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Parameter estimation for kinetic models of chemical reaction networks from partial experimental data of species’ concentrations

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Abstract
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 abovementioned 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.
Keywords
Bioengineering, systems biology, mathematical modeling, mass action kinetics, model reduction, least squares optimization, parameter identifiability

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MLA
Gasparyan, Manvel, and Shodhan Rao. “Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species’ Concentrations.” BIOENGINEERING-BASEL, vol. 10, no. 9, 2023, doi:10.3390/bioengineering10091056.
APA
Gasparyan, M., & Rao, S. (2023). Parameter estimation for kinetic models of chemical reaction networks from partial experimental data of species’ concentrations. BIOENGINEERING-BASEL, 10(9). https://doi.org/10.3390/bioengineering10091056
Chicago author-date
Gasparyan, Manvel, and Shodhan Rao. 2023. “Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species’ Concentrations.” BIOENGINEERING-BASEL 10 (9). https://doi.org/10.3390/bioengineering10091056.
Chicago author-date (all authors)
Gasparyan, Manvel, and Shodhan Rao. 2023. “Parameter Estimation for Kinetic Models of Chemical Reaction Networks from Partial Experimental Data of Species’ Concentrations.” BIOENGINEERING-BASEL 10 (9). doi:10.3390/bioengineering10091056.
Vancouver
1.
Gasparyan M, Rao S. Parameter estimation for kinetic models of chemical reaction networks from partial experimental data of species’ concentrations. BIOENGINEERING-BASEL. 2023;10(9).
IEEE
[1]
M. Gasparyan and S. Rao, “Parameter estimation for kinetic models of chemical reaction networks from partial experimental data of species’ concentrations,” BIOENGINEERING-BASEL, vol. 10, no. 9, 2023.
@article{01HFEC0VVNX90QTQ4YFAMJ651D,
  abstract     = {{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 abovementioned
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.}},
  articleno    = {{1056}},
  author       = {{Gasparyan, Manvel and Rao, Shodhan}},
  issn         = {{2306-5354}},
  journal      = {{BIOENGINEERING-BASEL}},
  keywords     = {{Bioengineering,systems biology,mathematical modeling,mass action kinetics,model reduction,least squares optimization,parameter identifiability}},
  language     = {{eng}},
  number       = {{9}},
  pages        = {{30}},
  title        = {{Parameter estimation for kinetic models of chemical reaction networks from partial experimental data of species’ concentrations}},
  url          = {{http://doi.org/10.3390/bioengineering10091056}},
  volume       = {{10}},
  year         = {{2023}},
}

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