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Mathematical Modeling of a Positive Connection in the p53-microRNA Tumor Marker System

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Abstract

A hierarchy of minimal mathematical models of the dynamics of the p53-Mdm2- microRNA system has been developed. The models are based on differential equations with a time delay, describing complex interaction mechanisms in the signal system of the p53 protein. We consider two types of interaction of p53 with microRNAs: a positive direct connection and a positive feedback. The feedback of microRNA-p53 is due to a negative effect of the microRNA on the Mdm2 protein, which is a negative regulator of p53. To approximate the direct positive effect of p53 on the microRNAs, a linear function or a representation of the Goldbeter-Koshland type is used. A comparison of numerical solutions with medical and biological data of a number of specific p53-dependent microRNAs is made, which proves that the models and the numerical analysis results are adequate. Special attention is given to analysis of a positive feedback of p53 and microRNAs. The minimal models allow us to consider the most general regularities of the p53-dependent microRNAs. Within the framework of these mathematical models it is shown that it is possible to neglect the Mdm2-miRNA connection for at least some of the most studied microRNAs associated with a direct positive connection with p53. However, those of the microRNAs that are an important negative regulator of Mdm2, can have the most significant impact on the entire p53-Mdm2-microRNA system. Conditions are obtained to manifest the regulatory function of microRNAs with respect to p53. The results of the numerical experiments indicate that such microRNAs can be used as a factor of an anticancer therapy.

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Authors and Affiliations

  1. Institute of Computational Technologies, Siberian Branch, Russian Academy of Sciences, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia

    S. D. Senotrusova & O. F. Voropaeva

Authors
  1. S. D. Senotrusova
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  2. O. F. Voropaeva
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Correspondence to S. D. Senotrusova or O. F. Voropaeva.

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Russian Text © The Author(s), 2019, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2019, Vol. 22, No. 3, pp. 317–334.

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Senotrusova, S.D., Voropaeva, O.F. Mathematical Modeling of a Positive Connection in the p53-microRNA Tumor Marker System. Numer. Analys. Appl. 12, 270–283 (2019). https://doi.org/10.1134/S1995423919030066

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  • DOI: https://doi.org/10.1134/S1995423919030066

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