Polynomials, polytopes, and steady states of reaction networks

Authors

  • Elisenda Feliu

Keywords:

reaction network, multistationarity, bistability, Newton polytope, positivity, real algebraic geometry

Abstract

In this paper we introduce the theory of the study of steady states of reaction networks, and we focus on examples from molecular biology. Steady states are the positive solutions to a system of polynomial equations containing numerous parameters. One of the objectives of the theory is to study steady states as a function of parameters, and, in particular, to determine their number. These problems can be solved using tools from real algebraic geometry and computational algebra, but the specific characteristics of the systems stemming from reaction networks have allowed more in-depth findings to be obtained. In this article we explain some of the recent effective results in this area, where the study of the system and of the parameter regions is possible thanks to the examination of the geometry of an associated polytope.

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Published

2023-10-10

How to Cite

Feliu, E. (2023). Polynomials, polytopes, and steady states of reaction networks. Butlletí De La Societat Catalana De Matemàtiques, 37(2), 101–136. Retrieved from https://revistes.iec.cat/index.php/BSCM/article/view/150652

Issue

Vol. 37 No. 2 (2022)

Section

Articles

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