### Abstract

Biochemical systems theory (BST) characterizes a given biochemical system based on the logarithmic gains, rate-constant sensitivities and kinetic-order sensitivities defined at a steady state. This paper describes an efficient method for calculation of the time courses of logarithmic gains, i.e. dynamic logarithmic gains L(X_{i}, X_{j}; t), which expresses the percentage change in the value of a dependent variable X_{i} at a time t in response to an infinitesimal percentage change in the value of an independent variable X_{j} at t=0. In this method, one first recasts the ordinary differential equations for the dependent variables into an exact canonical nonlinear representation (GMA system) through appropriate transformations of variables. Owing to the structured mathematical form of this representation, the recast system can be fully described by a set of numeric parameters, and the differential equations for the dynamic logarithmic gains can be set up automatically without resource to computer algebra. A simple general-purpose computer program can thus be written that requires only the relevant numeric parameters as input to calculate the time courses of the variables and of the dynamic logarithmic gains for both concentrations and fluxes. Unlike other methods, the proposed method does not require to derive any expression for the partial differentiation of flux expressions with respect to each independent variable. The proposed method has been applied to two kinds of reaction models to elucidate its usefulness.

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

Pages (from-to) | 79-85 |

Number of pages | 7 |

Journal | Journal of Theoretical Biology |

Volume | 234 |

Issue number | 1 |

DOIs | |

Publication status | Published - May 7 2005 |

Externally published | Yes |

### 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*,

*234*(1), 79-85. https://doi.org/10.1016/j.jtbi.2004.11.015

**An efficient method for calculation of dynamic logarithmic gains in biochemical systems theory.** / Shiraishi, Fumihide; Hatoh, Yuji; Irie, Toshinori.

Research output: Contribution to journal › Article

*Journal of Theoretical Biology*, vol. 234, no. 1, pp. 79-85. https://doi.org/10.1016/j.jtbi.2004.11.015

}

TY - JOUR

T1 - An efficient method for calculation of dynamic logarithmic gains in biochemical systems theory

AU - Shiraishi, Fumihide

AU - Hatoh, Yuji

AU - Irie, Toshinori

PY - 2005/5/7

Y1 - 2005/5/7

N2 - Biochemical systems theory (BST) characterizes a given biochemical system based on the logarithmic gains, rate-constant sensitivities and kinetic-order sensitivities defined at a steady state. This paper describes an efficient method for calculation of the time courses of logarithmic gains, i.e. dynamic logarithmic gains L(Xi, Xj; t), which expresses the percentage change in the value of a dependent variable Xi at a time t in response to an infinitesimal percentage change in the value of an independent variable Xj at t=0. In this method, one first recasts the ordinary differential equations for the dependent variables into an exact canonical nonlinear representation (GMA system) through appropriate transformations of variables. Owing to the structured mathematical form of this representation, the recast system can be fully described by a set of numeric parameters, and the differential equations for the dynamic logarithmic gains can be set up automatically without resource to computer algebra. A simple general-purpose computer program can thus be written that requires only the relevant numeric parameters as input to calculate the time courses of the variables and of the dynamic logarithmic gains for both concentrations and fluxes. Unlike other methods, the proposed method does not require to derive any expression for the partial differentiation of flux expressions with respect to each independent variable. The proposed method has been applied to two kinds of reaction models to elucidate its usefulness.

AB - Biochemical systems theory (BST) characterizes a given biochemical system based on the logarithmic gains, rate-constant sensitivities and kinetic-order sensitivities defined at a steady state. This paper describes an efficient method for calculation of the time courses of logarithmic gains, i.e. dynamic logarithmic gains L(Xi, Xj; t), which expresses the percentage change in the value of a dependent variable Xi at a time t in response to an infinitesimal percentage change in the value of an independent variable Xj at t=0. In this method, one first recasts the ordinary differential equations for the dependent variables into an exact canonical nonlinear representation (GMA system) through appropriate transformations of variables. Owing to the structured mathematical form of this representation, the recast system can be fully described by a set of numeric parameters, and the differential equations for the dynamic logarithmic gains can be set up automatically without resource to computer algebra. A simple general-purpose computer program can thus be written that requires only the relevant numeric parameters as input to calculate the time courses of the variables and of the dynamic logarithmic gains for both concentrations and fluxes. Unlike other methods, the proposed method does not require to derive any expression for the partial differentiation of flux expressions with respect to each independent variable. The proposed method has been applied to two kinds of reaction models to elucidate its usefulness.

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UR - http://www.scopus.com/inward/citedby.url?scp=13844253731&partnerID=8YFLogxK

U2 - 10.1016/j.jtbi.2004.11.015

DO - 10.1016/j.jtbi.2004.11.015

M3 - Article

C2 - 15721037

AN - SCOPUS:13844253731

VL - 234

SP - 79

EP - 85

JO - Journal of Theoretical Biology

JF - Journal of Theoretical Biology

SN - 0022-5193

IS - 1

ER -