The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.04 - July/August (2011 vol.8)
pp: 943-958
Nuno Tenazinha , Investigação e Desenvolvimento, INESC-ID, Lisboa
Susana Vinga , Investigação e Desenvolvimento, INESC-ID, Lisboa
ABSTRACT
Understanding how cellular systems build up integrated responses to their dynamically changing environment is one of the open questions in Systems Biology. Despite their intertwinement, signaling networks, gene regulation and metabolism have been frequently modeled independently in the context of well-defined subsystems. For this purpose, several mathematical formalisms have been developed according to the features of each particular network under study. Nonetheless, a deeper understanding of cellular behavior requires the integration of these various systems into a model capable of capturing how they operate as an ensemble. With the recent advances in the "omics” technologies, more data is becoming available and, thus, recent efforts have been driven toward this integrated modeling approach. We herein review and discuss methodological frameworks currently available for modeling and analyzing integrated biological networks, in particular metabolic, gene regulatory and signaling networks. These include network-based methods and Chemical Organization Theory, Flux-Balance Analysis and its extensions, logical discrete modeling, Petri Nets, traditional kinetic modeling, Hybrid Systems and stochastic models. Comparisons are also established regarding data requirements, scalability with network size and computational burden. The methods are illustrated with successful case studies in large-scale genome models and in particular subsystems of various organisms.
INDEX TERMS
Systems biology, survey, modeling methodologies, integrated biological networks.
CITATION
Nuno Tenazinha, Susana Vinga, "A Survey on Methods for Modeling and Analyzing Integrated Biological Networks", IEEE/ACM Transactions on Computational Biology and Bioinformatics, vol.8, no. 4, pp. 943-958, July/August 2011, doi:10.1109/TCBB.2010.117
REFERENCES
[1] D. Noble, The Music of Life: Biology Beyond the Genome. Oxford Univ. Press, 2006.
[2] F. Crick, “Central Dogma of Molecular Biology,” Nature, vol. 227, no. 5258, pp. 561-563, Aug. 1970.
[3] F.H. Crick, “On Protein Synthesis,” Proc. Symp. Soc. Experimental Biology, vol. 12, pp. 138-163, 1958.
[4] A.L. Barabasi and Z.N. Oltvai, “Network Biology: Understanding the Cell's Functional Organization,” Nature Rev. Genetics, vol. 5, no. 2, pp. 101-113, Feb. 2004.
[5] H. Kitano, “Systems Biology: A Brief Overview,” Science, vol. 295, no. 5560, pp. 1662-1624, Mar. 2002.
[6] B.H. ter Kuile and H.V. Westerhoff, “Transcriptome Meets Metabolome: Hierarchical and Metabolic Regulation of the Glycolytic Pathway,” Federation of European Biochemical Soc. Letters, vol. 500, no. 3, pp. 169-171, July 2001.
[7] U. Sauer, M. Heinemann, and N. Zamboni, “Genetics. Getting Closer to the Whole Picture,” Science, vol. 316, no. 5824, pp. 550-551, Apr. 2007.
[8] A. Quarteroni, “Mathematical Models in Science and Engineering,” Notices of the AMS, vol. 56, no. 1, pp. 10-19, 2009.
[9] M.J. Herrgard, N. Swainston, P. Dobson, W.B. Dunn, K.Y. Arga, M. Arvas, N. Bluthgen, S. Borger, R. Costenoble, M. Heinemann, M. Hucka, N. Le Novere, P. Li, W. Liebermeister, M.L. Mo, A.P. Oliveira, D. Petranovic, S. Pettifer, E. Simeonidis, K. Smallbone, I. Spasic, D. Weichart, R. Brent, D.S. Broomhead, H.V. Westerhoff, B. Kirdar, M. Penttila, E. Klipp, B.O. Palsson, U. Sauer, S.G. Oliver, P. Mendes, J. Nielsen, and D.B. Kell, “A Consensus Yeast Metabolic Network Reconstruction Obtained from a Community Approach to Systems Biology,” Nature Biotechnology, vol. 26, no. 10, pp. 1155-1160, Oct. 2008.
[10] B. Teusink, J. Passarge, C.A. Reijenga, E. Esgalhado, C.C. Van Der Weijden, M. Schepper, M.C. Walsh, B.M. Bakker, K. van Dam, H.V. Westerhoff, and J.L. Snoep, “Can Yeast Glycolysis Be Understood in Terms of in Vitro Kinetics of the Constituent Enzymes? Testing Biochemistry,” European J. Biochemistry, vol. 267, no. 17, pp. 5313-5329, Sept. 2000.
[11] S. Rinaldi and M. Scheffer, “Geometric Analysis of Ecological Models with Slow and Fast Processes,” Ecosystems, vol. 3, no. 6, pp. 507-521, Nov./Dec. 2000.
