Network Translation and Steady-State Properties of Chemical Reaction Systems

Abstract

Network translation has recently been used to establish steady-state properties of mass action systems by corresponding the given system to a generalized one which is either dynamically or steady-state equivalent. In this work, we further use network translation to identify network structures which give rise to the well-studied property of absolute concentration robustness in the corresponding mass action systems. In addition to establishing the capacity for absolute concentration robustness, we show that network translation can often provide a method for deriving the steady-state value of the robust species. We furthermore present a MILP algorithm for the identification of translated chemical reaction networks that improves on previous approaches, allowing for easier application of the theory.

Computing Weakly Reversible Deficiency Zero Network Translations Using Elementary Flux Modes

“…Applications exist, however, for translations which are not necessarily weakly reversible or deficiency zero (e.g. absolute concentration robustness, [37,35]). Future work will focus on adapting the procedure outlined in Section 3.3 to account for CRNs where some stoichiometric generators are not translated into cyclic generators.…”

“…We introduce the following structural notion of network translation, which is weaker than those presented in [21,22,37,23].…”

“…Network translation consists of restructuring a given CRN in such a way that the resulting network (a GCRN) can be used to guarantee dynamical and steady state properties of the original CRN. The process has been utilized to establish connections between chemical reaction network theory [9], the algebraic study of toric varieties [6,29,8], and biochemical reaction modeling [22,37,5]. Recent work has also established a deficiency-based method for constructing rational parametrizations of steady state sets for a broad class of mass-action systems [23].In this paper, we focus on computational methods for performing the structural component of network translation, which we call structural translation.…”

A Deficiency-Based Approach to Parametrizing Positive Equilibria of Biochemical Reaction Systems

“…Hence it takes the same value at every positive steady state. This property has been called absolute concentration robustness (ACR) in the literature, and the robust steady state value of Y p has been obtained by other methods in [23,17,25,19].…”

“…Example 19. Consider the model for the Shuttled WNT signaling pathway from [11], which has a deficiency of four (δ = 4), taken with the following translation scheme: (25) In the representation above, we have kept the indexing of the species X 1 through X 19 as in [11], but renamed the rate constants. Via Lemmas 16 and 10, the network corresponds to a weakly reversible, V * -directed GCRN: (26) Thereby, 17 → 16 and 18 → 19 (with labels σ 1 > 0 and σ 2 > 0) are phantom egdes since y(16) = y(17) = X 4 + X 6 + X 10 and y(18) = y(19) = X 4 + X 6 + X 11 .…”