Stability analysis of cell signaling on the example of the phenomenological model of the PI3K-Akt-mTOR cascade

Sapega T.S., Guria G.Th.

National Research Center for Hematology, 4a, Novozykovskii proezd, Moscow, 125167, Russian Federation Moscow Institute of Physics and Technology (State University), 9 Institutskiy per., Dolgoprudny, Moscow Region, 141701, Russian Federation

To provide a wide-spectrum cellular response (cell division, differentiation, alteration of metabolism, apoptosis or its evasion), there functions the network of signaling pathways in the cell, which are cascades of biochemical reactions. These cascades transmit information from the cell membrane to its nucleus. Some disruptions in cell signaling pathways lead to malignant cell transformation [1, 2]. Based on what, the stability of signal transduction in cell is extremely important.

The report will present a simplified graph-diagram of PI3K-Akt-mTOR signaling cascade, based on the data presented in [3]. The aim of the work was to find the conditions for the dynamic and parametric stability loss of this signal path. A phenomenological model of cascade activation was compiled and described by the ODE system. The study of the phase portrait of the stationary states of the system in the absence of exogenous stimulation made it possible to judge the conditions of instability in terms of the model. An analysis of the case with external stimulation made it possible to obtain an explicit expression for the magnitude of the dynamic destabilization threshold of the signal path PI3K-Akt-mTOR. Based on the data on the biochemical effects of a number of genetic mutations, these mutations were classified according to their effect on the magnitude of the dynamic destabilization threshold. A table was compiled containing estimates of the possible influence of a number of known therapeutic agents on the magnitude of the buckling threshold of the PI3K-Akt-mTOR cascade.


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3. I.A. Yakutik, L.S. Al-Radi, B.V. Biderman, E.A. Nikitin, A.B. Sudarikov. Mutations in the genes of MAP-kinases in hairy cell leukemia and lymphoma from cells of the red pulp of the spleen. Hematology and transfusiology. - 2018. - T. 63: p. 112

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