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Recent developments in parameter estimation and structure identification of biochemical and genomic systems. (English) Zbl 1168.92019
Summary: The organization, regulation and dynamical responses of biological systems are in many cases too complex to allow intuitive predictions and require the support of mathematical modeling for quantitative assessments and a reliable understanding of system functioning. All steps of constructing mathematical models for biological systems are challenging, but arguably the most difficult task among them is the estimation of model parameters and the identification of the structure and regulation of the underlying biological networks. Recent advancements in modern high-throughput techniques have been allowing the generation of time series data that characterize the dynamics of genomic, proteomic, metabolic, and physiological responses and enable us, at least in principle, to tackle estimation and identification tasks using ‘top-down’ or ‘inverse’ approaches. While the rewards of a successful inverse estimation or identification are great, the process of extracting structural and regulatory information is technically difficult. The challenges can generally be categorized into four areas, namely, issues related to the data, the model, the mathematical structure of the system, and the optimization and support algorithms.
Many recent articles have addressed inverse problems within the modeling framework of Biochemical Systems Theory (BST). BST was chosen for these tasks because of its unique structural flexibility and the fact that the structure and regulation of a biological system are mapped essentially one-to-one onto the parameters of the describing model. The proposed methods mainly focused on various optimization algorithms, but also on support techniques, including methods for circumventing the time consuming numerical integration of systems of differential equations, smoothing overly noisy data, estimating slopes of time series, reducing the complexity of the inference task, and constraining the parameter search space. Other methods targeted issues of data preprocessing, detection and amelioration of model redundancy, and model-free or model-based structure identification.
The total number of the proposed methods and their applications has by now exceeded one hundred, which makes it difficult for the newcomer, as well as the expert, to gain a comprehensive overview of available algorithmic options and limitations. To facilitate the entry into the field of inverse modeling within BST and related modeling areas, the article presented here reviews the field and proposes an operational ‘work-flow’ that guides the user through the estimation process, identifies possibly problematic steps, and suggests corresponding solutions based on the specific characteristics of the various available algorithms. The article concludes with a discussion of the present state of the art and with a description of open questions.

92C40 Biochemistry, molecular biology
92D10 Genetics and epigenetics
93B30 System identification
62P10 Applications of statistics to biology and medical sciences; meta analysis
Full Text: DOI
[1] Goel, G.; Chou, I-C.; Voit, E.O., Biological systems modeling and analysis: a biomolecular technique of the twenty-first century, J. biomol. tech., 17, 252, (2006)
[2] Voit, E.O.; Schwacke, J.H., Understanding through modeling, (), 27
[3] Veflingstad, S.R.; Dam, P.; Xu, Y.; Voit, E.O., Microbial pathway models, ()
[4] Wu, J.; Voit, E., Hybrid modeling in biochemical systems theory by means of functional Petri nets, J. bioinform. comput. biol., 7, 107, (2009)
[5] Wu, J.L.; Voit, E.O., Integrative biological systems modeling: challenges and opportunities, Frontiers comput. sci. chin., 3, 92, (2009)
[6] Vodovotz, Y.; Constantine, G.; Rubin, J.; Csete, M.; Voit, E.O.; An, G., Mechanistic simulations of inflammation: current state and future prospects, Math. biosci., 217, 1, (2009) · Zbl 1158.92318
[7] Gavalas, G.R., Nonlinear differential equations of chemically reacting systems, (1968), Springer Berlin · Zbl 0174.13401
[8] Heinrich, T.; Schuster, S., The regulation of cellular systems, (1996), Chapman and Hall New York · Zbl 0895.92013
[9] Palsson, B.Ø., Systems biology: properties of reconstructed networks, (2006), Cambridge University New York
[10] Stephanopoulos, G.; Aristidou, A.A.; Nielsen, J., Metabolic engineering: principles and methodologies, (1998), Academic Press San Diego, CA
[11] Varma, A.; Palsson, B.Ø., Metabolic flux balancing: basic concepts, scientific, and practical use, Bio/technology, 12, 994, (1994)
[12] Kauffman, K.J.; Prakash, P.; Edwards, J.S., Advances in flux balance analysis, Curr. opin. biotechnol., 14, 491, (2003)
[13] Bono, H.; Ogata, H.; Goto, S.; Kanehisa, M., Reconstruction of amino acid biosynthesis pathways from the complete genome sequence, Genome res., 8, 203, (1998)
[14] Edwards, J.S.; Palsson, B.Ø., The Escherichia coli MG1655 in silico metabolic genotype: its definition, characteristics, and capabilities, Proc. natl. acad. sci. USA, 97, 5528, (2000)
[15] Forster, J.; Famili, I.; Fu, P.; Palsson, B.Ø.; Nielsen, J., Genome-scale reconstruction of the saccharomyces cerevisiae metabolic network, Genome res., 13, 244, (2003)
[16] Selkov, E.; Maltsev, N.; Olsen, G.J.; Overbeek, R.; Whitman, W.B., A reconstruction of the metabolism of methanococcus jannaschii from sequence data, Gene, 197, GC11, (1997)
[17] Okamoto, M., System analysis of acetone – butanol – ethanol fermentation based on time-sliced metabolic flux analysis, Symposium on cellular systems biology, (2008), National Chung Cheng University Taiwan
[18] Teixeira, A.P.; Santos, S.S.; Carinhas, N.; Oliveira, R.; Alves, P.M., Combining metabolic flux analysis tools and 13C NMR to estimate intracellular fluxes of cultured astrocytes, Neurochem. int., 52, 478, (2008)
[19] Yang, C.; Hua, Q.; Shimizu, K., Quantitative analysis of intracellular metabolic fluxes using GC-MS and two-dimensional NMR spectroscopy, J. biosci. bioeng., 93, 78, (2002)
