Mathematical modeling of molecular-genetic systems regulatory mechanisms activity in malignant neoplasms

Abstract The paper presents the method for constructing systems of nonlinear functional-differential equations with delay of a cellular regulator in norm and in cancerous formations. The existence of stable stationary as well as self-oscillatory solutions to the regulator equations, chaotic solutions and the “black hole” effect is established. The results of the quantitative analysis of the developed equations show the possibility of existence of chaotic behavior (the emergence of various types of chromosomal aberrations), the effect of failure of solutions on the trivial attractor - the effect of “black hole” (metastasis). The opportunity for forecasting the basic modes characteristics allows establishing molecular-genetic bases in oncologic pathogenesis, carrying out diagnostics and predicting characteristic stages of malignant neoplasms current.

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