### Abstract

The calculation of steady-state metabolite concentrations in metabolic reaction network models is the first step in the sensitivity analy-sis 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 1500 differential equations. The complex-step method is also shown to contribute to shorten-ing the calculation time and enhancing the accuracy. The program code has been deposited to https://github.com/BioprocessdesignLab/Steadystateconc.

Original language | English |
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Journal | IEEE/ACM Transactions on Computational Biology and Bioinformatics |

DOIs | |

Publication status | Accepted/In press - Jul 10 2018 |

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### All Science Journal Classification (ASJC) codes

- Biotechnology
- Genetics
- Applied Mathematics

### Cite this

*IEEE/ACM Transactions on Computational Biology and Bioinformatics*. https://doi.org/10.1109/TCBB.2018.2853724

**A Promising Method for Calculating True Steady-State Metabolite Concentrations in Large-Scale Metabolic Reaction Network Models.** / Miyawaki-Kuwakado, Atsuko; Komori, Soichiro; Shiraishi, Fumihide.

Research output: Contribution to journal › Article

}

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

PY - 2018/7/10

Y1 - 2018/7/10

N2 - The calculation of steady-state metabolite concentrations in metabolic reaction network models is the first step in the sensitivity analy-sis 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 1500 differential equations. The complex-step method is also shown to contribute to shorten-ing 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 analy-sis 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 1500 differential equations. The complex-step method is also shown to contribute to shorten-ing the calculation time and enhancing the accuracy. The program code has been deposited to https://github.com/BioprocessdesignLab/Steadystateconc.

UR - http://www.scopus.com/inward/record.url?scp=85049850426&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049850426&partnerID=8YFLogxK

U2 - 10.1109/TCBB.2018.2853724

DO - 10.1109/TCBB.2018.2853724

M3 - Article

AN - SCOPUS:85049850426

JO - IEEE/ACM Transactions on Computational Biology and Bioinformatics

JF - IEEE/ACM Transactions on Computational Biology and Bioinformatics

SN - 1545-5963

ER -