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

[en] For the purpose of precise mathematical modelling of chemical reaction networks, useful techniques for estimating their parameters from experimental data are necessary. In this manuscript, we propose a new parameter estimation method for enzymatic chemical reaction networks from time-series experimental data of reaction rates. The main idea is based on retrieving time-series data of the species' concentrations from the available experimental data of reaction rates by making use of parametric Bézier curves. The least-squares method is applied to these retrieved data in order to determine the best-fitting values of the parameters in the corresponding mathematical model. Subsequently, we demonstrate the applicability of our parameter estimation method on three examples of enzymatic chemical reaction networks, including a model of ryanodine receptor adaptation and a model of protein kinase cascades. We also address the issue of identifiability of chemical reaction network models from reaction rates.

Disciplines :

Mathematics
Life sciences: Multidisciplinary, general & others

Author, co-author :

Gasparyan, Manvel

Van Messem, Arnout ; Université de Liège - ULiège > Département de mathématique > Statistique applquée aux sciences

Rao, Shodhan

Language :

English

Title :

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

Publication date :

26 October 2021

Journal title :

International Journal of Control

ISSN :

0020-7179

Publisher :

Taylor & Francis, United Kingdom

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 29 November 2021

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Bibliography

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 C-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). C-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 -induced release-dependent 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 C 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: C-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). C-metabolic flux analysis. Metabolic Engineering, 3 (3), 195–206. https://doi.org/10.1006/mben.2001.0187