Cited By
View all- Sun JGaribaldi JHodgman C(2012)Parameter Estimation Using Metaheuristics in Systems BiologyIEEE/ACM Transactions on Computational Biology and Bioinformatics10.1109/TCBB.2011.639:1(185-202)Online publication date: 1-Jan-2012
Metabolic Flux Estimation-A Self-Adaptive Evolutionary Algorithm with Singular Value Decomposition
Authors: 
Jing Yang, Sarawan Wongsa, Visakan Kadirkamanathan, Stephen A. Billings, Phillip C. WrightAuthors Info & Claims
Pages 126 - 138
Abstract
Metabolic flux analysis is important for metabolic system regulation and intracellular pathway identification. A popular approach for intracellular flux estimation involves using ^{13}{\rm C} tracer experiments to label states that can be measured by nuclear magnetic resonance spectrometry or gas chromatography mass spectrometry. However, the bilinear balance equations derived from ^{13}{\rm C} tracer experiments and the noisy measurements require a nonlinear optimization approach to obtain the optimal solution. In this paper, the flux quantification problem is formulated as an error-minimization problem with equality and inequality constraints through the ^{13}{\rm C} balance and stoichiometric equations. The stoichiometric constraints are transformed to a null space by singular value decomposition. Self-adaptive evolutionary algorithms are then introduced for flux quantification. The performance of the evolutionary algorithm is compared with ordinary least squares estimation by the simulation of the central pentose phosphate pathway. The proposed algorithm is also applied to the central metabolism of Corynebacterium glutamicum under lysine-producing conditions. A comparison between the results from the proposed algorithm and data from the literature is given. The complexity of a metabolic system with bidirectional reactions is also investigated by analyzing the fluctuations in the flux estimates when available measurements are varied.
References
[1]
{1} J.E. Bailey, "Toward a Science of Metabolic Engineering," Science, vol. 252, pp. 1668-1675, 1991.]]
[2]
{2} M.I. Klapa, J.C. Aon, and G. Stephanopoulos, "Ion-Trap Mass Spectrometry Used in Combination with Gas Chromatography for High-Resolution Metabolic Flux Determination," Biotechniques, vol. 34, no. 4, pp. 832-840, 2003.]]
[3]
{3} C. Zupke and G. Stephanopoulos, "Modeling of Isotope Distributions and Intracellular Fluxes in Metabolic Networks Using Atom Mapping Matrices," Biotechnology Programming, vol. 10, no. 5, pp. 489-498, 1994.]]
[4]
{4} A. Marx, A.A. de Graaf, W. Wiechert, L. Eggeling, and H. Sahm, "Determination of the Fluxes in the Central Metabolism of Corynebacterium Glutamicum by Nuclear Magnetic Resonance Spectroscopy Combined with Metabolite Balancing," Biotechnology Bioeng., vol. 49, pp. 111-129, 1996.]]
[5]
{5} G.N. Stephanopoulos, A.A. Aristidou, and J. Nielsen, Metabolic Engineering-Principles and Methodologies. Academic Press, 1998.]]
[6]
{6} J.J. Vallino and G. Stephanopoulos, "Metabolic Flux Distributions in Corynebacterium Glutamicum during Growth and Lysine Overproduction," Biotechnology Bioeng., vol. 41, pp. 633-646, 1993.]]
[7]
{7} A. Varma and B.O. Palsson, "Metabolic Flux Balancing: Basic Concepts, Scientific and Practical Use," Bio/Technology, vol. 12, pp. 994-998, 1994.]]
[8]
{8} H. Bonarius, G. Schmidt, and J. Tramper, "Flux Analysis of Underdetermined Metabolic Networks: The Quest of the Missing Constraints," Trends in Biotechnology, vol. 15, pp. 308-314, 1997.]]
[9]
{9} H. Jorgensen, J. Nielsen, J. Villadsen, and H. Nolgaard, "Metabolic Flux Distributions in Penicillium Chrysogenum during Fed-Batch Cultivations," Biotechnology Bioeng., vol. 46, pp. 117-131, 1995.]]
[10]
{10} W. Wiechert, "<sup>13</sup>C Metabolic Flux Analysis," Metabolic Eng., vol.3, no. 3, pp. 195-206, 2001.]]
[11]
{11} D.H. Anderson, "Compartmental Modeling and Tracer Kinetics," Lecture Notes in Biomath., vol. 50, Springer-Verlag, 1983.]]
[12]
{12} M.I. Klapa, J.C. Aon, and G. Stephanopoulos, "Systematic Quantification of Complex Metabolic Flux Networks Using Stable Isotopes and Mass Spectrometry," European J. Biochemistry, vol. 270, pp. 3525-3542, 2003.]]