[20] Vallino, J.J.; Stephanopoulos, G., Metabolic flux distributions in corynebacterium glutamicum during growth and lysine overproduction, Biotechnol. bioeng., 41, 633, (1993)
[21] Goel, G.; Chou, I-C.; Voit, E.O., System estimation from metabolic time series data, Bioinformatics, 24, 2505, (2008)
[22] Mahadevan, R.; Edwards, J.S.; Doyle, F.J., Dynamic flux balance analysis of diauxic growth in Escherichia coli, Biophys. J., 83, 1331, (2002)
[23] Covert, M.W.; Palsson, B.Ø., Constraints-based models: regulation of gene expression reduces the steady-state solution space, J. theor. biol., 221, 309, (2003)
[24] Gombert, A.K.; Nielsen, J., Mathematical modelling of metabolism, Curr. opin. biotechnol., 11, 180, (2000)
[25] Schulz, A.R., Enzyme kinetics: from diastase to multi-enzyme systems, (1994), Cambridge University Cambridge, New York
[26] Michaelis, L.; Menten, M.L., Die kinetik der invertinwirkung, Biochem. zeitschrift, 49, 333, (1913)
[27] Savageau, M.A., Biochemical systems analysis. I. some mathematical properties of the rate law for the component enzymatic reactions, J. theor. biol., 25, 365, (1969)
[28] Savageau, M.A., The behavior of intact biochemical control systems, Curr. top. cell. regul., 6, 63, (1972)
[29] Heinrich, R.; Rapoport, T.A., A linear steady-state treatment of enzymatic chains. general properties, control and effector strength, Eur. J. biochem., 42, 89, (1974)
[30] Lineweaver, H.; Burk, D., The determination of enzyme dissociation constants, J. am. chem. soc., 56, 658, (1934)
[31] Voit, E.O.; Sands, P.J., Modeling forest growth I. canonical approach, Ecol. model., 86, 51, (1996)
[32] Savageau, M.A., Biochemical systems analysis. II. the steady-state solutions for an n-pool system using a power-law approximation, J. theor. biol., 25, 370, (1969)
[33] Savageau, M.A., Biochemical systems analysis: A study of function and design in molecular biology, (1976), Addison-Wesley Pub. Co., Advanced Book Program Reading, Mass · Zbl 0398.92013
[34] Torres, N.V.; Voit, E.O., Pathway analysis and optimization in metabolic engineering, (2002), Cambridge University Cambridge, UK
[35] Voit, E.O., Computational analysis of biochemical systems: A practical guide for biochemists and molecular biologists, (2000), Cambridge University Cambridge, UK
[36] ()
[37] Chou, I-C.; Martens, H.; Voit, E.O., Parameter estimation in biochemical systems models with alternating regression, Theor. biol. med. model., 3, 25, (2006)
[38] Savageau, M.A.; Voit, E.O., Recasting nonlinear differential equations as S-systems: a canonical nonlinear form, Math. biosci., 87, 83, (1987) · Zbl 0631.34015
[39] Voit, E.O., S-system modeling of complex systems with chaotic input, Environmetrics, 4, 153, (1993)
[40] Atkinson, M.R.; Savageau, M.A.; Myers, J.T.; Ninfa, A.J., Development of genetic circuitry exhibiting toggle switch or oscillatory behavior in Escherichia coli, Cell, 113, 597, (2003)
[41] Savageau, M.A., Design principles for elementary gene circuits: elements, methods, and examples, Chaos, 11, 142, (2001) · Zbl 1020.92021
[42] Vera, J.; Balsa-Canto, E.; Wellstead, P.; Banga, J.R.; Wolkenhauer, O., Power-law models of signal transduction pathways, Cell. signal., 19, 1531, (2007)
[43] Irvine, D.H.; Savageau, M.A., Network regulation of the immune response: alternative control points for suppressor modulation of effector lymphocytes, J. immunol., 134, 2100, (1985)
[44] Irvine, D.H.; Savageau, M.A., Network regulation of the immune response: modulation of suppressor lymphocytes by alternative signals including contrasuppression, J. immunol., 134, 2117, (1985)
[45] Schwacke, J.H.; Voit, E.O., The potential for signal integration and processing in interacting MAP kinase cascades, J. theor. biol., 246, 604, (2007)
[46] Hatzimanikatis, V.; Bailey, J.E., MCA has more to say, J. theor. biol., 182, 233, (1996)
[47] Visser, D.; Heijnen, J.J., The mathematics of metabolic control analysis revisited, Metab. eng., 4, 114, (2002)
[48] Fell, D.A., Understanding the control of metabolism, (1997), Portland Press London
[49] Kacser, H.; Burns, J.A., The control of flux, Symp. soc. exp. biol., 27, 65, (1973)
[50] del Rosario, R.C.; Mendoza, E.; Voit, E.O., Challenges in lin-log modelling of glycolysis in lactococcus lactis, IET syst. biol., 2, 136, (2008)
[51] Heijnen, J.J., Approximative kinetic formats used in metabolic network modeling, Biotechnol. bioeng., 91, 534, (2005)
[52] Wang, F.-S.; Ko, C.-L.; Voit, E.O., Kinetic modeling using S-systems and lin-log approaches, Biochem. eng. J., 33, 238, (2007)
[53] Sorribas, A.; Hernandez-Bermejo, B.; Vilaprinyo, E.; Alves, R., Cooperativity and saturation in biochemical networks: a saturable formalism using Taylor series approximations, Biotechnol. bioeng., 97, 1259, (2007)
[54] Lotka, A., Elements of physical biology, (1925), Williams and Wilkins Baltimore · JFM 51.0416.06
[55] May, R.E., Theoretical ecology: principles and applications, (1976), Blackwell Oxford
[56] Volterra, V., Variazioni e fluttuazioni del numero d’individui in specie animali conviventi, Mem. R. accad. dei lincei., 2, 31, (1926) · JFM 52.0450.06
[57] Hernandez-Bermejo, B.; Fairen, V., Lotka – volterra representation of general nonlinear systems, Math. biosci., 140, 1, (1997) · Zbl 0902.92001
[58] Peschel, M.; Mende, W., The predator-prey model: do we live in a Volterra world?, (1986), Akademie-Verlag Berlin · Zbl 0576.92001
[59] Voit, E.O.; Savageau, M.A., Equivalence between S-systems and Volterra-systems, Math. biosci., 78, 47, (1986) · Zbl 0586.92003
[60] Savageau, M.A., Development of fractal kinetic theory for enzyme-catalysed reactions and implications for the design of biochemical pathways, Biosystems, 47, 9, (1998)
[61] de Jong, H., Modeling and simulation of genetic regulatory systems: a literature review, J. comput. biol., 9, 67, (2002)
[62] D’Haeseleer, P.; Wen, X.; Fuhrman, S.; Somogyi, R., Linear modeling of mrna expression levels during CNS development and injury, Pac. symp. biocomput., 41, (1999)
[63] Bower, J.M.; Bolouri, H., Computational modeling of genetic and biochemical networks computational molecular biology series, (2001), The MIT
[64] Barabasi, A.L.; Oltvai, Z.N., Network biology: understanding the cell’s functional organization, Nat. rev. genet., 5, 101, (2004)