[12] A. Kumar, P.D. Christofides, and P. Daoutidis, “Singular Perturbation Modeling of Nonlinear Processes with Nonexplicit Time-Scale Multiplicity,” Chemical Eng. Science, vol. 53, no. 8, pp. 1491-1504, Apr. 1998.
[13] M. Rizzi, M. Baltes, U. Theobald, and M. Reuss, “In Vivo Analysis of Metabolic Dynamics in Saccharomyces Cerevisiae.2. Mathematical Model,” Biotechnology and Bioeng., vol. 55, no. 4, pp. 592-608, Aug. 1997.
[14] U. Theobald, W. Mailinger, M. Baltes, M. Rizzi, and M. Reuss, “In Vivo Analysis of Metabolic Dynamics in Saccharomyces Cerevisiae.1. Experimental Observations,” Biotechnology and Bioeng., vol. 55, no. 2, pp. 305-316, July 1997.
[15] R. Thomas, “Boolean Formalization of Genetic Control Circuits,” J. Theoretical Biology, vol. 42, no. 3, pp. 563-585, Dec. 1973.
[16] F. Li, T. Long, Y. Lu, Q. Ouyang, and C. Tang, “The Yeast Cell-Cycle Network is Robustly Designed,” Proc. Nat'l Academy of Sciences USA, vol. 101, no. 14, pp. 4781-4786, Apr. 2004.
[17] A. Faure, A. Naldi, C. Chaouiya, and D. Thieffry, “Dynamical Analysis of a Generic Boolean Model for the Control of the Mammalian Cell Cycle,” Bioinformatics, vol. 22, no. 14, pp. e124-e131, July 2006.
[18] B.C. Goodwin, “Oscillatory Behavior in Enzymatic Control Processes,” Advances in Enzyme Regulation, vol. 3, pp. 425-438, 1965.
[19] S. Li, P. Brazhnik, B. Sobral, and J.J. Tyson, “A Quantitative Study of the Division Cycle of Caulobacter Crescentus Stalked Cells,” Plos Computational Biology, vol. 4, no. 1,article no. e9, Jan. 2008.
[20] K.C. Chen, L. Calzone, A. Csikasz-Nagy, F.R. Cross, B. Novak, and J.J. Tyson, “Integrative Analysis of Cell Cycle Control in Budding Yeast,” Molecular Biology of the Cell, vol. 15, no. 8, pp. 3841-3862, Aug. 2004.
[21] H. De Jong, J. Geiselmann, G. Batt, C. Hernandez, and M. Page, “Qualitative Simulation of the Initiation of Sporulation in Bacillus Subtilis,” Bull. Math. Biology, vol. 66, no. 2, pp. 261-299, Mar. 2004.
[22] D. Ropers, H. de Jong, M. Page, D. Schneider, and J. Geiselmann, “Qualitative Simulation of the Carbon Starvation Response in Escherichia Coli,” Biosystems, vol. 84, no. 2, pp. 124-152, May 2006.
[23] H.H. McAdams and A. Arkin, “Stochastic Mechanisms in Gene Expression,” Proc. Nat'l Academy of Sciences USA, vol. 94, no. 3, pp. 814-819, Feb. 1997.
[24] J. Paulsson, “Models of Stochastic Gene Expression,” Physics of Life Rev., vol. 2, no. 2, pp. 157-175, June 2005.
[25] E. Cinquemani, A. Milias-Argeitis, S. Summers, and J. Lygeros, “Stochastic Dynamics of Genetic Networks: Modelling and Parameter Identification,” Bioinformatics, vol. 24, no. 23, pp. 2748-2754, Dec. 2008.
[26] H. De Jong, “Modeling and Simulation of Genetic Regulatory Systems: A Literature Review,” J. Computational Biology, vol. 9, no. 1, pp. 67-103, 2002.
[27] G. Karlebach and R. Shamir, “Modelling and Analysis of Gene Regulatory Networks,” Nature Rev. Molecular Cell Biology, vol. 9, no. 10, pp. 770-780, Oct. 2008.
[28] E.P. Gianchandani, J.A. Papin, N.D. Price, A.R. Joyce, and B.O. Palsson, “Matrix Formalism to Describe Functional States of Transcriptional Regulatory Systems,” Plos Computational Biology, vol. 2, no. 8, pp. 902-917, Aug. 2006.
[29] R. Heinrich and S. Schuster, The Regulation of Cellular Systems. Chapman & Hall, 1996.
[30] J.S. Edwards, R.U. Ibarra, and B.O. Palsson, “In Silico Predictions of Escherichia Coli Metabolic Capabilities Are Consistent with Experimental Data,” Nature Biotechnology, vol. 19, no. 2, pp. 125-130, Feb. 2001.
