×

Biochemical systems theory: a review. (English) Zbl 1268.92045

Summary: Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. This paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of applications. The paper is intended as a guide for investigators entering the fascinating field of biological systems analysis and as a resource for practitioners and experts.

MSC:

92C40 Biochemistry, molecular biology
92C42 Systems biology, networks
Full Text: DOI

References:

[1] Savageau, M. A., Biochemical Systems Analysis: A Study of Function and Design in Molecular Biology, (1976), Addison-Wesley, Reading, Mass, USA · Zbl 0398.92013
[2] Voit, E. O., Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity, (1991), Van Nostrand Reinhold, New York, NY, USA · Zbl 0785.92004
[3] Voit, E. O., Computational Analysis of Biochemical Systems: A Practical Guide for Biochemists and Molecular Biologists, (2000), Cambridge University Press, Cambridge, UK
[4] Torres, N. V.; Voit, E. O., Pathway Analysis and Optimization in Metabolic Engineering, (2002), Cambridge University Press, Cambridge, UK · Zbl 1013.42001
[5] Goel, G., Reconstructing Biochemical Systems. Systems Modeling and Analysis Tools for Decoding Biological Designs, (2008), VDM Verlag Dr. Müller, Saarbrücken, Germany
[6] Voit, E. O., A First Course in Systems Biology, (2012), Garland Science, New York, NY, USA
[7] Voit, E. O., Computational Analysis of Biochemical Systems. A Practical Guide for Biochemists and Molecular Biologists, (2006), Cambridge University Press, Cambridge, UK
[8] Torres, N. V.; Voit, E. O., Pathway Analysis and Optimization in Metabolic Engineering, (2005), Cambridge University Press, Cambridge, UK
[9] Shiraishi, F., BST: Biochemical Systems Theory, (2007)
[10] Savageau, M. A., The behavior of intact biochemical control systems, Current Topics in Cellular Regulation, 6, 63-129, (1972)
[11] Savageau, M. A., Mathematics of organizationally complex systems, Biomedica Biochimica Acta, 44, 6, 839-844, (1985)
[12] Savageau, M. A.; Bittar, E. E., Critique of the Enzymologist’s test tube, Fundamentals of Medical Cell Biology, 3, 45-108, (1992), JAI Press, Greenwich, Conn, USA
[13] Savageau, M. A.; Bittar, E. E., Enzyme kinetics in vitro and in vivo: Michaelis-Menten revisited, Principles of Medical Biology, 4, 93-146, (1995), JAI Press, Greenwich, Conn, USA
[14] Savageau, M. A.; Collado-Vides, J.; Magasanik, B.; Smith, T. F., A kinetic formalism for integrative molecular biology: manifestation in biochemical systems theory and use in elucidating design principles for gene circuits, Integrative Approaches to Molecular Biology, 115-146, (1996), MIT Press, Cambridge, Mass, USA
[15] Savageau, M. A.; Voit, E. O., Power-law approach to modeling biological systems—I—theory, Journal of Fermentation Technology, 60, 221-228, (1982)
[16] Voit, E. O.; Savageau, M. A., Power-law approach to modeling biological systems—III—methods of analysis, Journal of Fermentation Technology, 60, 223-241, (1982)
[17] Voit, E. O., Canonical modeling: review of concepts with emphasis on environmental health, Environmental Health Perspectives, 108, 5, supplement, 895-909, (2000)
[18] Voit, E. O.; Savageau, M. A.; Capasso, V.; Grosso, E.; Paveri-Fontana, S. L., S-system analysis of biological systems, Mathematics in Biology and Medicine, Lecture Notes in Biomathematics, 57, 517-524, (1985), Heidelberg, Germany · Zbl 0566.92003
[19] Voit, E. O., Models-of-data and models-of-processes in the post-genomic era, Mathematical Biosciences, 180, 263-274, (2002) · Zbl 1015.92014 · doi:10.1016/S0025-5564(02)00115-3
[20] Marin-Sanguino, A.; Gupta, S. K.; Voit, E. O.; Vera, J., Biochemical pathway modeling tools for drug target detection in cancer and other complex diseases, Methods in Enzymology, 487, 319-369, (2011) · doi:10.1016/B978-0-12-381270-4.00011-1
[21] Peschel, M.; Mende, W.; Savageau, M. A.; Voit, E. O., Allgemeine systemkonzepte für homogene dynamische netzwerke, Messen-Steuern-Regeln, 32, 170-172, (1989)
[22] Sims, K. J.; Alvarez-Vasquez, F.; Voit, E. O.; Hannun, Y. A., A guide to biochemical systems modeling of sphingolipids for the biochemist, Methods in Enzymology, 432, 319-350, (2007) · doi:10.1016/S0076-6879(07)32013-2
[23] Savageau, M. A.; Lakshmikantham, V., Power-law formalism: a canonical nonlinear approach to modeling and analysis, Proceedings of the World Congress of Nonlinear Analysts, Walter de Gruyter Publishers · Zbl 0843.92001
[24] Volt, E. O., Control in perspective, Trends in Biochemical Sciences, 12, 221, (1987)
[25] Voit, E. O., Recasting nonlinear models as S-systems, Mathematical and Computer Modelling, 11, 140-145, (1988)
[26] Voit, E. O., Modelling metabolic networks using power-laws and S-systems, Essays in Biochemistry, 45, 29-40, (2008) · doi:10.1042/BSE0450029
[27] Voit, E. O.; Qi, Z.; Miller, G. W., Steps of modeling complex biological systems, Pharmacopsychiatry, 41, 1, S78-S84, (2008) · doi:10.1055/s-2008-1080911
[28] Voit, E. O.; Schubauer-Berigan, M. K.; Newman, M. C.; Stojan, C. L., The role of canonical modeling as a unifying framework for ecological and human risk assessment, Risk Assessment: Logic and Measurement, 101-139, (1998), Ann Arbor Press, Chelsea, Mich, USA
[29] Savageau, M. A., Introduction to S-systems and the underlying power-law formalism, Mathematical and Computer Modelling, 11, 546-551, (1988)
[30] Voit, E. O.; Schwacke, J. H.; Konopka, A. K., Understanding through modeling, Systems Biology: Principles, Methods, and Concepts, 27-82, (2007), CRC Press/Taylor & Francis Books, Boca Raton, Fla, USA
[31] Voit, E. O.; Veflingstad, S. R., Systems biology as an inspiration for mechatronics, Journal of Biomechatronics Engineering, 1, 55-69, (2008)
[32] Savageau, M. A., Biochemical systems theory: operational differences among variant representations and their significance, Journal of Theoretical Biology, 151, 4, 509-530, (1991)
[33] Voit, E. O., Tutorial on the structure of S-systems. tutorials of the iizuka, Proceedings of the 4th International Conference on Soft Computing, Lizuka
[34] Savageau, M. A., Reconstructionist molecular biology, New Biologist, 3, 2, 190-197, (1991)
[35] Savageau, M. A., The challenge of reconstruction, New Biologist, 3, 2, 101-102, (1991)
[36] Savageau, M. A., Design principles for elementary gene circuits: elements, methods, and examples, Chaos, 11, 1, 142-159, (2001) · Zbl 1020.92021 · doi:10.1063/1.1349892
[37] Shiraishi, F.; Savageau, M. A., The tricarboxylic acid cycle in dictyostelium discoideum. I. formulation of alternative kinetic representations, Journal of Biological Chemistry, 267, 32, 22912-22918, (1992)
[38] Wang, F.-S.; Wu, W.-H., Biomolecular pathway modeling, Systems Biology, 55-84, (2012), World Scientific, Singapore
[39] Alves, R.; Vilaprinyo, E.; Sorribas, A., Integrating bioinformatics and computational biology: perspectives and possibilities forin silico network reconstruction in molecular systems biology, Current Bioinformatics, 3, 98-129, (2008)
[40] Veflingstad, S. R.; Dam, P.; Xu, Y.; Voit, E. O.; Xu, Y.; Gogarten, J. P., Microbial pathway models, Computational Methods for Understanding Bacterial and Archaeal Genomes, 7, (2008), Imperial College Press, London, UK
[41] Vera, J.; Balsa-Canto, E.; Wellstead, P.; Banga, J. R.; Wolkenhauer, O., Power-law models of signal transduction pathways, Cellular Signalling, 19, 7, 1531-1541, (2007) · doi:10.1016/j.cellsig.2007.01.029
[42] Alves, R.; Vilaprinyo, E.; Hernández-Bermejo, B.; Sorribas, A., Mathematical formalisms based on approximated kinetic representations for modeling genetic and metabolic pathways, Biotechnology and Genetic Engineering Reviews, 25, 1-40, (2008)
[43] Voit, E. O., Metabolic modeling: a tool of drug discovery in the post-genomic era, Drug Discovery Today, 7, 11, 621-628, (2002) · doi:10.1016/S1359-6446(02)02280-8
[44] Voit, E. O.; Qi, Z.; Kikuchi, S., Mesoscopic models of neurotransmission as intermediates between disease simulators and tools for discovering design principles, Pharmacopsychiatry, 45, 1, supplement, S22-S30, (2012)
[45] Goel, G.; Chou, I. C.; Voit, E. O., Biological systems modeling and analysis: a biomolecular technique of the twenty-first century, Journal of Biomolecular Techniques, 17, 4, 252-269, (2006)
[46] Voit, E. O.; Ebeling, W.; Peschel, M., Theory and applications of S-systems, Dynamical Networks, 37-51, (1989), Akademie, Berlin, Germany
[47] Voit, E. O.; Savageau, M. A.; Irvine, D. H.; Voit, E. O., An introduction to S-systems, Canonical Nonlinear Modeling. S-system Approach to Understanding Complexity, 47-66, (1991), Van Nostrand Reinhold, New York, NY, USA
[48] Sims, K. J.; Spassieva, S. D.; Voit, E. O.; Obeid, L. M., Yeast sphingolipid metabolism: clues and connections, Biochemistry and Cell Biology, 82, 1, 45-61, (2004) · doi:10.1139/o03-086
[49] Voit, E. O., The dawn of a new era of metabolic systems analysis, Drug Discovery Today, 2, 5, 182-189, (2004) · doi:10.1016/S1741-8364(04)02419-9
[50] Tominaga, D.; Okamoto, M., Design of canonical model describing complex nonlinear dynamics, Proceedings of the 7th International Conference on Computer Applications in Biotechnology
[51] Voit, E. O., Canonical nonlinear simulation of complex systems, Proceedings of the European Simulation Multiconference
[52] Savageau, M. A.; Voit, E. O.; Irvine, D. H., Biochemical systems theory and metabolic control theory—1—fundamental similarities and differences, Mathematical Biosciences, 86, 2, 127-145, (1987) · Zbl 0645.92011
[53] Savageau, M. A.; Voit, E. O.; Irvine, D. H., Biochemical systems theory and metabolic control theory—2—the role of summation and connectivity relationships, Mathematical Biosciences, 86, 2, 147-169, (1987) · Zbl 0645.92012
[54] Sorribas, A.; Savageau, M. A., Strategies for representing metabolic pathways within biochemical systems theory: reversible pathways, Mathematical Biosciences, 94, 2, 239-269, (1989) · Zbl 0677.92004
[55] Sorribas, A.; Savageau, M. A., A comparison of variant theories of intact biochemical systems. II. flux-oriented and metabolic control theories, Mathematical Biosciences, 94, 2, 195-238, (1989) · Zbl 0696.92013
[56] Sorribas, A.; Savageau, M. A., A comparison of variant theories of intact biochemical systems. I. enzyme-enzyme interactions and biochemical systems theory, Mathematical Biosciences, 94, 2, 161-193, (1989) · Zbl 0696.92012
[57] Sorribas, A.; Voit, E. O., Optimal strategies for modeling biochemical systems, Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity, (1991), Van Nostrand Reinhold, New York, NY, USA · Zbl 0785.92004
[58] Wang, F. S.; Ko, C. L.; Voit, E. O., Kinetic modeling using S-systems and lin-log approaches, Biochemical Engineering Journal, 33, 3, 238-247, (2007) · doi:10.1016/j.bej.2006.11.002
[59] Savageau, M. A., Dominance according to metabolic control analysis: major achievement or house of cards?, Journal of Theoretical Biology, 154, 1, 131-136, (1992)
[60] Savageau, M. A., Michaelis-Menten mechanism reconsidered: implications of fractal kinetics, Journal of Theoretical Biology, 176, 1, 115-124, (1995) · doi:10.1006/jtbi.1995.0181
[61] Savageau, M. A., Metabolite channeling: implications for regulation of metabolism and for quantitative description of reactions in vivo, Journal of Theoretical Biology, 152, 1, 85-92, (1991)
[62] Heijnen, J. J., Approximative kinetic formats used in metabolic network modeling, Biotechnology and Bioengineering, 91, 5, 534-545, (2005) · doi:10.1002/bit.20558
[63] del Rosario, R. C. H.; Mendoza, E.; Voit, E. O., Challenges in lin-log modelling of glycolysis in lactococcus lactis, IET Systems Biology, 2, 3, 136-149, (2008) · doi:10.1049/iet-syb:20070030
[64] Voit, E. O.; Torres, N. V.; Breitenecker, F.; Husinsky, I., Simulation and steady-state optimization of integrated biochemical systems: theory and applications in biotechnology, Proceedings of the EUROSIM Simulation Congress, Elsevier Science B.V.
[65] Torres, N. V.; Alvarez-Vasquez, F.; Voit, E. O.; Arora, D. K., Optimization of biotechnological processes with S-system models. methodology and applications to fungal metabolism, Handbook of Fungal Biotechnology, (2002), Marcel Dekker, New York, NY, USA
[66] Torres, N. V.; Voit, E. O.; Glez-Alcón, C.; Rodríguez, F., A novel approach to design of overexpression strategy for metabolic engineering. application to the carbohydrate metabolism in the citric acid producing mould aspergillus niger, Food Technology and Biotechnology, 36, 3, 177-184, (1998)
[67] Voit, E. O.; Torres, N. V., Canonical modeling of complex pathways in biotechnology (invited review), Recent Research Developments in Biotechnology & Bioengineering, 1, 321-341, (1998)
[68] Chou, I. C.; Voit, E. O., Recent developments in parameter estimation and structure identification of biochemical and genomic systems, Mathematical Biosciences, 219, 2, 57-83, (2009) · Zbl 1168.92019 · doi:10.1016/j.mbs.2009.03.002
[69] Voit, E. O.; Marino, S.; Lall, R., Challenges for the identification of biological systems from in vivo time series data, In Silico Biology, 5, 2, 83-92, (2005)
[70] Voit, E. O.; Du, D.-Z.; Shang, X. S., Model identification: a key challenge is computational systems biology, Optimization and Systems Biology, 1-12, (2008), World Publishing Corp.
[71] Voit, E. O.; Chou, I.-C., Parameter estimation in canonical biological systems models, International Journal of Systems and Synthetic Biology, 1, 1-19, (2010)
[72] Voit, E. O.; Dehmer, M.; Emmert-Streib, F.; Salvador, A., What if the fit is unfit? criteria for biological systems estimation beyond residual errors, Applied Statistics for Biological Networks, 183-200, (2011), John Wiley and Sons, New York, NY, USA
[73] Savageau, M. A., A theory of alternative designs for biochemical control systems, Biomedica Biochimica Acta, 44, 6, 875-880, (1985)
[74] Savageau, M. A.; Calendar, R. R.; Gold, L., Coupled circuits of gene regulation, Sequence Specificity in Transcription and Translation, 633-642, (1985), A. R. Liss, New York, NY, USA
[75] Savageau, M. A.; Goodwin, B. C.; Saunders, P. T., Are there rules governing patterns of regulation?, Theoretical Biology-Epigenetic and Evolutionary Order, (1989), Edinburgh, UK, Edinburgh University Press
[76] Voit, E. O., Design principles and operating principles: the yin and Yang of optimal functioning, Mathematical Biosciences, 182, 1, 81-92, (2003) · Zbl 1012.92013 · doi:10.1016/S0025-5564(02)00162-1
[77] Voit, E. O.; Deutsch, A.; Howard, J.; Falcke, M.; Zimmermann, W., Design and operation: keys to understanding biological systems, Function and Regulation of Cellular Systems: Experiments and Models, (2004), Birkhäuser
[78] Alves, R.; Sorribas, A., Special issue on biological design principles, Mathematical Biosciences, 231, 1, 1-2, (2011) · doi:10.1016/j.mbs.2011.03.009
[79] Voit, E. O.; Rust, P. F., Invited tutorial: S-system analysis of continuous univariate probability distributions, Journal of Statistical Computing and Simulation, 42, 187-249, (1992) · Zbl 0775.65027
[80] Sorribas, A.; Voit, E. O.; Rust, P. F.; Sentis, J., S-systems: a useful representation for computing statistical distributions, Biometric Bulletin, 7, 19, (1990)
[81] Voit, E. O., Canonical modeling: a link between environmental models and statistics, Austrian Journal for Statistics, 27, 109-121, (1998)
[82] Savageau, M. A.; Voit, E. O., 20 years of S-systems, Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity, 1-44, (1991), Van Nostrand Reinhold, New York, NY, USA
[83] Voit, E. O.; Irvine, D. H.; Savageau, M. A., The User’s Guide to ESSYNS, (1989), Medical University of South Carolina Press, Charleston, SC, USA
[84] Irvine, D. H.; Voit, E. O.; Savageau, M. A.; Voit, E. O., Analysis of complex dynamic networks witrh ESSYNS, Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity, 133-141, (1991), Van Nostrand Reinhold, New York, NY, USA · Zbl 0785.92004
[85] Irvine, D. H.; Savageau, M. A.; Voit, E. O.; Voit, E. O., Numerical analysis of S-systems with ESSYNS, Canonical Nonlinear Modeling. S-system Approach to Understanding Complexity, 133-141, (1991), Van Nostrand Reinhold, New York, NY, USA · Zbl 0785.92004
[86] Irvine, D. H., Efficient solution of nonlinear models expressed in S-system canonical form, Mathematical and Computer Modelling, 11, 123-128, (1988)
[87] Irvine, D. H.; Savageau, M. A., Efficient solution of nonlinear ordinary differential equations expressed in S-system canonical form, SIAM Journal on Numerical Analysis, 27, 3, 704-735, (1990) · Zbl 0702.65068
[88] Shiraishi, F.; Takeuchi, H.; Hasegawa, T.; Nagasue, H., A Taylor-series solution in Cartesian space to GMA-system equations and its application to initial-value problems, Applied Mathematics and Computation, 127, 1, 103-123, (2002) · Zbl 1023.65064 · doi:10.1016/S0096-3003(01)00007-8
[89] Ferreira, A., Power Law Analysis and Simulation, (2000)
[90] Yamada, Y.; Kinoshita, A.; Nakayama, Y.; Tomita, M., Automatic transformation of kinetic equations into S-system and GMA forms, Genome Informatics, 13, 482-483, (2002)
[91] Okamoto, M.; Morita, Y.; Tominaga, D.; Tanaka, K.; Kinoshita, N.; Ueno, J. I.; Miura, Y.; Maki, Y.; Eguchi, Y., Design of virtual-labo-system for metabolic engineering: development of biochemical engineering system analyzing tool-kit (BEST KIT), Computers and Chemical Engineering, 21, 1, S745-S750, (1997)
[92] Yoshimura, J.; Shimonobou, T.; Sekiguchi, T.; Okamoto, M., Development of the parameter-Fitting module for web-based biochemical reaction simulator BEST-KIT, Chem-Bioinformatics Journal, 3, 114-129, (2003)
[93] Sekiguchi, T.; Okamoto, M., Winbest-KIT: windows-based biochemical reaction simulator for metabolic pathways, Journal of Bioinformatics and Computational Biology, 4, 3, 621-638, (2006) · doi:10.1142/S0219720006002132
[94] Vera, J.; Sun, C.; Oertel, Y.; Wolkenhauer, O., Plmaddon: a power-law module for the Matlab sbtoolbox, Bioinformatics, 23, 19, 2638-2640, (2007) · doi:10.1093/bioinformatics/btm245
[95] Luo, J. L.; Frank Hsu, D.; Kao, C. Y., Constructing a SMBL-based S-system simulation platform, Proceedings of the Emerging Information Technology Conference · doi:10.1109/EITC.2005.1544378
[96] Dräger, A.; Hassis, N.; Supper, J.; Schröder, A.; Zell, A., Sbmlsqueezer: a celldesigner plug-in to generate kinetic rate equations for biochemical networks, BMC Systems Biology, 2, article 39, (2008) · doi:10.1186/1752-0509-2-39
[98] Vera, J.; Torres, N. V., Metmap: an integrated Matlab package for analysis and optimization of metabolic systems, In Silico Biology, 4, 2, 97-108, (2004)
[99] Savageau, M. A., Software for design space analysis
[100] Savageau, M. A., Biochemical systems analysis—II. the steady-state solutions for an n-pool system using a power-law approximation, Journal of Theoretical Biology, 25, 3, 370-379, (1969)
[101] Savageau, M. A., Biochemical systems analysis. I. some mathematical properties of the rate law for the component enzymatic reactions, Journal of Theoretical Biology, 25, 3, 365-369, (1969)
