Authors : Debopam Ghosh

Volume/Issue : Volume 9 - 2024, Issue 5 - May

Google Scholar : https://tinyurl.com/5ev9ebd2

Scribd : https://tinyurl.com/38uzwmc5

DOI : https://doi.org/10.38124/ijisrt/IJISRT24MAY964

Abstract : The article presents a consolidated review of the mathematical framework for construction of Stoichiometric subspaces associated with Chemical Reaction Networks, based on theoretically imposed constraints, mechanistic considerations and data driven mathematical modeling; A rigorous mathematical treatment of the problem is presented and is illustrated using an appropriate numerical case study example.

Keywords : Stoichiometric Matrix, Chemical Reaction Networks, Fundamental Subspaces of a Matrix, Stoichiometric Subspaces, Chemical Factor Analysis.

References :

1. Aris, R., and Mah, R.H.S., Independence of chemical reactions, Ind. Engng Chem. Fundam. Vol 2, pp. 90-94 (1963)
2. Bjὂrnbom, P.H., The independent reactions in calculations of complex chemical equilibria, Ind. Engng Chem. Fundam. Vol 14, pp. 102-106 (1975) 
3. Bonvin, D., and Rippin, D.W.T., Target Factor Analysis for the Identification of Stoichiometric Models, Chemical Engineering Science, Vol 45, No. 12, pp. 3417-3426 (1990)
4. Feinberg, Martin, Foundations of Chemical Reaction Network Theory, Springer Maarleveld, Timo R., Khandelwal, Ruchir A., Olivier, Brett G., Teusink, Bas, Bruggeman, Frank J., Basic concepts and principles of Stoichiometric modeling of metabolic networks, Biotechnology Journal, Vol 8(9), pp. 997-1008 (2013)
5. Malinowski, Edmund. R., Factor Analysis in Chemistry, Third Edition, John Wiley and Sons Inc.
6. Meyer, Carl. D., Matrix Analysis and Applied Linear Algebra, SIAM
7. Nakhleh, Luay, Bioinformatics: Network Analysis-Analyzing Stoichiometric Matrices (Lecture Slides, Department of Computer Science, Rice University) (2013)
8. Palsson, Bernhard, Representing Reconstructed Networks Mathematically: The Stoichiometric Matrix (Lecture Slides, Department of Bioengineering, University of California, San Diego)  (2003)
9. Rawlings, James. B., Stoichiometry of  Chemical Reactions, (Lecture notes, Department of Chemical and Biological Engineering, University of Wisconsin-Madison) (2014)
10. Rawlings, J. B., and  Ekerdt, J. G., Chemical Reactor Analysis and Design Fundamentals, Second Edition, Nob Hill Publishing Strang,  Gilbert,  Linear Algebra and its Applications, Fourth Edition, Cengage Learning.