[31] C.H. Schilling, J.S. Edwards, D. Letscher, and B.O. Palsson, “Combining Pathway Analysis with Flux Balance Analysis for the Comprehensive Study of Metabolic Systems,” Biotechnology and Bioeng., vol. 71, no. 4, pp. 286-306, 2000.
[32] P. Wong, S. Gladney, and J.D. Keasling, “Mathematical Model of the Lac Operon: Inducer Exclusion, Catabolite Repression, and Diauxic Growth on Glucose and Lactose,” Biotechnology Progress, vol. 13, no. 2, pp. 132-143, Mar./Apr. 1997.
[33] E.O. Voit, J. Almeida, S. Marino, R. Lall, G. Goel, A.R. Neves, and H. Santos, “Regulation of Glycolysis in Lactococcus Lactis: An Unfinished Systems Biological Case Study,” Systems Biology, vol. 153, no. 4, pp. 286-298, July 2006.
[34] H.V. Westerhoff, A. Kolodkin, R. Conradie, S.J. Wilkinson, F.J. Bruggeman, K. Krab, J.H. van Schuppen, H. Hardin, B.M. Bakker, M.J. Mone, K.N. Rybakova, M. Eijken, H.J. van Leeuwen, and J.L. Snoep, “Systems Biology towards Life in Silico: Mathematics of the Control of Living Cells,” J Math. Biology, vol. 58, nos. 1/2, pp. 7-34, Jan. 2009.
[35] R. Alves, E. Vilaprinyo, B. Hernandez-Bermejo, and A. Sorribas, “Mathematical Formalisms Based on Approximated Kinetic Representations for Modeling Genetic and Metabolic Pathways,” Biotechnology and Genetic Eng. Rev., vol. 25, pp. 1-40, 2008.
[36] M. Durot, P.Y. Bourguignon, and V. Schachter, “Genome-Scale Models of Bacterial Metabolism: Reconstruction and Applications,” FEMS Microbiology Rev, vol. 33, no. 1, pp. 164-190, Jan. 2009.
[37] M. Terzer, N.D. Maynard, M.W. Covert, and J. Stelling, “Genome-Scale Metabolic Networks,” WIREs Systems Biology and Medicine, vol. 1, no. 3, pp. 285-297, 2009.
[38] M.A. Ovacik and I.P. Androulakis, “On the Potential for Integrating Gene Expression and Metabolic Flux Data,” Current Bioinformatics, vol. 3, no. 3, pp. 142-148, Sept. 2008.
[39] O. Mason and M. Verwoerd, “Graph Theory and Networks in Biology,” IET Systems Biology, vol. 1, no. 2, pp. 89-119, Mar. 2007.
[40] T. Aittokallio and B. Schwikowski, “Graph-Based Methods for Analysing Networks in Cell Biology,” Brief Bioinformatics, vol. 7, no. 3, pp. 243-255, Sept. 2006.
[41] R. Albert, “Network Inference, Analysis, and Modeling in Systems Biology,” Plant Cell, vol. 19, no. 11, pp. 3327-3338, Nov. 2007.
[42] S. Klamt, U.U. Haus, and F. Theis, “Hypergraphs and Cellular Networks,” Plos Computational Biology, vol. 5, no. 5,article no. e1000385, May 2009.
[43] C.H. Yeang and M. Vingron, “A Joint Model of Regulatory and Metabolic Networks,” BMC Bioinformatics, vol. 7, article no. 332, July 2006.
[44] S. Schuster, D.A. Fell, and T. Dandekar, “A General Definition of Metabolic Pathways Useful for Systematic Organization and Analysis of Complex Metabolic Networks,” Nature Biotechnology, vol. 18, no. 3, pp. 326-332, Mar. 2000.
[45] J. Stelling, S. Klamt, K. Bettenbrock, S. Schuster, and E.D. Gilles, “Metabolic Network Structure Determines Key Aspects of Functionality and Regulation,” Nature, vol. 420, no. 6912, pp. 190-193, Nov. 2002.
[46] J.A. Papin, J. Stelling, N.D. Price, S. Klamt, S. Schuster, and B.O. Palsson, “Comparison of Network-Based Pathway Analysis Methods,” Trends in Biotechnology, vol. 22, no. 8, pp. 400-405, Aug. 2004.
[47] M.W. Covert and B.O. Palsson, “Constraints-Based Models: Regulation of Gene Expression Reduces the Steady-State Solution Space,” J. Theoretical Biology, vol. 221, no. 3, pp. 309-325, Apr. 2003.
[48] M. Terzer and J. Stelling, “Elementary Flux Modes - State-of-the-Art implementation and Scope of Application,” BMC Systems Biology, vol. 1, Suppl 1:P2, 2007.
