2016 , Volume 21, ¹ 2, p.12-25
Voropaeva O.F., Kozlova A.O., Senotrusova S.D.
Numerical analysis of the transition from the equation with retarded argument to the ODE system in a mathematical model of the tumor markers network
The p53 protein (tumor necrosis factor) involved in many life and death processes is expressed in all cells of the organism including the formation of tumors and aging. Mdm2 protein is considered to be the key negative p53 regulator. The investigation of the mechanism of p53 and Mdm2 interaction is paramount for developing new approaches to cancer treatment and determining the prevention strategy for many diseases.
This paper is devoted to a development of the effective numerical technology for solution of a system of equations describing the dynamics of the p53-Mdm2 network. We consider two interrelated mathematical models of the p53-Mdm2 network. The first model of the proteins concentrations dynamics includes the system of two nonlinear differential equations with the retarded argument. The second model describes hypothetical stages of process and uses the simplest ODE system of sufficiently higher dimension. We numerically show that in the transition to the limit in which the second model has sufficiently many stages, we obtain model based equation with retarded argument. We examined the specific conditions of the numerical realization of this transition.
Keywords: numerical analysis, equation with retarded argument, tumor marker, p53-Mdm2 network
Voropaeva Olga Falaleevna
Position: Leading research officer
Office: Federal Research Centerfor Information and Computational Technologies
Address: 630090, Russia, Novosibirsk, ac. Lavrentyev Ave. 6
Phone Office: (383) 330-85-70
SPIN-code: 6550-0849Kozlova Alina Olegovna
Address: 630090, Russia, Novosibirsk, ac. Lavrentyev Ave. 6
Senotrusova Sofya Dmitrievna
Position: Junior Research Scientist
Address: 630090, Russia, Novosibirsk, Academician M.A. Lavrentiev avenue, 6
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Voropaeva O.F., Kozlova A.O., Senotrusova S.D. Numerical analysis of the transition from the equation with retarded argument to the ODE system in a mathematical model of the tumor markers network // Computational technologies. 2016. V. 21. ¹ 2. P. 12-25