[65] Kauffman, S.A., The origins of order: self-organization and selection in evolution, (1993), Oxford University New York
[66] Sachs, K.; Perez, O.; Pe’er, D.; Lauffenburger, D.A.; Nolan, G.P., Causal protein-signaling networks derived from multiparameter single-cell data, Science, 308, 523, (2005)
[67] Zhu, J.; Wiener, M.C.; Zhang, C.; Fridman, A.; Minch, E.; Lum, P.Y.; Sachs, J.R.; Schadt, E.E., Increasing the power to detect causal associations by combining genotypic and expression data in segregating populations, Plos comput. biol., 3, e69, (2007)
[68] Savageau, M.A., Genetic regulatory mechanisms and the ecological niche of Escherichia coli, Proc. natl. acad. sci. USA, 71, 2453, (1974)
[69] Elowitz, M.B.; Leibler, S., A synthetic oscillatory network of transcriptional regulators, Nature, 403, 335, (2000)
[70] Hasty, J.; Dolnik, M.; Rottschafer, V.; Collins, J.J., Synthetic gene network for entraining and amplifying cellular oscillations, Phys. rev. lett., 88, 148101, (2002)
[71] Hlavacek, W.S.; Savageau, M.A., Subunit structure of regulator proteins influences the design of gene circuitry: analysis of perfectly coupled and completely uncoupled circuits, J. mol. biol., 248, 739, (1995)
[72] Hlavacek, W.S.; Savageau, M.A., Rules for coupled expression of regulator and effector genes in inducible circuits, J. mol. biol., 255, 121, (1996)
[73] Hlavacek, W.S.; Savageau, M.A., Completely uncoupled and perfectly coupled gene expression in repressible systems, J. mol. biol., 266, 538, (1997)
[74] Savageau, M.A., A theory of alternative designs for biochemical control systems, Biomed. biochim. acta, 44, 875, (1985)
[75] Neidhardt, F.C.; Savageau, M.A., Regulation beyond the operon, (), 1310
[76] Savageau, M.A., Significance of autogenously regulated and constitutive synthesis of regulatory proteins in repressible biosynthetic systems, Nature, 258, 208, (1975)
[77] Savageau, M.A., Design of molecular control mechanisms and the demand for gene expression, Proc. natl. acad. sci. USA, 74, 5647, (1977)
[78] Savageau, M.A., Models of gene function: general methods of kinetic analysis and specific ecological correlates, (), 3
[79] Savageau, M.A., Demand theory of gene regulation. I. quantitative development of the theory, Genetics, 149, 1665, (1998)
[80] Savageau, M.A., Demand theory of gene regulation. II. quantitative application to the lactose and maltose operons of Escherichia coli, Genetics, 149, 1677, (1998)
[81] Maki, Y.; Tominaga, D.; Okamoto, M.; Watanabe, S.; Eguchi, Y., Development of a system for the inference of large scale genetic networks, Pac. symp. biocomput., 446, (2001)
[82] Kimura, S.; Ide, K.; Kashihara, A.; Kano, M.; Hatakeyama, M.; Masui, R.; Nakagawa, N.; Yokoyama, S.; Kuramitsu, S.; Konagaya, A., Inference of S-system models of genetic networks using a cooperative coevolutionary algorithm, Bioinformatics, 21, 1154, (2005)
[83] Kutalik, Z.; Tucker, W.; Moulton, V., S-system parameter estimation for noisy metabolic profiles using Newton-flow analysis, IET syst. biol., 1, 174, (2007)
[84] Mao, F.; Wu, H.; Dam, P.; Chou, I-C.; Voit, E.O.; Xu, Y., Prediction of biological pathways through data mining and information fusion, ()
[85] Voit, E.O., The dawn of a new era of metabolic systems analysis, Drug discovery today biosilico, 2, 182, (2004)
[86] E.O. Voit, G. Goel, I-C. Chou, L. da Fonseca, Estimation of metabolic pathway systems from different data sources, IET Systems Biol., accepted for publication.
[87] M. Kanehisa, The KEGG database, Novartis Foundation Symposium, 2002, p. 91.
[88] Kanehisa, M.; Goto, S.; Kawashima, S.; Okuno, Y.; Hattori, M., The KEGG resource for deciphering the genome, Nucleic acids res., 32, D277, (2004)
[89] Caspi, R.; Foerster, H.; Fulcher, C.A.; Hopkinson, R.; Ingraham, J.; Kaipa, P.; Krummenacker, M.; Paley, S.; Pick, J.; Rhee, S.Y.; Tissier, C.; Zhang, P.; Karp, P.D., Metacyc: a multiorganism database of metabolic pathways and enzymes, Nucleic acids res., 34, D511, (2006)
[90] Schomburg, I.; Chang, A.; Ebeling, C.; Gremse, M.; Heldt, C.; Huhn, G.; Schomburg, D., BRENDA, the enzyme database: updates and major new development, Nucleic acids res., 32, D431, (2004)
[91] Shiraishi, F.; Savageau, M.A., The tricarboxylic-acid cycle in dictyostelium discoideum. 1. formulation of alternative kinetic representations, J. biol. chem., 267, 22912, (1992)
[92] Torres, N.V., Modeling approach to control of carbohydrate-metabolism during citric-acid accumulation by aspergillus niger. 1. model definition and stability of the steady-state, Biotechnol. bioeng., 44, 104, (1994)
[93] Torres, N.V.; Voit, E.O.; Alcón, C.H., Optimization of nonlinear biotechnological processes with linear programming. application to citric acid production in aspergillus niger, Biotechnol. bioeng., 49, 247, (1996)
[94] Cascante, M.; Curto, R.; Sorribas, A., Comparative characterization of the fermentation pathway of saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: steady-state analysis, Math. biosci., 130, 51, (1995) · Zbl 0835.92016
[95] Curto, R.; Sorribas, A.; Cascante, M., Comparative characterization of the fermentation pathway of saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: model definition and nomenclature, Math. biosci., 130, 25, (1995) · Zbl 0835.92015
[96] Sorribas, A.; Curto, R.; Cascante, M., Comparative characterization of the fermentation pathway of saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: model validation and dynamic behavior, Math. biosci., 130, 71, (1995) · Zbl 0835.92017
[97] Curto, R.; Voit, E.O.; Cascante, M., Analysis of abnormalities in purine metabolism leading to gout and to neurological dysfunctions in man, Biochem. J., 329, Pt. 3, 477, (1998)
[98] Curto, R.; Voit, E.O.; Sorribas, A.; Cascante, M., Validation and steady-state analysis of a power-law model of purine metabolism in man, Biochem. J., 324, Pt. 3, 761, (1997)
[99] Curto, R.; Voit, E.O.; Sorribas, A.; Cascante, M., Mathematical models of purine metabolism in man, Math. biosci., 151, 1, (1998) · Zbl 0938.92015