[49] C.T. Trinh, A. Wlaschin, and F. Srienc, “Elementary Mode Analysis: A Useful Metabolic Pathway Analysis Tool for Characterizing Cellular Metabolism,” Applied Microbiology and Biotechnology, vol. 81, no. 5, pp. 813-826, Jan. 2009.
[50] F. Llaneras and J. Pico, “Stoichiometric Modelling of Cell Metabolism,” J. Bioscience and Bioeng., vol. 105, no. 1, pp. 1-11, Jan. 2008.
[51] Z. Szallasi, J. Stelling, and V. Periwal, System Modeling in Cell Biology : From Concepts to Nuts and Bolts. MIT Press, 2006.
[52] N.D. Price, J.A. Papin, C.H. Schilling, and B.O. Palsson, “Genome-Scale Microbial in Silico Models: The Constraints-Based Approach,” Trends in Biotechnology, vol. 21, no. 4, pp. 162-169, Apr. 2003.
[53] M.W. Covert, C.H. Schilling, and B. Palsson, “Regulation of Gene Expression in Flux Balance Models of Metabolism,” J. Theoretical Biology, vol. 213, no. 1, pp. 73-88, Nov. 2001.
[54] A. Varma and B.O. Palsson, “Stoichiometric Flux Balance Models Quantitatively Predict Growth and Metabolic By-Product Secretion in Wild-Type Escherichia-Coli W3110,” Applied and Environmental Microbiology, vol. 60, no. 10, pp. 3724-3731, Oct. 1994.
[55] M.W. Covert and B.O. Palsson, “Transcriptional Regulation in Constraints-Based Metabolic Models of Escherichia Coli,” J. Biological Chemistry, vol. 277, no. 31, pp. 28058-28064, Aug. 2002.
[56] M.W. Covert, E.M. Knight, J.L. Reed, M.J. Herrgard, and B.O. Palsson, “Integrating High-Throughput and Computational Data Elucidates Bacterial Networks,” Nature, vol. 429, no. 6987, pp. 92-96, May 2004.
[57] M.J. Herrgard, B.S. Lee, V. Portnoy, and B.O. Palsson, “Integrated Analysis of Regulatory and Metabolic Networks Reveals Novel Regulatory Mechanisms in Saccharomyces Cerevisiae,” Genome Research, vol. 16, no. 5, pp. 627-635, May 2006.
[58] T. Shlomi, Y. Eisenberg, R. Sharan, and E. Ruppin, “A Genome-Scale Computational Study of the Interplay between Transcriptional Regulation and Metabolism,” Molecular Systems Biology, vol. 3, p. 101, 2007.
[59] S. Rossell, C.C. Van Der Weijden, A. Lindenbergh, A. van Tuijl, C. Francke, B.M. Bakker, and H.V. Westerhoff, “Unraveling the Complexity of Flux Regulation: A New Method Demonstrated for Nutrient Starvation in Saccharomyces Cerevisiae,” Proc Nat'l Academy of Sciences USA, vol. 103, no. 7, pp. 2166-2171, Feb. 2006.
[60] M.W. Covert, N. Xiao, T.J. Chen, and J.R. Karr, “Integrating Metabolic, Transcriptional Regulatory and Signal Transduction Models in Escherichia Coli,” Bioinformatics, vol. 24, no. 18, pp. 2044-2050, Sept. 2008.
[61] A. Kremling, K. Bettenbrock, and E.D. Gilles, “Analysis of Global Control of Escherichia Coli Carbohydrate Uptake,” BMC Systems Biology, vol. 1, p. 42, 2007.
[62] J.M. Lee, E.P. Gianchandani, J.A. Eddy, and J.A. Papin, “Dynamic Analysis of Integrated Signaling, Metabolic, and Regulatory Networks,” Plos Computational Biology, vol. 4, no. 5,article no. e1000086, May 2008.
[63] S. Hohmann, “Osmotic Stress Signaling and Osmoadaptation in Yeasts,” Microbiology and Molecular Biology Rev., vol. 66, no. 2, pp. 300-372, June 2002.
[64] W. Fontana and L.W. Buss, “The Arrival of the Fittest”: toward a Theory of Biological Organization,” Bull. Math. Biology, vol. 56, pp. 1-64, 1994.
[65] P. Dittrich and P. Speroni di Fenizio, “Chemical Organization Theory,” Bull. Math. Biology, vol. 69, no. 4, pp. 1199-1231, 2007.
[66] C. Kaleta, F. Centler, and P. Dittrich, “Analyzing Molecular Reaction Networks,” Molecular Biotechnology, vol. 34, no. 2, pp. 117-123, Oct. 2006.
[67] F. Centler and P. Dittrich, “Chemical Organizations in Atmospheric Photochemistries—A New Method to Analyze Chemical Reaction Networks,” Planetary and Space Science, vol. 55, no. 4, pp. 413-428, Mar. 2007.
