Radulescu, O.; Gorban, A.N.; Zinovyev, A.; Noel, V. Reduction of dynamical biochemical reactions networks in computational biology. Front. Genet. 2012, 3, 131. [CrossRef] [PubMed]
Snowden, T.J.; van der Graaf, P.H.; Tindall, M.J. Methods of model reduction for large-scale biological systems: a survey of current methods and trends. Bull. Math. Biol. 2017, 79, 1449–1486. [CrossRef]
Cornish-Bowden, A. Fundamentals of Enzyme Kinetics; Wiley-Blackwell: Weinheim, Germany, 2012.
Segel, I. Biochemical Calculations; Wiley: Hoboken, NJ, USA, 1975.
Rao, S.; Van der Schaft, A.; Van Eunen, K.; Bakker, B.M.; Jayawardhana, B. A model reduction method for biochemical reaction networks. BMC Syst. Biol. 2014, 8, 52. [CrossRef] [PubMed]
Kron, G. Tensor Analysis of Networks; Macdonald: New York, NY, USA, 1939.
Zhang, F. The Schur Complement and Its Applications; Springer Science & Business Media: Berlin, Germany, 2006; Volume 4.
Gasparyan, M.; Van Messem, A.; Rao, S. A Novel Technique for Model Reduction of Biochemical Reaction Networks. IFAC-PapersOnLine 2018, 51, 28–31. [CrossRef]
Noether, E. Invariant variation problems. Transp. Theory Stat. Phys. 1971, 1, 186–207. [CrossRef]
Le Novere, N.; Bornstein, B.; Broicher, A.; Courtot, M.; Donizelli, M.; Dharuri, H.; Li, L.; Sauro, H.; Schilstra, M.; Shapiro, B.; et al. BioModels Database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems. Nucleic Acids Res. 2006, 34, D689–D691. [CrossRef] [PubMed]
Van der Schaft, A.; Rao, S.; Jayawardhana, B. A network dynamics approach to chemical reaction networks. Int. J. Control 2016, 89, 731–745. [CrossRef]
Feinberg, M. Lectures on chemical reaction networks. In Notes of Lectures Given at the Mathematics Research Center; University of Wisconsin-Madison: Madison, WI, USA, 1979; p. 49.
Michaelis, L.; Menten, M.L. Die kinetik der Invertinwirkung; Universitätsbibliothek Johann Christian Senckenberg: Frankfurt, Germany, 2007.
Monod, J.; Wyman, J.; Changeux, J.P. On the nature of allosteric transitions: a plausible model. J. Mol. Biol. 1965, 12, 88–118. [CrossRef]
Hill, A.V. The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves. J. Physiol. 1910, 40, 4–7.
Hofmeyr, J.H.; Cornish-Bowden, H. The reversible Hill equation: how to incorporate cooperative enzymes into metabolic models. Bioinformatics 1997, 13, 377–385. [CrossRef] [PubMed]
Cleland, W.W. Derivation of rate equations for multisite ping-pong mechanisms with ping-pong reactions at one or more sites. J. Biol. Chem. 1973, 248, 8353–8355. [PubMed]
Koshland, D.; Némethy, G.; Filmer, D. Comparison of experimental binding data and theoretical models in proteins containing subunits. Biochemistry 1966, 5, 365–385. [CrossRef] [PubMed]
Bapat, R.B. Graphs and Matrices; Springer: New York, NY, USA, 2010; Volume 27.
Feinberg, M. Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theorems. Chem. Eng. Sci. 1987, 42, 2229–2268. [CrossRef]
Horn, F.; Jackson, R. General mass action kinetics. Arch. Ration. Mech. Anal. 1972, 47, 81–116. [CrossRef]
Rao, S.; van der Schaft, A.; Jayawardhana, B. A graph-theoretical approach for the analysis and model reduction of complex-balanced chemical reaction networks. J. Math. Chem. 2013, 51, 2401–2422. [CrossRef]
Sivakumar, K.C.; Dhanesh, S.B.; Shobana, S.; James, J.; Mundayoor, S. A systems biology approach to model neural stem cell regulation by notch, shh, wnt, and EGF signaling pathways. Omics J. Integr. Biol. 2011, 15, 729–737. [CrossRef] [PubMed]
Cau, E.; Blader, P. Notch activity in the nervous system: to switch or not switch? BMC Neural Dev. 2009, 4, 36. [CrossRef] [PubMed]
Catherine, D.; Zhenwei, L.; Ji-Hun, K.; Sanders, C. Notch Transmembrane Domain: Secondary Structure and Topology. Biochemistry 2015, 54, 3565–3568.