Abstract
Equation-based algorithms make hypotheses regarding the biophysical dynamical laws that govern a biological system and in the form of a mathematical expression, aiming to interrelate the system components, in an effort to explain and verify the experimental observations. This approach is what we mainly regard as dynamical inference. Assumptions such as the deterministic or stochastic laws that govern the system dynamics, the degree of modeling spatial phenomena, the exact mathematical representations of these biophysical laws and constraints, comprise some of the main issues of the dynamical inference problem. Another class of algorithms considers the cell as a whole system that orchestrates its components under physio-chemical constraints towards the accomplishment of certain cellular functions. These approaches avoid the search of detailed equation forms as well as the demand of knowledge of the parameters involved in the kinetics, and produce a steady state dynamic picture of the complex, genome-scale metabolic network of chemical reactions at the flux level. The constraint-based methods are essential for the analysis of the metabolic capabilities of organisms as well as the elucidation of systemic properties that cannot be described by descriptions of individual components or sub-systems.
The current biological knowledge, the available data and the computer power, are the issues that actually determine the upper limit for the system size and its complexity that can be simulated, thus defining our level of understanding.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Suggested Reading
Chen, B.S., et al., A new measure of the robustness of biochemical networks. Bioinformatics, 2005. 21(11): p. 2698–2705.
Mahadevan, R. and C.H. Schilling, The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metab Eng, 2003. 4(5): p. 264–276.
Orphanides, G. and D. Reinberg, A unified theory of gene expression. Cell, 2002. 4(108): p. 439–451.
Ribeiro, A., R. Zhu, and S.A. Kauffman, A general modeling strategy for gene regulatory networks with stochastic dynamics. J Comput Biol, 2006. 9(13): p. 1630–1639.
Chen, K.C., et al., A stochastic differential equation model for quantifying transcriptional regulatory network in Saccharomyces cerevisiae. Bioinformatics, 2005. 12(21): p. 2883–2890.
McAdams, H.H. and A. Arkin, Stochastic mechanisms in gene expression. Proc Natl Acad Sci U S A, 1997. 3(94): p. 814–819.
Joshi, A. and B.O. Palsson, Metabolic dynamics in the human red cell. Part I—A comprehensive kinetic model. J Theor Biol, 1989. 4(141): p. 515–528.
Nakayama, Y., A. Kinoshita, and M. Tomita, Dynamic simulation of red blood cell metabolism and its application to the analysis of a pathological condition. Theor Biol Med Model, 2005. 1(2): p. 18.
Chen, K.C., et al., Integrative analysis of cell cycle control in budding yeast. Mol Biol Cell, 2004. 8(15): p. 3841–3862.
Ingram, P.J., M.P. Stumpf, and J. Stark, Network motifs: structure does not determine function. BMC Genomics, 2006. 7: p. 108.
Yang, C.R., et al., A mathematical model for the branched chain amino acid biosynthetic pathways of Escherichia coli K12. J Biol Chem, 2005. 12(280): p. 11224–11232.
Goryanin, I., T.C. Hodgman, and E. Selkov, Mathematical simulation and analysis of cellular metabolism and regulation. Bioinformatics, 1999. 9(15): p. 749–758.
Widder, S., J. Schicho, and P. Schuster, Dynamic patterns of gene regulation I: Simple two-gene systems. J Theor Biol, 2007.
Mocek, W.T., R. Rudnicki, and E.O. Voit, Approximation of delays in biochemical systems. Math Biosci, 2005. 2(198): p. 190–216.
Carey, M., The enhanceosome and transcriptional synergy. Cell, 1998. 1(92): p. 5–8.
Spudich, J.L. and D.E. Koshland, Jr., Non-genetic individuality: chance in the single cell. Nature, 1976. 5568(262): p. 467–471.
Hasty, J., et al., Noise-based switches and amplifiers for gene expression. Proc Natl Acad Sci U S A, 2000. 5(97): p. 2075–2080.
Elowitz, M.B., et al., Stochastic gene expression in a single cell. Science, 2002. 5584(297): p. 1183–1186.
Gillespie, D.T., Stochastic Simulation of Chemical Kinetics. Annu Rev Phys Chem, 2006.
Lacalli, T.C., Modeling the Drosophila pair-rule pattern by reaction-diffusion: gap input and pattern control in a 4-morphogen system. J Theor Biol, 1990. 2(144): p. 171–194.