[100] Ferreira, A.E.; Ponces Freire, A.M.; Voit, E.O., A quantitative model of the generation of N(epsilon)-(carboxymethyl)lysine in the maillard reaction between collagen and glucose, Biochem. J., 376, 109, (2003)
[101] Alves, R.; Herrero, E.; Sorribas, A., Predictive reconstruction of the mitochondrial iron – sulfur cluster assembly metabolism: I. the role of the protein pair ferredoxin – ferredoxin reductase (yah1-axh1), Proteins: structure function and bioinformatics, 56, 354, (2004)
[102] Alvarez-Vasquez, F.; Sims, K.J.; Cowart, L.A.; Okamoto, Y.; Voit, E.O.; Hannun, Y.A., Simulation and validation of modelled sphingolipid metabolism in saccharomyces cerevisiae, Nature, 433, 425, (2005)
[103] Alvarez-Vasquez, F.; Sims, K.J.; Hannun, Y.A.; Voit, E.O., Integration of kinetic information on yeast sphingolipid metabolism in dynamical pathway models, J. theor. biol., 226, 265, (2004)
[104] Alvarez-Vasquez, F.; Sims, K.J.; Voit, E.O.; Hannun, Y.A., Coordination of the dynamics of yeast sphingolipid metabolism during the diauxic shift, Theor. biol. med. model., 4, 42, (2007)
[105] Klapa, M.I.; Park, S.M.; Sinskey, A.J.; Stephanopoulos, G., Metabolite and isotopomer balancing in the analysis of metabolic cycles: I. theory, Biotechnol. bioeng., 62, 375, (1999)
[106] Ratcliffe, R.G.; Shachar-Hill, Y., Measuring multiple fluxes through plant metabolic networks, Plant J., 45, 490, (2006)
[107] Wiechert, W., 13C metabolic flux analysis, Metab. eng., 3, 195, (2001)
[108] Wiechert, W.; Möllney, M.; Isermann, N.; Wurzel, M.; de Graaf, A.A., Bidirectional reaction steps in metabolic networks: III. explicit solution and analysis of isotopomer labeling systems, Biotechnol. bioeng., 66, 69, (1999)
[109] Alvarez-Vasquez, F.; Hannun, Y.A.; Voit, E.O., Dynamics of positional enrichment: theoretical development and application to carbon labeling in zymomonas mobilis, Biochem. eng. J., 40, 157, (2008)
[110] Voit, E.O.; Alvarez-Vasquez, F.; Sims, K.J., Analysis of dynamic labeling data, Math. biosci., 191, 83, (2004) · Zbl 1072.92018
[111] Kacser, H.; Burns, J.A., Molecular democracy: who shares the controls?, Biochem. soc. trans., 7, 1149, (1979)
[112] Sorribas, A.; Cascante, M., Structure identifiability in metabolic pathways: parameter estimation in models based on the power-law formalism, Biochem. J., 298, Pt. 2, 303, (1994)
[113] Bozdech, Z.; Llinas, M.; Pulliam, B.L.; Wong, E.D.; Zhu, J.; DeRisi, J.L., The transcriptome of the intraerythrocytic developmental cycle of plasmodium falciparum, Plos biol., 1, E5, (2003)
[114] Du, X.; Callister, S.J.; Manes, N.P.; Adkins, J.N.; Alexandridis, R.A.; Zeng, X.; Roh, J.H.; Smith, W.E.; Donohue, T.J.; Kaplan, S.; Smith, R.D.; Lipton, M.S., A computational strategy to analyze label-free temporal bottom-up proteomics data, J. proteome res., 7, 2595, (2008)
[115] Neves, A.R.; Ventura, R.; Mansour, N.; Shearman, C.; Gasson, M.J.; Maycock, C.; Ramos, A.; Santos, H., Is the glycolytic flux in lactococcus lactis primarily controlled by the redox charge? kinetics of NAD(+) and NADH pools determined in vivo by 13C NMR, J. biol. chem., 277, 28088, (2002)
[116] Szyperski, T., 13C-NMR, MS and metabolic flux balancing in biotechnology research, Q. rev. biophys., 31, 41, (1998)
[117] Goodenowe, D., Metabolomic analysis with Fourier transform ion cyclotron resonance mass spectrometry, (), 125
[118] Plumb, R.S.; Stumpf, C.L.; Gorenstein, M.V.; Castro-Perez, J.M.; Dear, G.J.; Anthony, M.; Sweatman, B.C.; Connor, S.C.; Haselden, J.N., Metabonomics: the use of electrospray mass spectrometry coupled to reversed-phase liquid chromatography shows potential for the screening of rat urine in drug development, Rapid commun. mass spectrom., 16, 1991, (2002)
[119] Ostergaard, S.; Olsson, L.; Nielsen, J., in vivo dynamics of galactose metabolism in saccharomyces cerevisiae: metabolic fluxes and metabolite levels, Biotechnol. bioeng., 73, 412, (2001)
[120] Theobald, U.; Mailinger, W.; Baltes, M.; Rizzi, M.; Reuss, M., in vivo analysis of metabolic dynamics in saccharomyces cerevisiae: I. experimental observations, Biotechnol. bioeng., 55, 305, (1997)
[121] Voit, E.O.; Almeida, J.; Marino, S.; Lall, R.; Goel, G.; Neves, A.R.; Santos, H., Regulation of glycolysis in lactococcus lactis: an unfinished systems biological case study, IEE proc. syst. biol., 153, 286, (2006)
[122] Voit, E.O.; Marino, S.; Lall, R., Challenges for the identification of biological systems from in vivo time series data, In silico biol., 5, 83, (2005)
[123] Maki, Y.; Ueda, T.; Okamoto, M.; Uematsu, N.; Inamura, Y.; Eguchi, Y., Inference of genetic network using the expression profile time course data of mouse P19 cells, Genome inform., 13, 382, (2002)
[124] Kimura, S.; Hatakeyama, M.; Konagaya, A., Inference of S-system models of genetic networks from noisy time-series data, Chem-bio inform. J., 4, 1, (2004)
[125] Savageau, M.A., Enzyme kinetics in vitro and in vivo: michaelis – menten revisited, ()
[126] Hill, C.M.; Waight, R.D.; Bardsley, W.G., Does any enzyme follow the michaelis – menten equation?, Mol. cell biochem., 15, 173, (1977)
[127] Mendes, P.; Kell, D., Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation, Bioinformatics, 14, 869, (1998)
[128] Voit, E.O.; Almeida, J., Decoupling dynamical systems for pathway identification from metabolic profiles, Bioinformatics, 20, 1670, (2004)
[129] Voit, E.O., Symmetries of S-systems, Math. biosci., 109, 19, (1992) · Zbl 0765.92003
[130] Sands, P.J.; Voit, E.O., Flux-based estimation of parameters in S-systems, Ecol. model., 93, 75, (1996)
[131] Voit, E.O., Algebraic properties of canonical forms, Canonical nonlinear modeling. S-system approach to understanding complexity, (1991), Van Nostrand Reinhold NY, p. 278 · Zbl 0785.92004
[132] Berg, P.H.; Voit, E.O.; White, R.L., A pharmacodynamic model for the action of the antibiotic imipenem on pseudomonas aeruginosa populations in vitro, Bull. math. biol., 58, 923, (1996) · Zbl 0859.92008
[133] Gutenkunst, R.N.; Waterfall, J.J.; Casey, F.P.; Brown, K.S.; Myers, C.R.; Sethna, J.P., Universally sloppy parameter sensitivities in systems biology models, Plos comput. biol., 3, 1871, (2007)
