Miyawaki-Kuwakado A, Komori S, Shiraishi F. A Promising Method for Calculating True Steady-State Metabolite Concentrations in Large-Scale Metabolic Reaction Network Models.
IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2020;
17:27-36. [PMID:
30004883 DOI:
10.1109/tcbb.2018.2853724]
[Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
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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