Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species’ Concentrations
The current manuscript addresses the problem of parameter estimation for kinetic models of chemical reaction networks from observed time series partial experimental data of species concentrations. It is demonstrated how the Kron reduction method of kinetic models, in conjunction with the (weighted)...
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| Format: | Article |
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MDPI AG
2023-09-01
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| Series: | Bioengineering |
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| Online Access: | https://www.mdpi.com/2306-5354/10/9/1056 |
| _version_ | 1797581269032239104 |
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| author | Manvel Gasparyan Shodhan Rao |
| author_facet | Manvel Gasparyan Shodhan Rao |
| author_sort | Manvel Gasparyan |
| collection | DOAJ |
| description | The current manuscript addresses the problem of parameter estimation for kinetic models of chemical reaction networks from observed time series partial experimental data of species concentrations. It is demonstrated how the Kron reduction method of kinetic models, in conjunction with the (weighted) least squares optimization technique, can be used as a tool to solve the above-mentioned ill-posed parameter estimation problem. First, a new trajectory-independent measure is introduced to quantify the dynamical difference between the original mathematical model and the corresponding Kron-reduced model. This measure is then crucially used to estimate the parameters contained in the kinetic model so that the corresponding values of the species’ concentrations predicted by the model fit the available experimental data. The new parameter estimation method is tested on two real-life examples of chemical reaction networks: nicotinic acetylcholine receptors and Trypanosoma brucei trypanothione synthetase. Both weighted and unweighted least squares techniques, combined with Kron reduction, are used to find the best-fitting parameter values. The method of leave-one-out cross-validation is utilized to determine the preferred technique. For nicotinic receptors, the training errors due to the application of unweighted and weighted least squares are 3.22 and 3.61 respectively, while for Trypanosoma synthetase, the application of unweighted and weighted least squares result in training errors of 0.82 and 0.70 respectively. Furthermore, the problem of identifiability of dynamical systems, i.e., the possibility of uniquely determining the parameters from certain types of output, has also been addressed. |
| first_indexed | 2024-03-10T23:01:57Z |
| format | Article |
| id | doaj.art-eeb101bf60d140068d431ddc5b09a4b4 |
| institution | Directory Open Access Journal |
| issn | 2306-5354 |
| language | English |
| last_indexed | 2024-03-10T23:01:57Z |
| publishDate | 2023-09-01 |
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| series | Bioengineering |
| spelling | doaj.art-eeb101bf60d140068d431ddc5b09a4b42023-11-19T09:37:03ZengMDPI AGBioengineering2306-53542023-09-01109105610.3390/bioengineering10091056Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species’ ConcentrationsManvel Gasparyan0Shodhan Rao1School of Environmental Engineering, University of Seoul, Seoul 02504, Republic of KoreaCenter for Biosystems and Biotech Data Science, Ghent University Global Campus, Incheon 21985, Republic of KoreaThe current manuscript addresses the problem of parameter estimation for kinetic models of chemical reaction networks from observed time series partial experimental data of species concentrations. It is demonstrated how the Kron reduction method of kinetic models, in conjunction with the (weighted) least squares optimization technique, can be used as a tool to solve the above-mentioned ill-posed parameter estimation problem. First, a new trajectory-independent measure is introduced to quantify the dynamical difference between the original mathematical model and the corresponding Kron-reduced model. This measure is then crucially used to estimate the parameters contained in the kinetic model so that the corresponding values of the species’ concentrations predicted by the model fit the available experimental data. The new parameter estimation method is tested on two real-life examples of chemical reaction networks: nicotinic acetylcholine receptors and Trypanosoma brucei trypanothione synthetase. Both weighted and unweighted least squares techniques, combined with Kron reduction, are used to find the best-fitting parameter values. The method of leave-one-out cross-validation is utilized to determine the preferred technique. For nicotinic receptors, the training errors due to the application of unweighted and weighted least squares are 3.22 and 3.61 respectively, while for Trypanosoma synthetase, the application of unweighted and weighted least squares result in training errors of 0.82 and 0.70 respectively. Furthermore, the problem of identifiability of dynamical systems, i.e., the possibility of uniquely determining the parameters from certain types of output, has also been addressed.https://www.mdpi.com/2306-5354/10/9/1056systems biologymathematical modelingmass action kineticsmodel reductionleast squares optimizationparameter identifiability |
| spellingShingle | Manvel Gasparyan Shodhan Rao Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species’ Concentrations Bioengineering systems biology mathematical modeling mass action kinetics model reduction least squares optimization parameter identifiability |
| title | Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species’ Concentrations |
| title_full | Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species’ Concentrations |
| title_fullStr | Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species’ Concentrations |
| title_full_unstemmed | Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species’ Concentrations |
| title_short | Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species’ Concentrations |
| title_sort | parameter estimation for kinetic models of chemical reaction networks from partial experimental data of species concentrations |
| topic | systems biology mathematical modeling mass action kinetics model reduction least squares optimization parameter identifiability |
| url | https://www.mdpi.com/2306-5354/10/9/1056 |
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