307
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Parameter estimation for models of chemical reaction networks from experimental data of reaction rates

ORCID Icon, ORCID Icon & ORCID Icon
Pages 392-407 | Received 25 Jan 2021, Accepted 18 Oct 2021, Published online: 11 Nov 2021

References

  • Antoniewicz, M. R. (2015). Methods and advances in metabolic flux analysis: A mini-review. Journal of Industrial Microbiology & Biotechnology, 42(3), 317–325. https://doi.org/10.1007/s10295-015-1585-x
  • Antoniewicz, M. R. (2018). A guide to 13C-metabolic flux analysis for the cancer biologist. Experimental & Molecular Medicine, 50(4), 1–13. https://doi.org/10.1038/s12276-018-0060-y
  • Arlot, S., & Celisse, A. (2010). A survey of cross-validation procedures for model selection. Statistics Surveys, 4, 40–79. https://doi.org/10.1214/09-SS054
  • Bellman, R., & Åström, K. J. (1970). On structural identifiability. Mathematical Biosciences, 7(3–4), 329–339. https://doi.org/10.1016/0025-5564(70)90132-X
  • Bergmeir, C., & Benítez, J. M. (2012). On the use of cross-validation for time series predictor evaluation. Information Sciences, 191(3), 192–213. https://doi.org/10.1016/j.ins.2011.12.028
  • Bernard, O., & Bastin, G. (2005). Identification of reaction networks for bioprocesses: Determination of a partially unknown pseudo-stoichiometric matrix. Bioprocess and Biosystems Engineering, 27(5), 293–301. https://doi.org/10.1007/s00449-005-0407-3
  • Bernšteın, S. (1912). Démonstration du théoreme de Weierstrass fondée sur le calcul des probabilities. Communications of the Kharkov Mathematical Society, 13, 1–2.
  • Berry, T. G., & Patterson, R. R. (1997). The uniqueness of Bézier control points. Computer Aided Geometric Design, 14(9), 877–879. https://doi.org/10.1016/S0167-8396(97)00016-2
  • Bézier, P. E. (1986). The mathematical basis of the UNISURF CAD system. Butterworth-Heinemann.
  • Bézier, P. E., & Sioussiou, S. (1983). Semi-automatic system for defining free-form curves and surfaces. Computer-Aided Design, 15(2), 65–72. https://doi.org/10.1016/0010-4485(83)90170-7
  • Cobelli, C., & DiStefano, 3rd, J. J. (1980). Parameter and structural identifiability concepts and ambiguities: A critical review and analysis. American Journal of Physiology. Regulatory, Integrative and Comparative Physiology, 239(1), R7–R24. https://doi.org/10.1152/ajpregu.1980.239.1.R7
  • Craciun, G., & Pantea, C. (2008). Identifiability of chemical reaction networks. Journal of Mathematical Chemistry, 44(1), 244–259. https://doi.org/10.1007/s10910-007-9307-x
  • Crampin, E. J., Schnell, S., & McSharry, P. E. (2004). Mathematical and computational techniques to deduce complex biochemical reaction mechanisms. Progress in Biophysics and Molecular Biology, 86(1), 77–112. https://doi.org/10.1016/j.pbiomolbio.2004.04.002
  • Donnelly, J. K., & Quon, D. (1970). Identification of parameters in systems of ordinary differential equations using quasilinearization and data perturbation. The Canadian Journal of Chemical Engineering, 48(1), 114–119. https://doi.org/10.1002/cjce.v48:1
  • Edwards, L. M., & Thiele, I. (2013). Applying systems biology methods to the study of human physiology in extreme environments. Extreme Physiology & Medicine, 2(1), 8. https://doi.org/10.1186/2046-7648-2-8
  • Farin, G. (1993). Curves and surfaces for computer-aided geometric design: A practical guide (3rd ed.). Academic Press.
  • Farina, M., Findeisen, R., Bullinger, E., Bittanti, S., Allgower, F., & Wellstead, P. (2006). Results towards identifiability properties of biochemical reaction networks. In Proceedings of the 45th IEEE Conference on Decision & Control (pp. 2104–2109). Institute of Electrical and Electronics Engineers.
  • Fröhlich, F., Kaltenbacher, B., Theis, F. J., & Hasenauer, J. (2017). Scalable parameter estimation for genome-scale biochemical reaction networks. PLOS Computational Biology, 13(1), e1005331. https://doi.org/10.1371/journal.pcbi.1005331
  • Gasparyan, M., Van Messem, A., & Rao, S. (2018). A novel technique for model reduction of biochemical reaction networks. IFAC-PapersOnLine, 51(19), 28–31. https://doi.org/10.1016/j.ifacol.2018.09.024
  • Gasparyan, M., Van Messem, A., & Rao, S. (2020). An automated model reduction method for biochemical reaction networks. Symmetry-Basel, 12(8), 1321. https://doi.org/10.3390/sym12081321
  • Guo, W., Sheng, J., & Feng, X. (2016). 13C-metabolic flux analysis: An accurate approach to demystify microbial metabolism for biochemical production. Bioengineering-Basel, 3(1), 3. https://doi.org/10.3390/bioengineering3010003