[102] Savageau, M. A., Biochemical systems analysis—III—dynamic solutions using a power-law approximation, Journal of Theoretical Biology, 26, 2, 215-226, (1970)
[103] Garfinkel, D.; Garfinkel, L.; Pring, M.; Green, S. B.; Chance, B., Computer applications to biochemical kinetics, Annual Review of Biochemistry, 39, 473-498, (1970)
[104] Garfinkel, D., The role of computer simulation in biochemistry, Computers and Biomedical Research, 2, 31-44, (1968)
[105] Garfinkel, D., Computer-based modeling of biological systems which are inherently complex: problems, strategies, and methods, Biomedica Biochimica Acta, 44, 6, 823-829, (1985)
[106] Henri, M. V., Lois Générales de l’Action des Diastases, (1903), Hermann, Paris, France
[107] Michaelis, L.; Menten, M. L., Die kinetik der inver-tinwirkung, Biochemische Zeitschrift, 49, 333-369, (1913)
[108] Hill, A. V., Possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves, Journal of Physiology, 40, 4-8, (1910)
[109] Schulz, A. R., Enzyme Kinetics: From Diastase to Multi-Enzyme Systems, (1994), Cambridge University Press, New York, NY, USA
[110] Heinrich, R.; Rapoport, T. A., A linear steady state treatment of enzymatic chains: general properties, control and effector strength, European Journal of Biochemistry, 42, 1, 89-95, (1974)
[111] Heinrich, R.; Rapoport, S. M.; Rapoport, T. A., Metabolic regulation and mathematical models, Progress in Biophysics and Molecular Biology, 32, 1, 1-82, (1977)
[112] Bode, H. W., Network Analysis and Feedback Amplifier Design, (1945), Van Nostrand, Princeton, NJ, USA
[113] Savageau, M. A.; Voit, E. O., Recasting nonlinear differential equations as S-systems: a canonical nonlinear form, Mathematical Biosciences, 87, 1, 83-115, (1987) · Zbl 0631.34015
[114] Savageau, M. A., Demand theory of gene regulation—II—quantitative application to the lactose and maltose operons of Escherichia coli, Genetics, 149, 4, 1677-1691, (1998)
[115] Savageau, M. A., Demand theory of gene regulation—I—quantitative development of the theory, Genetics, 149, 4, 1665-1676, (1998)
[116] Craciun, G.; Feinberg, M., Multiple equilibria in complex chemical reaction networks: extensions to entrapped species models, IEE Proceedings, 153, 4, 179-186, (2006) · doi:10.1049/ip-syb:20050093
[117] Shinar, G.; Feinberg, M., Concordant chemical reaction networks, Mathematical Biosciences, 240, 2, 92-113, (2012) · Zbl 1316.92100
[118] Savageau, M. A., The power-law formalism: generic properties and relatedness to other canonical nonlinear formalisms, Proceedings of the 4th International Conference on Soft Computing, Fuzzy Logic Institute
[119] Voit, E. O.; Sands, P. J., Modeling forest growth—I. canonical approach, Ecological Modelling, 86, 1, 51-71, (1996)
[120] Shiraishi, F.; Fujiwara, S., An efficient method for solving two-point boundary value problems with extremely high accuracy, Journal of Chemical Engineering of Japan, 29, 1, 88-94, (1996)
[121] Shiraishi, F., Highly accurate solution of the axial dispersion model expressed in S-system canonical form by Taylor series method, Chemical Engineering Journal, 83, 3, 175-183, (2001) · doi:10.1016/S1385-8947(00)00252-7
[122] Shiraishi, F.; Voit, E. O., Solution of a two-point boundary value model of immobilized enzyme reactions, using an S-system-based root-finding method, Applied Mathematics and Computation, 127, 2-3, 289-310, (2002) · Zbl 1016.92013 · doi:10.1016/S0096-3003(01)00008-X
[123] Shiraishi, F.; Furuta, S.; Ishimatsu, T.; Akhter, J., A simple and highly accurate numerical differentiation method for sensitivity analysis of large-scale metabolic reaction systems, Mathematical Biosciences, 208, 2, 590-606, (2007) · Zbl 1119.92035 · doi:10.1016/j.mbs.2006.11.007
[124] Shiraishi, F.; Hatoh, Y.; Irie, T., An efficient method for calculation of dynamic logarithmic gains in biochemical systems theory, Journal of Theoretical Biology, 234, 1, 79-85, (2005) · Zbl 1445.92126 · doi:10.1016/j.jtbi.2004.11.015
[125] Schwacke, J. H.; Voit, E. O., Computation and analysis of time-dependent sensitivities in generalized mass action systems, Journal of Theoretical Biology, 236, 1, 21-38, (2005) · Zbl 1442.92061 · doi:10.1016/j.jtbi.2005.02.013
[126] Shiraishi, F.; Tomita, T.; Iwata, M.; Berrada, A. A.; Hirayama, H., A reliable Taylor series-based computational method for the calculation of dynamic sensitivities in large-scale metabolic reaction systems: algorithm and software evaluation, Mathematical Biosciences, 222, 2, 73-85, (2009) · Zbl 1178.92018 · doi:10.1016/j.mbs.2009.09.001
[127] Shiraishi, F.; Egashira, M.; Iwata, M.; Sriyudthsak, K.; Hattori, K., Highly reliable computation of dynamic sensitivities in metabolic reaction systems by a variable-step Taylor series method, Asia-Pacific Journal of Chemical Engineering, 7, S32-S38, (2012)
[128] Savageau, M. A., Growth of complex systems can be related to the properties of their underlying determinants, Proceedings of the National Academy of Sciences of the United States of America, 76, 11, 5413-5417, (1979) · Zbl 0411.92005
[129] Marino, S.; Voit, E. O., An automated procedure for the extraction of metabolic network information from time series data, Journal of Bioinformatics and Computational Biology, 4, 3, 665-691, (2006) · doi:10.1142/S0219720006002259
[130] Gavalas, G. R., Nonlinear Differential Equations of Chemically Reacting Systems, (1968), Springer, Berlin, Germany · Zbl 0174.13401
[131] Lotka, A., Elements of Physical Biology, (1924), Williams and Wilkins
[132] May, R. M., Stability and complexity in model ecosystems, Monographs in Population Biology, 6, 1-235, (1973)
[133] Odum, E. P., Fundamentals of Ecology, (1953), Saunders, Philadelphia, Pa, USA
[134] Peschel, M.; Mende, W., The Predator-Prey Model: Do We Live in a Volterra World?, (1986), Akademie, Berlin, Germany · Zbl 0576.92001
[135] Volterra, V., Variazioni e fluttuazioni del numero d’individui in specie animali conviventi, Memorie della Reale Accademia Nazionale dei Lincei, 2, 31-113, (1926) · JFM 52.0450.06
[136] Voit, E. O.; Savageau, M. A., Equivalence between S-systems and Volterra systems, Mathematical Biosciences, 78, 1, 47-55, (1986) · Zbl 0586.92003 · doi:10.1016/0025-5564(86)90030-1
[137] Sprott, J. C.; Vano, J. A.; Wildenberg, J. C.; Anderson, M. B.; Noel, J. K., Coexistence and chaos in complex ecologies, Physics Letters, Section A, 335, 2-3, 207-212, (2005) · Zbl 1123.37331 · doi:10.1016/j.physleta.2004.12.068
[138] Vano, J. A.; Wildenberg, J. C.; Anderson, M. B.; Noel, J. K.; Sprott, J. C., Chaos in low-dimensional Lotka-Volterra models of competition, Nonlinearity, 19, 10, article 006, 2391-2404, (2006) · Zbl 1107.92058 · doi:10.1088/0951-7715/19/10/006
[139] Bailey, J. E.; Ollis, D. F., Biochemical Engineering Fundamentals, (1977), McGraw-Hill, New York, NY, USA
[140] Aiba, S.; Shoda, A. I.; Nagatani, A. I., Kinetics of product inhibition in alcohol fermentation, Biotechnology and Bioengineering, 67, 6, 689-690, (2000)
[141] Aiba, S.; Shoda, A. I.; Nagatani, A. I., Reassessment of the product inhibition in alcohol fermentation, Journal of Fermentation Technology of Japan, 47, 790-805, (1969)
[142] Díaz-Sierra, R.; Hernández-Bermejo, B.; Fairén, V., Graph-theoretic description of the interplay between non-linearity and connectivity in biological systems, Mathematical Biosciences, 156, 1-2, 229-253, (1999) · Zbl 0954.92001 · doi:10.1016/S0025-5564(98)10068-8
[143] Fairén, V.; Hernández-Bermejo, B., Mass action law conjugate representation for general chemical mechanisms, Journal of Physical Chemistry, 100, 49, 19023-19028, (1996)
[144] Hernández-Bermejo, B.; Fairén, V., Lotka-Volterra representation of general nonlinear systems, Mathematical Biosciences, 140, 1, 1-32, (1997) · Zbl 0902.92001 · doi:10.1016/S0025-5564(96)00131-9
[145] Hernández-Bermejo, B.; Fairén, V., Simple evaluation of Casimir invariants in finite-dimensional Poisson systems, Physics Letters, Section A, 241, 3, 148-154, (1998) · Zbl 0928.37008
[146] Hernández-Bermejo, B.; Fairén, V., Hamiltonian structure and Darboux theorem for families of generalized Lotka-Volterra systems, Journal of Mathematical Physics, 39, 11, 6162-6174, (1998) · Zbl 0929.37021
[147] Hernández-Bermejo, B.; Fairén, V.; Brenig, L., Algebraic recasting of nonlinear systems of ODEs into universal formats, Journal of Physics A, 31, 10, 2415-2430, (1998) · Zbl 0923.34035 · doi:10.1088/0305-4470/31/10/016
[148] Hernández-Bermejo, B., Renormalization group approach to power-law modeling of complex metabolic networks, Journal of Theoretical Biology, 265, 3, 422-432, (2010) · Zbl 1461.92035 · doi:10.1016/j.jtbi.2010.04.024
[149] Hatzimanikatis, V.; Bailey, J. E., MCA has more to say, Journal of Theoretical Biology, 182, 3, 233-242, (1996) · doi:10.1006/jtbi.1996.0160
[150] Visser, D.; Heijnen, J. J., The mathematics of metabolic control analysis revisited, Metabolic Engineering, 4, 2, 114-123, (2002) · doi:10.1006/mben.2001.0216
[151] Wu, L.; Wang, W.; Van Winden, W. A.; Van Gulik, W. M.; Heijnen, J. J., A new framework for the estimation of control parameters in metabolic pathways using lin-log kinetics, European Journal of Biochemistry, 271, 16, 3348-3359, (2004) · doi:10.1111/j.0014-2956.2004.04269.x
[152] Voit, E. O.; Eisenfeld, J.; Witten, M., Accuracy of alternative nonlinear power-law models for biochemical systems: advantages of S-systems, IMACS Transactions on Scientific Computing: Modelling od Biomedical Systems, Elsevier
[153] Savageau, M. A., Control of metabolism: where is the theory?, Trends in Biochemical Sciences, 12, 219-220, (1987)
[154] Savageau, M. A.; Cornish-Bowden, A.; Cardenas, M. L., Biochemical systems theory—alternative views of metabolic control, Control of Metabolic Processes, 69-87, (1990), Elsevier, Amsterdam, The Netherlands
[155] Voit, E. O.; Cornish-Bowden, A.; Cárdenas, M. L., Comparison of accuracy of alternative models for biochemical pathways, Proceedings of the Advanced NATO Research Workshop on Control in Metabolic Systems, Plenum Press
[156] Sorribas, A., Discovering another view of control analysis, Trends in Biochemical Sciences, 12, 221-222, (1987)
[157] Sorribas, A., Alternative S-system representations for reversible biochemical pathways, Mathematical and Computer Modelling, 11, 129-133, (1988)
[158] Sorribas, A., Modeling intracellular biochemical pathways that involve multi-enzyme complexes. A critical evaluation of alternative theories of intact biochemical systems, Proceedings of the 1st IFAC Symposium on Modelling and Control in Biomedical Systems
[159] Visser, D.; Van Der Heijden, R.; Mauch, K.; Reuss, M.; Heijnen, S., Tendency modeling: a new approach to obtain simplified kinetic models of metabolism applied to saccharomyces cerevisiae, Metabolic Engineering, 2, 3, 252-275, (2000) · doi:10.1006/mben.2000.0150
[160] Marin-Sanguino, A.; Torres, N. V.; Mendoza, E. R.; Oesterhelt, D., Metabolic engineering with power-law and linear-logarithmic systems, Mathematical Biosciences, 218, 1, 50-58, (2009) · Zbl 1157.92018 · doi:10.1016/j.mbs.2008.12.010
[161] Omholt, S. W.; Plahte, E.; Øyehaug, L.; Xiang, K., Gene regulatory networks generating the phenomena of additivity, dominance and epistasis, Genetics, 155, 2, 969-980, (2000)
[162] Ao, P., Metabolic network modelling: including stochastic effects, Computers and Chemical Engineering, 29, 11-12, 2297-2303, (2005) · doi:10.1016/j.compchemeng.2005.05.007
[163] Kohn, M. C., Use of sensitivity analysis to assess reliability of metabolic and physiological models, Risk Analysis, 22, 3, 623-631, (2002) · doi:10.1111/0272-4332.00042
[164] Bewick, S.; Yang, R.; Zhang, M., Complex mathematical models of biology at the nanoscale, Wiley Interdisciplinary Reviews. Nanomedicine and Nanobiotechnology, 1, 6, 650-659, (2009) · doi:10.1002/wnan.61
[165] Huang, W. H.; Wang, F. S., Kinetic modeling of batch fermentation for mixed-sugar to ethanol production, Journal of the Taiwan Institute of Chemical Engineers, 41, 4, 434-439, (2010) · doi:10.1016/j.jtice.2010.03.002
[166] Shiraishi, F.; Sriyudthsak, K.; Suzuki, Y., Calculation errors of time-varying flux control coefficients obtained from elasticity coefficients by means of summation and connectivity theorems in metabolic control analysis, Mathematical Biosciences, 223, 2, 105-114, (2010) · Zbl 1183.92019 · doi:10.1016/j.mbs.2009.11.004
[167] Costa, R. S.; Machado, D.; Rocha, I.; Ferreira, E. C., Hybrid dynamic modeling of Escherichia coli central metabolic network combining Michaelis-Menten and approximate kinetic equations, BioSystems, 100, 2, 150-157, (2010) · doi:10.1016/j.biosystems.2010.03.001
[168] Sorribas, A.; Hernández-Bermejo, B.; Vilaprinyo, E.; Alves, R., Cooperativity and saturation in biochemical networks: a saturable formalism using Taylor series approximations, Biotechnology and Bioengineering, 97, 5, 1259-1277, (2007) · doi:10.1002/bit.21316
[169] Sorribas, A.; Vilaprinyo, E.; Alves, R., Approximate kinetic formalisms for modeling metabolic networks: does anything work?, Philippines Information Technology Journal, 1, (2008)
[170] Vinga, S.; Neves, A. R.; Santos, H.; Brandt, B. W.; Kooijman, S. A. L. M., Subcellular metabolic organization in the context of dynamic energy budget and biochemical systems theories, Philosophical Transactions of the Royal Society B, 365, 1557, 3429-3442, (2010) · doi:10.1098/rstb.2010.0156
[171] Tenazinha, N.; Vinga, S., A survey on methods for modeling and analyzing integrated biological networks, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 8, 4, 943-958, (2011) · doi:10.1109/TCBB.2010.117
[172] Wu, J.; Voit, E., Hybrid modelling in biochemical systems theory by means of functional Petri nets, Journal of Bioinformatics and Computational Biology, 7, 1, 107-134, (2009) · doi:10.1142/S0219720009004047
[173] Wu, J.; Voit, E., Integrative biological systems modeling: challenges and opportunities, Frontiers of Computer Science in China, 3, 1, 92-100, (2009) · doi:10.1007/s11704-007-0011-9
[174] Wu, J.; Qi, Z.; Voit, E. O., Investigation of delays and noise in dopamine signaling with hybrid functional Petri nets, In Silico Biology, 10, (2010)
[175] Marin-Sanguino, A.; Mendoza, E. R., Hybrid modeling in computational neuropsychiatry, Pharmacopsychiatry, 41, 1, supplement, S85-S88, (2008) · doi:10.1055/s-2008-1081464
[176] Wu, J.; Vidakovic, B.; Voit, E. O., Constructing stochastic models from deterministic process equations by propensity adjustment, BMC Systems Biology, 5, article 187, (2011)
[177] Paulsson, J., The stochastic nature of intracellular control circuits
[178] Mueller, K. M.; Burns, S. A.; Savageau, M. A., A comparison of the monomial method and the S-system method for solving systems of algebraic equations, Applied Mathematics and Computation, 90, 167-180, (1998) · Zbl 0907.65047
[179] Savageau, M. A., Finding multiple roots of nonlinear algebraic equations using S-system methodology, Applied Mathematics and Computation, 55, 2-3, 187-199, (1993) · Zbl 0771.65025
[180] Nabli, F.; Soliman, S., Steady-state solution of biochemical systems, beyond S-systems via T-invariants, Proceedings of the 8th International Conference on Computational Methods in Systems Biology (CMSB ’10) · doi:10.1145/1839764.1839768
[181] Torsella, J. A.; Bin Razali, A. M.; Voit, E. O., An analysis of forestry data, Canonical Nonlinear Modeling: S-System Approach to Understanding Complexity, 181-199, (1991), Van Nostrand Reinhold, New York, NY, USA · Zbl 0785.92004
[182] Voit, E. O.; Newstetter, W. C.; Kemp, M. L., A feel for systems, Molecular Systems Biology, 8, article 609, (2012) · doi:10.1038/msb.2012.41
[183] Torres, N. V., Modeling approach to control of carbohydrate metabolism during citric acid accumulation by aspergillus niger—II—sensitivity analysis, Biotechnology and Bioengineering, 44, 1, 112-118, (1994) · doi:10.1002/bit.260440116
[184] Torres, N. V., Modeling approach to control of carbohydrate metabolism during citric acid accumulation by aspergillus niger—I—model definition and stability of the steady state, Biotechnology and Bioengineering, 44, 1, 104-111, (1994) · doi:10.1002/bit.260440115
[185] 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, Mathematical Biosciences, 130, 1, 25-50, (1995) · Zbl 0835.92015 · doi:10.1016/0025-5564(94)00092-E
[186] Curto, R.; Voit, E. O.; Sorribas, A.; Cascante, M., Mathematical models of purine metabolism in man, Mathematical Biosciences, 151, 1, 1-49, (1998) · Zbl 0938.92015 · doi:10.1016/S0025-5564(98)10001-9
[187] Alvarez-Vasquez, F.; Sims, K. J.; Hannun, Y. A.; Voit, E. O., Integration of kinetic information on yeast sphingolipid metabolism in dynamical pathway models, Journal of Theoretical Biology, 226, 3, 265-291, (2004) · Zbl 1439.92099 · doi:10.1016/j.jtbi.2003.08.010
[188] Alvarez-Vasquez, F.; Riezman, H.; Hannun, Y. A.; Voit, E. O., Mathematical modeling and validation of the ergosterol pathway in saccharomyces cerevisiae, PloS ONE, 6, (2011)
[189] Hasegawa, T.; Shiraishi, F.; Yamakawa, T.; Matsumoto, G., Application of biochemical systems theory to determination of intrinsic kinetic parameters of an immobilized enzyme reaction following Michaelis-Menten kinetics, Methodologies for the Conception, Design, and Application of Intelligent Systems, (1996), World Scientific, Singapore
[190] Sorribas, A.; March, J.; Trujillano, J., A new parametric method based on S-distributions for computing receiver operating characteristic curves for continuous diagnosis tests, Statistics in Medicine, 21, 9, 1213-1235, (2002) · doi:10.1002/sim.1086
[191] Sorribas, A.; Lozano, J. B.; Fairén, V., Deriving chemical and biochemical model networks from experimental measurements, Recent Developments in Chemical Physics, 2, 553-573, (1998)
[192] Bermejo, B. H.; Fairén, V.; Sorribas, A., Power-law modeling based on least-squares minimization criteria, Mathematical Biosciences, 161, 1-2, 83-94, (1999) · Zbl 0953.92016 · doi:10.1016/S0025-5564(99)00035-8
[193] Hernández-Bermejo, B.; Fairén, V.; Sorribas, A., Power-law modeling based on least-squares criteria: consequences for system analysis and simulation, Mathematical Biosciences, 167, 2, 87-107, (2000) · Zbl 1009.92001 · doi:10.1016/S0025-5564(00)00039-0
[194] Díaz-Sierra, R.; Fairén, V., Simplified method for the computation of parameters of power-law rate equations from time-series, Mathematical Biosciences, 171, 1, 1-19, (2001) · Zbl 1006.92004 · doi:10.1016/S0025-5564(01)00051-7
[195] 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, Theoretical Biology and Medical Modelling, 3, article 24, (2006) · doi:10.1186/1742-4682-3-24
[196] Sorribas, A.; Cascante, M.; Lakshmikantham, V., Assessment of the regulatory properties of a metabolic pathway: parameter estimation from steady-state measurements, Proceedings of the World Congress of Nonlinear Analysts, Walter de Gruyter · Zbl 0842.92010