Aranda, J.S., E. Salgado, and A. Munoz-Diosdado, Multifractality in intracellular enzymatic reactions. J Theor Biol, 2006. 2(240): p. 209–217.
Schnell, S. and T.E. Turner, Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws. Prog Biophys Mol Biol, 2004. 85(2–3): p. 235–260.
Weiss, M., et al., Anomalous subdiffusion is a measure for cytoplasmic crowding in living cells. Biophys J, 2004. 5(87): p. 3518–3524.
de Hoon, M.J., et al., Inferring gene regulatory networks from time-ordered gene expression data of Bacillus subtilis using differential equations. Pac Symp Biocomput. 2003: p. 17–28.
D'Haeseleer, P., et al., Linear modeling of mRNA expression levels during CNS development and injury. Pac Symp Biocomput, 1999: p. 41–52.
van Someren, E.P., L.F. Wessels, and M.J. Reinders, Linear modeling of genetic networks from experimental data. Proc Int Conf Intell Syst Mol Biol, 2000. 8: p. 355–366.
Wu, F.X., W.J. Zhang, and A.J. Kusalik, Modeling gene expression from microarray expression data with state-space equations. Pac Symp Biocomput, 2004: p. 581–592.
Gustafsson, M., M. Hornquist, and A. Lombardi, Constructing and analyzing a large-scale gene-to-gene regulatory network–lasso-constrained inference and biological validation. IEEE/ACM Trans Comput Biol Bioinform, 2005. 3(2): p. 254–261.
Chen, T., H.L. He, and G.M. Church, Modeling gene expression with differential equations. Pac Symp Biocomput, 1999: p. 29–40.
Glass, L. and S.A. Kauffman, The logical analysis of continuous, non-linear biochemical control networks. J Theor Biol, 1973. 1(39): p. 103–129.
Drulhe, S., Ferrari-Trecate, G., H. de Jong, and A. Viari, Reconstruction of Switching Thresholds in Piece-wise-Affine Models of Genetic Regulatory Networks. LECTURE NOTES IN COMPUTER SCIENCE, 2006(3927): p. 184–199.
Vercruysse, S. and M. Kuiper, Simulating genetic networks made easy: network construction with simple building blocks. Bioinformatics, 2005. 2(21): p. 269–271.
Radde, N., J. Gebert, and C.V. Forst, Systematic component selection for gene-network refinement. Bioinformatics, 2006. 21(22): p. 2674–2680.
Mason, J., et al., Evolving complex dynamics in electronic models of genetic networks. Chaos, 2004. 3(14): p. 707–715.
Edwards, R., P. van den Driessche, and L. Wang, Periodicity in piece-wise-linear switching networks with delay. J Math Biol, 2007.
Casey, R., H. de Jong, and J.L. Gouze, Piece-wise-linear models of genetic regulatory networks: equilibria and their stability. J Math Biol, 2006. 1(52): p. 27–56.
Ben-Hur, A. and H.T. Siegelmann, Computation in gene networks. Chaos, 2004. 1(14): p. 145–151.
Mestl, T., E. Plahte, and S.W. Omholt, A mathematical framework for describing and analysing gene regulatory networks. J Theor Biol, 1995. 2(176): p. 291–300.
Hu, X., A. Maglia, and D. Wunsch, A general recurrent neural network approach to model genetic regulatory networks. Conf Proc IEEE Eng Med Biol Soc, 2005. 5: p. 4735–4738.
Vohradsky, J., Neural network model of gene expression. Faseb J, 2001. 3(15): p. 846–854.
Wahde, M. and J. Hertz, Modeling genetic regulatory dynamics in neural development. J Comput Biol, 2001. 4(8): p. 429–442.
Xu, R., X. Hu, and D. Wunsch Ii, Inference of genetic regulatory networks with recurrent neural network models. Conf Proc IEEE Eng Med Biol Soc, 2004. 4: p. 2905–2908.
Weaver, D.C., C.T. Workman, and G.D. Stormo, Modeling regulatory networks with weight matrices. Pac Symp Biocomput, 1999: p. 112–123.
Vohradsky, J., Neural model of the genetic network. J Biol Chem, 2001. 39(276): p. 36168–36173.
Sorribas, A., R. Curto, and M. Cascante, Comparative characterization of the fermentation pathway of Saccharomyces cerevisiae using biochemical systems theory and metabolic control analysis: model validation and dynamic behavior. Math Biosci, 1995. 1(130): p. 71–84.
