Balance dynamic model of the cell cycle

Authors

  • Анатолий Иванович Божков Researcher Institute to Biologies V.N. Karazin Kharkov national university sq. Svoboda, 4, Kharkov, 61022, Ukraine
  • Надежда Дмитриевна Гернет Researcher Institute of Biologies V.N.Karazin Kharkov national university sq. Svoboda, 4, Harkov, 61022, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2013.19190

Keywords:

living cell, mathematical modeling, balance model, cell cycle, the dynamics of the cell development

Abstract

The development of new mathematical and computer approaches and the needs of fundamental medicine and biology have raised a complicated issue of modelling a living cell. This may be solved today with achievements of theoretical and experimental methods. It is especially interesting to model a cell at different stages of its life cycle, including its division, differentiation and death. The paper considers mathematical modeling of cell cycle, being a dynamic sequence of events from one cell division to another.

Based on the system analysis of the available data on the living cell development and functioning, it is suggested to consider the cell cycle as an integrated dynamic process of the interaction of intracellular matter flow, energy, and information directed on the reproduction of the new live cell.

The work analyses the specifics and essential preconditions of the cell cycle description using the balance dynamic model, which sets the balance of reproduction, distribution and consumption of matter, energy, and information inside the cell for each temporary subinterval of the cell cycle.

The regularities and peculiarities of the cell development dynamics and their influence on the processes of organism aging are considered on the basis of formal mathematical properties for built dynamic model and its simplified modifications. The questions of practical using the offered model are discussed.

Author Biographies

Анатолий Иванович Божков, Researcher Institute to Biologies V.N. Karazin Kharkov national university sq. Svoboda, 4, Kharkov, 61022

Doctor of the Biological sciences, professor

Director of Researcher Institute to Biologies

Надежда Дмитриевна Гернет, Researcher Institute of Biologies V.N.Karazin Kharkov national university sq. Svoboda, 4, Harkov, 61022