[134] Kikuchi, S.; Tominaga, D.; Arita, M.; Takahashi, K.; Tomita, M., Dynamic modeling of genetic networks using genetic algorithm and S-system, Bioinformatics, 19, 643, (2003)
[135] Irvine, D.H.; Savageau, M.A., Efficient solution of nonlinear ordinary differential equations expressed in S-system canonical form, SIAM J. numer. anal., 27, 704, (1990) · Zbl 0702.65068
[136] Voit, E.O.; Savageau, M.A., Power-law approach to modeling biological systems: II. application to ethanol production, J. ferment. technol., 60, 229, (1982)
[137] Voit, E.O.; Savageau, M.A., Power-law approach to modeling biological systems: III. methods of analysis, J. ferment. technol., 60, 233, (1982)
[138] Matsubara, Y.; Kikuchi, S.; Sugimoto, M.; Tomita, M., Parameter estimation for stiff equations of biosystems using radial basis function networks, BMC bioinform., 7, 230, (2006)
[139] Rank, E., Application of Bayesian trained RBF networks to nonlinear time-series modeling, Signal process., 83, 1393, (2003) · Zbl 1144.94357
[140] Tsai, K.Y.; Wang, F.S., Evolutionary optimization with data collocation for reverse engineering of biological networks, Bioinformatics, 21, 1180, (2005)
[141] de Boor, C., A practical guide to splines, (1978), Springer New York · Zbl 0406.41003
[142] de Boor, C.; Höllig, K.; Riemenschneider, S.D., Box splines, (1993), Springer New York, Hong Kong · Zbl 0814.41012
[143] Green, P.J.; Silverman, B.W., Nonparametric regression and generalized linear models: A roughness penalty approach, (1994), Chapman and Hall London, New York · Zbl 0832.62032
[144] Seatzu, C., A Fitting based method for parameter estimation in S-systems, Dynam. syst. appl., 9, 77, (2000) · Zbl 1158.65329
[145] Burden, R.L.; Faires, J.D., Numerical analysis, (1993), PWS Boston, MA · Zbl 0788.65001
[146] Almeida, J.S., Predictive non-linear modeling of complex data by artificial neural networks, Curr. opin. biotechnol., 13, 72, (2002)
[147] Almeida, J.S.; Voit, E.O., Neural-network-based parameter estimation in S-system models of biological networks, Genome inform., 14, 114, (2003)
[148] Funahashi, K.-I., On the approximate realization of continuous mappings by neural networks, Neural networks, 2, 183, (1989)
[149] Hornik, K.; Stinchcombe, M.; White, H., Multilayer feedforward networks are universal approximators, Neural networks, 2, 359, (1989) · Zbl 1383.92015
[150] Mendes, P.; Kell, D.B., On the analysis of the inverse problem of metabolic pathways using artificial neural networks, Biosystems, 38, 15, (1996)
[151] Whittaker, E.T., On a new method of graduation, Proc. Edinburgh math. soc., 41, 63, (1923)
[152] Eilers, P.H.C., A perfect smoother, Anal. chem., 75, 3631, (2003)
[153] Vilela, M.; Borges, C.C.; Vinga, S.; Vasconcelos, A.T.; Santos, H.; Voit, E.O.; Almeida, J.S., Automated smoother for the numerical decoupling of dynamics models, BMC bioinform., 8, 305, (2007)
[154] M. Vilela, C.C. Borges, S. Vinga, A.T. Vasconcelos, H. Santos, E.O. Voit, J.S. Almeida, Automated smoother for the numerical decoupling of dynamics models. Available from: <http://autosmooth.sourceforge.net/>, 2007.
[155] Tucker, W.; Moulton, V., Parameter reconstruction for biochemical networks using interval analysis, Reliable comput., 12, 1, (2006)
[156] Tucker, W.; Kutalik, Z.; Moulton, V., Estimating parameters for generalized mass action models using constraint propagation, Math. biosci., 208, 607, (2007) · Zbl 1119.92031
[157] Jeong, H.; Tombor, B.; Albert, R.; Oltval, Z.N.; Barabási, A.-L., The large-scale organization of metabolic networks, Nature, 407, 651, (2000)
[158] Thieffry, D.; Huerta, A.M.; Perez-Rueda, E.; Collado-Vides, J., From specific gene regulation to genomic networks: a global analysis of transcriptional regulation in Escherichia coli, Bioessays, 20, 433, (1998)
[159] Vilela, M.; Chou, I-C.; Vinga, S.; Vasconcelos, A.T.; Voit, E.O.; Almeida, J.S., Parameter optimization in S-system models, BMC syst. biol., 2, 35, (2008)
[160] Voit, E.O.; Almeida, J.S., Dynamic profiling and canonical modeling: powerful partners in metabolic pathway identification, ()
[161] Noman, N.; Iba, H., Reverse engineering genetic networks using evolutionary computation, Genome inform., 16, 205, (2005)
[162] Runarsson, T.P.; Yao, X., Stochastic ranking for constrained evolutionary optimization, IEEE trans. evolut. comput., 4, 284, (2000)
[163] Cho, D.Y.; Cho, K.H.; Zhang, B.T., Identification of biochemical networks by S-tree based genetic programming, Bioinformatics, 22, 1631, (2006)
[164] Liu, P.K.; Wang, F.S., Inference of biochemical network models in S-system using multiobjective optimization approach, Bioinformatics, 24, 1085, (2008)
[165] Liu, P.K.; Wang, F.S., Inverse problems of biological systems using multi-objective optimization, Journal of the Chinese institute of chemical engineers, 39, 399, (2008)
[166] Noman, N.; Iba, H., Inference of genetic networks using S-system: information criteria for model selection, Proceedings of the 8th annual conference on genetic and evolutionary computation (GECCO’06), (2006), ACM Seattle, WA, USA
[167] Shin, A.; Iba, H., Construction of genetic network using evolutionary algorithm and combined fitness function, Genome inform., 14, 94, (2003)
[168] Björck, A., Numerical methods for least squares problems, (1996), SIAM Philadelphia, PA · Zbl 0847.65023
[169] Fletcher, R., Practical methods of optimization, (1987), Wiley New York · Zbl 0905.65002
[170] Nocedal, J.; Wright, S.J., Numerical optimization, (1999), Springer New York · Zbl 0930.65067
[171] Marino, S.; Voit, E.O., An automated procedure for the extraction of metabolic network information from time series data, J. bioinform. comput. biol., 4, 665, (2006)
[172] Moles, C.G.; Mendes, P.; Banga, J.R., Parameter estimation in biochemical pathways: a comparison of global optimization methods, Genome res., 13, 2467, (2003)
[173] Park, L.J.; Park, C.H.; Park, C.; Lee, T., Application of genetic algorithms to parameter estimation of bioprocesses, Med. biol. eng. comput., 35, 47, (1997)
[174] D. Tominaga, N. Koga, M. Okamoto, Efficient numerical optimization algorithm based on genetic algorithm for inverse problem, in: Proceedings of the Genetic and Evolutionary Computation Conference, 2000, p. 251.