Voit, E.O. and T. Radivoyevitch, Biochemical systems analysis of genome-wide expression data. Bioinformatics, 2000. 11(16): p. 1023–1037.
Alvarez-Vasquez, F., C. Gonzalez-Alcon, and N.V. Torres, Metabolism of citric acid production by Aspergillus niger: model definition, steady-state analysis and constrained optimization of citric acid production rate. Biotechnol Bioeng, 2000. 1(70): p. 82–108.
Kitayama, T., et al., A simplified method for power-law modelling of metabolic pathways from time-course data and steady-state flux profiles. Theor Biol Med Model, 2006. 3: p. 24.
Kimura, S., et al., Inference of S-system models of genetic networks using a cooperative coevolutionary algorithm. Bioinformatics, 2005. 7(21): p. 1154–1163.
Noman, N. and H. Iba, Reverse engineering genetic networks using evolutionary computation. Genome Inform, 2005. 2(16): p. 205–214.
Gonzalez, O.R., et al., Parameter estimation using Simulated Annealing for S-system models of biochemical networks. Bioinformatics, 2007. 4(23): p. 480–486.
Voit, E.O., Smooth bistable S-systems. Syst Biol (Stevenage), 2005. 4(152): p. 207–213.
Marino, S. and E.O. Voit, An automated procedure for the extraction of metabolic network information from time series data. J Bioinform Comput Biol, 2006. 3(4): p. 665–691.
Chou, I.C., H. Martens, and E.O. Voit, Parameter estimation in biochemical systems models with alternating regression. Theor Biol Med Model, 2006. 3: p. 25.
Hernandez-Bermejo, B., V. Fairen, and A. Sorribas, Power-law modeling based on least-squares minimization criteria. Math Biosci, 1999. 161(1–2): p. 83–94.
Savageau, M.A., A theory of alternative designs for biochemical control systems. Biomed Biochim Acta, 1985. 6(44): p. 875–80.
Cai, X. and Z. Xu, K-leap method for accelerating stochastic simulation of coupled chemical reactions. J Chem Phys, 2007. 7(126): p. 074102.
Cao, Y., D.T. Gillespie, and L.R. Petzold, Efficient step size selection for the tau-leaping simulation method. J Chem Phys, 2006. 4(124): p. 044109.
Chatterjee, A., et al., Time accelerated Monte Carlo simulations of biological networks using the binomial tau-leap method. Bioinformatics, 2005. 9(21): p. 2136–2137.
Tian, T. and K. Burrage, Binomial leap methods for simulating stochastic chemical kinetics. J Chem Phys, 2004. 21(121): p. 10356–10364.
Puchalka, J. and A.M. Kierzek, Bridging the gap between stochastic and deterministic regimes in the kinetic simulations of the biochemical reaction networks. Biophys J, 2004. 3(86): p. 1357–1372.
Simpson, M.L., C.D. Cox, and G.S. Sayler, Frequency domain chemical Langevin analysis of stochasticity in gene transcriptional regulation. J Theor Biol, 2004. 3(229): p. 383–394.
Haseltine, E.L. and J.B. Rawlings, On the origins of approximations for stochastic chemical kinetics. J Chem Phys, 2005. 16(123): p. 164115.
Salis, H. and Y. Kaznessis, Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions. J Chem Phys, 2005. 5(122): p. 54103.
Achimescu, S. and O. Lipan, Signal propagation in non-linear stochastic gene regulatory networks. Syst Biol (Stevenage), 2006. 3(153): p. 120–134.
Reinker, S., R.M. Altman, and J. Timmer, Parameter estimation in stochastic biochemical reactions. Syst Biol (Stevenage), 2006. 4(153): p. 168–178.
Wang, S.C., Reconstructing genetic networks from time ordered gene expression data using Bayesian method with global search algorithm. J Bioinform Comput Biol, 2004. 3(2): p. 441–458.
Goutsias, J., A hidden Markov model for transcriptional regulation in single cells. IEEE/ACM Trans Comput Biol Bioinform, 2006. 1(3): p. 57–71.
Inoue, L.Y., et al., Cluster-based network model for time-course gene expression data. Biostatistics, 2006.
Grima, R. and S. Schnell, A systematic investigation of the rate laws valid in intracellular environments. Biophys Chem, 2006. 1(124): p. 1–10.