Senior scientific employee

Scientifically

References

  1. Гернет, Н. Д. Информационная технология комплексной оценки процессов старения биологических организмов. [Текст] / Н. Д. Гернет, А. И. Божков // Восточно-Европейский журнал передовых технологий. – 2012. – №6/2. – C. 31-36.
  2. Лахно, В. Д. Математическая клетка. Концепции построения математических моделей переноса заряда в живой клетке [Текст] / В. Д. Лахно // Вестник РУДН. Серия Прикладная и компьютерная математика. 2003. – Т.2, №2. – С. 77-84.
  3. Терентьев, А. А. Динамическая протеомика в моделировании живой клетки. Белок-белковые взаимодействия [Текст] / А. А. Терентьев, Н. Т. Молдогазиева, К. В. Шайтан // Успехи биологической химии. – 2009. – Т.49. – С. 429-480.
  4. Smolen, P. Mathematical modelinng of gene networks [Текст] / P. Smolen, D. A. Baxter, J. H. Byrne // Neuron. – 2000. – Vol. 26. – P. 567-580.
  5. Hasty, J. Computational studies of gene regulatory networks in numero molecular biology. [Текст] / J. Hasty, D. McMillen, F. Isaacs, J. J. Collins // Nature Rev. Genet. – 2001. – Vol.2. – P. 268-297.
  6. Ризниченко, Г. Ю. Лекции по математическим моделям в биологии / Г. Ю. Ризниченко. – М., Ижевск: НИЦ «Регулярная и хаотическая динамика», 2011. – 560 с.
  7. Кривовичев, Г. В. Математическое моделирование плоских движений живой клетки [Текст] / Г. В. Кривовичев, В. П. Трегубов // Вестник Харьковского национального университета им. В. Н. Каразина. – 2009. – №850. – С. 91-102.
  8. Zhu, C. Cell mechanics: mechanical response, cell adhesion and molecular deformation [Текст] / C. Zhu, G. Bao, N. Wang // Annual Reviews of Biomedical Engineering. – 2000. – Vol. 02. – Р. 189-226.
  9. Petelin, D. V. Simple Model of Cell Cycle Dynamics. [Текст] / D. V. Petelin, M. Sadovsky // Journal of Siberian Federal University. Mathematical & Physics. – 2011. – №4(3). – Р. 382-384.
  10. Лахно, В. Информационно-вычислительная среда Mathcell для моделирования живой клетки [Текст] / В. Лахно, Н. Назипова, В. Ким, С. Филиппов, Н. Фиалко, Д. Устинин, А. Теплухин, Г. Тюльбашева, А. Зайцев, М. Устинин // Математическая биология и биоинформатика. – 2007. – Т. 2, №2. – С. 361-376.
  11. Халявкин, А. В. Старение: роль управляющих сигналов [Текст] / А. В. Халявкин, А. И. Яшин; ред. Г. И. Марчук и др. // Геронтология in silico: Становление новой дисциплины. Математические модели, анализ данных и вычислительные эксперименты. – М.: БИНОМ. Лаборатория знаний, 2007. – С. 114-147.
  12. Згуровский, М. З. / Системный анализ. Проблемы. Методология. Приложения [Текст] / М. З. Згуровский, Н. Д. Панкратова. – К.: Наукова думка, 2005. – 741 с.
  13. Savagean, M. A. Biochemacal System Analysis. [Текст] / M. A. Savagean. – Addison Wesley, Reading., 1976.
  14. Doyle, F. J. Systems interface biology. [Текст] / F. J. Doyle, J. Stelling // J. R. Soc. Interface. – 2006. – №3. – Р. 603-616.
  15. Voit, E. O. Biochemical Systems Theory: A Rewieu. [Текст] / E. O. Voit // ISRN Biochemicals. – Volume 2013. – Article ID897758. – 53 p.
  16. Voit, E. O. Canonical Nonlinear Modelling. S-System Approach to Understanding Complexity [Текст] / E. O. Voit // Van Nostrand Reinhold. – New York, NY, USA, 1991.
  17. Ярыгин, В. Н. Биология [Текст] / В. Н. Ярыгин, В. И. Васильева, И. Н. Волков, В. В.Синельщикова. – М.: Высш.шк., 2003. – 432 с.
  18. Атауллаханов, Ф. И. Клетка: координация молекулярных процессов деления [Текст] / Ф. И. Атауллаханов., Е. Л. Грищук // Журнал «Природа» . – 2012. – №01. – С. 37-44.
  19. Калашников, Ю. Я. Информационный микромир живой клетки (идеи, концепции, гипотезы) [Электронный ресурс] / Ю. Я. Калашников // Библиотека РГИУ. Философия информационной цивилизации. – Режим доступа: www/ URL: http://www/sciteclibarary.ru/rus/catalog/pages/9557.html. – 11.03.2009г.
  20. Малинецкий, Г. Г. Математические основы синергетики. Хаос, структуры. Вычислительный эксперимент [Текст] / Г. Г. Малинецкий. – М.: КомКнига, 2005. – 312 с.
  21. Гантмахер, Ф. Р. Теория матриц [Текст] / Ф. Р. Гантмахер. – М:. Наука, 1988.