[197] Sorribas, A.; Samitier, S.; Canela, E. I.; Cascante, M., Metabolic pathway characterization from transient response data obtained in situ: parameter estimation in S-system models, Journal of Theoretical Biology, 162, 1, 81-102, (1993) · doi:10.1006/jtbi.1993.1078
[198] Sorribas, A.; Cascante, M.; Schuster, S., Steady-state measurements and identifiability of regulatory patterns in metabolic studies, Modern Trends in Biothermokinetics, 125-131, (1993), Plenum Press, New York, NY, USA
[199] Sorribas, A.; Cascante, M., Structure identifiability in metabolic pathways: parameter estimation in models based on the power-law formalism, Biochemical Journal, 298, 2, 303-311, (1994)
[200] Savageau, M. A., Concepts relating the behavior of biochemical systems to their underlying molecular properties, Archives of Biochemistry and Biophysics, 145, 2, 612-621, (1971)
[201] Voit, E. O.; Savageau, M. A., Power-law approach to modeling biological systems—II. application to ethanol production, Journal of Fermentation Technology, 60, 229-232, (1982)
[202] Varah, J. M., A spline least squares method for numerical parameter estimation in differential equations, SIAM Journal on Scientific and Statistical Computing, 3, 28-46, (1982) · Zbl 0481.65050
[203] Voit, E. O.; Almeida, J., Decoupling dynamical systems for pathway identification from metabolic profiles, Bioinformatics, 20, 11, 1670-1681, (2004) · doi:10.1093/bioinformatics/bth140
[204] Brunel, N. J.-B., Parameter estimation of ODE’s via nonparametric estimators, Electronic Journal of Statistics, 2, 1242-1267, (2008) · Zbl 1320.62063
[205] Crampin, E. J.; Schnell, S.; McSharry, P. E., Mathematical and computational techniques to deduce complex biochemical reaction mechanisms, Progress in Biophysics and Molecular Biology, 86, 1, 77-112, (2004) · doi:10.1016/j.pbiomolbio.2004.04.002
[206] Gennemark, P.; Wedelin, D., Efficient algorithms for ordinary differential equation model identification of biological systems, IET Systems Biology, 1, 2, 120-129, (2007) · doi:10.1049/iet-syb:20050098
[207] Gennemark, P.; Wedelin, D., Benchmarks for identification of ordinary differential equations from time series data, Bioinformatics, 25, 6, 780-786, (2009) · doi:10.1093/bioinformatics/btp050
[208] Swain, M. T.; Mandel, J. J.; Dubitzky, W., Comparative study of three commonly used continuous deterministic methods for modeling gene regulation networks, BMC Bioinformatics, 11, article 459, (2010) · doi:10.1186/1471-2105-11-459
[209] Sun, J.; Garibaldi, J. M.; Hodgman, C., Parameter estimation using metaheuristics in systems biology: a comprehensive review, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 9, 185-202, (2012)
[210] Gugushvili, S.; Klaassen, C. A. J., n-consistent parameter estimation for systems of ordinary differential equations: bypassing numerical integration via smoothing, Bernoulli, 18, 1061-1098, (2012) · Zbl 1257.49033
[211] Sima, C.; Hua, J.; Jung, S., Inference of gene regulatory networks using time-series data: a survey, Current Genomics, 10, 6, 416-429, (2009) · doi:10.2174/138920209789177610
[212] Džeroski, S.; Todorovski, L., Equation discovery for systems biology: finding the structure and dynamics of biological networks from time course data, Current Opinion in Biotechnology, 19, 4, 360-368, (2008) · doi:10.1016/j.copbio.2008.07.002
[213] Todorovski, L.; Džeroski, S.; Choi, S., Modeling the dynamics of biological networks from time course data, Systems Biology for Signaling Networks, 1, 275-294, (2010), Springer
[214] Lee, W. P.; Tzou, W. S., Computational methods for discovering gene networks from expression data, Briefings in Bioinformatics, 10, 4, 408-423, (2009) · doi:10.1093/bib/bbp028
[215] Akutsu, T.; Miyano, S.; Kuhara, S., Automated construction and analysis of the design space for biochemical systems, Bioinformatics, 16, 8, 727-734, (2000)
[216] Maki, Y.; Tominaga, D.; Okamoto, M.; Watanabe, S.; Eguchi, Y., Development of a system for the inference of large scale genetic networks, Proceedings of the Pacific Symposium on Biocomputing
[217] Shin, A.; Iba, H., Construction of genetic network using evolutionary algorithm and combined fitness function, Genome Informatics, 14, 94-103, (2003)
[218] Maki, Y.; Takahashi, Y.; Arikawa, Y.; Watanabe, S.; Aoshima, K.; Eguchi, Y.; Ueda, T.; Aburatani, S.; Kuhara, S.; Okamoto, M., An integrated comprehensive workbench for inferring genetic networks: voyagene, Journal of Bioinformatics and Computational Biology, 2, 3, 533-550, (2004) · doi:10.1142/S0219720004000727
[219] Kikuchi, S.; Tominaga, D.; Arita, M.; Takahashi, K.; Tomita, M., Dynamics modeling of genetic networks using genetic algorithm and S-system, Bioinformatics, 19, 5, 643-650, (2003) · doi:10.1093/bioinformatics/btg027
[220] 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 Bioinformatics, 9, article 23, (2008) · doi:10.1186/1471-2105-9-23
[221] Noman, N.; Iba, H., Reverse engineering genetic networks using evolutionary computation, Genome Informatics, 16, 2, 205-214, (2005)
[222] 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 Informatiics, 13, 382-383, (2002)
[223] Kimura, S.; Hatakeyama, M.; Konagaya, A., Inference of S-system models of genetic networks from noisy time-series data, Chem-Bio Informatics Journal, 4, 1, 1-14, (2004) · doi:10.1273/cbij.4.1
[224] Noman, N.; Iba, H., Inference of gene regulatory networks using S-system and differential evolution, Proceedings of the Genetic and Evolutionary Computation Conference (GECCO ’05) · doi:10.1145/1068009.1068079
[225] Noman, N.; Iba, H., Inference of genetic networks using S-system: information criteria for model selection, Proceedings of the 8th Annual Genetic and Evolutionary Computation Conference 2006
[226] Wu, S. J.; Chou, C. H.; Wu, C. T.; Lee, T. T., Inference of genetic network of xenopus frog egg: improved genetic algorithm, Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society
[227] 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, 7, 1154-1163, (2005) · doi:10.1093/bioinformatics/bti071
[228] Kimura, S.; Matsumura, K.; Okada-Hatakeyama, M., Efficient parameter estimation for the inference of S-system models of genetic networks: proposition of further problem decomposition and alternate function optimization, Chem-Bio Informatics Journal, 9, (2009)
[229] Kimura, S.; Matsumura, K.; Okada-Hatakeyama, M., Efficient parameter estimation for the inference of S-system models of genetic networks: proposition of further problem decomposition and alternate function optimization, Chem-Bio Informatics Journal, 11, 1, 24-40, (2011)
[230] Kimura, S.; Sonoda, K.; Yamane, S.; Matsumura, K.; Hatakeyama, M., Function approximation approach to the inference of normalized Gaussian network models of genetic networks, Proceedings of the International Joint Conference on Neural Networks (IJCNN ’06)
[231] Kimura, S.; Sonoda, K.; Yamane, S.; Matsumura, K.; Hatakeyama, M., Function approximation approach to the inference of reduced ngnet models of genetic networks, IPSJ Transactions on Bioinformatics, 2007, 9-19, (2007) · doi:10.1186/1471-2105-9-23
[232] Kimura, S.; Nakayama, S.; Hatakeyama, M., Genetic network inference as a series of discrimination tasks, Bioinformatics, 25, 7, 918-925, (2009) · doi:10.1093/bioinformatics/btp072
[233] Kimura, S.; Shiraishi, Y.; Hatakeyama, M., Inference of genetic networks using linear programming machines: application of a priori knowledge, Proceedings of the International Joint Conference on Neural Networks (IJCNN ’09) · doi:10.1109/IJCNN.2009.5178679
[234] Kimura, S.; Shiraishi, Y.; Okada, M., Inference of genetic networks using LPMs: assessment of confidence values of regulations, Journal of Bioinformatics and Computational Biology, 8, 4, 661-677, (2010) · doi:10.1142/S0219720010004859
[235] Kimura, S.; Matsumura, K.; Okada-Hatakeyama, M., Bootstrap analysis of genetic networks inferred by the method using lpms, Proceedings of the International Conference on Computational Science and Its Applications (ICCSA ’10), IEEE Computer Society
[236] Kimura, S.; Amano, Y.; Matsumura, K.; Okada-Hatakeyama, M., Effective parameter estimation for S-system models using LPMs and evolutionary algorithms, Proceedings of the 6th IEEE World Congress on Computational Intelligence · doi:10.1109/CEC.2010.5586248
[237] Kimura, S.; Araki, D.; Matsumura, K.; Okada-Hatakeyama, M., Inference of S-system models of genetic networks by solving one-dimensional function optimization problems, Mathematical Biosciences, 235, 161-170, (2012) · Zbl 1402.92177
[238] Nakatsui, M.; Ueda, T.; Maki, Y.; Ono, I.; Okamoto, M., Method for inferring and extracting reliable genetic interactions from time-series profile of gene expression, Mathematical Biosciences, 215, 1, 105-114, (2008) · Zbl 1156.92020 · doi:10.1016/j.mbs.2008.06.007
[239] Nakatsui, M.; Ueda, T.; Okamoto, M., Integrated system for inference of gene expression network, Genome Informatics, 14, 282-283, (2003)
[240] Nakatsui, M.; Ueda, T.; Ono, I.; Okamoto, M., Control aspect of common interactions extracted from inferred network candidates of gene expression, Genome Informatics, P008-P009, (2004)
[241] Nakatsui, M.; Ueda, T.; Ono, I.; Okamoto, M., Efficient method for extracting common core binomial genetic interactions, Genome Informatics, 215, P148-P149, (2005)
[242] Tominaga, D.; Okamoto, M., Nonlinear mumerical optimization technique based on genetic algorithm for inverse problem, Kagaku Kougaku Ronbunshu, 25, 220-225, (1999)
[243] Tominaga, D.; Koga, N.; Okamoto, M., Efficient numerical optimization algorithm based on genetic algorithm for inverse problem, Proceedings of the Genetic and Evolutionary Computation Conference
[244] Ueda, T.; Koga, N.; Okamoto, M., Efficient numerical optimization technique based on real-coded genetic algorithm, Genome Informatics, 12, 451-453, (2001)
[245] Okamoto, M.; Tominaga, D.; Koga, N.; Maki, Y., Efficient numerical optimization algorithm based on genetic algorithm for inverse problem, Proceedings of the 1st International Conference on Systems Biology
[246] Ueda, T.; Ono, I.; Okamoto, M., Development of system identification technique based on real-coded genetic algorithm, Genome Informatics, 13, 386-387, (2002)
[247] Kikuchi, S.; Tominaga, D.; Arita, M.; Tomita, M., Pathway finding from given time-courses using genetic algorithm, Genome Informatics, 12, 304-305, (2001)
[248] Sakamoto, E.; Iba, H., Inferring a system of differential equations for a gene regulatory network by using genetic programming, Proceedings of the Congress on Evolutionary Computation
[249] Wang, H.; Qian, L.; Dougherty, E., Inference of gene regulatory networks using S-system: a unified approach, IET Systems Biology, 4, 2, 145-156, (2010) · doi:10.1049/iet-syb.2008.0175
[250] Yang, X.; Dent, J. E.; Nardini, C., An S-system parameter estimation method (SPEM) for biological networks, Journal of Computational Biology, 19, 175-187, (2012)
[251] Nakayama, T.; Seno, S.; Takenaka, Y.; Matsuda, H., Inference of S-system models of gene regulatory networks using immune algorithm, Journal of Bioinformatics and Computational Biology, 9, 1, supplement, 75-86, (2011)
[252] Liu, L. Z.; Wu, F. X.; Zhang, W. J., Inference of biological S-system using the separable estimation method and the genetic algorithm, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 9, 4, 955-965, (2012)
[253] Ando, S.; Iba, H., Real-coded GA with multimodal uniform distribution, Proceedings of the Congress on Evolutionary Computation (CEC ’04)
[254] Yeh, W. C.; Lin, W. B.; Hsieh, T. J.; Liu, S. L., Feasible prediction in S-system models of genetic networks, Expert Systems with Applications, 38, 1, 193-197, (2011) · doi:10.1016/j.eswa.2010.06.042
[255] Cho, D. Y.; Cho, K. H.; Zhang, B. T., Identification of biochemical networks by S-tree based genetic programming, Bioinformatics, 22, 13, 1631-1640, (2006) · doi:10.1093/bioinformatics/btl122
[256] Ono, I.; Ono, N.; Seike, Y.; Nakatsui, M.; Morishita, R.; Okamoto, M., An evolutionary algorithm taking account of mutual interactions among substances for inference of genetic networks, Proceedings of the Congress on Evolutionary Computation (CEC ’04)
[257] Noman, N.; Iba, H., Enhancing differential evolution performance with local search for high dimensional function optimization, Proceedings of the Genetic and Evolutionary Computation Conference · doi:10.1145/1068009.1068174
[258] Noman, N.; Iba, H., A new generation alternation model for differential evolution, Proceedings of the 8th Annual Genetic and Evolutionary Computation Conference
[259] Noman, N.; Iba, H., Inferring gene regulatory networks using differential evolution with local search heuristics, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 4, 4, 634-647, (2007) · doi:10.1109/TCBB.2007.1058
[260] Daisuke, T.; Horton, P., Inference of scale-free networks from gene expression time series, Journal of Bioinformatics and Computational Biology, 4, 2, 503-514, (2006) · doi:10.1142/S0219720006001886
[261] Hasegawa, T.; Yoshimura, J., An effective method to increase solvability in biochemical systems using S-system, Mathematical Biosciences, 201, 1-2, 125-142, (2006) · Zbl 1093.92039 · doi:10.1016/j.mbs.2005.12.009
[262] Ho, S. Y.; Hsieh, C. H.; Yu, F. C.; Huang, H. L., Evolutionary divide-and-conquer approach to inferring S-system models of genetic networks, Proceedings of the IEEE Congress on Evolutionary Computation (IEEE CEC ’05)
[263] Ho, S.-Y.; Shieh, C.-H.; Yu, F.-C., Inference of S-system models for large-scale genetic networks, Proceedings of the 21st International Conference on Data Engineering Workshops (ICDEW ’05), IEEE Computer Society
[264] Imade, H.; Mizuguchi, N.; Ono, I.; Ono, N.; Okamoto, M., “gridifying” an evolutionary algorithm for inference of genetic networks using the improved GOGA framework and its performance evaluation on OBI grid, Proceedings of the 1st International Workshop on Life Science Grid (LSGRID ’04)
[265] Kim, K.-Y.; Cho, D.-Y.; Zhang, B.-T., Multi-stage evolutionary algorithms for efficient identification of gene regulatory networks, Proceedings of the EvoWorkshops, Springer
[266] Kimura, S.; Hatakeyama, M.; Konagaya, A., Inference of S-system models of genetic networks using a genetic local search, Proceedings of the Congress on Evolutionary Computation (CEC ’03), IEEE Press
[267] Kimura, S.; Sonoda, K.; Yamane, S.; Yoshida, K.; Matsumura, K.; Hatakeyama, M., Inference of genetic networks using a reduced ngnet model, Proceedings of the International Joint Conference on Neural Networks (IJCNN ’07) · doi:10.1109/IJCNN.2007.4371083
[268] Matsubara, Y.; Kikuchi, S.; Sugimoto, M.; Tomita, M., Parameter estimation for stiff equations of biosystems using radial basis function networks, BMC Bioinformatics, 7, article 230, (2006) · doi:10.1186/1471-2105-7-230
[269] Morishita, R.; Imade, H.; Ono, I.; Ono, N.; Okamoto, M., Finding multiple solutions based on an evolutionary algorithm for inference of genetic networks by S-system, Proceedings of the The Congress on Evolutionary Computation (CEC ’03)
[270] Okamoto, M.; Nonaka, T.; Ochiai, S.; Tominaga, D., Nonlinear numerical optimization with use of a hybrid genetic algorithm incorporating the modified powell method, Applied Mathematics and Computation, 91, 1, 63-72, (1998)
[271] Ueda, T.; Koga, N.; Ono, I.; Okamoto, M., Application of numerical optimization technique based on real-coded genetic algorithm to inverse problem in biochemical systems, Proceedings of the Genetic and Evolutionary Computation Conference
[272] Zhang, Z.; Voit, E. O.; Schwacke, L. H.; Yamakawa, T.; Matsumoto, G., Parameter estimation and sensitivity analysis of S-systems using a genetic algorithm, Methodologies for the Conception, Design, and Application of Intelligent Systems, 155-158, World Scientific
[273] Shu, L.-S.; Huang, H.-L.; Ho, S.-J.; Ho, S.-Y., Establishing large-scale gene regulatory networks using a gene-knowledge-embedded evolutionary computation method, Proceedings of the IEEE International Conference on Computer Science and Automation Engineering (CSAE ’11)
[274] Hasan, M. M.; Noman, N.; Iba, H., A prior knowledge based approach to infer gene regulatory networks, Proceedings of the International Symposium on Biocomputing (ISB ’10) · doi:10.1145/1722024.1722069
[275] Chuang, C. H.; Lin, C. L., Estimation of noisy gene regulatory networks, Proceedings of the SICE Annual Conference
[276] Chowdhury, A. R.; Chetty, M., An improved method to infer gene regulatory networks using S-systems, Proceedings of the IEEE Congress on Evolutionary Computation (CEC ’11)
[277] Wu, S. J.; Wu, C. T.; Lee, T. T., Computation intelligent for eukaryotic cell-cycle gene network, Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society
[278] Wu, S. J.; Wu, C. T.; Chou, G. H.; Lee, T. T., Evolution—based gene regulatory network of yeast cell cycle, Proceedings of the IEEE International Conference on Systems, Man and Cybernetics · doi:10.1109/ICSMC.2006.384893
[279] Naval, P. C.; Sison, L. G.; Mendoza, E., Metabolic network parameter inference using particle swarm optimization, Proceedings of the International Conference on Molecular Systems Biology (ICMSB ’06)
[280] Naval, P. C.; Sison, L. G.; Mendoza, E. R., Parameter estimation with term-wise decomposition in biochemical network GMA models by hybrid regularized least squares-particle swarm optimization, Proceedings of the 6th IEEE World Congress on Computational Intelligence · doi:10.1109/CEC.2010.5585984
[281] Naval, P. C., Robust term-wise parameter estimation in biochemical Generalized Mass Action (GMA) models by hybrid regularized least squares-particle swarm optimization [Dissertation], (2007), University of the Philippines, Diliman, Quezon City
[282] Yang, B.; Jiang, M.; Chen, Y., A fast and efficient method for inferring structure and parameters of S-system models, Proceedings of the 11th International Conference on Hybrid Intelligent Systems (HIS ’11)
[283] Hsiao, Y.-T.; Lee, W.-P., Inferring robust gene networks from expression data by a sensitivity-based incremental evolution method, BMC Bioinformatics, 13, article S8, (2012)
[284] Zuñiga, P. C.; Pasia, J.; Adorna, H.; del Rosario, R. C. H.; Naval, P., An ant colony optimization algorithm for parameter estimation and network inference problems in S-system models, Proceedings of the International Conference on Molecular Systems Biology 2008 (ICMSB ’08)
[285] Zuniga, P. C. C., An ant colony optimization for the network inference and parameter estimation of S-systems, Proceedings of the 3rd International Conference on BioMedical Engineering and Informatics (BMEI ’10) · doi:10.1109/BMEI.2010.5639727
[286] Gonzalez, O. R.; Küper, C.; Jung, K.; Naval, P. C.; Mendoza, E., Parameter estimation using simulated annealing for S-system models of biochemical networks, Bioinformatics, 23, 4, 480-486, (2007) · doi:10.1093/bioinformatics/btl522
[287] Naval, P. C.; Gonzalez, O. R.; Mendoza, E.; Sison, L. G., Heuristic parameter estimation methods for S-system models of biochemical networks, Proceedings of the 2nd Humanoid, Nanotechnology, Information, Communication and Control, Environment and Management, IEEE-Philippine Section