  • Hedengren, J. (2021). Dynamic parameter estimation and confidence intervals. MATLAB Central File Exchange. Retrieved July 12, 2021, from https://www.mathworks.com/matlabcentral/fileexchange/45496-dynamic-parameter-estimation-and-confidence-intervals
  • Heirendt, L., Arreckx, S., Pfau, T., Mendoza, S. N., Richelle, A., Heinken, A., Haraldsdóttir, H. S., Wachowiak, J., Keating, S. M., Vlasov, V., Magnusdóttir, S., Ng, C. Y., Preciat, G., Žagare, A., Chan, S. H. J., Aurich, M. K., Clancy, C. M., Modamio, J., Sauls, J. T., … Fleming, R. M. (2019). Creation and analysis of biochemical constraint-based models using the COBRA toolbox v.3.0. Nature Protocols, 14(3), 639–702. https://doi.org/10.1038/s41596-018-0098-2
  • Himmelblau, D. M., & Riggs, J. B. (2012). Basic principles and calculations in chemical engineering (l8th ed.). Prentice Hall.
  • Hodges, A., & Chatelier, R. (2002). Electrochemical method for measuring chemical reaction rates (US Patent 6,444,115). Google Patents.
  • Keizer, J., & Levine, L. (1996). Ryanodine receptor adaptation and Ca2+-induced Ca2+ release-dependent Ca2+ oscillations. Biophysical Journal, 71(6), 3477–3487. https://doi.org/10.1016/S0006-3495(96)79543-7
  • Ljung, L. (1999). System identification: Theory for the user (2nd ed.). Prentice Hall.
  • Long, C. P., & Antoniewicz, M. R. (2019). High-resolution 13C metabolic flux analysis. Nature Protocols, 14(10), 2856–2877. https://doi.org/10.1038/s41596-019-0204-0
  • Loskot, P., Atitey, K., & Mihaylova, L. (2019). Comprehensive review of models and methods for inferences in bio-chemical reaction networks. Frontiers in Genetics, 10, 549. https://doi.org/10.3389/fgene.2019.00549
  • Malik-Sheriff, R. S., Glont, M., Nguyen, T. V. N., Tiwari, K., Roberts, M. G., Xavier, A., Vu, M. T., Men, J., Maire, M., Kananathan, S., Fairbanks, E. L., Meyer, J. P., Arankalle, C., Varusai, T. M., Knight-Schrijver, V., Li, L., Dueñas-Roca, C., Dass, G., Keating, S. M., … Hermjakob, H. (2020). BioModels – 15 years of sharing computational models in life science. Nucleic Acids Research, 48(D1), D407–D415.https://doi.org/10.1093/nar/gkz1055
  • Markevich, N. I., Hoek, J. B., & Kholodenko, B. N. (2004). Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades. The Journal of Cell Biology, 164(3), 353–359. https://doi.org/10.1083/jcb.200308060
  • Megchelenbrink, W., Rossell, S., Huynen, M. A., Notebaart, R. A., & Marchiori, E. (2015). Estimating metabolic fluxes using a maximum network flexibility paradigm. PLOS ONE, 10(10), e0139665. https://doi.org/10.1371/journal.pone.0139665
  • Miao, H., Xia, X., Perelson, A. S., & Wu, H. (2011). On identifiability of nonlinear ODE models and applications in viral dynamics. SIAM Review, 53(1), 3–39. https://doi.org/10.1137/090757009
  • Mock, A., Chiblak, S., & Herold-Mende, C. (2014). Lessons we learned from high-throughput and top-down systems biology analyses about glioma stem cells. Current Pharmaceutical Design, 20(1), 66–72. https://doi.org/10.2174/138161282001140113124343
  • Orth, J. D., Thiele, I., & Palsson, B. P. (2010). What is flux balance analysis?Nature Biotechnology, 28(3), 245–248. https://doi.org/10.1038/nbt.1614
  • Prautzsch, H., Boehm, W., & Paluszny, M. (2002). Bézier and B-spline techniques. Springer-Verlag.
  • Rao, S., van der Schaft, A., van Eunen, K., Bakker, B. M., & Jayawardhana, B. (2014). A model reduction method for biochemical reaction networks. BMC Systems Biology, 8(1), 52. https://doi.org/10.1186/1752-0509-8-52
  • Ross, J., Schreiber, I., & Vlad, M. O. (2005). Determination of complex reaction mechanisms: Analysis of chemical, biological, and genetic networks. Oxford University Press.
  • Sauer, U. (2006). Metabolic networks in motion: 13C-based flux analysis. Molecular Systems Biology, 2(1), 62. https://doi.org/10.1038/msb4100109
  • Sparkman, O. D., Penton, Z., & Kitson, F. G. (2011). Gas chromatography and mass spectrometry: A practical guide (2nd ed.). Academic Press.
  • Stanhope, S., Rubin, J. E., & Swigon, D. (2014). Identifiability of linear and linear-in-parameters dynamical systems from a single trajectory. SIAM Journal on Applied Dynamical Systems, 13(4), 1792–1815. https://doi.org/10.1137/130937913
  • Stone, M. (1974). Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society: Series B (Methodological), 36(2), 111–147.https://doi.org/10.1111/j.2517-6161.1974.tb00994.x
  • Waring, E. (1779). Problems concerning interpolations. Philosophical Transactions of the Royal Society of London, 69, 59–67. https://doi.org/10.1098/rstl.1779.0008
  • Wiechert, W. (2001). 13C-metabolic flux analysis. Metabolic Engineering, 3(3), 195–206. https://doi.org/10.1006/mben.2001.0187

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.