 102, No 41. - P. 14593-14598.
- Bracun D.A., Zaharov A.P. Modelirovanie prostranstvenno-vremennoj dinamiki cirkadiannyh ritmov Neurospora crassa // Komp’uternye issledovania i modelirovanie. - 2011. - T. 3, No 2. - S. 191-213.
- Bratsun D.A., Zakharov A.P. Spatial Effects of Delay-Induced Stochastic Oscillations in a Multi-scale Cellular System // Springer Proceedings in Complexity. - 2016. - P. 93-103.
- Bratsun D.A., Zakharov A.P., Pismen L.M. Chemo-mechanical modeling of Tumor Growth in Elastic Epithelial Tissue // AIP Conference Proceedings. - 2016. - Vol. 1760. - 020007.
- Bracun D.A., Zaharov A.P. Prostranstvenno-raspredelennye stohasticeskie kolebania s zapazdyvaniem v mnogokletocnoj sisteme // Vest. Perm. gos. gum.-ped. un-ta. Ser. No 2: Fiziko- matematiceskie i estestvennye nauki. - 2015. - Vyp. 1. - S. 73-87.
- Zakharov A.P., Pismen L.M. Reshaping nemato-elastic sheets // Eur. Phys. J. E Soft Matter. - 2015. - Vol. 38, No 7. - P. 75.
- Martinez-Torres C., Laperrousaz B., Berguiga L., Boyer-Provera E., Elezgaray J., Nicolini F.E., Maguer- Satta V., Arneodo A., Argoul F. Deciphering the internal complexity of living cells with quantitative phase microscopy: a multiscale approach // J. Biomed. Opt. - 2015. - Vol. 20, No 9. - P. 096005.
- Bracun D.A., Krasnakov I.V. Matematiceskoe modelirovanie processa terapii rakovoj opuholi s pomos’u nanocastic // Matematiceskoe modelirovanie v estestvennyh naukah: tez. dokl. - Perm’: izd-vo PNIPU, 2016 - S. 53-54.