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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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Metabolic network of the central metabolism of Bacillus subtilis utilizing glutamate and succinate as co-substrates. All flux values denoted in parentheses were generated by obeying the given stoichiometry. Effluxes and biomass yield were measured experimentally. The symbol 'ν' indicates the flux, the subscript 'r' the reverse flux of the bidirectional flux pair, the subscript 'ex' extracellular pools of substrates and products and YXS the biomass yield in g(biomass)/mmol(glutamate). All flux values are normalized by the glutamate uptake rate.
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Figure 2: Metabolic network of the central metabolism of Bacillus subtilis utilizing glutamate and succinate as co-substrates. All flux values denoted in parentheses were generated by obeying the given stoichiometry. Effluxes and biomass yield were measured experimentally. The symbol 'ν' indicates the flux, the subscript 'r' the reverse flux of the bidirectional flux pair, the subscript 'ex' extracellular pools of substrates and products and YXS the biomass yield in g(biomass)/mmol(glutamate). All flux values are normalized by the glutamate uptake rate.

Mentions: To evaluate the developed methods, a metabolic network of the wild type B.subtilis was constructed as shown in Figure 2 based on the Kyoto Encyclopedia of Genes and Genomes (KEGG) database specified for the strain. The network is composed of catabolic reactions of the central metabolism incorporating glycolysis/gluconeogenesis, pentose phosphate pathway, TCA cycle, C3/C4 inter-conversion and anabolic reactions. All effluxes including the biomass yield YXS in Figure 2 were assumed to be measured experimentally from a batch-cultivation on succinate and glutamate as carbon sources. All flux values specified in Figure 2 are generated from arbitrary values of Θdefault and normalized by the glutamate uptake rate. Note that each anabolic flux given in Figure 2 is the product of YXS (biomass production [gDW L-1 h-1] normalized by glutamate uptake [mM h-1]) and a value that specifies the precursor requirement for growth (mmol precursor per g biomass) adopted from literature data [34]. For bidirectional reactions, the fluxes in the gluconeogenetic direction were declared as forward.


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

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

Metabolic network of the central metabolism of Bacillus subtilis utilizing glutamate and succinate as co-substrates. All flux values denoted in parentheses were generated by obeying the given stoichiometry. Effluxes and biomass yield were measured experimentally. The symbol 'ν' indicates the flux, the subscript 'r' the reverse flux of the bidirectional flux pair, the subscript 'ex' extracellular pools of substrates and products and YXS the biomass yield in g(biomass)/mmol(glutamate). All flux values are normalized by the glutamate uptake rate.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 2: Metabolic network of the central metabolism of Bacillus subtilis utilizing glutamate and succinate as co-substrates. All flux values denoted in parentheses were generated by obeying the given stoichiometry. Effluxes and biomass yield were measured experimentally. The symbol 'ν' indicates the flux, the subscript 'r' the reverse flux of the bidirectional flux pair, the subscript 'ex' extracellular pools of substrates and products and YXS the biomass yield in g(biomass)/mmol(glutamate). All flux values are normalized by the glutamate uptake rate.
Mentions: To evaluate the developed methods, a metabolic network of the wild type B.subtilis was constructed as shown in Figure 2 based on the Kyoto Encyclopedia of Genes and Genomes (KEGG) database specified for the strain. The network is composed of catabolic reactions of the central metabolism incorporating glycolysis/gluconeogenesis, pentose phosphate pathway, TCA cycle, C3/C4 inter-conversion and anabolic reactions. All effluxes including the biomass yield YXS in Figure 2 were assumed to be measured experimentally from a batch-cultivation on succinate and glutamate as carbon sources. All flux values specified in Figure 2 are generated from arbitrary values of Θdefault and normalized by the glutamate uptake rate. Note that each anabolic flux given in Figure 2 is the product of YXS (biomass production [gDW L-1 h-1] normalized by glutamate uptake [mM h-1]) and a value that specifies the precursor requirement for growth (mmol precursor per g biomass) adopted from literature data [34]. For bidirectional reactions, the fluxes in the gluconeogenetic direction were declared as forward.

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