TY - JOUR
T1 - A Promising Method for Calculating True Steady-State Metabolite Concentrations in Large-Scale Metabolic Reaction Network Models
AU - Miyawaki-Kuwakado, Atsuko
AU - Komori, Soichiro
AU - Shiraishi, Fumihide
N1 - Funding Information:
This work was supported by JSPS Science Grant-in-Aid for JSPS Research Fellow Grant Number 17J04007.
Publisher Copyright:
© 2004-2012 IEEE.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - The calculation of steady-state metabolite concentrations in metabolic reaction network models is the first step in the sensitivity analysis of a metabolic reaction system described by differential equations. However, this calculation becomes very difficult when the number of differential equations is more than 100. In the present study, therefore, we investigated a calculation procedure for obtaining true steady-state metabolite concentrations both efficiently and accurately even in large-scale network models. For convenience, a linear pathway model composed of a simple Michaelis-Menten rate law and two TCA cycle models were used as case studies. The calculation procedure is as follows: first solve the differential equations by a numerical method for solving initial-value problems until the upper several digits of the calculated values stabilize, and then use these values as initial guesses for a root-finding technique. An intensive investigation indicates that the S-system technique, finding roots in logarithmic space and providing a broader convergence region, is superior to the Newton-Raphson technique, and the algorithm using the S-system technique successfully provides true steady-state values with machine accuracy even with 1,500 differential equations. The complex-step method is also shown to contribute to shortening the calculation time and enhancing the accuracy. The program code has been deposited to https://github.com/BioprocessdesignLab/Steadystateconc.
AB - The calculation of steady-state metabolite concentrations in metabolic reaction network models is the first step in the sensitivity analysis of a metabolic reaction system described by differential equations. However, this calculation becomes very difficult when the number of differential equations is more than 100. In the present study, therefore, we investigated a calculation procedure for obtaining true steady-state metabolite concentrations both efficiently and accurately even in large-scale network models. For convenience, a linear pathway model composed of a simple Michaelis-Menten rate law and two TCA cycle models were used as case studies. The calculation procedure is as follows: first solve the differential equations by a numerical method for solving initial-value problems until the upper several digits of the calculated values stabilize, and then use these values as initial guesses for a root-finding technique. An intensive investigation indicates that the S-system technique, finding roots in logarithmic space and providing a broader convergence region, is superior to the Newton-Raphson technique, and the algorithm using the S-system technique successfully provides true steady-state values with machine accuracy even with 1,500 differential equations. The complex-step method is also shown to contribute to shortening the calculation time and enhancing the accuracy. The program code has been deposited to https://github.com/BioprocessdesignLab/Steadystateconc.
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U2 - 10.1109/TCBB.2018.2853724
DO - 10.1109/TCBB.2018.2853724
M3 - Article
C2 - 30004883
AN - SCOPUS:85049850426
VL - 17
SP - 27
EP - 36
JO - IEEE/ACM Transactions on Computational Biology and Bioinformatics
JF - IEEE/ACM Transactions on Computational Biology and Bioinformatics
SN - 1545-5963
IS - 1
M1 - 8410022
ER -