[288] Sayol, J.; Nolle, L.; Schaefer, G.; Nakashima, T., Comparison of simulated annealing and SASS for parameter estimation of biochemical networks, Proceedings of the IEEE Congress on Evolutionary Computation (CEC ’08) · doi:10.1109/CEC.2008.4631280
[289] Yeh, W. C.; Hsieh, T. J., Artificial bee colony algorithm-neural networks for S-system models of biochemical networks approximation, Neural Computing and Applications, 21, 365-375, (2012) · doi:10.1007/s00521-010-0435-z
[290] del Rosario, R. C. H.; Echavez, M. T.; de Paz, M. T., Madman: a benchmarking framework for parameter estimation in biochemical systems theory models, Proceedings of the International Conference on Molecular Systems Biology (ICMSB ’08)
[291] McKinney, B. A.; Tian, D., Grammatical immune system evolution for reverse engineering nonlinear dynamic Bayesian models, Cancer Informatics, 6, 433-447, (2008)
[292] Lee, W. P.; Yang, K. C., A clustering-based approach for inferring recurrent neural networks as gene regulatory networks, Neurocomputing, 71, 4-6, 600-610, (2008) · doi:10.1016/j.neucom.2007.07.023
[293] Johnson, T.; Voit, E. O., Estimating parameters of S-systems, Canonical Nonlinear Modeling: S-System Approach to Understanding Complexity, 200-216, (1991), Van Nostrand Reinhold, New York, NY, USA · Zbl 0785.92004
[294] Vinga, S.; Thomaseth, K.; Lemos, J. M.; Neves, A. R.; Santos, H.; Freitas, A. T., Structural analysis of metabolic networks: a case study on lactococcus lactis, Proceedings of the 8th Portuguese Conference on Automatic Control (CONTROLO ’08), Lisbon: APCA-Associação Portuguesa de Controlo Automático
[295] Meskin, N.; Nounou, H.; Nounou, M.; Datta, A.; Dougherty, E. R., Parameter estimation of biological phenomenamodeled by S-systems: an extended Kalman filter approach, Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC ’11)
[296] Almeida, J. S.; Voit, E. O., Neural-network-based parameter estimation in S-system models of biological networks, Genome Informatics, 14, 114-123, (2003)
[297] Murata, H.; Koshino, M.; Mitamura, M.; Kimura, H., Inference of S-system models of genetic networks using product unit neural networks, Proceedings of the IEEE International Conference on Systems, Man and Cybernetics (SMC ’08) · doi:10.1109/ICSMC.2008.4811480
[298] Tucker, W.; Kutalik, Z.; Moulton, V., Estimating parameters for generalized mass action models using constraint propagation, Mathematical Biosciences, 208, 2, 607-620, (2007) · Zbl 1119.92031 · doi:10.1016/j.mbs.2006.11.009
[299] Tucker, W.; Moulton, V., Reconstructing metabolic networks using interval analysis, Proceedings of the 5th International Workshop on Algorithms in Bioinformatics (WABI ’05), Springer
[300] Tucker, W.; Moulton, V., Parameter reconstruction for biochemical networks using interval analysis, Reliable Computing, 12, 5, 389-402, (2006) · Zbl 1098.65082 · doi:10.1007/s11155-006-9009-2
[301] Kutalik, Z.; Cho, K. H.; Wolkenhauer, O., Optimal sampling time selection for parameter estimation in dynamic pathway modeling, BioSystems, 75, 1-3, 43-55, (2004) · doi:10.1016/j.biosystems.2004.03.007
[302] Kutalik, Z.; Tucker, W.; Moulton, V., S-system parameter estimation for noisy metabolic profiles using Newton-flow analysis, IET Systems Biology, 1, 3, 174-180, (2007) · doi:10.1049/iet-syb:20060064
[303] Chou, I. C.; Martens, H.; Voit, E. O., Parameter estimation in biochemical systems models with alternating regression, Theoretical Biology and Medical Modelling, 3, article 25, (2006) · doi:10.1186/1742-4682-3-25
[304] Chou, I. C.; Martens, H.; Voit, E. O., Parameter estimation of S-distributions with alternating regression, Statistics and Operations Research transactions, 31, 1, 55-74, (2007) · Zbl 1274.62437
[305] Mu, L., Parameter estimation methods for biological systems [M.S. thesis], (2010), University of Saskatchewan
[306] Tian, L. P.; Mu, L.; Wu, F. X., Alternating constraint least squares parameter estimation for S-system models of biological networks, Proceedings of the 4th International Conference on Bioinformatics and Biomedical Engineering (iCBBE ’10) · doi:10.1109/ICBBE.2010.5516917
[307] Lall, R.; Rutes, A.; Santos, H.; Almeida, J. S.; Voit, E. O., A new approach to parameter estimation using S-systems: modeling the glycolytic pathway of lactococcus lactis, Proceedings of the 4th Georgia Tech-UGA Conference on Bioinformatics
[308] Lall, R.; Voit, E. O., Parameter estimation in modulated, unbranched reaction chains within biochemical systems, Computational Biology and Chemistry, 29, 5, 309-318, (2005) · Zbl 1087.92027 · doi:10.1016/j.compbiolchem.2005.08.001
[309] Chen, S. F.; Juang, Y. L.; Chou, W. K.; Lai, J. M.; Huang, C. Y. F.; Kao, C. Y.; Wang, F. S., Inferring a transcriptional regulatory network of the cytokinesis-related genes by network component analysis, BMC Systems Biology, 3, article 110, (2009) · doi:10.1186/1752-0509-3-110
[310] 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, Industrial and Engineering Chemistry Research, 40, 13, 2876-2885, (2001)
[311] Tsai, K. Y.; Wang, F. S., Evolutionary optimization with data collocation for reverse engineering of biological networks, Bioinformatics, 21, 7, 1180-1188, (2005) · doi:10.1093/bioinformatics/bti099
[312] Wang, F. S., A modified collocation method for solving differential-algebraic equations, Applied Mathematics and Computation, 116, 3, 257-278, (2000) · Zbl 1023.65083
[313] Wang, F. S.; Liu, P.-K., Inverse problems of biochemical systems using hybrid differential evolution and data collocation, Journal of Systems and Synthetic Biology, 1, 21-38, (2010)
[314] Huang, W. H.; Yuh, C. H.; Wang, F. S., Reverse engineering for embryonic gene regulatory network in zebrafish via evolutionary optimization with data collocation, Proceedings of the 7th International Conference on Systems Biology
[315] Liu, P. K.; Wang, F. S., Inference of biochemical network models in S-system using multiobjective optimization approach, Bioinformatics, 24, 8, 1085-1092, (2008) · doi:10.1093/bioinformatics/btn075
[316] Liu, P. K.; Wang, F. S., Inverse problems of biological systems using multi-objective optimization, Journal of the Chinese Institute of Chemical Engineers, 39, 5, 399-406, (2008) · doi:10.1016/j.jcice.2008.05.001
[317] Wu, S. J.; Wu, C. T.; Chang, J. Y., Fuzzy-based self-interactive multi-objective evolution optimization for reverse engineering of biological networks, IEEE Transactions on Fuzzy Systems, 20, 5, 865-882, (2012)
[318] Wu, W.-H.; Wang, F. S.; Chang, M.-S., Multi-objective optimization of enzyme manipulations in metabolic networks considering resilience effects, BMC Systems Biology, 5, article 145, (2011)
[319] Polisetty, P. K.; Voit, E. O.; Gatzke, E. P., Identification of metabolic system parameters using global optimization methods, Theoretical Biology and Medical Modelling, 3, article 4, (2006) · doi:10.1186/1742-4682-3-4
[320] Pozo, C.; Guillén-Gosálbez, G.; Sorribas, A.; Jiménez, L., A spatial branch-and-bound framework for the global optimization of kinetic models of metabolic networks, Industrial and Engineering Chemistry Research, 50, 9, 5225-5238, (2011) · doi:10.1021/ie101368k
[321] Ando, S.; Sakamoto, E.; Iba, H., Evolutionary modeling and inference of gene network, Information Sciences, 145, 3-4, 237-259, (2002) · doi:10.1016/S0020-0255(02)00235-9
[322] Yin, W.; Voit, E. O., Function and design of the nox1 system in vascular smooth muscle cells
[323] Lee, Y.; Chen, F.; Gallego-Giraldo, L.; Dixon, R. A.; Voit, E. O., Integrative analysis of transgenic alfalfa (medicago sativa L.) suggests new metabolic control mechanisms for monolignol biosynthesis, PLoS Computational Biology, 7, 5, (2011) · doi:10.1371/journal.pcbi.1002047
[324] 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 Transactions on Computational Biology and Bioinformatics, 4, 4, 648-660, (2007) · doi:10.1109/tcbb.2007.1051
[325] Jia, G.; Stephanopoulos, G. N.; Gunawan, R., Parameter estimation of kinetic models from metabolic profiles: two-phase dynamic decoupling method, Bioinformatics, 27, 14, 1964-1970, (2011) · doi:10.1093/bioinformatics/btr293
[326] Wu, F. X.; Mu, L., Separable parameter estimation method for nonlinear biological systems, Proceedings of the 3rd International Conference on Bioinformatics and Biomedical Engineering (iCBBE ’09) · doi:10.1109/ICBBE.2009.5163379
[327] Hecker, M.; Lambeck, S.; Toepfer, S.; van Someren, E.; Guthke, R., Gene regulatory network inference: data integration in dynamic models-A review, BioSystems, 96, 1, 86-103, (2009) · doi:10.1016/j.biosystems.2008.12.004
[328] Mao, F.; Wu, H.; Dam, P.; Chou, I.-C.; Voit, E. O.; Xu, Y.; Xu, Y.; Gogarten, J. P., Prediction of biological pathways through data mining and information fusion, Computational Methods for Understanding Bacterial and Archaeal Genomes, 7, (2008), Imperial College Press, London, UK
[329] 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, 17, 3221-3235, (2004) · doi:10.1093/bioinformatics/bth389
[330] Thomas, R.; Paredes, C. J.; Mehrotra, S.; Hatzimanikatis, V.; Papoutsakis, E. T., A model-based optimization framework for the inference of regulatory interactions using time-course DNA microarray expression data, BMC Bioinformatics, 8, article 228, (2007) · doi:10.1186/1471-2105-8-228
[331] Lecca, P.; Palmisano, A.; Ihekwaba, A.; Priami, C., Calibration of dynamic models of biological systems with kinfer, European Biophysics Journal, 39, 6, 1019-1039, (2010) · doi:10.1007/s00249-009-0520-3
[332] Ko, C. L.; Voit, E. O.; Wang, F. S., Estimating parameters for generalized mass action models with connectivity information, BMC Bioinformatics, 10, article 140, (2009) · doi:10.1186/1471-2105-10-140
[333] Kresnowati, M. T. A. P.; Van Winden, W. A.; Heijnen, J. J., Determination of elasticities, concentration and flux control coefficients from transient metabolite data using linlog kinetics, Metabolic Engineering, 7, 2, 142-153, (2005) · doi:10.1016/j.ymben.2004.12.002
[334] Calçada, D.; Vinga, S.; Freitas, A. T.; Oliveira, A. L., Quantitative modeling of the saccharomyces cerevisiae FLR1 regulatory network using an S-system formalism, Journal of Bioinformatics and Computational Biology, 9, 613-630, (2011)
[335] Seatzu, C., A parameter estimation method for a special class of systems of ordinary differential equations, Proceedings of the 7th Mediterranean Conference on Control and Automation (MED ’99)
[336] Seatzu, C., A Fitting based method for parameter estimation in S-systems, Dynamic Systems and Applications, 9, 77-98, (2000) · Zbl 1158.65329
[337] Vilela, M.; Borges, C. C. H.; Vinga, S.; Vasconcelos, A. T. R.; Santos, H.; Voit, E. O.; Almeida, J. S., Automated smoother for the numerical decoupling of dynamics models, BMC Bioinformatics, 8, article 305, (2007) · doi:10.1186/1471-2105-8-305
[338] Vilela, M.; Chou, I. C.; Vinga, S.; Vasconcelos, A. T. R.; Voit, E. O.; Almeida, J. S., Parameter optimization in S-system models, BMC Systems Biology, 2, article 35, (2008) · doi:10.1186/1752-0509-2-35
[339] Wang, H.; Glover, J. E.; Qian, L., A comparative study of the time-series data for inference of gene regulatory networks using B-spline, Proceedings of the IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB ’10) · doi:10.1109/CIBCB.2010.5510596
[340] Nounou, M. N.; Nounou, H. N.; Meskin, N.; Datta, A.; Dougherty, E. R., Multiscale denoising of biological data: A comparative analysis, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 9, 1539-1544, (2012)
[341] Veflingstad, S. R.; Almeida, J.; Voit, E. O., Priming nonlinear searches for pathway identification, Theoretical Biology and Medical Modelling, 1, article 8, (2004) · doi:10.1186/1742-4682-1-8
[342] Srinath, S.; Gunawan, R., Parameter identifiability of power-law biochemical system models, Journal of Biotechnology, 149, 3, 132-140, (2010) · doi:10.1016/j.jbiotec.2010.02.019
[343] 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 Computational Biology, 3, 10, 1871-1878, (2007) · doi:10.1371/journal.pcbi.0030189
[344] Vilela, M.; Vinga, S.; Maia, M. A. G. M.; Voit, E. O.; Almeida, J. S., Identification of neutral biochemical network models from time series data, BMC Systems Biology, 3, article 47, (2009) · doi:10.1186/1752-0509-3-47
[345] Hatzimanikatis, V.; Floudas, C. A.; Bailey, J. E., Optimization of regulatory architectures in metabolic reaction networks, Biotechnology and Bioengineering, 52, 485-500, (1996)
[346] Hatzimanikatis, V.; Floudas, C. A.; Bailey, J. E., Analysis and design of metabolic reaction networks via mixed-integer linear optimization, AIChE Journal, 42, 5, 1277-1290, (1996)
[347] Khoury, M.; Guerin, F.; Coghill, G. M., Learning dynamic models of compartment systems by combining symbolic regression with fuzzy vector envisionment, Proceedings of the 9th Annual Genetic and Evolutionary Computation Conference (GECCO ’07) · doi:10.1145/1274000.1274050
[348] Spieth, C.; Streichert, F.; Speer, N.; Zell, A., Optimizing topology and parameters of gene regulatory tetwork models from time-series experiments, Proceedings of the Genetic and Evolutionary Computation (GECCO ’04)
[349] Spieth, C.; Streichert, F.; Speer, N.; Zell, A., A memetic inference method for gene regulatory networks based on S-systems, Proceedings of the Congress on Evolutionary Computation (CEC ’04)
[350] Spieth, C.; Streichert, F.; Speer, N.; Zell, A., Iteratively inferring gene regulatory networks with virtual knockout experiments, Proceedings of the 2nd European Workshop on Evolutionary Bioinformatics
[351] Spieth, C.; Streichert, F.; Speer, N.; Zell, A., Utilizing an island model for EA to preserve solution diversity for inferring gene regulatory networks, Proceedings of the Congress on Evolutionary Computation (CEC ’04)
[352] Spieth, C.; Streichelt, F.; Speer, N.; Zell, A., Multi-objective model optimization for inferring gene regulatory networks, Proceedings of the 3rd International Conference on Evolutionary Multi-Criterion Optimization (EMO ’05) · Zbl 1109.68636
[353] Spieth, C.; Streichert, F.; Supper, J.; Speer, N.; Zell, A., Feedback memetic algorithms for modeling gene regulatory networks, Proceedings of the IEEE Symposium on Computational Intelligence in Bioinformatics and Computational Biology (CIBCB ’05)
[354] Chowdhury, A. R.; Chetty, M.; Vinh, N. X., Adaptive regulatory genes cardinality for reconstructing genetic networks, Proceedings of the IEEE Congress on Evolutionary Computation (CEC ’12)
[355] Galbraith, S. J.; Tran, L. M.; Liao, J. C., Transcriptome network component analysis with limited microarray data, Bioinformatics, 22, 15, 1886-1894, (2006) · doi:10.1093/bioinformatics/btl279
[356] Liu, L. Z.; Wu, F. X.; Han, L. L.; Zhang, W. J., Structure identification and parameter estimation of biological s-systems, Proceedings of the IEEE International Conference on Bioinformatics and Biomedicine (BIBM 2’010) · doi:10.1109/BIBM.2010.5706586
[357] 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 Proceedings, 153, 4, 286-298, (2006) · doi:10.1049/ip-syb:20050087
[358] Srividhya, J.; Crampin, E. J.; McSharry, P. E.; Schnell, S., Reconstructing biochemical pathways from time course data, Proteomics, 7, 6, 828-838, (2007) · doi:10.1002/pmic.200600428
[359] Horne, S. J.; Searson, D. P.; Willis, M. J.; Wright, A. R., Modelling of chemical processes using S-systems, Proceedings of the 11th APCChe Congress
[360] Searson, D. P.; Willis, M. J.; Horne, S. J.; Wright, A. R., Inference of chemical reaction networks using hybrid S-system models, Chemical Product and Process Modeling, 2, 1, article 10, (2007)
[361] Kattas, G. D.; Gennemark, P.; Wedelin, D., Structural identification of GMA models: algorithm and model comparison, Proceedings of the 8th International Conference on Computational Methods in Systems Biology (CMSB ’10) · doi:10.1145/1839764.1839777
[362] Goel, G.; Chou, I. C.; Voit, E. O., System estimation from metabolic time-series data, Bioinformatics, 24, 21, 2505-2511, (2008) · doi:10.1093/bioinformatics/btn470
[363] Voit, E. O.; Goel, G.; Chou, I. C.; Fonseca, L. L., Estimation of metabolic pathway systems from different data sources, IET Systems Biology, 3, 6, 513-522, (2009) · doi:10.1049/iet-syb.2008.0180
[364] Chou, I.-C.; Voit, E. O., Estimation of dynamic flux profiles from metabolic time series data, BMC Systems Biology, 6, article 84, (2012)
[365] Dolatshahi, S.; Voit, E., Identifiation of dynamic fluxes from metabolic time series data
[366] Voit, E. O., Characterizability of metabolic pathway systems from time series data · Zbl 1308.92035
[367] Ndukum, J.; Fonseca, L. L.; Santos, H.; Voit, E. O.; Datta, S., Statistical inference methods for sparse biological time series data, BMC Systems Biology, 5, article 57, (2011) · doi:10.1186/1752-0509-5-57
[368] Kawagoe, K.; Bernecker, T.; Kriegel, H. P.; Renz, M.; Zimek, A.; Züfle, A., Similarity search in time series of dynamical model-based systems, Proceedings of the 21st International Workshop on Database and Expert Systems Applications (DEXA ’10) · doi:10.1109/DEXA.2010.41
[369] Lages, N. F.; Cordeiro, C.; Sousa Silva, M.; Ponces Freire, A.; Ferreira, A. E., Optimization of time-course experiments for kinetic model discrimination, PloS ONE, 7, (2012)
[370] Ni, T. C.; Savageau, M. A., Model assessment and refinement using strategies from biochemical systems theory: application to metabolism in human red blood cells, Journal of Theoretical Biology, 179, 4, 329-354, (1996) · doi:10.1006/jtbi.1996.0072
[371] Ni, T. C.; Savageau, M. A., Application of biochemical systems theory to metabolism in human red blood cells: signal propagation and accuracy of representation, Journal of Biological Chemistry, 271, 14, 7927-7941, (1996)
[372] Ni, T.-C.; Savageau, M. A.; Yamakawa, T.; Matsumoto, G., Scanning algorithm for refinement of complex biological models, Methodologies for the Conception, Design, and Application of Intelligent Systems, 147-150, (1996), World Scientific, Singapore
[373] Alves, R.; Herrero, E.; Sorribas, A., Predictive reconstruction of the mitochondrial iron-sulfur cluster assembly metabolism—II—role of glutaredoxin grx5, Proteins: Structure, Function and Genetics, 57, 3, 481-492, (2004) · doi:10.1002/prot.20228
[374] 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-arh1), Proteins, 56, 2, 354-366, (2004) · doi:10.1002/prot.20110
[375] Němcová, J., Rational systems in control and system theory [Doctoral dissertation], (2009), Vrije Universiteit Amsterdam
[376] Němcová, J., Structural identifiability of polynomial and rational systems, Mathematical Biosciences, 223, 2, 83-96, (2010) · Zbl 1183.92004 · doi:10.1016/j.mbs.2009.11.002
[377] Shiota, M., Nash Manifolds, (1987), Springer, New York, NY, USA · Zbl 0629.58002
[378] Papachristodoulou, A.; Recht, B., Determining interconnections in chemical reaction networks, Proceedings of the American Control Conference (ACC ’07) · doi:10.1109/ACC.2007.4283084
