Parameter Estimation for a Kinetic Model of a Cellular System Using Model Order Reduction Method
Abstract
:1. Introduction
2. Parameter Estimation for ODEs Using the POD Method
2.1. Creating the Snapshot Matrix
2.2. Computing the Reduced Basis
2.3. Construction of DataFitting Function
2.4. Estimating the Parameters
Algorithm 1 Parameter estimation for a kinetic model. 

3. Application of the Parameter Estimation Method to a Kinetic Model of CCR in E. coli
3.1. The Kinetic Model of the Carbon Catabolite Repression
3.2. Numerical Results
3.2.1. Estimation of the Parameter ${k}_{s1}$
3.2.2. Estimation of the Parameters ${k}_{s1}$ and ${k}_{s2}$
3.2.3. Estimation of the Parameters ${k}_{s1},{k}_{e1},{k}_{x1}$ and ${k}_{x2}$
4. Conclusions and Discussion
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
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Constant Rates  Value  Unit 

${K}_{1}$  $1\times {10}^{4}$  g/L 
${K}_{2}$  $0.2$  g/L 
${k}_{e1}$  6  mol/gDWh 
${k}_{e2}$  $8.69$  mol/gDWh 
${k}_{x1}$  10  1/h 
${k}_{x2}$  10  1/h 
${k}_{m}$  10  1/h 
${\beta}_{1}$  1  mol/gDW 
${\beta}_{2}$  $0.6$  mol/gDW 
$\alpha $  $11.05$  mol/gDW 
${Y}_{1}$  90  gDW/mol 
${Y}_{2}$  $102.6$  gDW/mol 
${w}_{1}$  180  gDW/mol 
${w}_{2}$  342  gDW/mol 
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Eshtewy, N.A.; Scholz, L.; Kremling, A. Parameter Estimation for a Kinetic Model of a Cellular System Using Model Order Reduction Method. Mathematics 2023, 11, 699. https://doi.org/10.3390/math11030699
Eshtewy NA, Scholz L, Kremling A. Parameter Estimation for a Kinetic Model of a Cellular System Using Model Order Reduction Method. Mathematics. 2023; 11(3):699. https://doi.org/10.3390/math11030699
Chicago/Turabian StyleEshtewy, Neveen Ali, Lena Scholz, and Andreas Kremling. 2023. "Parameter Estimation for a Kinetic Model of a Cellular System Using Model Order Reduction Method" Mathematics 11, no. 3: 699. https://doi.org/10.3390/math11030699