Kinetic discretization of the multidimensional PIDE model of gene regulatory networks

2023. 04. 18. 17:15
M. Vághy (Pázmány Péter Catholic Univ., Budapest)

Joint work with I. Otero-Muras, M. Pájaro, G. Szederkényi 

Gene expression is a fundamental process of actually realizing DNA information in the form of proteins in living organisms. Therefore, the (quantitative) modeling of gene expression has been the focus of research during the last decades. Based on [1], the so-called generalized Friedman (or multidimensional PIDE) model was introduced in [2] which describes the operation of a genetic circuit of $n$ genes expressed into $n$ different protein types. In this contribution, a special discretization scheme for the multidimensional PIDE model is proposed. It is shown that the obtained set of ODEs can be formally represented as a chemical reaction network (CRN) with a strongly connected reaction graph. This allows the direct application of the theory of CRNs and compartmental systems for the qualitative analysis of the approximating dynamics. In this framework, the existence, uniqueness, and stability of equilibria can be shown straightforwardly. Moreover, the stationary probability distribution of the system can be computed efficiently. Several illustrative examples will be presented to show the operation and precision of the approach.

[1] Friedman, N., Cai, L., & Xie, X. S. (2006). Linking stochastic dynamics to population distribution: an analytical framework of gene expression. Physical review letters, 97(16), 168302.

[2] Pájaro, M., Alonso, A. A., Otero-Muras, I., & Vázquez, C. (2017). Stochastic modeling and numerical simulation of gene regulatory networks with protein bursting. Journal of theoretical biology, 421, 51-70.

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