[379] Voit, E. O., A systems-theoretical framework for health and disease: inflammation and preconditioning from an abstract modeling point of view, Mathematical Biosciences, 217, 1, 11-18, (2009) · Zbl 1158.92029 · doi:10.1016/j.mbs.2008.09.005
[380] Lee, Y.; Chen, P. W.; Voit, E. O., Analysis of operating principles with S-system models, Mathematical Biosciences, 231, 1, 49-60, (2011) · Zbl 1214.92021 · doi:10.1016/j.mbs.2011.03.001
[381] Tournier, L., Approximation of dynamical systems using S-systems theory: application to biological systems, Proceedings of the International Symposium on Symbolic and Algebraic Computation · Zbl 1360.65202
[382] Hasegawa, T.; Takatani, H.; Yoshimura, J., Application of power-law formalism method to equilibrium computation of vapor growth epitaxy, Journal of Chemical Engineering of Japan, 32, 4, 506-513, (1999)
[383] Hasegawa, T.; Shiraishi, F.; Nagasue, H., Numerical tests for usefulness of power-law formalism method in parameter optimization problem of immobilized enzyme reaction, Journal of Chemical Engineering of Japan, 33, 2, 197-204, (2000)
[384] Lin, C. L.; Liu, Y. W.; Chuang, C. H., Control design for signal transduction networks, Bioinformatics and Biology Insights, 2009, 3, 1-14, (2009)
[385] Savageau, M. A., Alternative designs for a genetic switch: analysis of switching times using the piecewise power-law representation, Mathematical Biosciences, 180, 237-253, (2002) · Zbl 1020.92022 · doi:10.1016/S0025-5564(02)00113-X
[386] Voit, E. O., Smooth bistable S-systems, IEE Proceedings Systems Biology, 152, 4, 207-213, (2005) · doi:10.1049/ip-syb:20050063
[387] Igoshin, O. A.; Price, C. W.; Savageau, M. A., Signalling network with a bistable hysteretic switch controls developmental activation of the σF transcription factor in bacillus subtilis, Molecular Microbiology, 61, 1, 165-184, (2006) · doi:10.1111/j.1365-2958.2006.05212.x
[388] Igoshin, O. A.; Brody, M. S.; Price, C. W.; Savageau, M. A., Distinctive topologies of partner-switching signaling networks correlate with their physiological roles, Journal of Molecular Biology, 369, 5, 1333-1352, (2007) · doi:10.1016/j.jmb.2007.04.021
[389] Igoshin, O. A.; Alves, R.; Savageau, M. A., Hysteretic and graded responses in bacterial two-component signal transduction, Molecular Microbiology, 68, 5, 1196-1215, (2008) · doi:10.1111/j.1365-2958.2008.06221.x
[390] Salvado, B.; Vilaprinyo, E.; Karathia, H.; Sorribas, A.; Alves, R., Two component systems: physiological effect of a third component, PloS ONE, 7, (2012)
[391] Savageau, M. A., Parameter sensitivity as a criterion for evaluating and comparing the performance of biochemical systems, Nature, 229, 5286, 542-544, (1971) · doi:10.1038/229542a0
[392] Cascante, M.; Franco, R.; Canela, E.; Voit, E. O., Sensitivity analysis: a common foundation of theories for the quantitative study of metabolic control, Canonical Nonlinear Modeling: S-System Approach to Understanding Complexity, 76-89, (1991), Van Nostrand Reinhold, New York, NY, USA · Zbl 0785.92004
[393] Salvador, A.; Yamakawa, T.; Matsumoto, G., Steady-state synergisms in kinetic models: estimation and applications, Methodologies for the Conception, Design, and Application of Intelligent Systems, 143-146, (1996), World Scientific, Singapore
[394] Salvador, A., Development of methodology and software for analysis of kinetic models of metabolic processes. Application to the mitochondrial metabolism of lipid hydroperoxides [Doctoral thesis], (1997), Lisbon, Portugal
[395] Salvador, A., Synergism analysis of biochemical systems—II. tensor formulation and treatment of stoichiometric constraints, Mathematical Biosciences, 163, 2, 131-158, (2000) · Zbl 0946.92007 · doi:10.1016/S0025-5564(99)00057-7
[396] Salvador, A., Synergism analysis of biochemical systems—I. conceptual framework, Mathematical Biosciences, 163, 2, 105-129, (2000) · Zbl 0944.92015 · doi:10.1016/S0025-5564(99)00056-5
[397] Guebel, D. V., Canonical sensitivities: a useful tool to deal with large perturbations in metabolic network modeling, In Silico Biology, 4, 2, 163-182, (2004)
[398] Chen, B. S.; Wang, Y. C.; Wu, W. S.; Li, W. H., A new measure of the robustness of biochemical networks, Bioinformatics, 21, 11, 2698-2705, (2005) · doi:10.1093/bioinformatics/bti348
[399] Chen, B. S.; Wang, Y. C., On the attenuation and amplification of molecular noise in genetic regulatory netwoks, BMC Bioinformatics, 7, article 52, (2006) · doi:10.1186/1471-2105-7-52
[400] Chen, B. S.; Wu, W. S., Robust filtering circuit design for stochastic gene networks under intrinsic and extrinsic molecular noises, Mathematical Biosciences, 211, 2, 342-355, (2008) · Zbl 1130.92023 · doi:10.1016/j.mbs.2007.11.002
[401] Chen, B. S.; Wu, W. S.; Wang, Y. C.; Li, W. H., On the robust circuit design schemes of biochemical networks: steady-state approach, IEEE Transactions on Biomedical Circuits and Systems, 1, 2, 91-104, (2007) · doi:10.1109/TBCAS.2007.907060
[402] Chen, B.-S.; Wu, W.-S.; Wu, W.-S.; Li, W.-H., On the adaptive design rules of biochemical networks in evolution, Evolutionary Bioinformatics, 3, 27-29, (2007)
[403] Ma, L.; Iglesias, P. A., Quantifying robustness of biochemical network models, BMC Bioinformatics, 3, article 38, (2002) · doi:10.1186/1471-2105-3-38
[404] Chen, B. S.; Chang, Y. T.; Wang, Y. C., Robust \(H_\infty\)-stabilization design in gene networks under stochastic molecular noises: fuzzy-interpolation approach, IEEE Transactions on Systems, Man, and Cybernetics, Part B, 38, 1, 25-42, (2008) · doi:10.1109/TSMCB.2007.906975
[405] Chen, B. S.; Li, C. W., On the interplay between entropy and robustness of gene regulatory networks, Entropy, 12, 5, 1071-1101, (2010) · Zbl 1229.92037 · doi:10.3390/e12051071
[406] Shi, M.-G.; Lyu, M. R.; Lok, T.-M.; Huang, D.-S., Maximal-robustness-minimal-fragility controller: a compromise between robustness and fragility of biochemical networks, Proceedings of the Advanced Intelligent Computing Theories and Applications, Springer
[407] Wu, W. H.; Wang, F. S.; Chang, M. S., Dynamic sensitivity analysis of biological systems, BMC Bioinformatics, 9, 12, article S17, (2008) · doi:10.1186/1471-2105-9-S12-S17
[408] Shiraishi, F.; Hatoh, Y., Dynamic sensitivities in chaotic dynamical systems, Applied Mathematics and Computation, 186, 2, 1347-1359, (2007) · Zbl 1117.65167 · doi:10.1016/j.amc.2006.07.141
[409] Sriyudthsak, K.; Shiraishi, F., Identification of bottleneck enzymes with negative dynamic sensitivities: ethanol fermentation systems as case studies, Journal of Biotechnology, 149, 3, 191-200, (2010) · doi:10.1016/j.jbiotec.2010.01.015
[410] Shiraishi, F.; Suzuki, Y., Method for determination of the main bottleneck enzyme in a metabolic reaction network by dynamic sensitivity analysis, Industrial and Engineering Chemistry Research, 48, 1, 415-423, (2009) · doi:10.1021/ie8005963
[411] Sriyudthsak, K.; Shiraishi, F., Instantaneous and overall indicators for determination of bottleneck ranking in metabolic reaction networks, Industrial and Engineering Chemistry Research, 49, 5, 2122-2129, (2010) · doi:10.1021/ie901531d
[412] Chen, M. L.; Wang, F. S., Dynamic sensitivity analysis of oscillating biochemical systems using modified collocation method, Journal of the Taiwan Institute of Chemical Engineers, 40, 4, 371-379, (2009) · doi:10.1016/j.jtice.2009.01.004
[413] Horner, J. K., Sensitivity of blood serum uric acid concentration in HGPRT deficiency to initial conditions of the purine metabolism pathway, Proceedings of the International Conference on Scientific Computing, CSREA Press
[414] Drengstig, T.; Kjosmoen, T.; Ruoff, P., On the relationship between sensitivity coeffcients and transfer functions of reaction kinetic networks, Journal of Physical Chemistry B, 115, 19, 6272-6278, (2011) · doi:10.1021/jp200578e
[415] Weinberger, V.; Voit, E. O., Symbolic analysis of S-systems with MACSYMA, Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity, 110-132, (1991), Van Nostrand Reinhold, New York, NY, USA · Zbl 0785.92004
[416] Hopf, E., Abzweigung einer periodischen Lösung von einer stationären Lösung eines differentialsystems, Berichte der Mathematisch-Physikalischen Klasse der Sächsischen Akademie, 94, 1-22, (1942) · Zbl 0063.02065
[417] Wiggins, S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, (1990), Springer, New York, NY, USA · Zbl 0701.58001
[418] Lewis, D. C.; Voit, E. O., A qualitative analysis of S-systems: Hopf bifurcations, Canonical Nonlinear Modeling: S-System Approach to Understanding Complexity, 304-344, (1991), Van Nostrand Reinhold, New York, NY, USA · Zbl 0785.92004
[419] Yin, W.; Voit, E. O., Construction and customization of stable oscillation models in biology, Journal of Biological Systems, 16, 4, 463-478, (2008) · Zbl 1369.92009 · doi:10.1142/S0218339008002502
[420] Tyson, J. J., Some further studies of nonlinear oscillations in chemical systems, The Journal of Chemical Physics, 58, 9, 3919-3930, (1973)
[421] Morrison, M. S.; Voit, E., Recasting as a modeling tool, Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity, 258-277, (1991), Van Nostrand Reinhold, New York, NY, USA · Zbl 0785.92004
[422] Nikolov, S.; Lai, X.; Liebal, U. W.; Wolkenhauer, O.; Vera, J., Integration of sensitivity and bifurcation analysis to detect critical processes in a model combining signalling and cell population dynamics, International Journal of Systems Science, 41, 1, 81-105, (2010) · Zbl 1291.93028 · doi:10.1080/00207720903147746
[423] Voit, E. O.; Savageau, M. A., Analytical solutions to a generalized growth equation, Journal of Mathematical Analysis and Applications, 103, 2, 380-386, (1984) · Zbl 0588.92001
[424] Voit, E. O., Hierarchical Monte Carlo modeling with S-distributions: concepts and illustrative analysis of Mercury contamination in King mackerel, Environment International, 21, 5, 627-635, (1995) · doi:10.1016/0160-4120(95)00067-U
[425] Cascante, M.; Curto, R.; Sorribas, A., Testing the robustness of the steady-state characteristics of a metabolic pathway: parameter sensitivity as a basic feature for model validation, Journal of Biological Systems, 3, 105-113, (1995)
[426] 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, 7024, 425-430, (2005) · doi:10.1038/nature03232
[427] Mishra, B., A symbolic approach to modeling cellular behavior, Proceedings of the High Performance Computing (HIPC ’02), Springer · Zbl 1032.92502
[428] Mishra, B.; Cherepinsky, V.; Silver, N.; Casey, W.; Piazza, C.; Simeoni, M.; Barbano, P.; Spivak, M.; Feng, J.; Gill, O.; Venkatesh, M.; Daruwala, R. S.; Cheng, F.; Sun, B.; Ioniata, I.; Anantharaman, T.; Hubbard, E. J. A.; Pnueli, A.; Harel, D.; Chandru, V.; Hariharan, R.; Wigler, M.; Zhou, Y.; Park, F.; Lin, S. C.; Lazebnik, Y.; Winkler, F.; Cantor, C. R.; Carbone, A.; Gromov, M.; Ugel, N.; Policriti, A.; Antoniotti, M.; Paxia, S.; Rejali, M.; Rudra, A., A sense of life: computational and experimental investigations with models of biochemical and evolutionary processes, OMICS, 7, 3, 253-268, (2003)
[429] Antoniotti, M.; Policriti, A.; Ugel, N.; Mishra, B., XS-systems: extended S-systems and algebraic differential automata for modeling cellular behavior, Proceedings of the High performane computing (HIPC ’02) · Zbl 1032.68659
[430] Antoniotti, M.; Park, F.; Policriti, A.; Ugel, N.; Mishra, B., Foundations of a query and simulation system for the modeling of biochemical and biological processes, Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing, 116-127, (2003) · Zbl 1219.92018
[431] Antoniotti, M.; Policriti, A.; Ugel, N.; Mishra, B., Model building and model checking for biochemical processes, Cell Biochemistry and Biophysics, 38, 3, 271-286, (2003) · doi:10.1385/CBB:38:3:271
[432] Antoniotti, M.; Piazza, C.; Policriti, A.; Simeoni, M.; Mishra, B., Taming the complexity of biochemical models through bisimulation and collapsing: theory and practice, Theoretical Computer Science, 325, 1, 45-67, (2004) · Zbl 1070.68059 · doi:10.1016/j.tcs.2004.03.064
[433] Mishra, B.; Antoniotti, M.; Paxia, S.; Ugel, N.; Kriete, A.; Eils, R., Simpathica: a computational systems biology tool within the valis bioinformatics environment, Computational Systems Biology, 79-102, (2006), Elsevier Academic Press
[434] Mishra, B.; Anai, H.; Horimoto, K.; Kutsia, T., Algebraic systems biology: theses and hypotheses, Proceedings of the Algebraic Biology, Springer · Zbl 1126.92004
[435] Mishra, B., Intelligently deciphering unintelligible designs: algorithmic algebraic model checking in systems biology, Journal of the Royal Society Interface, 6, 36, 575-597, (2009) · doi:10.1098/rsif.2008.0546
[436] Antoniotti, M.; Mishra, B.; Piazza, C.; Policriti, A.; Simeoni, M., Modeling cellular behavior with hybrid automata: bisimulation and collapsing, Proceedings of the Computational Methods in Systems Biology · Zbl 1112.92300
[437] Elowitz, M. B.; Leibier, S., A synthetic oscillatory network of transcriptional regulators, Nature, 403, 6767, 335-338, (2000) · doi:10.1038/35002125
[438] Curto, R.; Voit, E. O.; Cascante, M., Analysis of abnormalities in purine metabolism leading to gout and to neurological dysfunctions in man, Biochemical Journal, 329, 3, 477-487, (1998)
[439] Curto, R.; Voit, E. O.; Sorribas, A.; Cascante, M., Validation and steady-state analysis of a power-law model of purine metabolism in man, Biochemical Journal, 324, 3, 761-775, (1997)
[440] Gentilini, R., Toward integration of systems biology formalism: the gene regulatory networks case, Genome Informatics, 16, 2, 215-224, (2005)
[441] Campagna, D.; Piazza, C., Hybrid automata in systems biology: how far can we go?, Electronic Notes in Theoretical Computer Science, 229, 1, 93-108, (2009) · Zbl 1283.92035 · doi:10.1016/j.entcs.2009.02.007
[442] Savageau, M. A., Comparison of classical and autogenous systems of regulation in inducible operons, Nature, 252, 5484, 546-549, (1974)
[443] Savageau, M. A.; Goldberger, R. F.; Berg, P.; Schimke, R. T.; Moldave, K.; Leder, P.; Hood, L. E., Autogenous and classical regulation of gene expression: a general theory and experimental evidence, Biological Regulation and Development, 1, 57-108, (1979), Plenum, New York, NY, USA
[444] Savageau, M. A., Genetic regulatory mechanisms and the ecological niche of Escherichia coli, Proceedings of the National Academy of Sciences of the United States of America, 71, 6, 2453-2455, (1974)
[445] Savageau, M. A., Significance of autogenously regulated and constitutive synthesis of regulatory proteins in repressible biosynthetic systems, Nature, 258, 5532, 208-214, (1975)
[446] Savageau, M. A., Design of molecular control mechanisms and the demand for gene expression, Proceedings of the National Academy of Sciences of the United States of America, 74, 12, 5647-5651, (1977)
[447] Savageau, M. A., Escherichia coli habitats, cell types, and molecular mechanisms of gene control, American Naturalist, 122, 6, 732-744, (1983) · doi:10.1086/284168
[448] Savageau, M. A.; Blanch, H. W.; Papoutsakis, E. T.; Stephanopoulos, G. N., Models of gene function: general methods of kinetic analysis and specific ecological correlates, Foundations of Biochemical Engineering Kinetics and Thermodynamics in Biological Systems, 3-25, (1983), American Chemical Society, Washington, DC, USA
[449] Savageau, M. A.; Sands, P. J.; Voit, E. O., Completely uncoupled and perfectly coupled circuits for inducible gene regulation, Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity, 145-165, (1991), Van Nostrand Reinhold, New York, NY, USA · Zbl 0785.92004
[450] Savageau, M. A., Rules for the evolution of gene circuitry, Proceedings of the Pacific Symposium on Biocomputing
[451] Savageau, M. A., Design of gene circuitry by natural selection: analysis of the lactose catabolic system in Escherichia coli, Biochemical Society Transactions, 27, 2, 264-270, (1999)
[452] Savageau, M. A., Regulation of gene expression: new theory and the experimental evidence, Zagadnienia Biofizyki Wsopolczesnej, 4, 129-143, (1979)
[453] Savageau, M. A., Design of the lac gene circuit revisited, Mathematical Biosciences, 231, 1, 19-38, (2011) · Zbl 1214.92026 · doi:10.1016/j.mbs.2011.03.008
[454] Savageau, M. A.; Sorribas, A., Constraints among molecular and systemic properties: implications for physiological genetics, Journal of Theoretical Biology, 141, 1, 93-115, (1989)
[455] Hlavecek, W. S.; Savageau, M. A., Subunit structure of regulator proteins influences the design of gene circuitry: analysis of perfectly coupled and completely uncoupled circuits, Journal of Molecular Biology, 248, 4, 739-755, (1995) · doi:10.1006/jmbi.1995.0257
[456] Hlavacek, W. S.; Savageau, M. A., Rules for coupled expression of regulator and effector genes in inducible circuits, Journal of Molecular Biology, 255, 1, 121-139, (1996) · doi:10.1006/jmbi.1996.0011
[457] Hlavacek, W. S.; Savageau, M. A., Completely uncoupled and perfectly coupled gene expression in repressible systems, Journal of Molecular Biology, 266, 3, 538-558, (1997) · doi:10.1006/jmbi.1996.0811
[458] Hlavacek, W. S.; Savageau, M. A.; Yamakawa, T.; Matsumoto, G., Comparison of completely uncoupled and perfectly coupled gene expression in repressible biosynthetic systems, Methodologies for the Conception, Design, amd Application of Intelligent Systems, 1, 167-170, (1996), World Scientific, Singapore
[459] Hlavacek, W. S.; Savageau, M. A., Method for determining natural design principles of biological control circuits, Journal of Intelligent and Fuzzy Systems, 6, 1, 147-160, (1998)
[460] Wall, M. E.; Hlavacek, W. S.; Savageau, M. A., Design principles for regulator gene expression in a repressible gene circuit, Journal of Molecular Biology, 332, 4, 861-876, (2003) · doi:10.1016/S0022-2836(03)00948-3
[461] Wall, M. E.; Hlavacek, W. S.; Savageau, M. A., Design of gene circuits: lessons from bacteria, Nature Reviews Genetics, 5, 1, 34-42, (2004) · doi:10.1038/nrg1244
[462] Irvine, D. H.; Savageau, M. A., Network regulation of the immune response: modulation of suppressor lymphocytes by alternative signals including contrasuppression, Journal of Immunology, 134, 4, 2117-2130, (1985)
[463] Irvine, D. H.; Savageau, M. A., Network regulation of the immune response: alternative control points for suppressor modulation of effector lymphocytes, Journal of Immunology, 134, 4, 2100-2116, (1985)
[464] Schwacke, J. H.; Voit, E. O., Improved methods for the mathematically controlled comparison of biochemical systems, Theoretical Biology and Medical Modelling, 1, article 1, (2004) · doi:10.1186/1742-4682-1-1
[465] Savageau, M. A., Regulation of differentiated cell-specific functions, Proceedings of the National Academy of Sciences of the United States of America, 80, 5 I, 1411-1415, (1983)
[466] 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, 5, 597-607, (2003) · doi:10.1016/S0092-8674(03)00346-5
