Numerical stochastic modelling of the proliferation process of naive T-lymphocytes in the lymph node
-
Nikolai V. Pertsev
and
Konstantin K. Loginov
Abstract
A continuously discrete stochastic model describing the proliferation process of naive T-lymphocytes during their contact with dendritic cells in a single lymph node is presented. Contact interaction is carried out between antigen-specific naive T-lymphocytes and antigen-presenting dendritic cells. The model is defined in terms of a random process whose components contain populations of different cells and families of unique cell types located in separate phases of the cell cycle. Model assumptions, recurrence relations for model variables, and a numerical simulation algorithm based on the Monte Carlo method are presented. The results of computational experiments with the model are presented illustrating the dynamics of the development of a population of cells formed from multiplying antigen-specific naive T-lymphocytes (memory and effector cells).
Funding statement: The research was supported by the Russian Science Foundation, project No. 23–11–00116.
References
[1] A. K. Abbas, E. G. Likhtman, and Sh. Pillai, Fundamentals of Immunology. Functions of the Immune System and their Disorders. Geotar-Media, Moscow, 2022 (in Russian).Search in Google Scholar
[2] P. Bousso and E. Robey, Dynamics of CD8+ T-cell priming by dendritic cells in intact lymph nodes. Nature Immunology 4 (2003), No. 6, 579–585.10.1038/ni928Search in Google Scholar PubMed
[3] T. Harris, Theory of Branching Random Processes. Vol. 6. Springer, Berlin, 1963.10.1007/978-3-642-51866-9Search in Google Scholar
[4] W.-Z. Huang, W.-H. Hu, Y. Wang, et al., A mathematical modelling of initiation of dendritic cells-induced T cell immune response. Int. J. Biol. Sci. 15 (2019), No. 7, 1396–1403.10.7150/ijbs.33412Search in Google Scholar PubMed PubMed Central
[5] O. Hyrien, R. Chen, and M. S. Zand, An age-dependent branching process model for the analysis of CFSE-labeling experiments. Biology Direct 5 (2010), 41.10.1186/1745-6150-5-41Search in Google Scholar PubMed PubMed Central
[6] M. Kimmel and D. E. Axelrod, Branching Processes in Biology. Springer-Verlag, New York, 2002.10.1007/b97371Search in Google Scholar
[7] G. Kramer, Mathematical Methods of Statistics. Mir, Moscow, 1975 (in Russian).Search in Google Scholar
[8] M. Marchenko, PARMONC — A software library for massively parallel stochastic simulation. Lecture Notes in Computer Science 6873 (2011), 302–315.10.1007/978-3-642-23178-0_27Search in Google Scholar
[9] M. A. Marchenko and G. A. Mikhailov, Parallel realization of statistical simulation and random number generators. Russ. J. Numer. Anal. Math. Modelling 17 (2002), No. 1, 113–124.10.1515/rnam-2002-0107Search in Google Scholar
[10] G. A. Mikhailov and A. V. Voitishek, Numerical Statistical Simulation. Monte Carlo Methods. Akademia, Moscow, 2006 (in Russian).Search in Google Scholar
[11] N. V. Pertsev, G. A. Bocharov, and K. K. Loginov, Numerical simulation of T-lymphocyte population dynamics in a lymph node. J. Appl. Industr. Math. 16 (2022), No. 4, 737–750.10.1134/S1990478922040147Search in Google Scholar
[12] B. J. Pichugin, N. V. Pertsev, V. A. Topchii, and K. K. Loginov, Stochastic modelling of age-structed population with time and size dependence of immigration rate. Russ. J. Numer. Anal. Math. Modelling 33 (2018), No. 5, 289–299.10.1515/rnam-2018-0024Search in Google Scholar
[13] I. M. Sobol, Numerical Monte Carlo methods. Nauka, Moscow, 1973 (in Russian).Search in Google Scholar
[14] A. A. Yarilin, Immunology. Geotar-Media, Moscow, 2010 (in Russian).Search in Google Scholar
© 2025 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- Self-similar mechanism of thrombin generation
- Reticular network as the lymph nodes railroad system: T cells migration modelling by the free energy minimization technique
- Personalization of parameters of electro-physiological model of the human heart
- Heterogeneous deformations of inflated hyperelastic membranes for data-driven constitutive modelling
- Numerical stochastic modelling of the proliferation process of naive T-lymphocytes in the lymph node
Articles in the same Issue
- Frontmatter
- Self-similar mechanism of thrombin generation
- Reticular network as the lymph nodes railroad system: T cells migration modelling by the free energy minimization technique
- Personalization of parameters of electro-physiological model of the human heart
- Heterogeneous deformations of inflated hyperelastic membranes for data-driven constitutive modelling
- Numerical stochastic modelling of the proliferation process of naive T-lymphocytes in the lymph node
