Response to stress via underlying deep gene regulation networks

Exposure of cells to non-optimal growth conditions or to any environment that reduces cell viability can be considered as a stress. In this paper, we are going to highlight the main factors that determine the danger of stress to a cell considered as a biochemical system. To this end, we introduce a new mathematical concept of biosystem stability, where we take into account a signal transduction by deep gene networks. Using this concept and known results on approximations by deep networks, we find asymptotic estimates of the size and the depth of gene regulation networks that define the stress response. We propose a new algorithm to find the gene network approximating a prescribed output. It allows us, with the help of Kolmogorov epsilon$$ \epsilon $$-entropy and the deep neural network theory, to estimate the number of genes involved in regulation of responses on a stress (for example, a heat shock). We show that the main factors that increase the sensitivity of the systems with respect to a stress are the number of biochemical network parameters affected by the stress and sensitivities of kinetic rates with respect to these parameters.

Automated summary

In this paper, the main factors determining the danger of stress to a cell as a biochemical system are highlighted, introducing a new mathematical concept of biosystem stability. An algorithm is proposed to find the gene network approximating a prescribed output, using Kolmogorov epsilon $$ \epsilon $$-entropy and deep neural network theory to estimate the number of genes involved in regulating responses to stress. It is shown that the sensitivity of systems to stress is increased by the number of biochemical network parameters affected by stress and the sensitivities of kinetic rates to these parameters.