[467] Savageau, M. A., Optimal design of feedback control by inhibition. steady state considerations, Journal of Molecular Evolution, 4, 2, 139-156, (1974)
[468] Savageau, M. A., Optimal design of feedback control by inhibition: dynamic considerations, Journal of Molecular Evolution, 5, 3, 199-222, (1975)
[469] Savageau, M. A., Feedforward inhibition in biosynthetic pathways: inhibition of the aminoacyl-trna synthetase by the penultimate product, Journal of Theoretical Biology, 77, 4, 385-404, (1979)
[470] Savageau, M. A.; Jacknow, G., Feedforward inhibition in biosynthetic pathways: inhibition of the aminoacyl-trna synthetase by intermediates of the pathway, Journal of Theoretical Biology, 77, 4, 405-425, (1979)
[471] Alves, R.; Savageau, M. A., Effect of overall feedback inhibition in unbranched biosynthetic pathways, Biophysical Journal, 79, 5, 2290-2304, (2000)
[472] Alves, R.; Savageau, M. A., Systemic properties of ensembles of metabolic networks: application of graphical and statistical methods to simple unbranched pathways, Bioinformatics, 16, 6, 534-547, (2000)
[473] Alves, R.; Savageau, M. A., Comparing systemic properties of ensembles of biological networks by graphical and statistical methods, Bioinformatics, 16, 6, 527-533, (2000)
[474] Alves, R.; Savageau, M. A., Irreversibility in unbranched pathways: preferred positions based on regulatory considerations, Biophysical Journal, 80, 3, 1174-1185, (2001)
[475] Alves, R.; Savageau, M. A., Comparative analysis of prototype two-component systems with either bifunctional or monofunctional sensors: differences in molecular structure and physiological function, Molecular Microbiology, 48, 1, 25-51, (2003) · doi:10.1046/j.1365-2958.2003.03344.x
[476] Alves, R.; Savageau, M. A., Evidence of selection for low cognate amino acid bias in amino acid biosynthetic enzymes, Molecular Microbiology, 56, 4, 1017-1034, (2005) · doi:10.1111/j.1365-2958.2005.04566.x
[477] Savageau, M. A.; Voigt, H. M.; Mühlenbein, H.; Schwefel, H. P., Evolution of regulation examined with a novel strategy for comparative optimization, Evolution and Optimization, 9-30, (1990), Akademie, Berlin, Germany · Zbl 0708.92012
[478] Salvador, A.; Savageau, M. A., Quantitative evolutionary design of glucose 6-phosphate dehydrogenase expression in human erythrocytes, Proceedings of the National Academy of Sciences of the United States of America, 100, 2, 14463-14468, (2003) · doi:10.1073/pnas.2335687100
[479] Salvador, A.; Savageau, M. A., Evolution of enzymes in a series is driven by dissimilar functional demands, Proceedings of the National Academy of Sciences of the United States of America, 103, 7, 2226-2231, (2006) · doi:10.1073/pnas.0510776103
[480] Coelho, P. M. B. M.; Salvador, A.; Savageau, M. A., Quantifying global tolerance of biochemical systems: design implications for moiety-transfer cycles, PLoS Computational Biology, 5, 3, (2009) · doi:10.1371/journal.pcbi.1000319
[481] Coelho, P. M. B. M.; Salvador, A.; Savageau, M. A., Relating mutant genotype to phenotype via quantitative behavior of the NADPH redox cycle in human erythrocytes, PLoS ONE, 5, 9, (2010) · doi:10.1371/journal.pone.0013031
[482] Alves, R.; Vilaprinyo, E.; Sorribas, A.; Herrero, E., Evolution based on domain combinations: the case of glutaredoxins, BMC Evolutionary Biology, 9, 1, article 66, (2009) · doi:10.1186/1471-2148-9-66
[483] Salvado, B.; Karathia, H.; Chimenos, A. U.; Vilaprinyo, E.; Omholt, S.; Sorribas, A.; Alves, R., Methods for and results from the study of design principles in molecular systems, Mathematical Biosciences, 231, 1, 3-18, (2011) · Zbl 1214.92025 · doi:10.1016/j.mbs.2011.02.005
[484] Guillén-Gosálbez, G.; Sorribas, A., Identifying quantitative operation principles in metabolic pathways: a systematic method for searching feasible enzyme activity patterns leading to cellular adaptive responses, BMC Bioinformatics, 10, article 386, (2009) · doi:10.1186/1471-2105-10-386
[485] Martinez-Antonio, A.; Lomnitz, J. G.; Sandoval, S.; Aldana, M.; Savageau, M. A., Regulatory design governing progression of population growth phases in bacteria, PloS ONE, 7, (2012)
[486] Voit, E. O., Biochemical and genomic regulation of the trehalose cycle in yeast: review of observations and canonical model analysis, Journal of Theoretical Biology, 223, 1, 55-78, (2003) · Zbl 1464.92152 · doi:10.1016/S0022-5193(03)00072-9
[487] Lee, Y.; Escamilla-Treviño, L.; Dixon, R. A.; Voit, E. O., Functional analysis of metabolic channeling and regulation in lignin biosynthesis: a computationalapproach, PLoS Computational Biology, 8, 11
[488] Puigjaner, J.; Cascante, M.; Sorribas, A., Assessing optimal designs in metabolic pathways, Journal of Biological Systems, 3, 197-206, (1995)
[489] Zhang, Q.; Bhattacharya, S.; Andersen, M. E.; Conolly, R. B., Computational systems biology and dose-response modeling in relation to new directions in toxicity testing, Journal of Toxicology and Environmental Health Part B, 13, 2-4, 253-276, (2010) · doi:10.1080/10937404.2010.483943
[490] Alves, R.; Savageau, M. A., Extending the method of mathematically controlled comparison to include numerical comparisons, Bioinformatics, 16, 9, 786-798, (2000)
[491] Savageau, M. A., Biomedical engineering strategies in system design space, Annals of Biomedical Engineering, 39, 4, 1278-1295, (2011) · doi:10.1007/s10439-010-0220-2
[492] Savageau, M. A.; Coelho, P. M. B. M.; Fasani, R. A.; Tolla, D. A.; Salvador, A., Phenotypes and tolerances in the design space of biochemical systems, Proceedings of the National Academy of Sciences of the United States of America, 106, 16, 6435-6440, (2009) · doi:10.1073/pnas.0809869106
[493] Savageau, M. A.; Fasani, R. A., Qualitatively distinct phenotypes in the design space of biochemical systems, FEBS Letters, 583, 24, 3914-3922, (2009) · doi:10.1016/j.febslet.2009.10.073
[494] Fasani, R. A.; Savageau, M. A., Automated construction and analysis of the design space for biochemical systems, Bioinformatics, 26, 20, 2601-2609, (2010) · doi:10.1093/bioinformatics/btq479
[495] Tolla, D. A.; Savageau, M. A., Regulation of aerobic-to-anaerobic transitions by the FNR cycle in Escherichia coli, Journal of Molecular Biology, 397, 4, 893-905, (2010) · doi:10.1016/j.jmb.2010.02.015
[496] Tolla, D. A.; Savageau, M. A., Phenotypic repertoire of the FNR regulatory network in Escherichia coli, Molecular Microbiology, 79, 1, 149-165, (2011) · doi:10.1111/j.1365-2958.2010.07437.x
[497] Chen, B.-S.; Wu, W.-S., Underlying principles of natural selection in network evolution: systems biology approach, Evolutionary Bioinformatics, 3, 245-262, (2007)
[498] Wu, R.; Cao, J.; Huang, Z.; Wang, Z.; Gai, J.; Vallejos, E., Systems mapping: how to improve the genetic mapping of complex traits through design principles of biological systems, BMC Systems Biology, 5, article 84, (2011) · doi:10.1186/1752-0509-5-84
[499] Savageau, M. A., Accuracy of proofreading with zero energy cost, Journal of Theoretical Biology, 93, 1, 179-195, (1981)
[500] Savageau, M. A.; Freter, R. R., On the evolution of accuracy and cost of proofreading trna aminoacylation, Proceedings of the National Academy of Sciences of the United States of America, 76, 9, 4507-4510, (1979)
[501] Savageau, M. A.; Freter, R. R., Energy cost of proofreading to increase fidelity of transfer ribonucleic acid aminoacylation, Biochemistry, 18, 16, 3486-3493, (1979)
[502] Savageau, M. A.; Lapointe, D. S., Optimization of kinetic proofreading: a general method for derivation of the constraint relations and an exploration of a specific case, Journal of Theoretical Biology, 93, 1, 157-177, (1981)
[503] Freter, R. R.; Savageau, M. A., Proofreading systems of multiple stages for improved accuracy of biological discrimination, Journal of Theoretical Biology, 85, 1, 99-123, (1980)
[504] Okamoto, M.; Yoshii, J. J.; Hayasji, K.; Voit, E. O., GTP-dependent kinetic proofreading, Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity, 166-180, (1991), Van Nostrand Reinhold, New York, NY, USA · Zbl 0785.92004
[505] Okamoto, M.; Savageau, M. A., Integrated function of a kinetic proofreading mechanism: dynamic analysis separating the effects of speed and substrate competition on accuracy, Biochemistry, 23, 8, 1710-1715, (1984)
[506] Okamoto, M.; Savageau, M. A., Integrated function of a kinetic proofreading mechanism: steady-state analysis testing internal consistency of data obtained in vivo and in vitro and predicting parameter values, Biochemistry, 23, 8, 1701-1709, (1984)
[507] Okamoto, M.; Savageau, M. A., Integrated function of a kinetic proofreading mechanism: double-stage proofreading by isoleucyl-trna synthetase, Biochemistry, 25, 8, 1969-1975, (1986)
[508] 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, Mathematical Biosciences, 130, 1, 51-69, (1995) · Zbl 0835.92016 · doi:10.1016/0025-5564(94)00093-F
[509] Cascante, M.; Curto, R.; Sorribas, A., Comparative characterization of the fermentation pathway of saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: model validation and dynamic behavior, Mathematical Biosciences, 130, 1, 71-84, (1995) · Zbl 0835.92017 · doi:10.1016/0025-5564(94)00094-G
[510] Rodríguez-Acosta, F.; Regalado, C. M.; Torres, N. V., Non-linear optimization of biotechnological processes by stochastic algorithms. application to the maximization of the production rate of ethanol, glycerol and carbohydrates by saccharomyces cerevisiae, Journal of Biotechnology, 68, 1, 15-28, (1999) · doi:10.1016/S0168-1656(98)00178-3
[511] Torres, N. V.; Voit, E. O.; Glez-Alcón, C.; Rodríguez, F., An indirect optimization method for biochemical systems: description of method and application to the maximization of the rate of ethanol, glycerol, and carbohydrate production in saccharomyces cerevisiae, Biotechnology and Bioengineering, 55, 758-772, (1997)
[512] 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, Biotechnology and Bioengineering, 83, 3, 335-343, (2003) · doi:10.1002/bit.10676
[513] Polisetty, P. K.; Gatzke, E. P.; Voit, E. O., Yield optimization of regulated metabolic systems using deterministic branch-and-reduce methods, Biotechnology and Bioengineering, 99, 5, 1154-1169, (2008) · doi:10.1002/bit.21679
[514] Polisetty, P. K.; Voit, E. O.; Gatzke, E. P., Yield optimization of saccharomyces cerevisiae using a GMA model and a MILP-based piecewise linear relaxation method, Proceedings of the Foundations of Systems Biology in Engineering
[515] Polisetty, P. K.; Voit, E.; Gatzke, E. P., Deterministic global optimization techniques for solution of nlp and MINLP problems using piecewise linear relaxations with applications in metabolic engineering, Proceedings of the AIChE Annual Meeting and Fall Showcase
[516] Lall, R.; Donohue, T. J.; Marino, S.; Mitchell, J. C., Optimizing ethanol production selectivity, Mathematical and Computer Modelling, 53, 7-8, 1363-1373, (2011) · doi:10.1016/j.mcm.2010.01.016
[517] Chang, Y.; Sahinidis, N. V., Optimization of metabolic pathways under stability considerations, Computers and Chemical Engineering, 29, 3, 467-479, (2005) · doi:10.1016/j.compchemeng.2004.08.013
[518] Xu, G., Bi-objective optimization of biochemical systems by linear programming, Applied Mathematics and Computation, 218, 7562-7572, (2012) · Zbl 1242.92023
[519] Sendín, O. H.; Vera, J.; Torres, N. V.; Banga, J. R., Mathematical and computer modelling of dynamical systems: methods, tools and applications in engineering and related sciences, Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences, 12, 469-487, (2006) · Zbl 1126.92016
[520] Xu, G., An iterative strategy for yield optimization of metabolic pathways, Proceedings of the 4rth International Joint Conference on Computational Sciences and Optimization (CSO ’10) · doi:10.1109/CSO.2010.225
[521] Ko, C. L.; Wang, F. S.; Chao, Y. P.; Chen, T. W., S-system approach to modeling recombinant Escherichia coli growth by hybrid differential evolution with data collocation, Biochemical Engineering Journal, 28, 1, 10-16, (2006) · doi:10.1016/j.bej.2005.08.032
[522] Ko, C. L.; Wang, F. S., On-line estimation of biomass and intracellular protein for recombinant Escherichia coli cultivated in batch and fed-batch modes, Journal of the Chinese Institute of Chemical Engineers, 38, 3-4, 197-203, (2007) · doi:10.1016/j.jcice.2007.04.005
[523] Alvarez-Vasquez, F.; Cánovas, M.; Iborra, J. L.; Torres, N. V., Modeling, optimization and experimental assessment of continuous L-(-)-carnitine production by Escherichia coli cultures, Biotechnology and Bioengineering, 80, 7, 794-805, (2002) · doi:10.1002/bit.10436
[524] Lall, R.; Mitchell, J., Metal reduction kinetics in shewanella, Bioinformatics, 23, 20, 2754-2759, (2007) · doi:10.1093/bioinformatics/btm400
[525] Sheridan, R.; Jackson, G. A.; Regan, L.; Ward, J.; Dunhill, P., Rational engineering of the TOL meta-cleavage pathway, Biotechnology and Bioengineering, 58, 240-249, (1998)
[526] Sun, Y. Q.; Qi, W. T.; Teng, H.; Xiu, Z. L.; Zeng, A. P., Mathematical modeling of glycerol fermentation by klebsiella pneumoniae: concerning enzyme-catalytic reductive pathway and transport of glycerol and 1,3-propanediol across cell membrane, Biochemical Engineering Journal, 38, 1, 22-32, (2008) · doi:10.1016/j.bej.2007.06.002
[527] Voit, E.; Neves, A. R.; Santos, H., The intricate side of systems biology, Proceedings of the National Academy of Sciences of the United States of America, 103, 25, 9452-9457, (2006) · doi:10.1073/pnas.0603337103
[528] Horner, J. K.; Wolinsky, M. A., A power-law sensitivity analysis of the hydrogen-producing metabolic pathway in chlamydomonas reinhardtii, International Journal of Hydrogen Energy, 27, 11-12, 1251-1255, (2002) · doi:10.1016/S0360-3199(02)00129-5
[529] Jorquera, O.; Kiperstok, A.; Sales, E. A.; Embiruçu, M.; Ghirardi, M. L., S-systems sensitivity analysis of the factors that may influence hydrogen production by sulfur-deprived chlamydomonas reinhardtii, International Journal of Hydrogen Energy, 33, 9, 2167-2177, (2008) · doi:10.1016/j.ijhydene.2008.01.054
[530] Zhang, T., Dynamics modeling of hydrogen production by sulfur-deprived chlamydomonas reinhardtii culture in tubular photobioreactor, International Journal of Hydrogen Energy, 36, 12177-12185, (2011)
[531] Zhang, T., Effects of culture parameters, light, and mixing on H2 production by sulfur-deprived chlamydomonas reinhardtii in flat plate reactor, International Journal of Hydrogen Energy, 36, 15168-15176, (2011)
[532] Streichert, F.; Spieth, C.; Ulmer, H.; Zell, A., How to evolve the head-tail pattern from reaction-diffusion systems, Proceedings of the NASA/DoD Conference on Evolvable Hardware · doi:10.1109/EH.2004.1310839
[533] Berovic, M.; Legisa, M., Citric acid production, Biotechnology Annual Review, 13, 303-343, (2007) · doi:10.1016/S1387-2656(07)13011-8
[534] Licht, F. O.
[535] Alvarez-Vasquez, F.; Gonzalez-Alcon, C.; Torres, N. V., Metabolism of citric acid production by aspergillus niger: model definition, steady-state analysis and constrained optimization of citric acid production rate, Biotechnology and Bioengineering, 70, 82-108, (2000)
[536] García, J.; Torres, N., Mathematical modelling and assessment of the ph homeostasis mechanisms in aspergillus niger while in citric acid producing conditions, Journal of Theoretical Biology, 282, 1, 23-35, (2011) · Zbl 1397.92285 · doi:10.1016/j.jtbi.2011.04.028
[537] Guebel, D. V.; Torres Darias, N. V., Optimization of the citric acid production by aspergillus niger through a metabolic flux balance model, Electronic Journal of Biotechnology, 4, 1, 3-19, (2001)
[538] Torres, N. V.; González-Alcón, C.; Voit, E. O.; Yamakawa, T.; Matsumoto, G., Optimization of metabolic systems with linear programming. application to biotechnological processes, Methodologies for the Conception, Design, and Application of Intelligent Systems, 171-174, (1996), World Scientific, Singapore
[539] Papagianni, M., Advances in citric acid fermentation by aspergillus niger: biochemical aspects, membrane transport and modeling, Biotechnology Advances, 25, 3, 244-263, (2007) · doi:10.1016/j.biotechadv.2007.01.002
[540] de Jongh, W. A.; Nielsen, J., Enhanced citrate production through gene insertion in aspergillus niger, Metabolic Engineering, 10, 2, 87-96, (2008) · doi:10.1016/j.ymben.2007.11.002
[541] Alves, R.; Sorribas, A., In silico pathway reconstruction: iron-sulfur cluster biogenesis in saccharomyces cerevisiae, BMC Systems Biology, 1, article 10, (2007) · doi:10.1186/1752-0509-1-10
[542] Alvarez-Vasquez, F.; Sims, K. J.; Voit, E. O.; Hannun, Y. A., Coordination of the dynamics of yeast sphingolipid metabolism during the diauxic shift, Theoretical Biology and Medical Modelling, 4, article 42, (2007) · doi:10.1186/1742-4682-4-42
[543] Voit, E. O.; Radivoyevitch, T., Biochemical systems analysis of genome-wide expression data, Bioinformatics, 16, 11, 1023-1037, (2000)
[544] Vilaprinyo, E.; Alves, R.; Sorribas, A., Use of physiological constraints to identify quantitative design principles for gene expression in yeast adaptation to heat shock, BMC Bioinformatics, 7, article 184, (2006) · doi:10.1186/1471-2105-7-184
[545] Vilaprinyo, E.; Alves, R.; Sorribas, A., Minimization of biosynthetic costs in adaptive gene expression responses of yeast to environmental changes, PLoS Computational Biology, 6, 2, (2010) · doi:10.1371/journal.pcbi.1000674
[546] Guillén-Gosálbez, G.; Pozo, C.; Jiménez, L.; Sorribas, A., A global optimization strategy to identify quantitative design principles for gene expression in yeast adaptation to heat shock, Computer Aided Chemical Engineering, 26, 1045-1050, (2009) · doi:10.1016/S1570-7946(09)70174-9
[547] Fonseca, L. L.; Sánchez, C.; Santos, H.; Voit, E. O., Complex coordination of multi-scale cellular responses to environmental stress, Molecular BioSystems, 7, 3, 731-741, (2011) · doi:10.1039/c0mb00102c
[548] Voit, E. O.; Alvarez-Vasquez, F.; Hannun, Y. A., Computational analysis of sphingolipid pathway systems, Advances in Experimental Medicine and Biology, 688, 264-275, (2010) · doi:10.1007/978-1-4419-6741-1_19
[549] Chen, P.-W.; Fonseca, L.; Hannun, Y. A.; Voit, E. O., Coordination of rapid sphingolipid responses to heat stress in yeast
[550] Fonseca, L. L.; Chen, P.-W.; Voit, E. O., Canonical modeling of the multi-scale regulation of the heat stress response in yeast, Metabolites, 2, 221-241, (2012)
[551] Shiraishi, F.; Savageau, M. A., The tricarboxylic acid cycle in dictyostelium discoideum—4. resolution of discrepancies between alternative methods of analysis, Journal of Biological Chemistry, 267, 32, 22934-22943, (1992)
[552] Shiraishi, F.; Savageau, M. A., The tricarboxylic acid cycle in dictyostelium discoideum—III. analysis of steady state and dynamic behavior, Journal of Biological Chemistry, 267, 32, 22926-22933, (1992)
[553] Shiraishi, F.; Savageau, M. A., The tricarboxylic acid cycle in dictyostelium discoideum—II. evaluation of model consistency and robustness, Journal of Biological Chemistry, 267, 32, 22919-22925, (1992)
