Current rates and reaction rates
in the Stoichiometric Network Analysis (SNA)

Maćešić, Stevan; Čupić, Željko; Blagojević, Stevan; Pejić, Nataša; Anić, Slobodan; Kolar-Anić, Ljiljana

doi:10.1515/chem-2015-0077

Cited by 6 publications

(3 citation statements)

References 48 publications

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“…1,21,22 The overall process can be represented as a linear combination of several elementary reaction pathways known as extreme currents E i and they all contribute to the steady-state values of reaction rates. The contributions of the extreme currents E i , denoted as the current rates j i , are the components of the corresponding current rate vector j, whereas the extreme currents E i are the columns of the extreme current matrix E. 1,2,6,17,18,[20][21][22][23][24] Thus,…”

Section: Sna Of Oscillatory Carbonylation Of Pegamentioning

confidence: 99%

Stoichiometric network analysis of a reaction system with conservation constraints

Čupić

Maćešić

Novakovic

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Stoichiometric Network Analysis (SNA) is a powerful method that can be used to examine instabilities in modelling a broad range of reaction systems without knowing the explicit values of reaction rate constants. Due to a lack of understanding, SNA is rarely used and its full potential is not yet fulfilled. Using the oscillatory carbonylation of a polymeric substrate [poly(ethylene glycol)methyl ether acetylene] as a case study, in this work, we consider two mathematical methods for the application of SNA to the reaction models when conservation constraints between species have an important role. The first method takes conservation constraints into account and uses only independent intermediate species, while the second method applies to the full set of intermediate species, without the separation of independent and dependent variables. Both methods are used for examination of steady state stability by means of a characteristic polynomial and related Jacobian matrix. It was shown that both methods give the same results. Therefore, as the second method is simpler, we suggest it as a more straightforward method for the applications.

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Section: Sna Of Oscillatory Carbonylation Of Pegamentioning

confidence: 99%

Stoichiometric network analysis of a reaction system with conservation constraints

Čupić

Maćešić

Novakovic

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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show abstract

“…It depends very much on the system under consideration. For this purpose, theory of the Stoichiometric Network Analysis was improved and used for identification of the instability regions in several models of the oscillatory reactions (Jelić et al 2008;Schmitz et al 2008;Jelić et al 2009;Kolar-Anić et al 2010;Čupić et al 2011;Marković et al 2011a;Maćešić et al 2012;Maćešić et al 2015a;Maćešić et al 2015b;Maćešić et al 2016;Čupić et al 2016b;Čupić et al 2016c). Here, as in the case of formal kinetics, the main steps in modelling procedure were developed on the BL reaction and then applied to the other systems.…”

Section: Modelingmentioning

confidence: 99%

Advances made by Belgrade's group in research of oscillatory reactions

Kolar‐Anić¹,

Čupić²,

Anić³

2016

J Serb Soc Comp Mech

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Oscillatory dynamic states as one form of selforganization of nonlinear systems can be found in almost all sciences, like mechanics, physical chemistry or biomedicine. Although origin of these oscillations is different, computational challenges in modelling oscillatory phenomena remain similar in all fields. Since 1979 researchers from Belgrade's group perform systematic examinations of oscillatory reactions. As stability of steady states is the central point in modelling oscillatory reactions, in last 10 years they have adapted and improved powerful tool of the Stoichiometric Network Analysis for this goal. Moreover, bifurcations of few types were identified in several models of oscillatory reactions. Even very complex chaotic motions in phase space were characterized and quantified by several numerical techniques. Multiple time scale behaviour is found within the core of the complex dynamic behaviour of mixed-mode oscillations. Analytical applications were developed, too.

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“…seja, se houver um ou mais autovalores positivos, o estado estacionário é instável, o que pode levar a bifurcações nos estados estacionários. Os autovalores de M são as raízes de seu polinômio característico 73. Retrato de fase de equação.…”

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Análise estequiométrica da dinâmica não-linear de redes de reações químicas

Silva¹

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The state of a living body is mainly characterized by the presence of a constant flow of chemical reactions, and therefore living beings are formed by several reactions, linked to each other in a kind of network. The theory of biochemical networks provides a mathematical and computational framework used to analyze and simulate reactions such networks. It is a building model, diagnosis and network analysis based on ordinary differential equations. Some chemical reactions networks are studied mainly for the complex dynamic behavior. Far from equilibrium, such nonlinear dynamical systems exhibit phenomena such as, multiple steady states and oscillations. Some chemical networks of biochemical interest were analyzed, such as calcium networks in the cilia of olfactory receptor neurons, the glycolytic pathway, oxidase-peroxidase and network granting a multistable dynamics in the fruit fly embryogenesis, Drosophila melanogaster, as well as networks theoretical. To study them, the method Stoichiometric Network Analysis, or SNA, provided a systematic approach to the dynamics of chemical mechanisms or other systems containing stoichiometry. First it was necessary to understand the biochemical systems that exhibit complex dynamics and the importance of such in maintaining metabolic and cellular communication in living creatures to then assess the effectiveness of the stoichiometric analysis of technical networks in the investigation of nonlinear phenomena. The graphical variant of the SNA method was used to create subnets that exhibit unusual behaviors and the consequent use of the same in modeling elementary easy to grasp networks. Finally, the methods have been shown effective in analyzing complex dynamic, moreover, it can verify the bifurcation analysis for some networks. In addition to the necessary and sufficient conditions for observing complex dynamics, the SNA by technique could even expose another biological properties of the models.

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Current rates and reaction rates in the Stoichiometric Network Analysis (SNA)

Cited by 6 publications

References 48 publications

Stoichiometric network analysis of a reaction system with conservation constraints

Stoichiometric network analysis of a reaction system with conservation constraints

Advances made by Belgrade's group in research of oscillatory reactions

Análise estequiométrica da dinâmica não-linear de redes de reações químicas

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