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Hybrid optimization for 13C metabolic flux analysis using systems parametrized by compactification.

Yang TH, Frick O, Heinzle E - BMC Syst Biol (2008)

Bottom Line: To solve the problem more efficiently, improved numerical optimization techniques are necessary.In the metabolic network studied, some fluxes were found to be either non-identifiable or nonlinearly correlated.In this way, it contributes to future quantitative studies of central metabolic networks in the framework of systems biology.

View Article: PubMed Central - HTML - PubMed

Affiliation: James Graham Brown Cancer Center & Department of Surgery, 2210 S, Brook St, Rm 342, Belknap Research Building, University of Louisville, Louisville, KY 40208, USA. th.yang@louisville.edu

ABSTRACT

Background: The importance and power of isotope-based metabolic flux analysis and its contribution to understanding the metabolic network is increasingly recognized. Its application is, however, still limited partly due to computational inefficiency. 13C metabolic flux analysis aims to compute in vivo metabolic fluxes in terms of metabolite balancing extended by carbon isotopomer balances and involves a nonlinear least-squares problem. To solve the problem more efficiently, improved numerical optimization techniques are necessary.

Results: For flux computation, we developed a gradient-based hybrid optimization algorithm. Here, independent flux variables were compactified into [0, 1)-ranged variables using a single transformation rule. The compactified parameters could be discriminated between non-identifiable and identifiable variables after model linearization. The developed hybrid algorithm was applied to the central metabolism of Bacillus subtilis with only succinate and glutamate as carbon sources. This creates difficulties caused by symmetry of succinate leading to limited introduction of 13C labeling information into the system. The algorithm was found to be superior to its parent algorithms and to global optimization methods both in accuracy and speed. The hybrid optimization with tolerance adjustment quickly converged to the minimum with close to zero deviation and exactly re-estimated flux variables. In the metabolic network studied, some fluxes were found to be either non-identifiable or nonlinearly correlated. The non-identifiable fluxes could correctly be predicted a priori using the model identification method applied, whereas the nonlinear flux correlation was revealed only by identification runs using different starting values a posteriori.

Conclusion: This fast, robust and accurate optimization method is useful for high-throughput metabolic flux analysis, a posteriori identification of possible parameter correlations, and also for Monte Carlo simulations to obtain statistical qualities for flux estimates. In this way, it contributes to future quantitative studies of central metabolic networks in the framework of systems biology.

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Related in: MedlinePlus

Developed hybrid optimization algorithm with tolerance adjustment consisting of the features: initialization within the feasible region (A); initial optimization using the SQP (B); interactive hybrid process using SQP (C); STRiN (D); and optimization control algorithm (E). f(Θ*k): objective function value at the current local minimizer Θ*k; χ2UL: upper limit of f(Θ*k) to invoke STRiN (if fΘ*k) <χ2UL; α: parameter scaling constant; Θ0: initial guess; Θ*: local minimizer from a successful sub-optimization; Θ°: iterate recorded for the smallest function value up to the current optimization trial; : ultimate minimizer.
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Figure 1: Developed hybrid optimization algorithm with tolerance adjustment consisting of the features: initialization within the feasible region (A); initial optimization using the SQP (B); interactive hybrid process using SQP (C); STRiN (D); and optimization control algorithm (E). f(Θ*k): objective function value at the current local minimizer Θ*k; χ2UL: upper limit of f(Θ*k) to invoke STRiN (if fΘ*k) <χ2UL; α: parameter scaling constant; Θ0: initial guess; Θ*: local minimizer from a successful sub-optimization; Θ°: iterate recorded for the smallest function value up to the current optimization trial; : ultimate minimizer.

Mentions: To solve the above constrained NLSP, we developed a logical algorithm (Figure 1) that interactively hybridizes two gradient-based local optimization methods, that is, the sequential quadratic programming (SQP) [31] and the subspace trust-region method based on the interior-reflective Newton method (STRiN) [32]. The developed method performs a series of sub-optimization trials by interactively switching between SQP and STRiN using the following features.


