Detection of Hopf bifurcations in chemical reaction networks using convex coordinates

Errami, Hassan; Eiswirth, M.; Grigoriev, Dima; Seiler, Werner M.; Sturm, Thomas; Weber, Andreas

doi:10.1016/j.jcp.2015.02.050

Cited by 51 publications

(64 citation statements)

References 45 publications

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“…The vast majority of chemical and biological models as they can be found, e.g., in the BioModels database 23 is considerably larger with respect to both dimension and degrees than our example here. in Sect.…”

Section: Life Sciencesmentioning

confidence: 90%

“…Therefore we may assume in 22 For independent reasons one knows with the first Hopf bifurcation at n = 9 that there will be Hopf bifurcations for all n > 9. 23 http://www.ebi.ac.uk/biomodels-main/. the sequel that f (1, .…”

Section: Subtropical Methodsmentioning

confidence: 99%

“…An alternative formulation using the same approach can be found in [23]. Figure 8 shows that original system in combination with an application of methylene blue as a dye.…”

Section: Methylene Blue Oscillator (Mbo)mentioning

confidence: 99%

“…The overall computation time was 200 s. The largest reaction system considered with our approach so far is the Mitogen-Activated Protein Kinase (MAPK) cascade, which is well studied in cell biology. Details can be found in [23].…”

Section: Methylene Blue Oscillator (Mbo)mentioning

confidence: 99%

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A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications

Sturm

2017

Math.Comput.Sci.

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Effective quantifier elimination procedures for first-order theories provide a powerful tool for generically solving a wide range of problems based on logical specifications. In contrast to general first-order provers, quantifier elimination procedures are based on a fixed set of admissible logical symbols with an implicitly fixed semantics. This admits the use of sub-algorithms from symbolic computation. We are going to focus on quantifier elimination for the reals and its applications giving examples from geometry, verification, and the life sciences. Beyond quantifier elimination we are going to discuss recent results with a subtropical procedure for an existential fragment of the reals. This incomplete decision procedure has been successfully applied to the analysis of reaction systems in chemistry and in the life sciences.

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Section: Life Sciencesmentioning

confidence: 90%

Section: Subtropical Methodsmentioning

confidence: 99%

“…An alternative formulation using the same approach can be found in [23]. Figure 8 shows that original system in combination with an application of methylene blue as a dye.…”

Section: Methylene Blue Oscillator (Mbo)mentioning

confidence: 99%

Section: Methylene Blue Oscillator (Mbo)mentioning

confidence: 99%

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A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications

Sturm

2017

Math.Comput.Sci.

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“…But what about the oscillatory behavior of the system? Indeed, Errami et al detected Hopf bifurcations in this system [2]. Jolley et al considered a variant of the dual futile cycle, in which the two phosphate groups are added in the same order as they are removed (rather than the reverse order), thus, there are four phosphoforms rather than three.…”

Section: Introductionmentioning

confidence: 99%

No oscillations in the Michaelis-Menten approximation of the dual futile cycle under a sequential and distributive mechanism

Morales¹

2017

SIURO

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Protein phosphorylation and dephosphorylation are important intracellular processes. The main object of study in this paper is the dual futile cycle, a network that describes the dual-site phosphorylation/dephosphorylation of a protein by a kinase/phosphatase pair in a sequential and distributive mechanism. Specifically, we analyze the 2-dimensional Michaelis-Menten (M-M) approximation of this system. It has been previously shown that this system is bistable. We also know, from monotone systems theory, that every solution converges to some steady state. Here, we give a new and simpler proof of this convergence result by using Bendixon's criterion to rule out oscillations. Ultimately, understanding the behavior of this system could help us understand the original dual futile cycle (or MAPK cascades that contain it), which has recently been shown to admit oscillations via Hopf bifurcations.

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Response to stress via underlying deep gene regulation networks

Vakulenko,

Grigoriev,

Suchkov

et al. 2023

Math Methods in App Sciences

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Exposure of cells to non‐optimal growth conditions or to any environment that reduces cell viability can be considered as a stress. In this paper, we are going to highlight the main factors that determine the danger of stress to a cell considered as a biochemical system. To this end, we introduce a new mathematical concept of biosystem stability, where we take into account a signal transduction by deep gene networks. Using this concept and known results on approximations by deep networks, we find asymptotic estimates of the size and the depth of gene regulation networks that define the stress response. We propose a new algorithm to find the gene network approximating a prescribed output. It allows us, with the help of Kolmogorov ‐entropy and the deep neural network theory, to estimate the number of genes involved in regulation of responses on a stress (for example, a heat shock). We show that the main factors that increase the sensitivity of the systems with respect to a stress are the number of biochemical network parameters affected by the stress and sensitivities of kinetic rates with respect to these parameters.

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Detection of Hopf bifurcations in chemical reaction networks using convex coordinates

Cited by 51 publications

References 45 publications

A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications

A Survey of Some Methods for Real Quantifier Elimination, Decision, and Satisfiability and Their Applications

No oscillations in the Michaelis-Menten approximation of the dual futile cycle under a sequential and distributive mechanism

Response to stress via underlying deep gene regulation networks

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