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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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Related in: MedlinePlus

Simplification results (III). Concentrations of c8 and c8* for the caspase system; (a) the solution profile of c8, from the full ODE model (c8) and from the reduced model (c8_red) and (b) the solution profile of c8*, from the full ODE model (c8*) and from the reduced model (c8*_red).
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Figure 4: Simplification results (III). Concentrations of c8 and c8* for the caspase system; (a) the solution profile of c8, from the full ODE model (c8) and from the reduced model (c8_red) and (b) the solution profile of c8*, from the full ODE model (c8*) and from the reduced model (c8*_red).

Mentions: The reaction rate equations for equation (12) are written as v1 = k1[c8*][c3], v2 = k2[c3*][c8], v3 = k3[c3*][IAP] - k-3 [c3*~IAP], v4 = k4[c3*][IAP], v5 = k5[c8*], v6 = k6[c3*], v7 = k7[c3*~IAP], v8 = k8[IAP] - k-8, v9 = k9[C8] - k-9, v10 = k10[c3] - k-10, v11 = k11[c8*][BAR] - k-11 [c8*~BAR], v12 = k12[BAR] - k-12 and v13 = k13[c8a~BAR], where the kinetic constants are listed in [26]. There are also two boundary layers at the initial and internal regions, but with a much larger δt relative to the former cases; δt ≈ O(10-1) at the initial area and δt ≈ O(1) at the internal boundary layer (Figure 4).


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

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

Simplification results (III). Concentrations of c8 and c8* for the caspase system; (a) the solution profile of c8, from the full ODE model (c8) and from the reduced model (c8_red) and (b) the solution profile of c8*, from the full ODE model (c8*) and from the reduced model (c8*_red).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 4: Simplification results (III). Concentrations of c8 and c8* for the caspase system; (a) the solution profile of c8, from the full ODE model (c8) and from the reduced model (c8_red) and (b) the solution profile of c8*, from the full ODE model (c8*) and from the reduced model (c8*_red).
Mentions: The reaction rate equations for equation (12) are written as v1 = k1[c8*][c3], v2 = k2[c3*][c8], v3 = k3[c3*][IAP] - k-3 [c3*~IAP], v4 = k4[c3*][IAP], v5 = k5[c8*], v6 = k6[c3*], v7 = k7[c3*~IAP], v8 = k8[IAP] - k-8, v9 = k9[C8] - k-9, v10 = k10[c3] - k-10, v11 = k11[c8*][BAR] - k-11 [c8*~BAR], v12 = k12[BAR] - k-12 and v13 = k13[c8a~BAR], where the kinetic constants are listed in [26]. There are also two boundary layers at the initial and internal regions, but with a much larger δt relative to the former cases; δt ≈ O(10-1) at the initial area and δt ≈ O(1) at the internal boundary layer (Figure 4).

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