NUMERICAL RESEARCH OF DEGENERATE DYNAMIC BALANCE MODEL OF THE CELL CYCLE

S. I. Ebel

Abstract


The mathematical model of the cell cycle is considered. It is shown that a balance dynamic model of the cell cycle for the mitotic cell division is degenerate.  The method of constructing of the degenerate balance dynamic model of the cell cycle is submitted.  The methods of the theory of degenerate groups and the numerical methods for the initial value problem for the Leontiev type systems are applied to the studied model. The numerical investigation of a model example of a degenerate balance dynamic model of the cell cycle is performed. The construction of the mathematical model will allow to reduce a time of studying of the processes occurring in the cell, to develop the possible scenarios of development in accordance with the changing of environmental factors and to optimize the process of removing of the division defect.

Keywords


model of the cell cycle, numerical solution, Leontieff type models, computational efficiency of the algorithm.

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References


Sviridyuk G.A., Zagrebina S.A. The Showalter - Sidorov Problem as Phenomena of the Sobolev-Type Equations. The Bulletin of Irkutsk State Universy. Series "Mathematics", 2010, vol. 3, no. 1, pp. 104-125. (in Russian)

Zagrebina S.A. On the Showalter - Sidorov problem. Izv. Vyssh. Uchebn. Zaved. Mat., 2007, no. 3, pp. 22-28. (in Russian)

Zamyshlyaeva A.A. The Higher-Order Sobolev Type Models. Bulletin of the South Ural State Universy. Series "Mathematical Modelling, Programming & Computer Software", 2014, vol. 7, no. 2, pp. 5-28. doi:10.14529/mmp140201 (in Russian)

Sagadeeva M.A. A Existance and a Stabily of Solutions for Semilinear Sobolev Type Equations in Relatively Radial Case. The Bulletin of Irkutsk State Universy. Series "Mathematics", 2013, vol. 6, no. 1, pp. 78-88. (in Russian)

Manakova N.A., Bogonos E.A. Optimal Control to Solutions of the Showalter - Sidorov Problem for a Sobolev Type Equation. The Bulletin of Irkutsk State Universy. Series "Mathematics", 2010, vol. 3, no. 1, pp. 42-53. (in Russian)

Sviridyuk G.A., Brychev S.V. Numerical Solution of Systems of Equations of Leontieff Type. Izv. Vyssh. Uchebn. Zaved. Mat., 2003, no. 8, pp. 46-52. (in Russian)

Burlachko I.V., Sviridyuk G.A. On the Numerical Solution of the Cauchy Problem for a Degenerate Linear System of Ordinary Differential Equations. Tambov Universy Reports. Series: Natural and Technical Sciences, 2003, vol. 8, no. 3, p. 353. (in Russian)

Keller A.V., Shishkina T.A. The Method of Constructing Dynamic and Static Balance Models at the Enterprise Level. Bulletin of the South Ural State Universy. Series "Economics and Management", 2013, vol. 7, no. 3, pp. 6-10. (in Russian)

Shestakov A.L., Sviridyuk G.A. A New Approach to the Measurement of Dynamically Perturbed Signals. Bulletin of the South Ural State Universy. Series "Mathematical Modeling and Programming & Computer Software", 2010, no. 16(192), pp. 116-120. (in Russian)

Keller A.V., Nazarova E.I. The Regularization Property and the Computational Solution of the Dynamic Measure Problem. Bulletin of the South Ural State Universy. Series "Mathematical Modeling and Programming & Computer Software", 2010, no. 16(192), pp. 32-38. (in Russian)

Shestakov A.L., Sviridyuk G.A., Khudyakov Y.V. Dinamic Measurement in Spaces of "Noise". Bulletin of the South Ural State Universy. Series "Computer Technologies, Automatic Control & Radioelectronics", 2013, vol. 13, no. 2, pp. 4-11. (in Russian)

Gernet N.D. Carrying a Dynamic Model of the Cell Cycle. Eastern-European Journal of Enterprise Technologies, 2013, vol. 6, no. 4(66), pp. 42-47. (in Russian)

Leontieff V.V. Interindustry Economics. Moscow, Ekonomika Publ., 1997. (in Russian)

Vysotskaya L.V. Motic Cycle and s Regulation. The Vavilov Journal of Genetics and Breeding, 2014, vol. 18, no. 1, pp. 81-92. (in Russian)

Antonova E.I., Berkova D.I., Sagalbaeva L.E., Shpak O.J. The Dynamics of Cellular Cycle Indices of Ecto- and Endothermic Animals. Journal of New Medical Technologies, 2011, vol. 18, no. 2, pp. 18-20. (in Russian)

Keller A.V., Ebel S.I. About Degenerate Discrete Dynamic Model of the Balance of the Cell Cycle. Yuzhno-Uralskaya Molodezhnaya Shkola po Matematicheskomu Modelirovaniyu, Chelyabinsk, 29-30 Maya 2014. South Ural Youth School on Mathematical Modeling, Chelyabinsk, 29-30 May 2014. Chelyabinsk, Publishing center of SUSU, 2014, pp. 74-79. (in Russian)

Keller A.V. The Algorhm for Solution of the Showalter - Sidorov Problem for Leontieff Type Models. Bulletin of the South Ural State Universy. Series "Mathematical Modeling and Programming & Computer Software", 2011, no. 4(221), pp. 40-46. (in Russian)


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