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New time-scale criteria for model simplification of bio-reaction systems.

Choi J, Yang KW, Lee TY, Lee SY - BMC Bioinformatics (2008)

Bottom Line: Therefore, an iterative procedure was also developed to find the possible multiple boundary layers and to derive an appropriate reduced model.By successive calculation of the newly derived time-scale criteria, it was possible to detect multiple boundary layers of full ordinary differential equation (ODE) models.Besides, the iterative procedure could derive the appropriate reduced differential algebraic equation (DAE) model with consistent initial values, which was tested with simple examples and a practical example.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Chemical and Biomolecular Engineering (BK21 Program), KAIST, 335 Gwahangro, Yuseong-gu, Daejeon, 305-701, Republic of Korea. martial@kaist.ac.kr

ABSTRACT

Background: Quasi-steady state approximation (QSSA) based on time-scale analysis is known to be an effective method for simplifying metabolic reaction system, but the conventional analysis becomes time-consuming and tedious when the system is large. Although there are automatic methods, they are based on eigenvalue calculations of the Jacobian matrix and on linear transformations, which have a high computation cost. A more efficient estimation approach is necessary for complex systems.

Results: This work derived new time-scale factor by focusing on the problem structure. By mathematically reasoning the balancing behavior of fast species, new time-scale criteria were derived with a simple expression that uses the Jacobian matrix directly. The algorithm requires no linear transformation or decomposition of the Jacobian matrix, which has been an essential part for previous automatic time-scaling methods. Furthermore, the proposed scale factor is estimated locally. Therefore, an iterative procedure was also developed to find the possible multiple boundary layers and to derive an appropriate reduced model.

Conclusion: By successive calculation of the newly derived time-scale criteria, it was possible to detect multiple boundary layers of full ordinary differential equation (ODE) models. Besides, the iterative procedure could derive the appropriate reduced differential algebraic equation (DAE) model with consistent initial values, which was tested with simple examples and a practical example.

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Simplification results (II). Concentrations of e, es1, es2, and ei for the Michaelis-Menten system with inhibition; (a) full ODE model solution and (b) reduced model solution.
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Figure 3: Simplification results (II). Concentrations of e, es1, es2, and ei for the Michaelis-Menten system with inhibition; (a) full ODE model solution and (b) reduced model solution.

Mentions: The second example, the Michaelis-Menten kinetics with inhibition, shows a boundary layer at the initial area only (see equation (11) and Figure 3) with a similar scale of δt to that of the non-inhibition case. The dynamic behavior of the second model in the inner region of the initial boundary layer is more complex because of the effect of the inhibition. These complex dynamics of the second example require a few more iterations than that of the first example to exit the initial boundary layer.


New time-scale criteria for model simplification of bio-reaction systems.

Choi J, Yang KW, Lee TY, Lee SY - BMC Bioinformatics (2008)

Simplification results (II). Concentrations of e, es1, es2, and ei for the Michaelis-Menten system with inhibition; (a) full ODE model solution and (b) reduced model solution.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2553091&req=5

Figure 3: Simplification results (II). Concentrations of e, es1, es2, and ei for the Michaelis-Menten system with inhibition; (a) full ODE model solution and (b) reduced model solution.
Mentions: The second example, the Michaelis-Menten kinetics with inhibition, shows a boundary layer at the initial area only (see equation (11) and Figure 3) with a similar scale of δt to that of the non-inhibition case. The dynamic behavior of the second model in the inner region of the initial boundary layer is more complex because of the effect of the inhibition. These complex dynamics of the second example require a few more iterations than that of the first example to exit the initial boundary layer.

Bottom Line: Therefore, an iterative procedure was also developed to find the possible multiple boundary layers and to derive an appropriate reduced model.By successive calculation of the newly derived time-scale criteria, it was possible to detect multiple boundary layers of full ordinary differential equation (ODE) models.Besides, the iterative procedure could derive the appropriate reduced differential algebraic equation (DAE) model with consistent initial values, which was tested with simple examples and a practical example.

View Article: PubMed Central - HTML - PubMed

Affiliation: Department of Chemical and Biomolecular Engineering (BK21 Program), KAIST, 335 Gwahangro, Yuseong-gu, Daejeon, 305-701, Republic of Korea. martial@kaist.ac.kr

ABSTRACT

Background: Quasi-steady state approximation (QSSA) based on time-scale analysis is known to be an effective method for simplifying metabolic reaction system, but the conventional analysis becomes time-consuming and tedious when the system is large. Although there are automatic methods, they are based on eigenvalue calculations of the Jacobian matrix and on linear transformations, which have a high computation cost. A more efficient estimation approach is necessary for complex systems.

Results: This work derived new time-scale factor by focusing on the problem structure. By mathematically reasoning the balancing behavior of fast species, new time-scale criteria were derived with a simple expression that uses the Jacobian matrix directly. The algorithm requires no linear transformation or decomposition of the Jacobian matrix, which has been an essential part for previous automatic time-scaling methods. Furthermore, the proposed scale factor is estimated locally. Therefore, an iterative procedure was also developed to find the possible multiple boundary layers and to derive an appropriate reduced model.

Conclusion: By successive calculation of the newly derived time-scale criteria, it was possible to detect multiple boundary layers of full ordinary differential equation (ODE) models. Besides, the iterative procedure could derive the appropriate reduced differential algebraic equation (DAE) model with consistent initial values, which was tested with simple examples and a practical example.

Show MeSH
Related in: MedlinePlus