[68] N. Matsumaru, F. Centler, P.S. Di Fenizio, and P. Dittrich, “Chemical Organization Theory Applied to Virus Dynamics,” it—Information Technology, vol. 48, no. 3, pp. 154-160, 2006.
[69] F. Centler, P.S. di Fenizio, N. Matsumaru, and P. Dittrich, “Chemical Organizations in the Central Sugar Metabolism of Escherichia Coli,” Math. Modeling of Biological Systems, Vol I, pp. 105-119, vol. 379, 2007.
[70] C. Kaleta, F. Centler, P.S. di Fenizio, and P. Dittrich, “Phenotype Prediction in Regulated Metabolic Networks,” BMC Systems Biology, vol. 2, article no. 37, Apr. 2008.
[71] F. Centler, C. Kaleta, P.S. di Fenizio, and P. Dittrich, “Computing Chemical Organizations in Biological Networks,” Bioinformatics, vol. 24, no. 14, pp. 1611-1618, July 2008.
[72] J.A. Asenjo, P. Ramirez, I. Rapaport, J. Aracena, E. Goles, and B.A. Andrews, “A Discrete Mathematical Model Applied to Genetic Regulation and Metabolic Networks,” J. Microbiology and Biotechnology, vol. 17, no. 3, pp. 496-510, Mar. 2007.
[73] I. Koch and M. Heiner, “Petri Nets,” Analysis of Biological Networks, B.H. Junker and F. Schreiber, eds., pp. 139-180, John Wiley & Sons, 2008.
[74] C. Chaouiya, “Petri Net Modelling of Biological Networks,” Briefings in Bioinformatics, vol. 8, no. 4, pp. 210-219, July 2007.
[75] W. Reisig, Petri Nets: An Introduction. Springer, 1985.
[76] I. Koch, B.H. Junker, and M. Heiner, “Application of Petri Net Theory for Modelling and Validation of the Sucrose Breakdown Pathway in the Potato Tuber,” Bioinformatics, vol. 21, no. 7, pp. 1219-1226, Apr. 2005.
[77] D.W. Ding and L.N. Li, “Modeling and Analyzing the Metabolism of Riboflavin Production Using Petri Nets,” J. Biological Systems, vol. 17, no. 3, pp. 479-490, Sept. 2009.
[78] M. Heiner, I. Koch, and R. Will, “Model Validation of Biological Pathways Using Petri Nets—Demonstrated for Apoptosis,” Biosystems, vol. 75, nos. 1-3, pp. 15-28, July 2004.
[79] A. Sackmann, M. Heiner, and I. Koch, “Application of Petri Net Based Analysis Techniques to Signal Transduction Pathways,” BMC Bioinformatics, vol. 7, article no. 482, Nov. 2006.
[80] R. Srivastava, M.S. Peterson, and W.E. Bentley, “Stochastic Kinetic Analysis of the Escherichia Coli Stress Circuit Using Sigma(32)-Targeted Antisense,” Biotechnology and Bioeng., vol. 75, no. 1, pp. 120-129, Oct. 2001.
[81] L.J. Steggles, R. Banks, and A. Wipat, “Modelling and Analysing Genetic Networks: From Boolean Networks to Petri Nets,” Proc. Conf. Computational Methods in Systems Biology, pp. 127-141, 2006.
[82] C. Chaouiya, E. Remy, P. Ruet, and D. Thieffry, “Qualitative Modelling of Genetic Networks: From Logical Regulatory Graphs to Standard Petri Nets,” Proc. Int'l Conf. Applications and Theory of Petri Nets '04, pp. 137-156, 2004.
[83] C. Chaouiya, E. Remy, and D. Thieffry, “Qualitative Petri Net Modelling of Genetic Networks,” Trans. Computational Systems Biology VI, vol. 4220, pp. 95-112, 2006.
[84] E. Simao, E. Remy, D. Thieffry, and C. Chaouiya, “Qualitative Modelling of Regulated Metabolic Pathways: Application to the Tryptophan Biosynthesis in E.Coli,” Bioinformatics, vol. 21, pp. 190-196, Sept. 2005.
[85] H. Genrich, R. Kueffner, and K. Voss, “Executable Petri Net Models for the Analysis of Metabolic Pathways,” Int'l J. Software Tools for Technology Transfer, vol. 3, pp. 394-404, 2001.
[86] C. Li, Q.W. Ge, M. Nakata, H. Matsuno, and S. Miyano, “Modelling and Simulation of Signal Transductions in an Apoptosis Pathway by Using Timed Petri Nets,” J Biosciences, vol. 32, no. 1, pp. 113-127, Jan. 2007.
[87] H. Matsuno, R. Murakami, R. Yamane, N. Yamasaki, S. Fujita, H. Yoshimori, and S. Miyano, “Boundary Formation by Notch Signaling in Drosophila Multicellular Systems: Experimental Observations and Gene Network Modeling by Genomic Object Net,” Proc. Pac Symp. Biocomputing, pp. 152-163, 2003.