  22. Гернет, Н. Д. Прогнозирование динамики процессов старения биологических систем. [Текст]: материалы 13-й Междунар. междисциплинарной науч.-практ. школы-конф., 26 апреля – 05 мая 2013г. / Н. Д. Гернет, А. И. Божков // Современные проблемы науки и образования. – Харьков: Украинская Ассоциация “Женщины в науке и образовании“, Харьковский национальный университет имени В. Н. Каразина, 2013. – С.196-197.
  23. Gernet, N., Bozhkov, А. (2012). Informational technology for the complex estimation of the biological organism ageing processes. Eastern-European Journal of Enterprise Technologies, 6(2(60)), 31-36.
  24. Lakhno, V. (2003). Mathematical cell. Concepts of mathematical models creation of charge transfer in living cell. Messenger of RUDN. Series Applied and computer mathematics, V.2, №2, 77-84.
  25. Terentyev, A., Moldogaziyeva, N., Shaitan, K. (2009). Dynamic proteomika in living cell modeling. Protein-proteinaceous interactions. Successes of biological chemistry, 49, 429-480.
  26. Smolen, P., Baxter, D., Byrne, J. (2000). Mathematical modelinng of gene networks. Neuron, 26, 567-580.
  27. Hasty, J., McMillen, D., Isaacs, F., Collins, J. (2001). Computational studies of gene regulatory networks in numero molecular biology. Nature Rev. Genet, 2, 268-297.
  28. Riznichenko, G. (2011). Lectures on mathematical models in biology. M., Izhevsk: Research Center “Regular and chaotic dynamics”, 560.
  29. Krivovichev, G., Tregubov, V. (2009). Mathematical modeling of flat movements of living cell. The messenger of V.N. Karazin Kharkov national university, 850, 91-102.
  30. Zhu, C., Bao, G., Wang, N. (2000). Cell mechanics: mechanical response, cell adhesion and molecular deformation. Annual Reviews of Biomedical Engineering, 02, 189-226.
  31. Petelin, D., Sadovsky, M. (2011). Simple Model of Cell Cycle Dynamics. Journal of Siberian Federal University. Mathematical & Physics., 4(3), 382-384.
  32. Lakhno, V., Nazipov, N., Kim, V., Filippov, S., Fialko, N, Ustinin, D., Teplukhin, A., Tyulbasheva, G., Zaytsev, A., Ustinin, M. (2007). Information computing Mathcell environment for modeling of living cell. Mathematical biology and bioinformatics, Vol. 2, No. 2, 361-376.
  33. Halyavkin, A., Yashin, A.; In: Marchuk, G. I., etc. (2007). Aging: role of operating signals. “In silico” gerontology: Formation of new discipline. Mathematical models, analysis of data and computing experiments. M: BINOM. Laboratory of knowledge, 114-147.
  34. Zgurovsky, M., Pankratov, N. (2005). System analysis. Problems. Methodology. Appendices. Naukova thought, 741.
  35. Savagean, M. (1976). Biochemical System Analysis. Addison Wesley, Reading.
  36. Doyle, F. J., Stelling, J. (2006). Systems interface biology. J. R. Soc. Interface, 3, 603-616.
  37. Voit, E. O.(2003). Biochemical Systems Theory: A Rewieu. ISRN Biochemicals, Volume 2013, Article ID897758, 53.
  38. Voit, E. O. (1991). Canonical Nonlinear Modelling. S-System Approach to Understanding Complexity. Van Nostrand Reinhold. New York, NY, USA.
  39. Yarygin, V., Vasilyeva, V., Volkov, I., Sinelshchikova, V. (2003). Biology. M: Higher school, 432.
  40. Ataullakhanov, F., Grishchuk, E. (2012). Cell: coordination of molecular processes of division. “Priroda” magazine, 01, 37-44.
  41. Kalashnikov, Yu. (2009). Information microcosm of living cell (idea, concept, hypothesis). RGIU Library. Philosophy of information civilization. http://www/sciteclibarary.ru/rus/catalog/pages/9557.html.
  42. Malinetsky, G. G. (2005). Mathematical bases of synergetrics. Chaos, structures. Computing experiment. M: КомBook, 312.
  43. Gantmakher, F. R. (1988). The Theory of matrixes.
  44. Gernet, N., Bozhkov, A. (2013). Forecasting of aging processes dynamics of biological systems. Modern problems of science and education. Materials 13th International interdisciplinary scientific and practical conference, 196-197.

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Published

2013-12-16

How to Cite

Божков, А. И., & Гернет, Н. Д. (2013). Balance dynamic model of the cell cycle. Eastern-European Journal of Enterprise Technologies, 6(4(66), 42–47. https://doi.org/10.15587/1729-4061.2013.19190

Issue

Vol. 6 No. 4(66) (2013): Mathematics and cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2014 Анатолий Иванович Божков, Надежда Дмитриевна Гернет

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