[13]
{13} K. Sonntag, L. Eggeling, A.A. de Graaf, and H. Sahm, "Flux Partitioning in the Split Pathway of Lysine Synthesis in Corynebacterium Glutamicum: Quantification by <sup>13</sup>C and <sup>1</sup>H NMR Spectroscopy," European J. Biochemistry, vol. 213, pp. 1325- 1331, 1993.]]
[14]
{14} T. Szyperski, "Biosynthetically Directed <sup>13</sup>C-Fractional Labeling of Proteinogenic Amino Acids," European J. Biochemistry, vol. 232, pp. 433-448, 1995.]]
[15]
{15} A.P.L. Snijders, M.G.J. de Vos, and P.C. Wright, "Novel Approach for Peptide Quantitation and Sequencing Based on <sup>15</sup>N and <sup>13</sup>C Metabolic Labeling," J. Proteome Research, vol. 4, no. 2, pp. 578-585, 2005.]]
[16]
{16} K. Schmidt, M. Carlsen, J. Nielsen, and J. Villadsen, "Modeling Isotopomer Distributions in Metabolic Networks Using Isotopomer Mapping Matrices," Biotechnology Bioeng., vol. 55, no. 6, pp. 831-840, 1997.]]
[17]
{17} K. Schmidt, J. Nielsen, and J. Villadsen, "Quantitative Analysis of Metabolic Fluxes in Escherichia Coli Using Two-Dimensional NMR Spectroscopy and Complete Isotopomer Models," J. Biotechnology, vol. 71, nos. 1-3, pp. 175-189, 1999.]]
[18]
{18} K. Schmidt, L.C. Norregaard, B. Pedersen, A. Meissner, J.O. Duus, J.O. Nielsen, and J. Villadsen, "Quantification of Intracellular Metabolic Fluxes from Fractional Enrichment and <sup>13</sup>C-<sup>13</sup>C Coupling Constraints on the Isotopomer Distribution in Labeled Biomass Components," Metabolic Eng., vol. 1, no. 2, pp. 166-179, 1999.]]
[19]
{19} M.J. Araúzo-Bravo and K. Shimizu, "An Improved Method for Statistical Analysis of Metabolic Flux Analysis Using Isotopomer Mapping Matrices with Analytical Expressions," J. Biotechnology, vol. 105, pp. 117-133, 2003.]]
[20]
{20} W. Wiechert and A.A. de Graaf, "Bidirectional Reaction Steps in Metabolic Networks: I. Modeling and Simulation of Carbon Isotope Labeling Experiments," Biotechnology Bioeng., vol. 55, no. 1, pp. 101-117, 1997.]]
[21]
{21} W. Wiechert, C. Siefke, A.A. de Graaf, and A. Marx, "Bidirectional Reaction Steps in Metabolic Networks: II. Flux Estimation and Statistical Analysis," Biotechnology Bioeng., vol. 55, no. 1, pp. 118- 135, 1997.]]
[22]
{22} M. Koffas and G.N. Stephanopoulos, "Strain Improvement by Metabolic Engineering: Lysine Production as a Case Study for Systems Biology," Current Opinions in Biotechnology, vol. 16, no. 3, pp. 361-366, 2005.]]
[23]
{23} W.J. Blake, M. Kaern, C.R. Cantor, and J.J. Collins, "Noise in Eukaryotic Gene Expression," Nature, vol. 422, pp. 633-637, 2003.]]
[24]
{24} M.B. Elowitz, A.J. Levine, E.D. Siggia, and P.S. Swain, "Stochastic Gene Expression in a Single Cell," Science, vol. 297, pp. 1183-1186, 2002.]]
[25]
{25} E.M. Ozbudak, M. Thattai, I. Kurtser, A.D. Grossman, and A. van Oudenaarden, "Regulation of Noise in the Expression of a Single Gene," Nature Genetics, vol. 31, pp. 69-73, 2002.]]
[26]
{26} Encyclopedia of Nuclear Magnetic Resonance, D.M. Grant and R.K. Harris, eds. Wiley, 2002.]]
[27]
{27} K. Schmidt and S.H. Issacs, "An Evolutionary Algorithm for Initial State and Parameter Estimation in Complex Biochemical Models," Proc. Sixth Int'l Conf. Computer Applications in Biotechnology, 1995.]]
