Concentration Robustness in LP Kinetic Systems

Abstract

For a reaction network N with species set S , a log-parametrized (LP) set is a non-empty set of the form E(P, x * ) = {x ∈ R S > | log x − log x * ∈ P ⊥ } where P (called the LP set's flux subspace) is a subspace of R S , x * (called the LP set's reference point) is a given element of R S > , and P ⊥ (called the LP set's parameter subspace) is the orthogonal complement of P . A network N with kinetics K is a positive equilibria LP (PLP) system if its set of positive equilibria is an LP set, i.e., E+(N , K) = E(PE, x * ) where PE is the flux

Complex Balanced Equilibria of Weakly Reversible Poly-Pl Systems: Existence, Stability, and Robustness

“…Hence, balanced concentration robustness in such PYK systems can be determined by the results reviewed above. Proposition 6.4 of [18] shows that the samd conclusion as in Proposition (10) holds even if the CLP summands are not necessarily PL-RDK. A class pf such PLK systems is given by the following result of [11]:…”

“…Proposition 21 (Prop. 5.3, [18]). Let (N , K) be a power law system with a positive equilibrium and an independent decomposition…”

“…Z }, with x * a given complex balanced equilibrium, P Z the system's flux subspace and P ⊥ Z its parameter subspace. Lao et al derived the following "Species Hyperplane Criterion for BCR": Theorem 18 (Theorem 3.12, [18]). Let (N , K) be a kinetic system, m ACR and m BCR be the number of species with ACR and BCR, respectively.…”

“…We have the following sufficient condition for ACR in larger and higher deficiency PLK systems [18]:…”

“…• Section 6: Analogues of the results of Fortun and Mendoza [8] involving absolute concentration robustness (ACR) and Lao et al [18] on balanced concentration robustness (BCR) for power law kinetic systems to poly-PL kinetic systems are established. Sufficient conditions for concentration robustness in higher deficiency systems are also derived (Section 6.2).…”