Concentration robustness in LP kinetic systems

College

College of Science

Department/Unit

Mathematics and Statistics Department

Document Type

Article

Source Title

arXiv Preprint

Volume

2110

Publication Date

2021

Abstract

For a reaction network with species set 𝒮, a log-parametrized (LP) set is a non-empty set of the form E(P,x∗)={x∈ℝ𝒮>∣logx−logx∗∈P⊥} where P (called the LP set's flux subspace) is a subspace of ℝ𝒮, x∗ (called the LP set's reference point) is a given element of ℝ𝒮>, and P⊥ (called the LP set's parameter subspace) is the orthogonal complement of P. A network with kinetics K is a positive equilibria LP (PLP) system if its set of positive equilibria is an LP set. Analogously, it is a complex balanced equilibria LP (CLP) system if its set of complex balanced equilibria is an LP set. An LP kinetic system is a PLP or CLP system. This paper studies concentration robustness of a species on subsets of equilibria. We present the "species hyperplane criterion", a necessary and sufficient condition for absolute concentration robustness (ACR) for a species of a PLP system. An analogous criterion holds for balanced concentration robustness (BCR) for species of a CLP system. These criteria also lead to interesting necessary properties of LP systems with concentration robustness. Furthermore, we show that PLP and CLP power law systems with Shinar-Feinberg reaction pairs in species X in a linkage class have ACR and BCR in X, respectively. This leads to a broadening of the "low deficiency building blocks" framework to include LP systems of Shinar-Feinberg type with arbitrary deficiency. Finally, we apply our results to species concentration robustness in LP systems with poly-PL kinetics.

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Disciplines

Algebraic Geometry

Keywords

Equilibrium; Geometry, Algebraic

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