Mayawala, K., D.G. Vlachos, and J.S. Edwards, Spatial modeling of dimerization reaction dynamics in the plasma membrane: Monte Carlo vs. continuum differential equations. Biophys Chem, 2006. 3(121): p. 194–208.
Loew, L.M. and J.C. Schaff, The virtual cell: a software environment for computational cell biology. Trends Biotechnol, 2001. 10(19): p. 401–406.
Slepchenko, B.M., et al., Quantitative cell biology with the virtual cell. Trends Cell Biol, 2003. 11(13): p. 570–576.
Hirschberg, K., et al., Kinetic analysis of secretory protein traffic and characterization of golgi to plasma membrane transport intermediates in living cells. J Cell Biol, 1998. 6(143): p. 1485–1503.
Von Dassow, G. and G.M. Odell, Design and constraints of the Drosophila segment polarity module: robust spatial patterning emerges from intertwined cell state switches. J Exp Zool, 2002. 3(294): p. 179–215.
Schaff, J., et al., A general computational framework for modeling cellular structure and function. Biophys J, 1997. 3(73): p. 1135–1346.
Wylie, D.C., et al., A hybrid deterministic-stochastic algorithm for modeling cell signaling dynamics in spatially inhomogeneous environments and under the influence of external fields. J Phys Chem B Condens Matter Mater Surf Interfaces Biophys, 2006. 25(110): p. 12749–12765.
Vitaly V. Gursky, J.J., Konstantin N. Kozlov, John Reinitz, Alexander M. Samsonova, Pattern formation and nuclear divisions are uncoupled in Drosophila segmentation: comparison of spatially discrete and continuous models. Physica D, 2004. 197: p. 286–302.
Smith, A.E., et al., Systems analysis of Ran transport. Science, 2002. 5554(295): p. 488–491.
Broderick, G., et al., A life-like virtual cell membrane using discrete automata. In Silico Biol, 2005. 2(5): p. 163–178.
Weimar, J.R. and J.P. Boon, Class of cellular automata for reaction-diffusion systems. Physical Review. E. Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 1994. 2(49): p. 1749–1752.
Shimizu, T.S., S.V. Aksenov, and D. Bray, A spatially extended stochastic model of the bacterial chemotaxis signalling pathway. J Mol Biol, 2003. 2(329): p. 291–309.
Dab, D., et al., Cellular-automaton model for reactive systems. Physical Review Letters, 1990. 20(64): p. 2462–2465.
Wishart, D.S., et al., Dynamic cellular automata: an alternative approach to cellular simulation. In Silico Biol, 2005. 2(5): p. 139–161.
Kier, L.B., et al., A cellular automata model of enzyme kinetics. J Mol Graph, 1996. 4(14): p. 227–231, 226.
Andrews, S.S. and D. Bray, Stochastic simulation of chemical reactions with spatial resolution and single molecule detail. Phys Biol, 2004. 1(3–4): p. 137–151.
Erban, R. and S.J. Chapman, Reactive boundary conditions for stochastic simulations of reaction-diffusion processes. Phys Biol, 2007. 1(4): p. 16–28.
Elf, J. and M. Ehrenberg, Spontaneous separation of bi-stable biochemical systems into spatial domains of opposite phases. Syst Biol (Stevenage), 2004. 2(1): p. 230–236.
Chiam, K.H., et al., Hybrid simulations of stochastic reaction-diffusion processes for modeling intracellular signaling pathways. Phys Rev E Stat Nonlin Soft Matter Phys, 2006. 74(5 Pt 1): p. 051910.
Sanbonmatsu, K.Y. and C.S. Tung, High performance computing in biology: multimillion atom simulations of nanoscale systems. J Struct Biol, 2007. 3(157): p. 470–480.
Phillips, J.C., et al., Scalable molecular dynamics with NAMD. J Comput Chem, 2005. 16(26): p. 1781–1802.
Covert Markus, Schilling Christophe, and P. Bernhard, Regulation of Gene Expression in Flux Balance Models of Metabolism. 2001: p. 73–78.
Varma, A. and B.O. Palsson, Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110. Appl Environ Microbiol, 1994. 10(60): p. 3724–3731.
Cakir, T., B. Kirdar, and K.O. Ulgen, Metabolic pathway analysis of yeast strengthens the bridge between transcriptomics and metabolic networks. Biotechnol Bioeng, 2004. 3(86): p. 251–260.
Klamt, S. and J. Stelling, Combinatorial complexity of pathway analysis in metabolic networks. Mol Biol Rep, 2002. 29(1–2): p. 233–236.
