Abstract
Stoichiometric network analysis (SNA) is a method of studying stability of steady states of reaction systems obeying mass action kinetics. Reaction rates are expressed as a linear combination of elementary subnetworks with nonnegative coefficients (convex parameters) as opposed to standard formulation using rate coefficients and input parameters (kinetic parameters). We present examples of core reaction subnetworks that provide for oscillatory instability. Frequently there is an autocatalytic cycle in the core subnetwork, but in biochemical reactions such cycle is often replaced by a pathway called competitive autocatalysis. Rate coefficients in complex networks are often only partly known. We present a method of estimating the unknown rate coefficients, in which known/measured kinetic parameters and steady state concentrations are used to determine convex parameters, which in turn allows for determination of unknown rate coefficients by solving a set of constraint equations.
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References
Albers, C.J., Critchley, F., Gower, J.C.: Quadratic minimisation problems in statistics. J. Multivar. Anal. 102(3), 698–713 (2011)
Cerveny, J., Salagovic, J., Muzika, F., Safranek, D., Schreiber, I.: Influence of circadian clocks on optimal regime of central C-N metabolism of cyanobacteria. In: Mishra, A.K., Tiwari, D.N., Rai, A.N. (eds.) Cyanobacteria: From Basic Science to Applications, Chap. 9, pp. 193–206. Academic Press, London (2019)
Clarke, B.L.: Stability of complex reaction networks. Adv. Chem. Phys. 43, 1–278 (1980)
Eiswirth, M., Bürger, J., Strasser, P., Ertl, G.: Oscillating Langmuir-Hinshelwood mechanisms. J. Phys. Chem. 100(49), 19118–19123 (1996)
Eiswirth, M., Freund, A., Ross, J.: Mechanistic classification of chemical oscillators and the role of species. Adv. Chem. Phys. 80, 127–199 (1991)
Errami, H., Eiswirth, M., Grigoriev, D., Seiler, W.M., Sturm, T., Weber, A.: Detection of Hopf bifurcations in chemical reaction networks using convex coordinates. J. Comput. Phys. 291, 279–302 (2015)
Gonze, D.: Modeling circadian clocks: from equations to oscillations. Cent. Eur. J. Biol. 6(5), 699–711 (2011)
Hadac, O., Muzika, F., Nevoral, V., Pribyl, M., Schreiber, I.: Minimal oscillating subnetwork in the Huang-Ferrell model of the MAPK cascade. Plos One 12(6) (2017)
Hadley, G.: Linear Programming. Addison-Wesley Publishing Company (1962)
Marsden, J.E., McCracken, M.: The Hopf Bifurcation and Its Applications. Springer, New York (1976)
Muzika, F., Jurasek, R., Schreiberova, L., Radojkovic, V., Schreiber, I.: Identifying the oscillatory mechanism of the glucose oxidase-catalase coupled enzyme system. J. Phys. Chem. A 121(40), 7518–7523 (2017)
Noyes, R.M., Field, R.J., Koros, E.: Oscillations in chemical systems. 1. Detailed mechanism in a system showing temporal oscillations. J. Am. Chem. Soc. 94(4), 1394–1395 (1972)
Palsson, B.: Systems Biology: Properties of Reconstructed Networks. Cambridge University Press, Cambridge, New York (2006)
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes in Fortran. Cambridge University Press, Cambridge (1986, 1992)
Radojkovic, V., Schreiber, I.: Constrained stoichiometric network analysis. PCCP 20, 9910–9921 (2018)
Ross, J., Schreiber, I., Vlad, M.O.: Determination of Complex Reaction Mechanisms. Oxford University Press Inc., New York (2006)
Schilling, C.H., Letscher, D., Palsson, B.Ø.: Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective. J. Theor. Biol. 203(3), 229–248 (2000)
Schreiber, I., Ross, J.: Mechanisms of oscillatory reactions deduced from bifurcation diagrams. J. Phys. Chem. A 107(46), 9846–9859 (2003)
Zhabotinskii, A.M.: Periodic course of the oxidation of malonic acid in a solution (studies on the kinetics of Belousov’s reaction). Biofizika 9, 306–11 (1964)
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This work has been supported by the grant 18-24397S from the Czech Science Foundation.
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Schreiber, I., Radojković, V., Muzika, F., Jurašek, R., Schreiberová, L. (2020). The Use of Reaction Network Theory for Finding Network Motifs in Oscillatory Mechanisms and Kinetic Parameter Estimation. In: Roy, P., Cao, X., Li, XZ., Das, P., Deo, S. (eds) Mathematical Analysis and Applications in Modeling. ICMAAM 2018. Springer Proceedings in Mathematics & Statistics, vol 302. Springer, Singapore. https://doi.org/10.1007/978-981-15-0422-8_2
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