# Concentration Robustness in LP Kinetic Systems

Source: [Concentration Robustness in LP Kinetic Systems](<https://www.sota2.com/research/paper/68fa58a61e209131ce9b0098>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T15:26:32.456Z

Authors: Angelyn R. Lao, Patrick Vincent N. Lubenia, Daryl M. Magpantay, Eduardo R. Mendoza

Published: 2021-10-26T16:43:48.000Z

## Abstract

For a reaction network with species set $\\mathscr{S}$, a log-parametrized (LP) set is a non-empty set of the form $E(P, x^\*) = \\{x \\in \\mathbb{R}^\\mathscr{S}\_\> \\mid \\log x - \\log x^\* \\in P^\\perp\\}$ where $P$ (called the LP set's flux subspace) is a subspace of $\\mathbb{R}^\\mathscr{S}$, $x^\*$ (called the LP set's reference point) is a given element of $\\mathbb{R}^\\mathscr{S}\_\>$, and $P^\\perp$ (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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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2110.13845>)

[PDF](<https://arxiv.org/pdf/2110.13845.pdf>)