[175] Okamoto, M.; Nonaka, T.; Ochiai, S.; Tominaga, D., Nonlinear numerical optimization with use of a hybrid genetic algorithm incorporating the modified powell method, Appl. math. comput., 91, 63, (1998)
[176] Nakatsui, M.; Ueda, T.; Okamoto, M., Integrated system for inference of gene expression network, Genome inform., 14, 282, (2003)
[177] Ueda, T.; Koga, N.; Okamoto, M., Efficient numerical optimization technique based on real-coded genetic algorithm, Genome inform., 12, 451, (2001)
[178] Ueda, T.; Ono, I.; Okamoto, M., Development of system identification technique based on real-coded genetic algorithm, Genome inform., 13, 386, (2002)
[179] Daisuke, T.; Horton, P., Inference of scale-free networks from gene expression time series, J. bioinform. comput. biol., 4, 503, (2006)
[180] Ho, S.Y.; Hsieh, C.H.; Yu, F.C.; Huang, H.L., An intelligent two-stage evolutionary algorithm for dynamic pathway identification from gene expression profiles, IEEE/ACM trans. comput. biol. bioinform., 4, 648, (2007)
[181] C. Spieth, F. Streichert, N. Speer, A. Zell, A memetic inference method for gene regulatory networks based on S-Systems, Congress on Evolutionary Computation 2004 (CEC2004), 2004, p. 152. · Zbl 1109.68636
[182] C. Spieth, F. Streichert, N. Speer, A. Zell, Optimizing topology and parameters of gene regulatory network models from time-series experiments, Genetic and Evolutionary Computation-GECCO 2004 (LNCS), Springer, Berlin/Heidelberg, 2004, p. 461.
[183] Spieth, C.; Streichert, F.; Supper, J.; Speer, N.; Zell, A., Feedback memetic algorithms for modeling gene regulatory networks, IEEE symposium on computational intelligence in bioinformatics and computational biology (CIBCB), (2005), IEEE, p. 61
[184] H. Imade, N. Mizuguchi, I. Ono, N. Ono, M. Okamoto, ‘Gridifying’ an evolutionary algorithm for inference of genetic networks using the improved GOGA framework and its performance evaluation on OBI grid, in: A. Konagaya, K. Satou (Eds.), Grid Computing in Life Science: First International Workshop on Life Science Grid, LSGRID 2004 Kanazawa, Japan, May 31-June 1, 2004, Springer, Berlin/Heidelberg, 2005, p. 171.
[185] R. Morishita, H. Imade, I. Ono, N. Ono, M. Okamoto, Finding multiple solutions based on an evolutionary algorithm for inference of genetic networks by S-system, Congress on Evolutionary Computation 2003 (CEC2003), 2003, p. 615. · Zbl 1084.68505
[186] I. Ono, Y. Seike, R. Morishita, N. Ono, M. Nakatsui, M. Okamoto, An evolutionary algorithm taking account of mutual interactions among substances for inference of genetic networks, Congress on Evolutionary Computation 2004 (CEC2004) 2004, p. 2060.
[187] N. Noman, H. Iba, Inference of gene regulatory networks using s-system and differential evolution, in: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, Washington, DC, 2005, p. 439.
[188] N. Noman, H. Iba, Enhancing differential evolution performance with local search for high dimensional function optimization, in: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, Washington, DC, 2005, p. 967.
[189] Noman, N.; Iba, H., Inferring gene regulatory networks using differential evolution with local search heuristics, IEEE/ACM trans. comput. biol. bioinform., 4, 634, (2007)
[190] Koza, J.R.; Mydlowec, W.; Lanza, G.; Yu, J.; Keane, M.A., Reverse engineering of metabolic pathways from observed data using genetic programming, Pac. symp. biocomput., 434, (2001)
[191] Koza, J.R., Genetic programming: on the programming of computers by means of natural selection, (1992), MIT Cambridge, MA · Zbl 0850.68161
[192] Sakamoto, E.; Iba, H., Inferring a system of differential equations for a gene regulatory network by using genetic programming, Proceedings of the 2001 congress on evolutionary computation (CEC2001), (2001), IEEE Seoul, South Korea, p. 720
[193] Sugimoto, M.; Kikuchi, S.; Tomita, M., Reverse engineering of biochemical equations from time-course data by means of genetic programming, Biosystems, 80, 155, (2005)
[194] Kim, K.-Y.; Cho, D.-Y.; Zhang, B.-T., Multi-stage evolutionary algorithms for efficient identification of gene regulatory networks, Evoworkshops 2006, (2006), Springer, p. 45
[195] Spieth, C.; Worzischek, R.; Streichert, F., Comparing evolutionary algorithms on the problem of network inference, Proceedings of the 8th annual conference on genetic and evolutionary computation (GECCO’06), (2006), ACM Seattle, WA, USA
[196] Salamon, P.; Sibani, P.; Frost, R., Facts, conjectures, and improvements for simulated annealing, (2002), SIAM New York · Zbl 1070.90137
[197] Gonzalez, O.R.; Kuper, C.; Jung, K.; Naval, P.C.; Mendoza, E., Parameter estimation using simulated annealing for S-system models of biochemical networks, Bioinformatics, 23, 480, (2007)
[198] M. Dorigo, G. Di Caro, Ant colony optimization: a new meta-heuristic, in: Proceedings of the 1999 Congress on Evolutionary Computation (CEC1999), Washington, DC, 1999, p. 1470.
