The Inheritance of Nondegenerate Multistationarity in Chemical Reaction Networks

Banaji, Murad; Pantea, Casian

doi:10.1137/16m1103506

Cited by 47 publications

(80 citation statements)

References 27 publications

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“…Our perspective is slightly different; instead of allowing parameter values to change, we modify the network itself. Accordingly, our work is similar in spirit to recent investigations into minimal oscillatory or bistable networks [3,4,27,28,34].…”

Section: Erksupporting

confidence: 59%

“…Returning to our bistability criterion (Theorem 4.6), recall that this result elucidates which reactions can be safely deleted while preserving bistability -in contrast to standard results concerning reactions that can be added [4,20,32]. We desire more results of this type, so we comment on how we proved our result.…”

Section: Discussionmentioning

confidence: 79%

“…Our focus here -on determining which operations on the ERK network preserve oscillations and bistability -is similar in spirit to the recent approach of Sadeghimanesh and Feliu [41]. Indeed, there has been significant interest in understanding which operations on networks preserve oscillations [3], bistability [4,20,32], and other properties [24].…”

Section: Erkmentioning

confidence: 90%

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Oscillations and bistability in a model of ERK regulation

et al. 2019

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This work concerns the question of how two important dynamical properties, oscillations and bistability, emerge in an important biological signaling network. Specifically, we consider a model for dual-site phosphorylation and dephosphorylation of extracellular signal-regulated kinase (ERK). We prove that oscillations persist even as the model is greatly simplified (reactions are made irreversible and intermediates are removed). Bistability, however, is much less robust -this property is lost when intermediates are removed or even when all reactions are made irreversible. Moreover, bistability is characterized by the presence of two reversible, catalytic reactions: as other reactions are made irreversible, bistability persists as long as one or both of the specified reactions is preserved. Finally, we investigate the maximum number of steady states, aided by a network's "mixed volume" (a concept from convex geometry). Taken together, our results shed light on the question of how oscillations and bistability emerge from a limiting network of the ERK network -namely, the fully processive dual-site network -which is known to be globally stable and therefore lack both oscillations and bistability. Our proofs are enabled by a Hopf bifurcation criterion due to Yang, analyses of Newton polytopes arising from Hurwitz determinants, and recent characterizations of multistationarity for networks having a steady-state parametrization.

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Section: Erksupporting

confidence: 59%

Section: Discussionmentioning

confidence: 79%

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Oscillations and bistability in a model of ERK regulation

et al. 2019

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“…By [5], if F has multiple positive non-degenerate steady states, then so does the fully open extension, provided the reaction rate constants of the flow reactions of G that are not in F are chosen small enough. By [1], the maximal number of exponentially stable positive steady states of F within a stoichiometric compatibility class is also a lower bound of the maximal number of exponentially stable positive steady states G admits for arbitrary reaction rate constants of the flow reactions. Here we relax the condition that all missing inflow and outflow reactions must be added to preserve these characteristics.…”

Section: Partially Open Extensions and Lifting Steady Statesmentioning

confidence: 99%

Addition of flow reactions preserving multistationarity and bistability

Cappelletti

Feliu

Wiuf

2020

Mathematical Biosciences

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We consider the question whether a chemical reaction network preserves the number and stability of its positive steady states upon inclusion of inflow and outflow reactions. Often a model of a reaction network is presented without inflows and outflows, while in fact some of the species might be degraded or leaked to the environment, or be synthesized or transported into the system. We provide a sufficient and easy-to-check criterion based on the stoichiometry of the reaction network alone and discuss examples from systems biology.

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“…Moreover, no way to explicitly determine the ACR value was given in [40], and we fill the gap by proposing a fast linear method to calculate it. Furthermore, a substantial effort in the Reaction Network community is devoted to understand under what conditions dynamical properties of single systems can be lifted to larger systems [9,24,25,29,32]. Our contribution in this sense consist in proving that, under certain conditions, if an ACR system of the class studied in this paper is part of a larger model, the ACR species is still so in the lager system and its ACR value is maintained.…”

Section: Introductionmentioning

confidence: 96%

A hidden integral structure endows Absolute Concentration Robust systems with resilience to dynamical concentration disturbances

Cappelletti

Gupta

Khammash

2019

Preprint

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Biochemical systems that express certain chemical species of interest at the same level at any positive equilibrium are called "absolute concentration robust" (ACR). These species behave in a stable, predictable way, in the sense that their expression is robust with respect to sudden changes in the species concentration, regardless the new positive equilibrium reached by the system. Such a property has been proven to be fundamentally important in certain gene regulatory networks and signaling systems. In the present paper, we mathematically prove that a well-known class of ACR systems studied by Shinar and Feinberg in 2010 hides an internal integral structure. This structure confers these systems with a higher degree of robustness that what was previously unknown. In particular, disturbances much more general than sudden changes in the species concentrations can be rejected, and robust perfect adaptation is achieved. Significantly, we show that these properties are maintained when the system is interconnected with other chemical reaction networks. This key feature enables design of insulator devices that are able to buffer the loading effect from downstream systems -a crucial requirement for modular circuit design in synthetic biology.

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The Inheritance of Nondegenerate Multistationarity in Chemical Reaction Networks

Cited by 47 publications

References 27 publications

Oscillations and bistability in a model of ERK regulation

Oscillations and bistability in a model of ERK regulation

Addition of flow reactions preserving multistationarity and bistability

A hidden integral structure endows Absolute Concentration Robust systems with resilience to dynamical concentration disturbances

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