[88] E. Grafahrend-Belau, F. Schreiber, M. Heiner, A. Sackmann, B.H. Junker, S. Grunwald, A. Speer, K. Winder, and I. Koch, “Modularization of Biochemical Networks Based on Classification of Petri Net T-Invariants,” BMC Bioinformatics, vol. 9, article no. 90, Feb. 2008.
[89] M. Heiner and I. Koch, “Petri Net Based Model Validation in Systems Biology,” Proc. Applications and Theory of Petri Nets '04, vol. 3099, pp. 216-237, 2004.
[90] J. Heath, M. Kwiatkowska, G. Norman, D. Parker, and O. Tymchyshyn, “Probabilistic Model Checking of Complex Biological Pathways,” Theoretical Computer Science, vol. 391, no. 3, pp. 239-257, Feb. 2008.
[91] J.S. Ferreira, R. Lozano, S. Mondie, and A. Friboulet, “Bifurcation Analysis of a Biochemical Network,” Proc. Positive Systems, vol. 341, pp. 279-286, 2006.
[92] E. Klipp, Systems Biology in Practice : Concepts, Implementation and Application. Wiley-VCH, 2005.
[93] S. Goutelle, M. Maurin, F. Rougier, X. Barbaut, L. Bourguignon, M. Ducher, and P. Maire, “The Hill Equation: A Review of Its Capabilities in Pharmacological Modelling,” Fundamental and Clinical Pharmacology, vol. 22, no. 6, pp. 633-648, Dec. 2008.
[94] M.A. Savageau, Biochemical Systems Analysis : A Study of Function and Design in Molecular Biology. Addison-Wesley Pub. Co., 1976.
[95] E.O. Voit, Computational Analysis of Biochemical Systems : A Practical Guide for Biochemists and Molecular Biologists. Cambridge Univ. Press, 2000.
[96] V. Hatzimanikatis and J.E. Bailey, “Effects of Spatiotemporal Variations on Metabolic Control: Approximate Analysis Using (Log)Linear Kinetic Models,” Biotechnology and Bioeng., vol. 54, no. 2, pp. 91-104, Apr. 1997.
[97] J.J. Heijnen, “Approximative Kinetic Formats Used in Metabolic Network Modeling,” Biotechnol Bioeng, vol. 91, no. 5, pp. 534-545, Sept. 2005.
[98] A. Sorribas, B. Hernandez-Bermejo, E. Vilaprinyo, and R. Alves, “Cooperativity and Saturation in Biochemical Networks: A Saturable Formalism Using Taylor Series Approximations,” Biotechnology Bioeng, vol. 97, no. 5, pp. 1259-1277, Aug. 2007.
[99] C.G. Moles, P. Mendes, and J.R. Banga, “Parameter Estimation in Biochemical Pathways: A Comparison of Global Optimization Methods,” Genome Research, vol. 13, no. 11, pp. 2467-2474, Nov. 2003.
[100] A. Babloyan and M. Sanglier, “Chemical Instabilities of All-or-None Type in Beta-Galactosidase Induction and Active Transport,” Federation of the Soc. of Biochemistry Letters, vol. 23, no. 3, pp. 364-366, 1972.
[101] M. Santillan and M.C. Mackey, “Influence of Catabolite Repression and Inducer Exclusion on the Bistable Behavior of the Lac Operon,” Biophysical J., vol. 86, no. 3, pp. 1282-1292, Mar. 2004.
[102] M.J.A. van Hoek and P. Hogeweg, “In Silico Evolved Lac Operons Exhibit Bistability for Artificial Inducers, but Not for Lactose,” Biophysical J., vol. 91, no. 8, pp. 2833-2843, Oct. 2006.
[103] M. van Hoek and P. Hogeweg, “The Effect of Stochasticity on the Lac Operon: An Evolutionary Perspective,” Plos Computational Biology, vol. 3, no. 6, pp. 1071-1082, June 2007.
[104] E. Klipp, B. Nordlander, R. Kruger, P. Gennemark, and S. Hohmann, “Integrative Model of the Response of Yeast to Osmotic Shock,” Nature Biotechnology, vol. 23, no. 8, pp. 975-982, Aug. 2005.
[105] O. Demir and I.A. Kurnaz, “An Integrated Model of Glucose and Galactose Metabolism Regulated by the Gal Genetic Switch,” Computational Biology and Chemistry, vol. 30, no. 3, pp. 179-192, June 2006.
[106] J. Lygeros, K.H. Johansson, S.N. Simic, J. Zhang, and S.S. Sastry, “Dynamical Properties of Hybrid Automata,” IEEE Trans. Automatic Control, vol. 48, no. 1, pp. 2-17, Jan. 2003.