[554] Shiraishi, F.; Savageau, M. A., The tricarboxylic acid cycle in dictyostelium discoideum. systemic effects of including protein turnover in the current model, Journal of Biological Chemistry, 268, 23, 16917-16928, (1993)
[555] Shiraishi, F.; Savageau, M. A., The tricarboxylic acid cycle in dictyostelium discoideum—two methods of analysis applied to the same model, Journal of Theoretical Biology, 178, 2, 219-222, (1996) · doi:10.1006/jtbi.1996.0018
[556] Vera, J.; Bachmann, J.; Pfeifer, A. C.; Becker, V.; Hormiga, J. A.; Darias, N. V. T.; Timmer, J.; Klingmüller, U.; Wolkenhauer, O., A systems biology approach to analyse amplification in the JAK2-STAT5 signalling pathway, BMC Systems Biology, 2, article 38, (2008) · doi:10.1186/1752-0509-2-38
[557] Vera, J.; Wolkenhauer, O., A system biology approach to understand functional activity of cell communication systems, Methods in Cell Biology, 90, 399-415, (2009) · doi:10.1016/S0091-679X(08)00817-0
[558] Vera, J.; Wolkenhauer, O.; Ramaswamy, B., A system biology approach to understand functional activity of cell communication systems, Methods in Nano Cell Biology, (2008), Elsevier
[559] Vera, J.; Millat, T.; Kolch, W.; Wolkenhauer, O., Dynamics of receptor and protein transducer homodimerisation, BMC Systems Biology, 2, article 92, (2008) · doi:10.1186/1752-0509-2-92
[560] Vera, J.; Rath, O.; Balsa-Canto, E.; Banga, J. R.; Kolch, W.; Wolkenhauer, O., Investigating dynamics of inhibitory and feedback loops in ERK signalling using power-law models, Molecular BioSystems, 6, 11, 2174-2191, (2010) · doi:10.1039/c0mb00018c
[561] Lai, X.; Nikolov, S.; Wolkenhauer, O.; Vera, J., A multi-level model accounting for the effects of JAK2-STAT5 signal modulation in erythropoiesis, Computational Biology and Chemistry, 33, 4, 312-324, (2009) · Zbl 1403.92027 · doi:10.1016/j.compbiolchem.2009.07.003
[562] Nikolov, S.; Vera, J.; Rath, O.; Kolch, W.; Wolkenhauer, O., Role of inhibitory proteins as modulators of oscillations in NFκB signalling, IET Systems Biology, 3, 2, 59-76, (2009) · doi:10.1049/iet-syb.2008.0105
[563] Liu, Y.-W.; Chen, C.-K.; Lin, C.-L., Signal transduction networks in biological systems based on Michaelis-Menten equation and S-system, Proceedings of the 7th WSEAS International Conference on Computational Intelligence, Man-Made Machine Systems and Cybernetics
[564] Boykin, E. R.; Ogle, W. O., Using heterogeneous data sources in a systems biology approach to modeling the sonic hedgehog signaling pathway, Molecular BioSystems, 6, 10, 1993-2003, (2010) · doi:10.1039/c0mb00006j
[565] Ray, J. C. J.; Kirschner, D. E., Requirement for multiple activation signals by anti-inflammatory feedback in macrophages, Journal of Theoretical Biology, 241, 2, 276-294, (2006) · Zbl 1447.92104 · doi:10.1016/j.jtbi.2005.11.037
[566] Schwacke, J. H.; Voit, E. O., Concentration-dependent effects on the rapid and efficient activation of the MAP kinase signaling cascade, Proteomics, 7, 6, 890-899, (2007) · doi:10.1002/pmic.200600927
[567] Schwacke, J. H.; Voit, E. O., The potential for signal integration and processing in interacting MAP kinase cascades, Journal of Theoretical Biology, 246, 4, 604-620, (2007) · Zbl 1451.92136 · doi:10.1016/j.jtbi.2006.12.035
[568] Sorribas, A.; Yamakawa, T.; Matsumoto, G., Exploring the properties of signal transduction pathways by mathematical controlled comparisons based on power-law models, Methodologies for the Conception, Design, and Application of Intelligent Systems, 179-182, (1996), World Scientific, Singapore
[569] Lin, C.-L.; Liu, Y.-W.; Chuang, C.-H., Analysis of signal transduction networks in Michaelis-Menten equations and S-systems, International Journal of Biology and Biomedical Engineering, 2, 69-78, (2008)
[570] Smith, D. F., Quantitative analysis of the functional relationships existing between ecosystem components—I. analysis of the linear intercomponent mass transfers, Oecologia, 16, 2, 97-106, (1974) · doi:10.1007/BF00345575
[571] Smith, D. F., Quantitative analysis of the functional relationships existing between ecosystem components—II. analysis of non-linear relationships, Oecologia, 16, 2, 107-117, (1974) · doi:10.1007/BF00345576
[572] Smith, D. F., Quantitative analysis of the functional relationships existing between ecosystem components—III. analysis of ecosystem stability, Oecologia, 21, 1, 17-29, (1975) · doi:10.1007/BF00345890
[573] Torres, N. V., S-system modelling approach to ecosystem: application to a study of magnesium flow in a tropical forest, Ecological Modelling, 89, 1-3, 109-120, (1996)
[574] Sands, P. J.; Voit, E. O., Flux-based estimation of parameters in S-systems, Ecological Modelling, 93, 1-3, 75-88, (1996) · doi:10.1016/0304-3800(95)00215-4
[575] Voit, E. O., Dynamic trends in distributions, Biometrical Journal, 38, 5, 587-603, (1996) · Zbl 0859.62018
[576] Voit, E. O.; Sands, P. J., Modeling forest growth—II. biomass partitioning in scots pine, Ecological Modelling, 86, 1, 73-89, (1996)
[577] Kaitaniemi, P., A canonical model of tree resource allocation after defoliation and bud consumption, Ecological Modelling, 129, 2-3, 259-272, (2000) · doi:10.1016/S0304-3800(00)00236-2
[578] Martin, P. G., The use of canonical S-system modelling for condensation of complex dynamic models, Ecological Modelling, 103, 1, 43-70, (1997) · doi:10.1016/S0304-3800(97)00075-6
[579] Renton, M.; Hanan, J.; Burrage, K., Using the canonical modelling approach to simplify the simulation of function in functional-structural plant models, New Phytologist, 166, 3, 845-857, (2005) · doi:10.1111/j.1469-8137.2005.01330.x
[580] Renton, M.; Kaitaniemi, P.; Hanan, J., Functional-structural plant modelling using a combination of architectural analysis, L-systems and a canonical model of function, Ecological Modelling, 184, 2-4, 277-298, (2005) · doi:10.1016/j.ecolmodel.2004.10.008
[581] Renton, M.; Thornby, D.; Hanan, J.; Vos, J.; Marcelis, L. F. M.; Visser, P. H. B. d.; Struik, P. C.; Evers, J. B., Canonical modeling, Functional-Structural Plant Modelling in Crop Production, 151-164, (2007), Springer
[582] Voit, E. O., Dynamics of self-thinning plant stands, Annals of Botany, 62, 1, 67-78, (1988)
[583] Pittman, S. D.; Turnblom, E. C., A study of self-thinning using coupled allometric equations: implications for coastal Douglas-fir stand dynamics, Canadian Journal of Forest Research, 33, 9, 1661-1669, (2003) · doi:10.1139/x03-086
[584] Voit, E. O.; Sorribas, A., Computer modeling of dynamically changing distributions of random variables, Mathematical and Computer Modelling, 31, 4-5, 217-225, (2000) · doi:10.1016/S0895-7177(00)00041-8
[585] Johnson, T., Estimation and simulation of 3-systems, Mathematical and Computer Modelling, 11, 134-139, (1988)
[586] Johnson, T., Modeling growth for economic analysis of dynamic agricultural systems, Departmental Report, (1985), Department of Agricultural and Resource Economics, North Carolina State University, Raleigh, NC, USA
[587] Lee, Y.; Voit, E. O., Mathematical modeling of monolignol biosynthesis in populus xylem, Mathematical Biosciences, 228, 1, 78-89, (2010) · Zbl 1200.92019 · doi:10.1016/j.mbs.2010.08.009
[588] Chaudhuri, K.; Johnson, T., Bioeconomic dynamics of a fishery modeled as an S-system, Mathematical Biosciences, 99, 2, 231-249, (1990) · Zbl 0699.92024 · doi:10.1016/0025-5564(90)90006-K
[589] Ganguly, S.; Chaudhuri, K. S., Regulation of a single-species fishery by taxation, Ecological Modelling, 82, 1, 51-60, (1995) · doi:10.1016/0304-3800(94)00079-W
[590] Brown, A. B., Determining the economically optimum slaughter age and time paths for dietary energy and protein [Doctoral dissertation], (1991), North Carolina State University, Raleigh, NC, USA
[591] Brown, A. B.; Johnson, T., Use of an S-System in Optimal Control of a Biological System, (1992), Department of Agricultural and Resource Economics, North Carolina State University, Raleigh, NC, USA
[592] Hormiga, J. A.; Almansa, E.; Sykes, A. V.; Torres, N. V., Model based optimization of feeding regimens in aquaculture: application to the improvement of octopus vulgaris viability in captivity, Journal of Biotechnology, 149, 3, 209-214, (2010) · doi:10.1016/j.jbiotec.2009.12.008
[593] Torres, N. V., Modelization and experimental studies on the control of the glycolytic- glycogenolytic pathway in rat liver, Molecular and Cellular Biochemistry, 132, 2, 117-126, (1994) · doi:10.1007/BF00926920
[594] Ervadi-Radhakrishnan, A.; Voit, E. O., Controllability of non-linear biochemical systems, Mathematical Biosciences, 196, 1, 99-123, (2005) · Zbl 1071.92013 · doi:10.1016/j.mbs.2005.03.012
[595] Nounou, H. N.; Meskin, N., Fuzzy intervention in biological phenomena, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 9, 6, 1819-1825, (2012) · doi:10.1109/TCBB.2012.113
[596] Meskin, N.; Nounou, H. N.; Nounou, M.; Datta, A.; Dougherty, E. R., Intervention in biological phenomena modeled by S-systems, IEEE Transactions on Biomedical Engineering, 58, 5, 1260-1267, (2011) · doi:10.1109/TBME.2010.2099658
[597] Meskin, N.; Nounou, H.; Nounou, M.; Datta, E. R.; Dougherty, A. E. R., Intervention in biological phenomena modeled by S-systems: A model predictive control approach, Proceedings of the American Control Conference
[598] Reilly, S. L.; Sing, C. F.; Savageau, M. A.; Turner, S. T., Analysis of systems influencing renal hemodynamics and sodium excretion. I. biochemical systems theory, Integrative Physiological and Behavioral Science, 29, 1, 55-73, (1994) · doi:10.1007/BF02691281
[599] Yin, W.; Jo, H.; Voit, E. O., Systems analysis of the role of bone morphogenic protein 4 in endothelial inflammation, Annals of Biomedical Engineering, 38, 2, 291-307, (2010) · doi:10.1007/s10439-009-9822-y
[600] Sorribas, A.; González, A., The power-law formalism as a tool for modeling hormonal systems, Journal of Theoretical Medicine, 2, 2, 19-38, (2000) · Zbl 0940.92012
[601] Thomas, G. M. H., Modelling the effects of inhibitors of guanine nucleotide synthesis: implications for studies of cellular differentiation pathways, Biochemical Society Transactions, 38, 5, 1314-1318, (2010) · doi:10.1042/BST0381314
[602] Qi, Z.; Kikuchi, S.; Tretter, F.; Voit, E. O., Effects of dopamine and glutamate on synaptic plasticity: a computational modeling approach for drug abuse as comorbidity in mood disorders, Pharmacopsychiatry, 44, 1, S62-S75, (2011) · doi:10.1055/s-0031-1273707
[603] Qi, Z.; Miller, G. W.; Voit, E. O., A mathematical model of presynaptic dopamine homeostasis: implications for schizophrenia, Pharmacopsychiatry, 41, 1, S89-S98, (2008) · doi:10.1055/s-2008-1080936
[604] Qi, Z.; Miller, G. W.; Voit, E. O., Computational systems analysis of dopamine metabolism, PLoS ONE, 3, 6, (2008) · doi:10.1371/journal.pone.0002444
[605] Qi, Z.; Miller, G. W.; Voit, E. O., Computational analysis of determinants of dopamine (DA) dysfunction in DA nerve terminals, Synapse, 63, 12, 1133-1142, (2009) · doi:10.1002/syn.20686
[606] Qi, Z.; Miller, G. W.; Voit, E. O., Computational modeling of synaptic neurotransmission as a tool for assessing dopamine hypotheses of schizophrenia, Pharmacopsychiatry, 43, 1, S50-S60, (2010) · doi:10.1055/s-0030-1248317
[607] Qi, Z.; Miller, G. W.; Voit, E. O., The internal state of medium spiny neurons varies in response to different input signals, BMC Systems Biology, 4, article 26, (2010) · doi:10.1186/1752-0509-4-26
[608] Qi, Z.; Miller, G. W.; Voit, E. O.; Ritsner, M. S., Mathematical models in schizophrenia, Textbook of Schizophrenia Spectrum Disorders, 1, (2011), Springer, New York, NY, USA
[609] Qi, Z.; Miller, G. W.; Voit, E. O.; Cloutier, P. W. A. M., Mathematical models of dopamine metabolism in parkinson’s disease, The Systems Biology of Parkinson’s Disease, (2012), Springer, New York, NY, USA
[610] Dulam-Banawa, B.; Marin-Sanguino, A.; Mendoza, E., The evolution of synapse models from numbers to networks to spaces, Pharmacopsychiatry, 43, 1, S42-S49, (2010) · doi:10.1055/s-0030-1249025
[611] Mendoza, E. R.; Tretter, F.; Gebicke-Härter, P.; Winterer, G.; Mendoza, E. R., From communicational to computational: systems modeling approaches for psychiatric research, Systems Biology and Psychiatric Research, (2010), Wiley VCH
[612] Marin-Sanguino, A.; del Rosario, R. C.; Mendoza, E. R., Concept maps and canonical models in neuropsychiatry, Pharmacopsychiatry, 42, S110-117, (2009)
[613] Sass, M. B.; Lorenz, A. N.; Green, R. L.; Coleman, R. A., A pragmatic approach to biochemical systems theory applied to an α-synuclein-based model of Parkinson’s disease, Journal of Neuroscience Methods, 178, 2, 366-377, (2009) · doi:10.1016/j.jneumeth.2008.12.014
[614] Liu, S.; Tao, C.; Huang, Z.; Huang, S., Modeling of p53 signaling pathway based on S-system equations, Journal of Biomedical Engineering, 27, 505-510, (2010)
[615] Vera, J.; Schultz, J.; Ibrahim, S.; Raatz, Y.; Wolkenhauer, O.; Kunz, M., Dynamical effects of epigenetic silencing of 14-3-3σ expression, Molecular BioSystems, 6, 1, 264-273, (2009) · doi:10.1039/b907863k
[616] Broome, T. M.; Coleman, R. A., A mathematical model of cell death in multiple sclerosis, Journal of Neuroscience Methods, 201, 420-425, (2011)
[617] Ferreira, A. E. N.; Ponces Freire, A. M. J.; Voit, E. O., A quantitative model of the generation of N-(carboxymethyl)lysine in the maillard reaction between collagen and glucose, Biochemical Journal, 376, 1, 109-121, (2003) · doi:10.1042/BJ20030496
[618] Garcia, J.; Shea, J.; Alvarez-Vasquez, F.; Qureshi, A.; Luberto, C.; Voit, E. O.; Del Poeta, M., Mathematical modeling of pathogenicity of cryptococcus neoformans, Molecular Systems Biology, 4, article 183, (2008) · doi:10.1038/msb.2008.17
[619] Garcia, J.; Sims, K. J.; Schwacke, J. H.; Poeta, M. D., Biochemical systems analysis of signaling pathways to understand fungal pathogenicity, Methods in Molecular Biology, 734, 173-200, (2011) · doi:10.1007/978-1-61779-086-7_9
[620] 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, Bulletin of Mathematical Biology, 58, 5, 923-938, (1996) · Zbl 0859.92008
[621] Vera, J.; Curto, R.; Cascante, M.; Torres, N. V., Detection of potential enzyme targets by metabolic modelling and optimization: application to a simple enzymopathy, Bioinformatics, 23, 17, 2281-2289, (2007) · doi:10.1093/bioinformatics/btm326
[622] Langer, B. M.; Pou-Barreto, C.; Gonzalez-Alcon, C.; Valladares, B.; Wimmer, B.; Torres, N. V., Modeling of leishmaniasis infection dynamics: novel application to the design of effective therapies, BMC Systems Biology, 6, article 1, (2012)
[623] Magombedze, G.; Mulder, N., Understanding TB latency using computational and dynamic modelling procedures
[624] Voit, E. O., S-system modelling of endemic infections, Computers and Mathematics with Applications, 20, 4-6, 161-173, (1990) · Zbl 0728.92019
[625] Balthis, W. L.; Voit, E. O.; Meaburn, G. M., Setting prediction limits for Mercury concentrations in fish having high bioaccumulation potential, Environmetrics, 7, 429-439, (1996)
[626] Voit, E. O.; Knapp, R. G., Derivation of the linear-logistic model and Cox’s proportional hazard model from a canonical system description, Statistics in Medicine, 16, 1705-1729, (1997)
[627] Voit, E. O., Utility of biochemical systems theory for the analysis of metabolic effects from low-dose chemical exposure, Risk Analysis, 20, 3, 393-402, (2000) · doi:10.1111/0272-4332.203038
[628] Voit, E. O.; Brigham, K. L., The role of systems biology in predictive health and personalized medicine, The Open Pathology Journal, 2, 68-70, (2008)
[629] Vodovotz, Y.; Constantine, G.; Rubin, J.; Csete, M.; Voit, E. O.; An, G., Mechanistic simulations of inflammation: current state and future prospects, Mathematical Biosciences, 217, 1, 1-10, (2009) · Zbl 1158.92318 · doi:10.1016/j.mbs.2008.07.013
[630] Faratian, D.; Clyde, R. G.; Crawford, J. W.; Harrison, D. J., Systems pathology—taking molecular pathology into a new dimension, Nature Reviews Clinical Oncology, 6, 8, 455-464, (2009) · doi:10.1038/nrclinonc.2009.102
[631] Faratian, D.; Bown, J. L.; Smith, V. A.; Langdon, S. P.; Harrison, D. J., Cancer systems biology, Stem Cells: The Importance of Modelling, Methods in Molecular Biology, 662, 245-263, (2010), Springer
[632] Athale, C. A.; Christensen, M. O.; Eils, R.; Boege, F.; Mielke, C., Inferring a system model of subcellular topoisomerase IIβ localization dynamics, OMICS, 8, 2, 167-175, (2004) · doi:10.1089/1536231041388339
[633] Palsson, B. Ø., Systems Biology: Properties of Reconstructed Networks, (2006), Cambridge University Press, New York, NY, USA
[634] Voit, E. O., Optimization in integrated biochemical systems, Biotechnology and Bioengineering, 40, 5, 572-582, (1992)
[635] Regan, L.; Bogle, I. D. L.; Dunnill, P., Simulation and optimization of metabolic pathways, Computers and Chemical Engineering, 17, 5-6, 627-637, (1993)
[636] Voit, E. O.; Signore, M. D., Assessment of effects of experimental imprecision on optimized biochemical systems, Biotechnology and Bioengineering, 74, 5, 443-448, (2001) · doi:10.1002/bit.1135
[637] Marín-Sanguino, A.; Torres, N. V., Optimization of biochemical systems by linear programming and general mass action model representations, Mathematical Biosciences, 184, 2, 187-200, (2003) · Zbl 1017.92017 · doi:10.1016/S0025-5564(03)00046-4
[638] Vera, J.; Torres, N. V.; Moles, C. G.; Banga, J., Integrated nonlinear optimization of bioprocesses via linear programming, AIChE Journal, 49, 12, 3173-3187, (2003) · doi:10.1002/aic.690491217
[639] Xu, G.; Shao, C.; Xiu, Z., A modified iterative IOM approach for optimization of biochemical systems, Computers and Chemical Engineering, 32, 7, 1546-1568, (2008) · doi:10.1016/j.compchemeng.2007.07.008
[640] Xu, G., Optimization of biochemical networks under uncertainty, Proceedings of the IEEE Biomedical Circuits and Systems Conference (BioCAS ’09) · doi:10.1109/BIOCAS.2009.5372061
[641] Xu, G., Comparison of iterative IOM approaches for optimization of biological systems under uncertainty, Proceedings of the 2nd International Conference on Intelligent Computing Technology and Automation (ICICTA ’09) · doi:10.1109/ICICTA.2009.756
[642] Marin-Sanguino, A.; Voit, E. O.; Gonzalez-Alcon, C.; Torres, N. V., Optimization of biotechnological systems through geometric programming, Theoretical Biology and Medical Modelling, 4, article 38, (2007) · doi:10.1186/1742-4682-4-38
[643] Sorribas, A.; Pozo, C.; Vilaprinyo, E.; Guillén-Gosálbez, G.; Jiménez, L.; Alves, R., Optimization and evolution in metabolic pathways: global optimization techniques in generalized mass action models, Journal of Biotechnology, 149, 3, 141-153, (2010) · doi:10.1016/j.jbiotec.2010.01.026
[644] Guillén-Gosálbez, G.; Pozo, C.; Jiménez, L.; Sorribas, A.; de Brito Alves, T. M.; Oller, C. A.; Biscaia, E. C., An outer approximation algorithm for the global optimization of regulated metabolic systems, Proceedings of the 10th International Symposium on Process Systems Engineering, Elsevier B.V.
