title: Investigation of kinetic-order sensitivities in metabolic reaction networks.
abstract: Kinetic-order sensitivity (the ratio of relative change in a dependent variable to the relative change in a kinetic order in a power-law-type differential equation) has recently become an important indicator in metabolic pathway analysis using mathematical models with parameter values determined from time-series data on cellular metabolite concentrations. Here, we discuss a potential problem in calculating kinetic-order sensitivities. When the steady-state metabolite concentration is less than unity, a slight increase in the kinetic order changes the metabolite concentration in the incorrect direction, yielding a kinetic-order sensitivity value with an incorrect sign. This is caused by a property of the power-law function (y=Xn): when X is less than unity, y decreases for a larger positive n or for a smaller absolute value of negative n. We propose two solutions. The first is to directly calculate the kinetic-order sensitivities and then reverse the sign of the relevant value if a steady-state metabolite concentration less than unity is involved. The second involves calculation of the kinetic-order sensitivities after setting all metabolite concentrations to values greater than unity (e.g., by changing the units from mM to μM). The latter method changes the absolute values of the kinetic-order sensitivities according to the magnitude of a multiplication factor, because kinetic-order sensitivities do not have unique values. Nevertheless, since the normalized absolute values exhibit an almost identical distribution, it should not be difficult to identify which kinetic order has greater effect, although kinetic order rankings may change slightly under different calculation conditions.
authors.affiliation: Section of Bio-process design, Department of Bioscience and Biotechnology, Graduate School of Bioresource and Bioenvironmental Sciences, Kyushu University, 6-10-1, Hakozaki, Higashi-Ku, Fukuoka 820-8581, Japan.
authors.forename: Masatsugu
authors.initials: M
authors.lastname: Yamada
authors.affiliation: Section of Bio-process design, Department of Bioscience and Biotechnology, Graduate School of Bioresource and Bioenvironmental Sciences, Kyushu University, 6-10-1, Hakozaki, Higashi-Ku, Fukuoka 820-8581, Japan.
authors.forename: Masashi
authors.initials: M
authors.lastname: Iwanaga
authors.affiliation: RIKEN Center for Sustainable and Resource Science,1-7-22 Suehiro, Tsurumi, Yokohama, Kanagawa 230-0045, Japan.
authors.forename: Kansuporn
authors.initials: K
authors.lastname: Sriyudthsak
authors.affiliation: RIKEN Center for Sustainable and Resource Science,1-7-22 Suehiro, Tsurumi, Yokohama, Kanagawa 230-0045, Japan.
authors.forename: Masami Y
authors.initials: MY
authors.lastname: Hirai
authors.affiliation: Section of Bio-process design, Department of Bioscience and Biotechnology, Graduate School of Bioresource and Bioenvironmental Sciences, Kyushu University, 6-10-1, Hakozaki, Higashi-Ku, Fukuoka 820-8581, Japan. Electronic address: fumishira@brs.kyushu-u.ac.jp.
authors.forename: Fumihide
authors.initials: F
authors.lastname: Shiraishi
mesh_terms: D006801:Humans; D007700:Kinetics; D053858:Metabolic Networks and Pathways; D008954:Models, Biological; D008962:Models, Theoretical
keywords: Kinetic-order sensitivity; Metabolic reaction network; Power-law function; Steady state