[107] P. Lincoln and A. Tiwari, “Symbolic Systems Biology: Hybrid Modeling and Analysis of Biological Networks,” Proc. Hybrid Systems: Computation and Control, vol. 2993, pp. 660-672, 2004.
[108] K.H. Cho, K.H. Johansson, and O. Wolkenhauer, “A Hybrid Systems Framework for Cellular Processes,” Biosystems, vol. 80, no. 3, pp. 273-282, June 2005.
[109] R. Rosen, “Some Realizations of (M, R)-Systems and Their Interpretation,” Bull. Math. Biophysics, vol. 33, no. 3, pp. 303-319, 1971.
[110] J.L. Casti, “The Theory of Metabolism-Repair Systems,” Applied Math. and Computation, vol. 28, no. 2, pp. 113-154, Nov. 1988.
[111] M. Belta, P. Finin, L.C.G.J.M. Habets, A.M. Halasz, M. Imielinski, R.V. Kumar, and H. Rubin, “Understanding the Bacterial Stringent Response Using Reachability Analysis of Hybrid Systems,” Proc. Conf. Hybrid Systems: Computation and Control, vol. 2993, pp. 111-125, 2004.
[112] A. Halasz, V. Kumar, M. Imielinski, C. Belta, O. Sokolsky, S. Pathak, and H. Rubin, “Analysis of Lactose Metabolism in E.Coli Using Reachability Analysis of Hybrid Systems,” IET Systems Biology, vol. 1, no. 2, pp. 130-148, Mar. 2007.
[113] H. Matsuno, Y. Tanaka, H. Aoshima, A. Doi, M. Matsui, and S. Miyano, “Biopathways Representation and Simulation on Hybrid Functional Petri Net,” In Silico Biology, vol. 3, no. 3, pp. 389-404, 2003.
[114] M. Chen and R. Hofestadt, “Quantitative Petri Net Model of Gene Regulated Metabolic Networks in the Cell,” In Silico Biology, vol. 3, no. 3, pp. 347-365, 2003.
[115] W. Marwan, A. Sujatha, and C. Starostzik, “Reconstructing the Regulatory Network Controlling Commitment and Sporulation in Physarum Polycephalum Based on Hierarchical Petri Net Modelling and Simulation,” J. Theoretical Biology, vol. 236, no. 4, pp. 349-365, Oct. 2005.
[116] S. Troncale, F. Tahi, D. Campard, J.P. Vannier, and J. Guespin, “Modeling and Simulation with Hybrid Functional Petri Nets of the Role of Interleukin-6 in Human Early Haematopoiesis,” Proc. Pac Symp. Biocomputing, pp. 427-438, 2006.
[117] J. Wu and E. Voit, “Hybrid Modeling in Biochemical Systems Theory by Means of Functional Petri Nets,” J. Bioinformatics Computer Biology, vol. 7, no. 1, pp. 107-134, Feb. 2009.
[118] J. Wu and E. Voit, “Integrative Biological Systems Modeling: Challenges and Opportunities,” Frontiers Computer Science in China, vol. 3, no. 1, pp. 92-100, 2009.
[119] P.S. Swain, M.B. Elowitz, and E.D. Siggia, “Intrinsic and Extrinsic Contributions to Stochasticity in Gene Expression,” Proc. Nat'l Academy of Sciences USA, vol. 99, no. 20, pp. 12795-12800, Oct. 2002.
[120] S. Kar, W.T. Baumann, M.R. Paul, and J.J. Tyson, “Exploring the Roles of Noise in the Eukaryotic Cell Cycle,” Proc. Nat'l Academy of Sciences USA, vol. 106, no. 16, pp. 6471-6476, Apr. 2009.
[121] A. Arkin, J. Ross, and H.H. McAdams, “Stochastic Kinetic Analysis of Developmental Pathway Bifurcation in Phage Lambda-Infected Escherichia Coli Cells,” Genetics, vol. 149, no. 4, pp. 1633-1648, Aug. 1998.
[122] D. Gonze and A. Goldbeter, “Circadian Rhythms and Molecular Noise,” Chaos, vol. 16, no. 2,article no. 026110, June 2006.
[123] D. Schultz, E. Ben Jacob, J.N. Onuchic, and P.G. Wolynes, “Molecular Level Stochastic Model for Competence Cycles in Bacillus Subtilis,” Proc. Nat'l Academy of Sciences USA, vol. 104, no. 45, pp. 17582-17587, Nov. 2007.
[124] L.S. Weinberger, J.C. Burnett, J.E. Toettcher, A.P. Arkin, and D.V. Schaffer, “Stochastic Gene Expression in a Lentiviral Positive-Feedback Loop: Hiv-1 Tat Fluctuations Drive Phenotypic Diversity,” Cell, vol. 122, no. 2, pp. 169-182, July 2005.