[645] Pozo, C.; Guillén-Gosálbez, G.; Sorribas, A.; Jiménez, L., Outer approximation-based algorithm for biotechnology studies in systems biology, Computers and Chemical Engineering, 34, 10, 1719-1730, (2010) · doi:10.1016/j.compchemeng.2010.03.001
[646] Pozo, C.; Marin-Sanguino, A.; Alves, R.; Guillen-Gosalbez, G.; Jimenez, L.; Sorribas, A., Steady-state global optimization of metabolic non-linear dynamic models through recasting into power-law canonical models, BMC Systems Biology, 5, article 137, (2011)
[647] Zheng, Y.; Yeh, C. W.; Yang, C. D.; Jang, S. S.; Chu, I. M., On the local optimal solutions of metabolic regulatory networks using information guided genetic algorithm approach and clustering analysis, Journal of Biotechnology, 131, 2, 159-167, (2007) · doi:10.1016/j.jbiotec.2007.06.019
[648] Sriyudthsak, K.; Shiraishi, F., Investigation of the performance of fermentation processes using a mathematical model including effects of metabolic bottleneck and toxic product on cells, Mathematical Biosciences, 228, 1, 1-9, (2010) · Zbl 1200.92016 · doi:10.1016/j.mbs.2010.08.001
[649] Sriyudthsak, K.; Shiraishi, F., Selection of best indicators for ranking and determination of bottleneck enzymes in metabolic reaction systems, Industrial and Engineering Chemistry Research, 49, 20, 9738-9742, (2010) · doi:10.1021/ie100911h
[650] Vera, J.; González-Alcón, C.; Marín-Sanguino, A.; Torres, N., Optimization of biochemical systems through mathematical programming: methods and applications, Computers and Operations Research, 37, 8, 1427-1438, (2010) · Zbl 1183.90372 · doi:10.1016/j.cor.2009.02.021
[651] Link, H.; Vera, J.; Weuster-Botz, D.; Torres Darias, N.; Franco-Lara, E., Multi-objective steady state optimization of biochemical reaction networks using a constrained genetic algorithm, Computers and Chemical Engineering, 32, 8, 1707-1713, (2008) · doi:10.1016/j.compchemeng.2007.08.009
[652] Vera, J.; Moles, C. G.; Banga, J.; Torres, N. V.; Pons, M.-N.; Van Impe, J. F. M., Optimal non-linear design and control of bioprocesses via linear programming, Computer Applications in Biotechnology, 469-472, (2004), Elsevier IFAC Publications
[653] Torres, N. V.; Voit, E. O.; Glez-Alcón, C.; Rodríguez, F., Optimization of nonlinear biotechnological processes with linear programming. application to citric acid production in aspergillus niger, Biotechnology and Bioengineering, 49, 247-258, (1996)
[654] Sevilla, A.; Vera, J.; Díaz, Z.; Cánovas, M.; Torres, N. V.; Iborra, J. L., Design of metabolic engineering strategies for maximizing L-(-)-carnitine production by Escherichia coli. integration of the metabolic and bioreactor levels, Biotechnology Progress, 21, 2, 329-337, (2005) · doi:10.1021/bp0497583
[655] Cánovas, M.; Bernal, V.; Sevilla, Á.; Iborra, J. L., Role of wet experiment design in data generation: from in vivo to in silico and back, In Silico Biology, 7, 2, 3-16, (2007)
[656] Hormiga, J.; González-Alcón, C.; Sevilla, A.; Cánovas, M.; Torres, N. V., Quantitative analysis of the dynamic signaling pathway involved in the camp mediated induction of L-carnitine biosynthesis in E. coli cultures, Molecular BioSystems, 6, 4, 699-710, (2010) · doi:10.1039/b913063b
[657] Santos, G.; Hormiga, J. A.; Arense, P.; Canovas, M.; Torres, N. V., Modelling and analysis of central metabolism operating regulatory interactions in salt stress conditions in a L-carnitine overproducing E. coli strain, PloS ONE, 7, (2012)
[658] Marín-Sanguino, A.; Torres, N. V., Optimization of tryptophan production in bacteria. design of a strategy for genetic manipulation of the tryptophan operon for tryptophan flux maximization, Biotechnology Progress, 16, 2, 133-145, (2000) · doi:10.1021/bp990144l
[659] Nguyen, L. K.; Kulasiri, D., On multiple regulatory mechanisms in the tryptophan operon system in Escherichia coli: in silico study of perturbation dynamics, In Silico Biology, 8, 5-6, 485-510, (2008)
[660] Sun, Y.; Mu, X.; Li, Z.; Teng, H.; Xiu, Z., Robustness and nonlinear dynamic analysis for trp operan and optimization of tryptophan production: an integrated model considering gene regulation, genes interaction and product excretion, Proceedings of the 4th International Conference on Bioinformatics and Biomedical Engineering (iCBBE ’10) · doi:10.1109/ICBBE.2010.5517954
[661] Marín-Sanguino, A.; Torres, N. V., Modelling, steady state analysis and optimization of the catalytic efficiency of the triosephosphate isomerase, Bulletin of Mathematical Biology, 64, 2, 301-326, (2002) · Zbl 1334.92178 · doi:10.1006/bulm.2001.0276
[662] Meskin, N.; Nounou, H.; Nounou, M.; Datta, A.; Dougherty, E., Output-feedback model predictive control of biological phenomena modeled by S-systems, Proceedings of the American Control Conference
[663] Domingues, A.; Vinga, S.; Lemos, J. M., Optimization strategies for metabolic networks, BMC Systems Biology, 4, article 113, (2010) · doi:10.1186/1752-0509-4-113
[664] Long, C. E.; Voit, E. O.; Gatzke, E. P., A mixed integer moving horizon formulation for prioritized objective inferential control of a bioprocess system, Proceedings of the American Control Conference
[665] Cascante, M.; Sorribas, A.; Canela, E. I., Enzyme-enzyme interactions and metabolite channelling: alternative mechanisms and their evolutionary significance, Biochemical Journal, 298, 2, 313-320, (1994)
[666] Klymko, P. W.; Kopelman, R., Fractal reaction kinetics: exciton fusion on clusters, Journal of Physical Chemistry, 87, 23, 4565-4567, (1983)
[667] Anacker, L. W.; Kopelman, R., Fractal chemical kinetics: simulations and experiments, The Journal of Chemical Physics, 81, 12, 6402-6403, (1984)
[668] Kopelman, R., Reaction kinetics in restricted spaces, Israel Journal of Chemistry, 31, 147-157, (1991)
[669] Kopelman, R., Rate processes on fractals: theory, simulations, and experiments, Journal of Statistical Physics, 42, 1-2, 185-200, (1986) · doi:10.1007/BF01010846
[670] Kopelman, R., Fractal reaction kinetics, Science, 241, 4873, 1620-1626, (1988)
[671] Savageau, M. A., Influence of fractal kinetics on molecular recognition, Journal of Molecular Recognition, 6, 4, 149-157, (1993)
[672] Savageau, M. A., Development of fractal kinetic theory for enzyme-catalysed reactions and implications for the design of biochemical pathways, BioSystems, 47, 1-2, 9-36, (1998) · doi:10.1016/S0303-2647(98)00020-3
[673] Savageau, M. A.; Yamakawa, T.; Matsumoto, G., Fractal kinetic effects on equilibrium, Methodologies for the Conception, Design, amd Application of Intelligent Systems, 1, 187-190, (1996), World Scientific, Singapore
[674] Bajzer, Ž.; Huzak, M.; Neff, K. L.; Prendergast, F. G., Mathematical analysis of models for reaction kinetics in intracellular environments, Mathematical Biosciences, 215, 1, 35-47, (2008) · Zbl 1160.92018 · doi:10.1016/j.mbs.2008.05.003
[675] Neff, K. L., Biochemical reaction kinetics in dilute and crowded solutions: predictions of macroscopic and mesoscopic models and experimental observations [Doctoral dissertation], (2010), Mayo Clinic, Rochester, Minn, USA
[676] Neff, K. L.; Offord, C. P.; Caride, A. J.; Strehler, E. E.; Prendergast, F. G.; Bajzer, Ž., Validation of fractal-like kinetic models by time-resolved binding kinetics of dansylamide and carbonic anhydrase in crowded media, Biophysical Journal, 100, 10, 2495-2503, (2011) · doi:10.1016/j.bpj.2011.04.016
[677] Voit, E. O.; Ferreira, A. E. N., Buffering in models of integrated biochemical systems, Journal of Theoretical Biology, 191, 4, 429-437, (1998) · doi:10.1006/jtbi.1997.0605
[678] Mocek, W. T.; Rudnicki, R.; Voit, E. O., Approximation of delays in biochemical systems, Mathematical Biosciences, 198, 2, 190-216, (2005) · Zbl 1089.92021 · doi:10.1016/j.mbs.2005.08.001
[679] Voit, E. O., S-system modelling of complex systems with chaotic input, Environmetrics, 4, 2, 153-186, (1993)
[680] Voit, E. O.; Alvarez-Vasquez, F.; Sims, K. J., Analysis of dynamic labeling data, Mathematical Biosciences, 191, 1, 83-99, (2004) · Zbl 1072.92018 · doi:10.1016/j.mbs.2004.04.004
[681] Alvarez-Vasquez, F.; Hannun, Y. A.; Voit, E. O., Dynamics of positional enrichment: theoretical development and application to carbon labeling in zymomonas mobilis, Biochemical Engineering Journal, 40, 1, 157-174, (2008) · doi:10.1016/j.bej.2007.12.003
[682] Voit, E. O.; Yi, P. N., Comparison of isoeffect relationships in radiotherapy, Bulletin of Mathematical Biology, 52, 5, 657-675, (1990) · Zbl 0704.92009 · doi:10.1016/S0092-8240(05)80372-6
[683] Feinendegen, L.; Hahnfeldt, P.; Schadt, E. E.; Stumpf, M.; Voit, E. O., Systems biology and its potential role in radiobiology, Radiation and Environmental Biophysics, 47, 1, 5-23, (2008) · doi:10.1007/s00411-007-0146-8
[684] Marin-Sanguino, A.; Mendoza, E. R.; Voit, E. O., Flux duality in nonlinear GMA systems: implications for metabolic engineering, Journal of Biotechnology, 149, 3, 166-172, (2010) · doi:10.1016/j.jbiotec.2009.12.009
[685] Kreyszig, E., Advanced Engineering Mathematics, (1993), John Wiley and Sons, New York, NY, USA · Zbl 0803.00001
[686] de Atauri, P.; Sorribas, A.; Cascante, M., Analysis and prediction of the effect of uncertain boundary values in modeling a metabolic pathway, Biotechnology and Bioengineering, 68, 18-30, (2000)
[687] De Atauri, P.; Curto, R.; Puigjaner, J.; Cornish-Bowden, A.; Cascante, M., Advantages and disadvantages of aggregating fluxes into synthetic and degradative fluxes when modelling metabolic pathways, European Journal of Biochemistry, 265, 2, 671-679, (1999) · doi:10.1046/j.1432-1327.1999.00760.x
[688] Machina, A.; Ponosov, A.; Voit, E. O., Automated piecewise power-law modeling of biological systems, Journal of Biotechnology, 149, 3, 154-165, (2010) · doi:10.1016/j.jbiotec.2009.12.016
[689] Cascante, M.; Sorribas, A.; Franco, R.; Canela, E. I., Biochemical systems theory: increasing predictive power by using second-order derivatives measurements, Journal of Theoretical Biology, 149, 4, 521-535, (1991)
[690] Kaddi, C.; Quo, C. F.; Wang, M. D., Quantitative metrics for bio-modeling algorithm selection, Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society
[691] Dräger, A.; Kronfeld, M.; Ziller, M. J.; Supper, J.; Planatscher, H.; Magnus, J. B.; Oldiges, M.; Kohlbacher, O.; Zell, A., Modeling metabolic networks in C. glutamicum: a comparison of rate laws in combination with various parameter optimization strategies, BMC Systems Biology, 3, article 5, (2009) · doi:10.1186/1752-0509-3-5
[692] Hadlich, F.; Noack, S.; Wiechert, W., Translating biochemical network models between different kinetic formats, Metabolic Engineering, 11, 2, 87-100, (2009) · doi:10.1016/j.ymben.2008.10.002
[693] Grima, R.; Schnell, S., How reaction kinetics with time-dependent rate coefficients differs from generalized mass action, ChemPhysChem, 7, 7, 1422-1424, (2006) · doi:10.1002/cphc.200600081
[694] Wolkenhauer, O.; Ullah, M.; Kolch, W.; Cho, K. H., Modeling and simulation of intracellular dynamics: choosing an appropriate framework, IEEE Transactions on Nanobioscience, 3, 3, 200-207, (2004) · doi:10.1109/TNB.2004.833694
[695] Voit, E. O.; Savageau, M. A., Accuracy of alternative representations for integrated biochemical systems, Biochemistry, 26, 21, 6869-6880, (1987)
[696] Vlad, M. O.; Corlan, A. D.; Morán, F.; Spang, R.; Oefner, P.; Ross, J., Kinetic laws, phase-phase expansions, renormalization group, and INR calibration, Proceedings of the National Academy of Sciences of the United States of America, 106, 16, 6465-6470, (2009) · doi:10.1073/pnas.0809855106
[697] Savageau, M. A., Allometric morphogenesis of complex systems: derivation of the basic equations from first principles, Proceedings of the National Academy of Sciences of the United States of America, 76, 12, 6023-6025, (1979) · Zbl 0421.92002
[698] Savageau, M. A., Growth equations: a general equation and a survey of special cases, Mathematical Biosciences, 48, 3-4, 267-278, (1980) · Zbl 0419.92001 · doi:10.1016/0025-5564(80)90061-9
[699] Voit, E. O.; Eisenfeld, J.; Levine, D. S.; Witten, M., Selecting a model for integrated biomedical systems, Biomedical Modeling and Simulation, 465-472, (1992), Elsevier Science Publishers, Amsterdam, The Netherlands
[700] West, G. B.; Brown, J. H.; Enquist, B. J., A general model for the origin of allometric scaling laws in biology, Science, 276, 5309, 122-126, (1997) · doi:10.1126/science.276.5309.122
[701] West, G. B.; Brown, J. H.; Enquist, B. J., A general model for ontogenetic growth, Nature, 413, 6856, 628-631, (2001) · doi:10.1038/35098076
[702] Sorribas, A.; March, J.; Voit, E. O., Estimating age-related trends in cross-sectional studies using S-distributions, Statistics in Medicine, 19, 697-713, (2000)
[703] Voit, E. O., Cell cycles and growth laws: the CCC model, Journal of Theoretical Biology, 114, 4, 589-599, (1985)
[704] Voit, E. O., Generic modeling of population dynamics with S-systems, Proceedings of the 2nd International Conference on Mathematical Population Dynamics, Marcel Dekker
[705] Voit, E. O.; Anton, H. J.; Blecker, J., Regenerative growth curves, Mathematical Biosciences, 73, 2, 253-269, (1985) · Zbl 0567.62090 · doi:10.1016/0025-5564(85)90015-X
[706] Voit, E. O.; Voit, E. O., Recasting of nonlinearities as S-systems, Canonical Nonlinear Modeling. S-system Approach to Understanding Complexity, 213-237, (1991), Van Nostrand, Reinhold, NY, USA · Zbl 0785.92004
[707] Kerner, E. H., Universal formats for nonlinear ordinary differential systems, Journal of Mathematical Physics, 22, 7, 1366-1371, (1980) · Zbl 0462.34019
[708] Brenig, L., Complete factorisation and analytic solutions of generalized Lotka-Volterra equations, Physics Letters A, 133, 7-8, 378-382, (1988)
[709] Brenig, L., New special functions solfing nonlinear autonomous dynamical systems
[710] Brenig, L.; Goriely, A., Universal canonical forms for time-continuous dynamical systems, Physical Review A, 40, 7, 4119-4122, (1989) · doi:10.1103/PhysRevA.40.4119
[711] Papachristodoulou, A.; Prajna, S.; Henrion, D.; Garuli, A., Analysis of non-polynomial systems using the sum of squares decomposition, Positive Polynomials in Control, 23-43, (2005), Springer, Berlin, Germany · Zbl 1138.93391
[712] Voit, E. O.; Lakshmikantham, V., How many variables? some comments on the dimensionality of nonlinear systems, Proceedings of the World Congress of Nonlinear Analysts, Walter de Gruyter & Co · Zbl 0846.34030
[713] Voit, E. O.; Voit, E. O., Algebraic properties of S-systems, Canonical Nonlinear Modeling. S-system Approach to Understanding Complexity, 278-303, (1991), Van Nostrand, Reinhold, NY, USA · Zbl 0785.92004
[714] Voit, E. O., Symmetries of S-systems, Mathematical Biosciences, 109, 1, 19-37, (1992) · Zbl 0765.92003 · doi:10.1016/0025-5564(92)90050-7
[715] Savageau, M. A., A suprasystem of probability distributions, Biometrical Journal, 24, 323-330, (1982) · Zbl 0493.62026
[716] Rust, P. F.; Voit, E. O., Non-central chi-square distributions computed by S-system differential equations, Proceedings of the Annual Meeting of the American Statistical Association, Statistical Computing Section
[717] Rust, P. F.; Voit, E. O., S-system computation of central and noncentral F densities and cumulatives, Proceedings of the Annual Meeting of the American Statistical Association, Statistical Computing Section
[718] Rust, P. F.; Voit, E. O., S-system analysis of the noncentral t distribution with fractional degrees of freedom, Proceedings of the Annual Meeting of the American Statistical Association, Statistical Computing Section
[719] Rust, P. F.; Voit, E. O., Statistical densities, cumulatives, quantiles, and power obtained by S-system differential equations, Journal of the American Statistical Association, 85, 572-578, (1990)
[720] Voit, E. O.; Rust, P. F., Evaluation of the noncentral t distribution with S-systems, Biometrical Journal, 32, 681-695, (1990) · Zbl 0716.62027
[721] Rust, P. F., Modeling approximately normal distributions with S-systems, Annual Meeting of the American Statistical Association, Statistical Computing Section
[722] Rust, P. F.; Voit, E. O., Applications of recasting in statistical distributions, Canonical Nonlinear Modeling. S-System Approach to Understanding Complexity, 238-257, (1991), Van Nostrand Reinhold · Zbl 0785.92004
[723] Chou, Y. C.; Chang, P. L.; Chen, Z. Y., Comparing S-system with existing methods for the computation of noncentral beta distribution, International Journal of Information and Management Sciences, 11, 2, 37-48, (2000) · Zbl 0995.62011
[724] Chen, Z. Y.; Chou, Y. C., Computing the noncentral beta distribution with S-system, Computational Statistics and Data Analysis, 33, 4, 343-360, (2000) · Zbl 1061.62513
[725] Chen, Z. Y.; Chen, C. C.; Lai, C. Y., On the S-system computation of statistical distributions, Journal of the Chinese Statistical Association, 37, 222-201, (1999)
[726] Chen, Z. Y., On the statistical computation of the sample multiple correlation coefficient, Journal of Statistical Computation and Simulation, 70, 4, 299-324, (2001) · Zbl 1098.62500
[727] Chen, Z. Y., Computing the distribution of the squared sample multiple correlation coefficient with S-systems, Communications in Statistics Part B, 32, 3, 873-898, (2003) · Zbl 1081.62505 · doi:10.1081/SAC-120017866
[728] Lee, M. H.; Ahmad Mahir, B. R., Penggunaan pendekatan sistem-S dan ESSYNS dalam analisis taburan normal, Pertanika Journal of Science & Technology, 2, 165-173, (1994)
[729] Lee, M. H.; Ahmad Mahir, B. R., Analisis berangka bagi taburan khi kuasa dua melalui persamaan terbitan sistem-S, Sains Malaysiana, 23, 4, 129-147, (1994)
[730] Chen, Z. Y., The S-system computation of non-central gamma distribution, Journal of Statistical Computation and Simulation, 75, 10, 813-829, (2005) · Zbl 1330.62075 · doi:10.1080/00949650410001687190
[731] Voit, E. O., The S-distribution. A tool for approximation and classification of univariate, unimodal probability distributions, Biometrical Journal, 34, 855-878, (1992) · Zbl 0775.62027
[732] Voit, E. O.; Yu, S., The S-distribution. approximation of discrete distributions, Biometrical Journal, 36, 205-219, (1994) · Zbl 0960.62508
[733] Voit, E. O.; Yu, S., A new tool for distribution approximation and classification, Annual Meeting of the American Statistical Association
[734] He, Q., Completing the Kaplan-Meier estimator when there is extreme right censoring [Ph.D. Dissertation], (1997), Medical University of South Carolina
[735] Yu, S.; Voit, E. O., A graphical classification of classic survival distributions, Proceedings of the International Research Conference on Lifetime Data Models in Reliability and Survival Analysis
[736] Yu, S.; Voit, E. O., A simple, flexible failure model, Biometrical Journal, 37, 595-609, (1995) · Zbl 0837.62097
[737] Yu, S. S.; Voit, E. O.; Jewell, N. P.; Kimber, A. C.; Lee, M.-L. T.; Whitmore, G. A., A graphical classification of survival distributions, Lifetime Data: Models in Reliability and Survival Analysis, 385-392, (1996), Kluwer Academic Publishers, Dordrecht, The Netherlands · Zbl 0909.62120
[738] He, Q.; Voit, E. O., Estimation and completion of survival data with piecewise linear models and S-distributions, Journal of Statistical Computation and Simulation, 75, 4, 287-305, (2005) · Zbl 1059.62101 · doi:10.1080/00949650410001729418
[739] Voit, E. O.; Schwacke, L. H., Random number generation from right-skewed, symmetric, and left-skewed distributions, Risk Analysis, 20, 1, 59-71, (2000) · doi:10.1111/0272-4332.00006
[740] Hernández-Bermejo, B.; Sorribas, A., Analytical quantile solution for the S-distribution, random number generation and statistical data modeling, Biometrical Journal, 43, 1007-1025, (2001) · Zbl 1083.62503
[741] Aksenov, S. V.; Savageau, M. A., Mathematica and C programs for minimum distance estimation of the S distribution and for calculation of goodness-of-fit by bootstrap
[742] Aksenov, S. V.; Savageau, M. A., Statistical inference and modeling with the S-distribution
[743] Balthis, W. L., Application of hierarchical Monte Carlo simulation to the estimation of human exposure to mercury via consumption of King Mackerel (Scomberomorus cavalla) [Doctoral dissertation], (1998), Medical University of South Carolina
[744] Bangerter, J. K., Uncertainty and variability analysis in the estimation of human exposure to mercury from seafood consumption using two-dimensional Monte Carlo simulations [Doctoral dissertation], (1998), Medical University of South Carolina
[745] Voit, E. O.; Schwacke, L. H., Scalability properties of the S-distribution, Biometrical Journal, 40, 6, 665-684, (1998) · Zbl 0914.62008
[746] Voit, E. O., A maximum likelihood estimator for shape parameters of S-distributions, Biometrical Journal, 42, 4, 471-479, (2000) · Zbl 0959.62023
[747] Yu, L.; Voit, E. O., Construction of bivariate S-distributions with copulas, Computational Statistics and Data Analysis, 51, 3, 1822-1839, (2006) · Zbl 1157.62409 · doi:10.1016/j.csda.2005.11.021
[748] Muiño, J. M.; Voit, E. O.; Sorribas, A., GS-distributions: a new family of distributions for continuous unimodal variables, Computational Statistics and Data Analysis, 50, 10, 2769-2798, (2006) · Zbl 1445.62031 · doi:10.1016/j.csda.2005.04.016
[749] Trujillano, J.; Muiño, J. M.; March, J.; Sorribas, A., A more flexible parametric estimation of univariate reference intervals: a new method based on the GS-distribution, Clinica Chimica Acta, 379, 1-2, 71-80, (2007) · doi:10.1016/j.cca.2006.12.010
[750] March, J.; Trujillano, J.; Tor, M.; Sorribas, A., Estimating conditional distributions using a method based on S-distributions reference percentile curves for body mass index in Spanish children, Growth, Development, and Aging, 67, 2, 59-72, (2003)
[751] Sorribas, A.; Muiño, J. M.; Rué, M., Univariate parametric survival analysis using GS-distributions, Statistics and Operations Research Transactions, 30, 2, 205-218, (2006) · Zbl 1274.62654
[752] Voit, E. O.; Schwacke, L. H.; Simpson, K. N., Application of S-distributions to resource use and cost data in clinical economic studies, Proceedings of the Annual Meeting of the American Statistical Association, Section on Survery Research methods
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.