[199] P.C. Zuñiga, J. Pasia, H. Adorna, R.C.H. del Rosario, P. Naval, An ant colony optimization algorithm for parameter estimation and network inference problems in S-system models, in: International Conference on Molecular Systems Biology 2008 (ICMSB08), Manila, Philippines, 2008, p. 105.
[200] R. Eberhart, J. Kennedy, A new optimizer using particle swarm theory, in: Proceedings of the Sixth International Symposium on Micro Machine and Human Science (MHS’95), 1995, p. 39.
[201] P.C. Naval, L.G. Sison, E. Mendoza, Metabolic network parameter inference using particle swarm optimization, in: International Conference on Molecular Systems Biology 2006 (ICMSB06), Munich, Germany, 2006.
[202] Lall, R.; Voit, E.O., Parameter estimation in modulated, unbranched reaction chains within biochemical systems, Comput. biol. chem., 29, 309, (2005) · Zbl 1087.92027
[203] Polisetty, P.K.; Voit, E.O.; Gatzke, E.P., Identification of metabolic system parameters using global optimization methods, Theor. biol. med. model., 3, 4, (2006)
[204] Chou, I-C.; Martens, H.; Voit, E.O., Parameter estimation of S-distributions with alternating regression, Stat. operations res. trans. (SORT), 31, 55, (2007) · Zbl 1274.62437
[205] Liao, J.C.; Boscolo, R.; Yang, Y.L.; Tran, L.M.; Sabatti, C.; Roychowdhury, V.P., Network component analysis: reconstruction of regulatory signals in biological systems, Proc. natl. acad. sci. USA, 100, 15522, (2003)
[206] Srividhya, J.; Crampin, E.J.; McSharry, P.E.; Schnell, S., Reconstructing biochemical pathways from time course data, Proteomics, 7, 828, (2007)
[207] Stelling, J.; Klamt, S.; Bettenbrock, K.; Schuster, S.; Gilles, E.D., Metabolic network structure determines key aspects of functionality and regulation, Nature, 420, 190, (2002)
[208] Thomas, R.; Mehrotra, S.; Papoutsakis, E.T.; Hatzimanikatis, V., A model-based optimization framework for the inference on gene regulatory networks from DNA array data, Bioinformatics, 20, 3221, (2004)
[209] Tran, L.M.; Brynildsen, M.P.; Kao, K.C.; Suen, J.K.; Liao, J.C., Gnca: a framework for determining transcription factor activity based on transcriptome: identifiability and numerical implementation, Metab. eng., 7, 128, (2005)
[210] Yeung, M.K.; Tegner, J.; Collins, J.J., Reverse engineering gene networks using singular value decomposition and robust regression, Proc. natl. acad. sci. USA, 99, 6163, (2002)
[211] Milo, R.; Shen-Orr, S.; Itzkovitz, S.; Kashtan, N.; Chklovskii, D.; Alon, U., Network motifs: simple building blocks of complex networks, Science, 298, 824, (2002)
[212] Wagner, A.; Fell, D.A., The small world inside large metabolic networks, Proc. biol. sci., 268, 1803, (2001)
[213] Chevalier, T.; Schreiber, I.; Ross, J., Toward a systematic determination of complex reaction mechanisms, J. phys. chem., 97, 6776, (1993)
[214] Sorribas, A.; Lozano, J.B.; Fairén, V., Deriving chemical and biochemical model networks from experimental measurements, Recent res. dev. phys. chem., 2, 553, (1998)
[215] Dı´az-Sierra, R.; Lozano, J.B.; Fairén, V., Deduction of chemical mechanisms from the linear response around steady state, J. phys. chem., 103, 337, (1999)
[216] Veflingstad, S.R.; Almeida, J.; Voit, E.O., Priming nonlinear searches for pathway identification, Theor. biol. med. model., 1, 8, (2004)
[217] Kitayama, T.; Kinoshita, A.; Sugimoto, M.; Nakayama, Y.; Tomita, M., A simplified method for power-law modelling of metabolic pathways from time-course data and steady-state flux profiles, Theor. biol. med. model., 3, 24, (2006)
[218] Hatzimanikatis, V.; Floudas, C.A.; Bailey, J.E., Optimization of regulatory architectures in metabolic reaction networks, Biotechnol. bioeng., 52, 485, (1996)
[219] Hatzimanikatis, V.; Floudas, C.A.; Bailey, J.E., Analysis and design of metabolic reaction networks via mixed-integer linear optimization, Aiche j., 42, 1277, (1996)
[220] Regan, L.; Bogle, I.D.L.; Dunhill, P., Simulation and optimization of metabolic pathways, Comput. chem. eng., 17, 627, (1993)
[221] Voit, E.O., Optimization in integrated biochemical systems, Biotechnol. bioeng., 40, 572, (1992)
[222] Vance, W.; Arkin, A.; Ross, J., Determination of causal connectivities of species in reaction networks, Proc. natl. acad. sci. USA, 99, 5816, (2002)
[223] Torralba, A.S.; Yu, K.; Shen, P.; Oefner, P.J.; Ross, J., Experimental test of a method for determining causal connectivities of species in reactions, Proc. natl. acad. sci. USA, 100, 1494, (2003)
[224] Pearl, J., Causality: models, reasoning, and inference, (2000), Cambridge University · Zbl 0959.68116
[225] Spirtes, P.; Glymour, C.; Scheines, R., Causation, prediction, and search, (1993), Springer New York · Zbl 0806.62001
[226] Arkin, A.; Ross, J., Statistical construction of chemical-reaction mechanisms from measured time-series, J. phys. chem., 99, 970, (1995)
[227] Arkin, A.; Shen, P.D.; Ross, J., A test case of correlation metric construction of a reaction pathway from measurements, Science, 277, 1275, (1997)
[228] Samoilov, M.; Arkin, A.; Ross, J., On the deduction of chemical reaction pathways from measurements of time series of concentrations, Chaos, 11, 108, (2001) · Zbl 0997.92041
[229] Pearl, J., Probabilistic reasoning in intelligent systems: networks of plausible inference, (1988), Morgan Kaufman San Mateo, CA
[230] Akaike, H., New look at statistical-model identification, IEEE trans. automat. contr. AC19, 716, (1974) · Zbl 0314.62039
[231] Judd, K.; Mees, A., On selecting models for nonlinear time-series, Physica D, 82, 426, (1995) · Zbl 0888.58034
[232] Hendry, D.F.; Krolzig, H.M., New developments in automatic general-to-specific modelling, () · Zbl 0978.91073
[233] Crampin, E.J.; McSharry, P.E.; Schnell, S., Extracting biochemical reaction kinetics from time series data, Lecture notes in artificial intelligence, (2004), Springer, p. 329
[234] Crampin, E.J.; Schnell, S.; McSharry, P.E., Mathematical and computational techniques to deduce complex biochemical reaction mechanisms, Prog. biophys. mol. biol., 86, 77, (2004)
[235] Barabási, A.-L.; Albert, R.; Jeong, H.; Bianconi, G., Power-law distribution of the world wide web, Science, 287, 2115, (2000)
[236] Podani, J.; Oltvai, Z.N.; Jeong, H.; Tombor, B.; Barabasi, A.L.; Szathmary, E., Comparable system-level organization of archaea and eukaryotes, Nat. genet., 29, 54, (2001)
[237] Kimura, S.; Sonoda, K.; Yamane, S.; Maeda, H.; Matsumura, K.; Hatakeyama, M., Function approximation approach to the inference of reduced ngnet models of genetic networks, BMC bioinform., 9, 23, (2008)
[238] R.C.H. del Rosario, M.T. Echavez, M.T. de Paz, P.C. Zuñiga, M.C.R. Bargo, C.O. Talaue, C. Arellano, J.M. Pasia, P.C. Naval, E.O. Voit, E. Mendoza, MADMan: a benchmarking framework for parameter estimation in biochemical systems theory models, in: International Conference on Molecular Systems Biology 2008 (ICMSB08), Manila, Philippines, 2008, p. 10.