[28]
{28} J. Yang, S. Wongsa, V. Kadirkamanathan, S.A. Billings, and P.C. Wright, "Self-Adaptive Evolutionary Algorithm Based Methods for Quantification in Metabolic Systems," Proc. 2004 IEEE Symp. Computational Intelligence in Bioinformatics and Computational Biology, pp. 260-267, 2004.]]
[29]
{29} H.-G. Beyer and H.-P. Schwefel, "Evolution Strategies-A Comprehensive Introduction," Natural Computing, vol. 1, no. 1, pp. 3-52, 2002.]]
[30]
{30} J.H. Holland, "Outline for a Logical Theory of Adaptive Systems," J. ACM, vol. 9, no. 3, pp. 297-314, 1962.]]
[31]
{31} I. Rechenberg, Cybernetic Solution Path of an Experimental Problem, Farnborough, U.K.: Library Translation 1122, Royal Aircraft Establishment, 1965.]]
[32]
{32} L.J. Fogel, "Autonomous Automata," Industrial Research, vol. 4, pp. 14-19, 1962.]]
[33]
{33} D.B. Fogel, K. Chellapilla, and P.J. Angeline, "Inductive Reasoning and Bounded Rationality Reconsidered," IEEE Trans. Evolutionary Computing, vol. 3, no. 2, pp. 142-146, 1999.]]
[34]
{34} H.-P. Schwefel, Numerical Optimization of Computer Models. Wiley, 1981.]]
[35]
{35} H. Mühlenbein and D. Schlierkamp-Voosen, "Predictive Models for the Breeder Genetic Algorithm I. Continuous Parameter Optimization," Evolutionary Computation, vol. 1, pp. 25-49, 1993.]]
[36]
{36} D.B. Fogel, L. Fogel, and W. Atmar, "Meta-Evolutionary Programming," Proc. 25th Asilomar Conf. Signals, Systems, and Computing, pp. 540-545, 1991.]]
[37]
{37} N. Saravanan, D.B. Fogel, and K.M. Nelson, "A Comparison of Methods for Self-Adaptation in Evolutionary Algorithms," Bio-Systems , vol. 36, pp. 157-166, 1995.]]
[38]
{38} S. Draghici and R.B. Potter, "Predicting HIV Drug Resistance with Neural Networks," Bioinformatics, vol. 19, pp. 98-107, 2003.]]
[39]
{39} Y.S. Song, Y. Wu, and D. Gusfield, "Efficient Computation of Close Lower and Upper Bounds on the Minimum Number of Recombinations in Biological Sequence Evolution," Bioinformatics, pp. 1-9, 2005.]]
[40]
{40} Evolutionary Computation in Bioinformatics, G.B. Fogel and D.W. Corne, eds. Morgan Kaufmann, 2003.]]
[41]
{41} O. Ebenhöh and R. Heinrich, "Evolutionary Optimization of Metabolic Pathways. Theoretical Reconstruction of the Stoichiometry of ATP and NADH Producing Systems," Bull. Math. Biology, no. 63, pp. 21-55, 2001.]]
[42]
{42} S.J.V. Dien, T. Strovas, and M.E. Lidstrom, "Quantification of Central Metabolic Fluxes in the Facultative Methylotroph Methylobacterium Extorquens am1 Using <sup>13</sup>C-Label Tracing and Mass Spectrometry," Biotechnology Bioeng., vol. 84, no. 1, pp. 45-55, 2003.]]
[43]
{43} C.H. Schilling, S. Schuster, B.O. Palsson, and R. Heinrich, "Metabolic Pathway Analysis: Basic Concepts and Scientific Applications in the Post-Genomic Era," Biotechnology Programming , vol. 15, pp. 296-303, 1999.]]
[44]
{44} M.L. Mavrovouniotis, G. Stephanopoulos, and G. Stephanopoulos, "Computer-Aided Synthesis of Biochemical Pathways," Biotechnology Bioeng., vol. 36, pp. 1119-1132, 1990.]]
[45]
{45} C.H. Schilling and B.O. Palsson, "The Underlying Pathway Structure of Biochemcial Reaction Networks," Proc. Nat'l Academy of Sciences USA, vol. 95, pp. 4193-4198, 1998.]]
[46]
{46} S. Schuster, T. Dandeker, and D.A. Fell, "Detection of Elementary Flux Modes in Biochemical Networks: A Promising Tool for Pathway Analysis and Metabolic Engineering," Trends in Biotechnology , vol. 17, pp. 53-60, 1999.]]
[47]
{47} S. Schuster, D.A. Fell, and T. Dandekar, "A General Definition of Metabolic Pathways Useful for Systematic Organization and Analysis of Complex Metabolic Networks," Nature Biotechnology, vol. 18, pp. 326-332, 2000.]]
