A sample of mathematical modeling of gene regulatory networks

What is it about?

Gene regulatory networks (GRN) form and regulate the main processes in living organisms. Elements of such a network are identified with genes, a segment of a genetic sequence. Each gene is assumed to communicate with other genes. Together, they form the reaction to internal and external events. Promoted functions in an organism are also managed by the GRN. Mathematically, GRN is usually modeled as a graph with vertices (genes) and edges (connections). To get information about the possible evolution of GRN, a system of ordinary differential equations is composed, which has amounts of proteins expressed by a gene as unknowns. These protein messages can be sent to other elements of a network. As a result, stable regimes may be established, for example, some rhythmic (periodic ) processes. Mathematically, this is described by attractors. They are subsets of a phase space, which have the remarkable properties of attracting other trajectories. Knowing all or a part of attractors allows predicting the behavior of a network in finite periods of time. This preprint shows a sample of mathematical research of that kind. It tells about attractors in the form of stable equilibria and stable periodic solutions, and provides an extensive reference list of recent articles concerning this subject.

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Photo by Vladislav Osterman on Unsplash

Photo by Vladislav Osterman on Unsplash

Why is it important?

It allows us to study the genetic network in a model and test the model by varying multiple parameters. The future behavior of GRN on a finite time interval can be predicted. Comparison with available experimental data allows us to judge the adequacy of a model.

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