Hybrid optimization for 13C metabolic flux analysis using systems parametrized by compactification.

Yang TH, Frick O, Heinzle E - BMC Syst Biol (2008)

Developed hybrid optimization algorithm with tolerance adjustment consisting of the features: initialization within the feasible region (A); initial optimization using the SQP (B); interactive hybrid process using SQP (C); STRiN (D); and optimization control algorithm (E). f(Θ*k): objective function value at the current local minimizer Θ*k; χ2UL: upper limit of f(Θ*k) to invoke STRiN (if fΘ*k) <χ2UL; α: parameter scaling constant; Θ0: initial guess; Θ*: local minimizer from a successful sub-optimization; Θ°: iterate recorded for the smallest function value up to the current optimization trial; : ultimate minimizer.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC2333969&req=5

Figure 1: Developed hybrid optimization algorithm with tolerance adjustment consisting of the features: initialization within the feasible region (A); initial optimization using the SQP (B); interactive hybrid process using SQP (C); STRiN (D); and optimization control algorithm (E). f(Θ*k): objective function value at the current local minimizer Θ*k; χ2UL: upper limit of f(Θ*k) to invoke STRiN (if fΘ*k) <χ2UL; α: parameter scaling constant; Θ0: initial guess; Θ*: local minimizer from a successful sub-optimization; Θ°: iterate recorded for the smallest function value up to the current optimization trial; : ultimate minimizer.
Mentions: To solve the above constrained NLSP, we developed a logical algorithm (Figure 1) that interactively hybridizes two gradient-based local optimization methods, that is, the sequential quadratic programming (SQP) [31] and the subspace trust-region method based on the interior-reflective Newton method (STRiN) [32]. The developed method performs a series of sub-optimization trials by interactively switching between SQP and STRiN using the following features.

Bottom Line: To solve the problem more efficiently, improved numerical optimization techniques are necessary.In the metabolic network studied, some fluxes were found to be either non-identifiable or nonlinearly correlated.In this way, it contributes to future quantitative studies of central metabolic networks in the framework of systems biology.

View Article: PubMed Central - HTML - PubMed

Affiliation: James Graham Brown Cancer Center & Department of Surgery, 2210 S, Brook St, Rm 342, Belknap Research Building, University of Louisville, Louisville, KY 40208, USA. th.yang@louisville.edu

ABSTRACT

Background: The importance and power of isotope-based metabolic flux analysis and its contribution to understanding the metabolic network is increasingly recognized. Its application is, however, still limited partly due to computational inefficiency. 13C metabolic flux analysis aims to compute in vivo metabolic fluxes in terms of metabolite balancing extended by carbon isotopomer balances and involves a nonlinear least-squares problem. To solve the problem more efficiently, improved numerical optimization techniques are necessary.

Results: For flux computation, we developed a gradient-based hybrid optimization algorithm. Here, independent flux variables were compactified into [0, 1)-ranged variables using a single transformation rule. The compactified parameters could be discriminated between non-identifiable and identifiable variables after model linearization. The developed hybrid algorithm was applied to the central metabolism of Bacillus subtilis with only succinate and glutamate as carbon sources. This creates difficulties caused by symmetry of succinate leading to limited introduction of 13C labeling information into the system. The algorithm was found to be superior to its parent algorithms and to global optimization methods both in accuracy and speed. The hybrid optimization with tolerance adjustment quickly converged to the minimum with close to zero deviation and exactly re-estimated flux variables. In the metabolic network studied, some fluxes were found to be either non-identifiable or nonlinearly correlated. The non-identifiable fluxes could correctly be predicted a priori using the model identification method applied, whereas the nonlinear flux correlation was revealed only by identification runs using different starting values a posteriori.

Conclusion: This fast, robust and accurate optimization method is useful for high-throughput metabolic flux analysis, a posteriori identification of possible parameter correlations, and also for Monte Carlo simulations to obtain statistical qualities for flux estimates. In this way, it contributes to future quantitative studies of central metabolic networks in the framework of systems biology.

Show MeSH
Related in: MedlinePlus