[48]
{48} R. Urbanczik and C. Wagner, "An Improved Algorithm for Stoichiometric Network Analysis: Theory and Applications," Bioinformatics, vol. 21, pp. 1203-1210, 2005.]]
[49]
{49} R. Schwarz, P. Musch, A. von Kamp, B. Engels, H. Schirmer, S. Schuster, and T. Dandekar, "Yana--A Software Tool for Analyzing Flux Modes, Gene-Expression and Enzyme Activities," BMC Bioinformatics, vol. 6, no. 1, p. 135, 2005.]]
[50]
{50} N.D. Price, J.A. Papin, and B.O. Palsson, "Determination of Redundancy and Systems Properties of the Metabolic Network of Helicobacter Pylori Using Genome-Scale Extreme Pathway Analysis," Genetics Research, vol. 12, no. 5, pp. 760-769, 2002.]]
[51]
{51} N.D. Price, J.L. Reed, J.A. Papin, I. Famili, and B.O. Palsson, "Analysis of Metabolic Capabilities Using Singular Value Decomposition of Extreme Pathway Matrices," Biophysics J., vol. 84, no. 2, pp. 794-804, 2003.]]
[52]
{52} S.J. Wiback, R. Mahadevan, and B.O. Palsson, "Using Metabolic Flux Data to Further Constrain the Metabolic Solution Space and Predict Internal Flux Patterns: The Escherichia Coli Spectrum," Biotechnology Bioeng., vol. 86, no. 3, pp. 317-331, 2004.]]
[53]
{53} B.G.W. Craenen, A.E. Eiben, and E. Marchiori, "How to Handle Constraints with Evolutionary Algortihms," Practical Handbook of Genetic Algorithms: Applications, L. Chambers, ed., pp. 341-361, CRC Press LLC, 2001.]]
[54]
{54} Á.E. Eiben, "Evolutionary Algorithms and Constraint Satisfaction: Definitions, Survey, Methodology, and Research Directions," Theoretical Aspects of Evolutionary Computing, Natural Computing Series, L. Kallel, B. Naudts, and A. Rogers, eds., pp. 13-58, Springer, 2001.]]
[55]
{55} Á.E. Eiben and J.E. Smith, Introduction to Evolutionary Computing. Springer, 2003.]]
[56]
{56} T. Shirai, A. Nakato, N. Izutani, K. Nagahisa, S. Shioya, E. Kimura, Y. Kawarabayasi, A. Yamagishi, T. Gojobori, and H. Shimizu, "Comparative Study of Flux Redistribution of Metabolic Pathway in Glutamate Production by Two Coryneform Bacteria," Metabolic Eng., vol. 7, pp. 59-69, 2005.]]
Index Terms
- Metabolic Flux Estimation-A Self-Adaptive Evolutionary Algorithm with Singular Value Decomposition
Recommendations
Biclustering of microarray data based on singular value decomposition
PAKDD'07: Proceedings of the 2007 international conference on Emerging technologies in knowledge discovery and data miningBiclustering is an important approach in microarray data analysis. Using biclustering algorithms, one can identify sets of genes sharing compatible expression patterns across subsets of samples. These patterns may provide clues about the main biological ...
Functional visualisation of genes using singular value decomposition
AusDM '12: Proceedings of the Tenth Australasian Data Mining Conference - Volume 134Progress in understanding core pathways and processes of cancer requires thorough analysis of many coding regions of the genome. New insights are hampered due to the lack of tools to make sense of large lists of genes identified using high throughput ...
Robust biclustering by sparse singular value decomposition incorporating stability selection
Motivation: Over the past decade, several biclustering approaches have been published in the field of gene expression data analysis. Despite of huge diversity regarding the mathematical concepts of the different biclustering methods, many of them can ...
Comments
Please enable JavaScript to view thecomments powered by Disqus.Information & Contributors
Information
Published In
Publisher
IEEE Computer Society Press
Washington, DC, United States
Publication History
Published: 01 January 2007
Published in TCBB Volume 4, Issue 1
Author Tags
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- View Citations1Total Citations
- 392Total Downloads
- Downloads (Last 12 months)3
- Downloads (Last 6 weeks)0
Reflects downloads up to 13 Dec 2024
Other Metrics
Citations
Cited By
View all- Sun JGaribaldi JHodgman C(2012)Parameter Estimation Using Metaheuristics in Systems BiologyIEEE/ACM Transactions on Computational Biology and Bioinformatics10.1109/TCBB.2011.639:1(185-202)Online publication date: 1-Jan-2012
View Options
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in