### 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=X^{n}): 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.

Original language | English |
---|---|

Pages (from-to) | 32-40 |

Number of pages | 9 |

Journal | Journal of Theoretical Biology |

Volume | 415 |

DOIs | |

Publication status | Published - Feb 21 2017 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Modelling and Simulation
- Biochemistry, Genetics and Molecular Biology(all)
- Immunology and Microbiology(all)
- Agricultural and Biological Sciences(all)
- Applied Mathematics

### Cite this

*Journal of Theoretical Biology*,

*415*, 32-40. https://doi.org/10.1016/j.jtbi.2016.12.001

**Investigation of kinetic-order sensitivities in metabolic reaction networks.** / Yamada, Masatsugu; Iwanaga, Masashi; Sriyudthsak, Kansuporn; Hirai, Masami Y.; Shiraishi, Fumihide.

Research output: Contribution to journal › Article

*Journal of Theoretical Biology*, vol. 415, pp. 32-40. https://doi.org/10.1016/j.jtbi.2016.12.001

}

TY - JOUR

T1 - Investigation of kinetic-order sensitivities in metabolic reaction networks

AU - Yamada, Masatsugu

AU - Iwanaga, Masashi

AU - Sriyudthsak, Kansuporn

AU - Hirai, Masami Y.

AU - Shiraishi, Fumihide

PY - 2017/2/21

Y1 - 2017/2/21

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85003443871&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85003443871&partnerID=8YFLogxK

U2 - 10.1016/j.jtbi.2016.12.001

DO - 10.1016/j.jtbi.2016.12.001

M3 - Article

C2 - 27939412

AN - SCOPUS:85003443871

VL - 415

SP - 32

EP - 40

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

ER -