Carlson, R., D. Fell, and F. Srienc, Metabolic pathway analysis of a recombinant yeast for rational strain development. Biotechnol Bioeng, 2002. 2(79): p. 121–134.
Wiback, S.J. and B.O. Palsson, Extreme pathway analysis of human red blood cell metabolism. Biophys J, 2002. 2(83): p. 808–818.
Papin, J.A., et al., The genome-scale metabolic extreme pathway structure in Haemophilus influenzae shows significant network redundancy. J Theor Biol, 2002. 1(215): p. 67–82.
Schilling, C.H., et al., Combining pathway analysis with flux balance analysis for the comprehensive study of metabolic systems. Biotechnol Bioeng, 2000. 4(71): p. 286–306.
Henry, C.S., L.J. Broadbelt, and V. Hatzimanikatis, Thermodynamics-based metabolic flux analysis. Biophys J, 2007. 5(92): p. 1792–1805.
Shlomi, T., O. Berkman, and E. Ruppin, Regulatory on/off minimization of metabolic flux changes after genetic perturbations. Proc Natl Acad Sci U S A, 2005. 21(102): p. 7695–7700.
Herrgard, M.J., S.S. Fong, and B.O. Palsson, Identification of genome-scale metabolic network models using experimentally measured flux profiles. PLoS Comput Biol, 2006. 7(2): p. e72.
Mahadevan, R., J.S. Edwards, and F.J. Doyle, 3rd, Dynamic flux balance analysis of diauxic growth in Escherichia coli. Biophys J, 2002. 3(83): p. 1331–1340.
Herrgard, M.J., et al., Integrated analysis of regulatory and metabolic networks reveals novel regulatory mechanisms in Saccharomyces cerevisiae. Genome Res, 2006. 5(16): p. 627–635.
Patil, K.R., et al., Evolutionary programming as a platform for in silico metabolic engineering. BMC Bioinformatics, 2005. 6: p. 308.
Knorr, A.L., R. Jain, and R. Srivastava, Bayesian-based selection of metabolic objective functions. Bioinformatics, 2007. 3(23): p. 351–357.
Forster, J., et al., Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network. Genome Res, 2003. 2(13): p. 244–253.
Borodina, I., P. Krabben, and J. Nielsen, Genome-scale analysis of Streptomyces coelicolor A3(2) metabolism. Genome Res, 2005. 6(15): p. 820–829.
Edwards, J.S., R.U. Ibarra, and B.O. Palsson, In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data. Nat Biotechnol, 2001. 2(19): p. 125–130.
Feist, A.M., et al., Modeling methanogenesis with a genome-scale metabolic reconstruction of Methanosarcina barkeri. Mol Syst Biol, 2006. 2: p. 2006 0004.
Becker, S.A. and B.O. Palsson, Genome-scale reconstruction of the metabolic network in Staphylococcus aureus N315: an initial draft to the two-dimensional annotation. BMC Microbiol, 2005. 1(5): p. 8.
Duarte, N.C., M.J. Herrgard, and B.O. Palsson, Reconstruction and validation of Saccharomyces cerevisiae iND750, a fully compartmentalized genome-scale metabolic model. Genome Res, 2004. 7(14): p. 1298–1309.
Almaas, E., Z. Oltvai, and A. Barabasi, The Activity Reaction Core and Plasticity of Metabolic Networks. PloS Computational Biology, 2005. 1(7).
Hoops, S., et al., COPASI–a COmplex PAthway SImulator. Bioinformatics, 2006. 24(22): p. 3067–3674.
Snoep, J.L., et al., Towards building the silicon cell: a modular approach. Biosystems, 2006. 83(2–3): p. 207–216.
Klipp, E., et al., Integrative model of the response of yeast to osmotic shock. Nat Biotechnol, 2005. 8(23): p. 975–982.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Humana Press, a part of Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Tzamali, E., Poirazi, P., Reczko, M. (2009). Methods for Dynamical Inference in Intracellular Networks. In: Krawetz, S. (eds) Bioinformatics for Systems Biology. Humana Press. https://doi.org/10.1007/978-1-59745-440-7_28
Download citation
DOI: https://doi.org/10.1007/978-1-59745-440-7_28
Publisher Name: Humana Press
Print ISBN: 978-1-934115-02-2
Online ISBN: 978-1-59745-440-7
eBook Packages: Biomedical and Life SciencesBiomedical and Life Sciences (R0)