[239] Sekiguchi, T.; Okamoto, M., Winbest-KIT: windows-based biochemical reaction simulator for metabolic pathways, J. bioinform. comput. biol., 4, 621, (2006)
[240] Cadlive, CADLIVE (Computer-Aided Design of LIVing systEms). Available from: <www.cadlive.jp>, 2009.
[241] J.S. Almeida, Bioinformatics Station. Available from: <http://bioinformaticstation.org>, 2008.
[242] Voit, E.O., The S-distribution. A tool for approximation and classification of univariate, unimodal probability distributions, Biometr. J., 34, 855, (1992) · Zbl 0775.62027
[243] Voit, E.O.; Yu, S., The S-distribution: approximation of discrete distributions, Biometr. J., 36, 205, (1994) · Zbl 0960.62508
[244] Yu, S.S.; Voit, E.O., A graphical classification of survival distributions, (), 385 · Zbl 0909.62120
[245] Sorribas, A.; March, J.; Voit, E.O., Estimating age-related trends in cross-sectional studies using S-distributions, Stat. med., 19, 697, (2000)
[246] Voit, E.O., Dynamic trends in distributions, Biometr. J., 38, 587, (1996) · Zbl 0859.62018
[247] Voit, E.O.; Sorribas, A., Computer modeling of dynamically changing distributions of random variables, Math. comput. model., 31, 217, (2000)
[248] Marin-Sanguino, A.; Voit, E.O.; Gonzalez-Alcon, C.; Torres, N.V., Optimization of biotechnological systems through geometric programming, Theor. biol. med. model., 4, 38, (2007)
[249] Neves, A.R.; Ramos, A.; Nunes, M.C.; Kleerebezem, M.; Hugenholtz, J.; de Vos, W.M.; Almeida, J.; Santos, H., in vivo nuclear magnetic resonance studies of glycolytic kinetics in lactococcus lactis, Biotechnol. bioeng., 64, 200, (1999)
[250] Neves, A.R.; Ramos, A.; Shearman, C.; Gasson, M.J.; Almeida, J.S.; Santos, H., Metabolic characterization of lactococcus lactis deficient in lactate dehydrogenase using in vivo 13C-NMR, Eur. J. biochem., 267, 3859, (2000)
[251] Vera, J.; de Atauri, P.; Cascante, M.; Torres, N.V., Multicriteria optimization of biochemical systems by linear programming: application to production of ethanol by saccharomyces cerevisiae, Biotechnol. bioeng., 83, 335, (2003)
[252] Sutton, M.D.; Smith, B.T.; Godoy, V.G.; Walker, G.C., The SOS response: recent insights into umudc-dependent mutagenesis and DNA damage tolerance, Annu. rev. genet., 34, 479, (2000)
[253] Barrett, T.; Suzek, T.O.; Troup, D.B.; Wilhite, S.E.; Ngau, W.C.; Ledoux, P.; Rudnev, D.; Lash, A.E.; Fujibuchi, W.; Edgar, R., NCBI GEO: mining millions of expression profiles – database and tools, Nucleic acids res., 33, D562, (2005)
[254] Kuper, C.; Jung, K., Cadc-mediated activation of the cadba promoter in Escherichia coli, J. mol. microbiol. biotechnol., 10, 26, (2005)
[255] Xiu, Z.L.; Chang, Z.Y.; Zeng, A.P., Nonlinear dynamics of regulation of bacterial trp operon: model analysis of integrated effects of repression, feedback inhibition, and attenuation, Biotechnol. prog., 18, 686, (2002)
[256] Cho, R.J.; Campbell, M.J.; Winzeler, E.A.; Steinmetz, L.; Conway, A.; Wodicka, L.; Wolfsberg, T.G.; Gabrielian, A.E.; Landsman, D.; Lockhart, D.J.; Davis, R.W., A genome-wide transcriptional analysis of the mitotic cell cycle, Mol. cell, 2, 65, (1998)
[257] Neves, A.R.; Pool, W.A.; Kok, J.; Kuipers, O.P.; Santos, H., Overview on sugar metabolism and its control in lactococcus lactis - the input from in vivo NMR, FEMS microbiol. rev., 29, 531, (2005)
[258] Wang, F.S.; Su, T.L.; Jang, H.J., Hybrid differential evolution for problems of kinetic parameter estimation and dynamic optimization of an ethanol fermentation process, Indust. eng. chem. res., 40, 2876, (2001)
[259] Ingalls, B.P., Autonomously oscillating biochemical systems: parametric sensitivity of extrema and period, Syst. biol. (stevenage), 1, 62, (2004)
[260] W.H. Huang, C.H. Yuh, F.S. Wang, Reverse engineering for embryonic gene regulatory network in zebrafish via evolutionary optimization with data collocation, in: Seventh International Conference on Systems Biology, Yokohama, Japan, 2006.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.