[125] V. Prasad and K.V. Venkatesh, “Stochastic Analysis of the Gal Genetic Switch in Saccharomyces Cerevisiae: Modeling and Experiments Reveal Hierarchy in Glucose Repression,” BMC Systems Biology, vol. 2, article no. 97, Nov. 2008.
[126] D.T. Gillespie, “General Method for Numerically Simulating Stochastic Time Evolution of Coupled Chemical-Reactions,” J. Computational Physics, vol. 22, no. 4, pp. 403-434, 1976.
[127] D.T. Gillespie, “The Chemical Langevin Equation,” J. Chemical Physics, vol. 113, no. 1, pp. 297-306, July 2000.
[128] M. Rathinam, L.R. Petzold, Y. Cao, and D.T. Gillespie, “Stiffness in Stochastic Chemically Reacting Systems: The Implicit Tau-Leaping Method,” J. Chemical Physics, vol. 119, no. 24, pp. 12784-12794, Dec. 2003.
[129] A. Chatterjee, K. Mayawala, J.S. Edwards, and D.G. Vlachos, “Time Accelerated Monte Carlo Simulations of Biological Networks Using the Binomial Tau-Leap Method,” Bioinformatics, vol. 21, no. 9, pp. 2136-2137, May 2005.
[130] A. Chatterjee and D.G. Vlachos, “Multiscale Spatial Monte Carlo Simulations: Multigriding, Computational Singular Perturbation, and Hierarchical Stochastic Closures,” J. Chemical Physics, vol. 124, no. 6,article no. 64110, Feb. 2006.
[131] C.S. Gillespie, “Moment-Closure Approximations for Mass-Action Models,” IET Systems Biology, vol. 3, no. 1, pp. 52-58, Jan. 2009.
[132] B. Munsky and M. Khammash, “The Finite State Projection Algorithm for the Solution of the Chemical Master Equation,” J. Chemical Physics, vol. 124, no. 4,article no. 044104, Jan. 2006.
[133] B. Munsky and M. Khammash, “The Finite State Projection Approach for the Analysis of Stochastic Noise in Gene Networks,” IEEE Trans. Circuits and Systems I-Regular Papers, pp. 201-214, Jan. 2008.
[134] I.C. Chou and E.O. Voit, “Recent Developments in Parameter Estimation and Structure Identification of Biochemical and Genomic Systems,” Math. Bioscience, vol. 219, no. 2, pp. 57-83, June 2009.
[135] S. Audoly, G. Bellu, L. D'Angio, M.P. Saccomani, and C. Cobelli, “Global Identifiability of Nonlinear Models of Biological Systems,” IEEE Trans Biomedical Eng, vol. 48, no. 1, pp. 55-65, Jan. 2001.
[136] L. Ljung and S.T. Glad, “On Global Identifiability for Arbitrary Model Parameterizations,” Automatica, vol. 30, no. 2, pp. 265-276, 1994.
[137] M.P. Saccomani, S. Audoly, G. Bellu, and L. D'Angio, “Parameter Identifiability of Nonlinear Biological Systems,” Positive Systems, pp. 87-93, 2004.
[138] S. Hengl, C. Kreutz, J. Timmer, and T. Maiwald, “Data-Based Identifiability Analysis of Non-Linear Dynamical Models,” Bioinformatics, vol. 23, no. 19, pp. 2612-8, Oct. 2007.
[139] L. Pu, J. Hu, and B. Chen, “Information Theoretical Approach to Identification of Hybrid Systems,” Proc. Int'l Workshop Hybrid Systems: Computation and Control, pp. 650-653, 2008.
[140] F. Lauer and G. Bloch, “Switched and Piecewise Nonlinear Hybrid System Identification,” Proc. Int'l Workshop Hybrid Systems: Computation and Control, pp. 330-343, 2008.
[141] N. Nandola and S. Bhartiya, “Hybrid System Identification Using a Structural Approach and Its Model Based Control: An Experimental Validation,” Nonlinear Analysis: Hybrid Systems, vol. 3, no. 2, pp. 87-100, 2009.
[142] J.D. Young, K.L. Henne, J.A. Morgan, A.E. Konopka, and D. Ramkrishna, “Integrating Cybernetic Modeling with Pathway Analysis Provides a Dynamic, Systems-Level Description of Metabolic Control,” Biotechnology and Bioeng., vol. 100, no. 3, pp. 542-59, June 2008.
[143] J.I. Kim, J.D. Varner, and D. Ramkrishna, “A Hybrid Model of Anaerobic E. Coli Gjt001: Combination of Elementary Flux Modes and Cybernetic Variables,” Biotechnology Progress, vol. 24, no. 5, pp. 993-1006, Sept./Oct. 2008.
6 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool