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Modeling and Model Simplification to Facilitate Biological Insights and Predictions

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Uncertainty in Biology

Part of the book series: Studies in Mechanobiology, Tissue Engineering and Biomaterials ((SMTEB,volume 17))

Abstract

Mathematical dynamical models of intracellular signaling networks are continuously increasing in size and model complexity due in large part to the data explosion in biology. However, the sheer complexity of the relationship between state-variables through numerous parameters constitutes a significant barrier against obtaining insight into which parts of a model govern a certain read-out, and the uncertainty in model structure and especially model parameters is here a further complicating factor. To meet these two challenges of complexity and uncertainty, systematic construction of simplified models from complex models is a central area of investigation within systems biology as well as for personalized medicine. Model complexity makes the task of deriving predictions difficult in general and in particular when different read-outs depend on combinations of parameters, since exhaustive computer simulations are not sufficient for understanding nor feasible in practice. Construction of simplified models is therefore an important complementary approach to this end, while also facilitating the identifiability of over-parameterized models. Within this chapter we discuss different methods for model simplification, and we specifically summarize a recently developed simplification method based on an iterative “tearing, zooming and simplifying” approach. We also look into the modeling process in general. In the “tearing, zooming and simplifying” approach the original model is divided into modules (tearing), the modules are considered as input-output systems (zooming), which then are replaced by simplified transfer functions (simplifying). The idea behind the simplification is to utilize biological features such as modularity and robustness as well as abundance of typical dynamical behaviors in biology such as switch-like responses. The methodology is illustrated using a relatively complex model of the cell division cycle, where the resulting simplification corresponds to a piecewise linear system with delay, facilitating an understanding of the underlying core dynamics and enabling the prediction of combinations of parameters that can change different model features like the size of the cell. Hence, the existence of biological organization principles enables a simplified description of intracellular dynamics.

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References

  1. Adamczyk, M., van Eunen, K., Bakker, B.M., Westerhoff, H.V.: Enzyme kinetics for systems biology: When, why and how. Methods. Enzymol. 500, 233–257 (2011)

    Article  Google Scholar 

  2. Albert, R., Othmer, H.G.: The topology of the regulatory interactions predicts the expression pattern of the Drosophila segment polarity genes. J. Theor. Biol. 223, 1–18 (2003)

    Article  MathSciNet  Google Scholar 

  3. Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., Watson, J.D.: Molecular biology of the cell. Garland, New York (1994)

    Google Scholar 

  4. Alexander, R.P., Kim, P.M., Emonet, T., Gerstein, M.B.: Understanding modularity in molecular networks requires dynamics. Sci. Signal. 2, pp. pe44 (2009)

    Google Scholar 

  5. Apri, M., de Gee, M., Molenaar, J.: Complexity reduction preserving dynamical behavior of biochemical networks. J. Theor. Biol. 304, 16–26 (2012)

    Article  Google Scholar 

  6. Bagowski, C.P., Besser, J., Frey, C.R., Ferrell Jr, J.E.: The JNK cascade as a biochemical switch in mammalian cells: ultrasensitive and all-or-none responses. Curr. Biol. 13, 315–320 (2003)

    Article  Google Scholar 

  7. Barabasi, A.L., Oltvai, Z.N.: Network biology: understanding the cell’s functional organization. Nat. Rev. Genet. 5, 101–113 (2004)

    Article  Google Scholar 

  8. Behar, M., Dohlman, H.G., Elston, T.C.: Kinetic insulation as an effective mechanism for achieving pathway specificity in intracellular signaling networks. Proc. Nat. Acad. Sci. 104, 16146–16151 (2007)

    Article  Google Scholar 

  9. Bornholdt, S.: Less is more in modeling large genetic networks. Science 310, 449–451 (2005)

    Article  Google Scholar 

  10. Bruggeman, F.J., Westerhoff, H.V.: The nature of systems biology. Trends Microbiol. 15, 45–50 (2007)

    Article  Google Scholar 

  11. Cedersund, G.: Core-box modelling, theoretical contributions and applications to glucose homeostasis related systems. Ph.D. thesis, Chalmers University of Technology, Sweden, 2006

    Google Scholar 

  12. Chen, W.W., Schoeberl, B., Jasper, P.J., Niepel, M., Nielsen, U.B., Lauffenburger, D.A., Sorger, P.K.: Input-output behavior of ErbB signaling pathways as revealed by a mass action model trained against dynamic data. Mol. Syst. Biol. 5, 239 (2009)

    Google Scholar 

  13. Christensen, C., Thakar, J., Albert, R.: Systems-level insights into cellular regulation: inferring, analysing, and modelling intracellular networks. IET Syst. Biol. 1, 61–77 (2007)

    Article  Google Scholar 

  14. Csete, M.E., Doyle, J.C.: Reverse engineering of biological complexity. Science 295, 1664–1669 (2002)

    Article  Google Scholar 

  15. Davidich, M., Bornholdt, S.: The transition from differential equations to boolean networks: A case study in simplifying a regulatory network model. J. Theor. Biol. 255, 269–277 (2008)

    Article  Google Scholar 

  16. de Jong, H.: Modeling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol. 9, 67–103 (2002)

    Google Scholar 

  17. de Jong, H., Gouzé, J.L., Hernandez, C., Page, M., Sari, T., Geiselmann, J.: Qualitative simulation of genetic regulatory networks using piecewise-linear models. Bull. Math. Biol. 66, 301–340 (2004)

    Article  MathSciNet  Google Scholar 

  18. Del Vecchio, D., Ninfa, A.J., Sontag, E.D.: Modular cell biology: Retroactivity and insulation. Mol. Syst. Biol. 4, (2008)

    Google Scholar 

  19. Dokoumetzidis, A., Aarons, L.: Proper lumping in systems biology models. IET Syst. Biol. 3, 40–51 (2009)

    Article  Google Scholar 

  20. Duarte, N.C., Becker, S.A., Jamshidi, N., Thiele, I., Mo, M.L., Vo, T.D., Srivas, R., Palsson, B.Ø.: Global reconstruction of the human metabolic network based on genomic and bibliomic data. Proc. Nat. Acad. Sci. 104, 1777–1782 (2007)

    Article  Google Scholar 

  21. Ehrenberg, M., Elf, J., Aurell, E., Sandberg, R., Tegnér, J.: Systems biology is taking off. Genome Res. 13, 2377–2380 (2003)

    Article  Google Scholar 

  22. Eriksson, O., Zhou, Y., Tegnér, J.: ‘Modeling complex cellular networks - robust switching in the cell cycle ensures a piecewise linear reduction of the regulatory network’. CDC: IEEE Conf. Decis. Contr. 2004(1), 117–123 (2004)

    Google Scholar 

  23. Eriksson, O., Brinne, B., Zhou, Y., Björkegren, J., Tegnér, J.: Deconstructing the core dynamics from a complex time-lagged regulatory biological circuit. IET Syst. Biol. 3, 113–129 (2009)

    Article  Google Scholar 

  24. Eriksson, O., Andersson, T., Zhou, Y., Tegnér, J.: Decoding complex biological networks - tracing essential and modulatory parameters in complex and simplified models of the cell cycle. BMC Syst. Biol. 5, 123 (2011)

    Article  Google Scholar 

  25. Ermentrout, B.: Simplifying and reducing complex models. In Bower, J.M., Bolouri, H. (Eds.) Computational Modeling of Genetic and Biochemical Networks, MIT Press, Cambridge, MA, pp. 307–323

    Google Scholar 

  26. Faeder, J.R., Blinov, M.L., Goldstein, B., Hlavacek, W.S.: Combinatorial complexity and dynamical restriction of network flows in signal transduction. Syst. Biol. (Stevenage) 2, 5–15 (2005)

    Article  Google Scholar 

  27. Feng, Y., Mitchison, T.J., Bender, A., Young, D.W., Tallarico, J.A.: Multi-parameter phenotypic profiling: using cellular effects to characterize small-molecule compounds. Nat. Rev. Drug Discov. 8, 567–578 (2009)

    Article  Google Scholar 

  28. Ferrell Jr, J.E.: Tripping the switch fantastic: how a protein kinase cascade can convert graded inputs into switch-like outputs. Trends Biochem. Sci. 21, 460–466 (1996)

    Article  Google Scholar 

  29. Glass, L.: Classification of biological networks by their qualitative dynamics. J. Theor. Biol. 54, 85–107 (1975)

    Article  Google Scholar 

  30. Glass, L., Kauffman, S.A.: The logical analysis of continuous, non-linear biochemical control networks. J. Theor. Biol. 39, 103–129 (1973)

    Article  Google Scholar 

  31. Gonçalves, J.: Constructive global analysis of hybrid systems. Ph.D. Thesis, Massachusetts Institute of Technology, 2000

    Google Scholar 

  32. Gureasko, J., Galush, W.J., Boykevisch, S., Sondermann, H., Bar-sagi, D., Groves, J.T., Kuriyan, J.: Membrane-dependent signal integration by the Ras activator Son of sevenless. Nat. Struct. Mol. Biol. 15, 452–461 (2008)

    Article  Google Scholar 

  33. Gutierrez-Arenas, O., Eriksson, O., and Hellgren Kotaleski, J.: Segregation and crosstalk of D1 receptor-mediated activation of ERK in striatal medium spiny neurons upon acute administration of psychostimulants. PLoS Comput. Biol. 10, pp. e1003445 (2014)

    Google Scholar 

  34. Halász, A., Kumar, V., Imieliński, M., Belta, C., Sokolsky, O., Pathak, S., Rubin, H.: Analysis of lactose metabolism in E.coli using reachability analysis of hybrid systems. IET Syst. Biol. 1, 130–148 (2007)

    Article  Google Scholar 

  35. Han, J.D., Bertin, N., Hao, T., Goldberg, D.S., Berriz, G.F., Zhang, L.V., Dupuy, D., Walhout, A.J., Cusick, M.E., Roth, F.P., Vidal, M.: Evidence for dynamically organized modularity in the yeast protein-protein interaction network. Nature 430, 88–93 (2004)

    Article  Google Scholar 

  36. Hardie, D.G., Salt, I.P., Hawley, S.A., Davies, S.P.: AMP-activated protein kinase: an ultrasensitive system for monitoring cellular energy charge. Biochem. J. 338, 717–722 (1999)

    Article  Google Scholar 

  37. Härdin, H.M., Zagaris, A., Krab, K., Westerhoff, H.V.: Simplified yet highly accurate enzyme kinetics for cases of low substrate concentrations. FEBS J. 276, 5491–5506 (2009)

    Article  Google Scholar 

  38. Harper, J.W.: A phosphorylation-driven ubiquitination switch for cell-cycle control. Trends Cell Biol. 12, 104–107 (2002)

    Article  Google Scholar 

  39. Hartwell, L.H., Hopfield, J.J., Leibler, S., Murray, A.W.: From molecular to modular cell biology. Nature 402, c47–c52 (1999)

    Article  Google Scholar 

  40. Huang, C.Y., Ferrell, J.E. Jr.: Ultrasensitivity in the mitogen-activated protein kinase cascade. Proc. Natl. Acad. Sci. U.S.A. 93, pp. 10078–10083 (1996)

    Google Scholar 

  41. Iyengar, R.: Why we need quantitative dynamic models. Sci. Signal. 2, eg3 (2009)

    Google Scholar 

  42. Karr, J.R., Sanghvi, J.C., Macklin, D.N., Gutschow, M.V., Jacobs, J.M., Bolival Jr, B., Assad-Garcia, N., Glass, J.I., Covert, M.W.: A whole-cell computational model predicts phenotype from genotype. Cell 150, 389–401 (2012)

    Article  Google Scholar 

  43. Kawai, J., et al.: Functional annotation of a full-length mouse cDNA collection. Nature 409, 685–690 (2001)

    Article  Google Scholar 

  44. Kepler, T.B., Abbott, L.F., Marder, E.: Reduction of conductance-based neuron models. Biol. Cybern. 66, 381–387 (1992)

    Article  MATH  Google Scholar 

  45. Kirk, P., Silk, D., Stumpf, M.P.H.: Reverse engineering under uncertainty. In: Uncertainty in Biology, A Computational Modeling Approach. Springer, Chem (2016, this volume)

    Google Scholar 

  46. Kitano, H.: Systems biology: A brief overview. Science 295, 1662–1664 (2002)

    Article  Google Scholar 

  47. Koschorreck, M., Conzelmann, H., Ebert, S., Ederer, M., Gilles, E.D.: Reduced modeling of signal transduction - a modular approach. BMC Bioinform. 8, 336 (2007)

    Article  Google Scholar 

  48. LeBeau, A.P., Robson, A.B., McKinnon, A.E., Sneyd, J.: Analysis of a reduced model of corticotroph action potentials. J. Theor. Biol. 192, 319–339 (1998)

    Article  Google Scholar 

  49. Lee, T.I., et al.: Transcriptional regulatory networks in Saccharomyces cerevisiae. Science 298, 799–804 (2002)

    Article  Google Scholar 

  50. Leloup, J.C., Goldbeter, A.: A model for circadian rhythms in Drosophila incorporating the formation of a complex between the PER and TIM proteins. J. Biol. Rhythms. 13, 70–87 (1998)

    Article  Google Scholar 

  51. Liu, G., Swihart, M.T., Neelamegham, S.: Sensitivity, principal component and flux analysis applied to signal transduction: the case of epidermal growth factor mediated signaling. Bioinformatics 21, 1194–1202 (2005)

    Article  Google Scholar 

  52. Liu, Y.-Y., Slotine, J.-J., Barabási, A.-L.: Observability of complex systems. Proc. Natl. Acad. Sci. U.S.A. 110, 2460–2465 (2013)

    Article  MATH  Google Scholar 

  53. Lohse, M.J., Nikolaev, V.O., Hein, P., Hoffmann, C., Vilardaga, J.P., Bünemann, M.: Optical techniques to analyze real-time activation and signaling of G-protein-coupled receptors. Trends Pharmacol. Sci. 29, 159–165 (2008)

    Article  Google Scholar 

  54. Luscombe, N.M., Babu, M.M., Yu, H., Snyder, M., Teichmann, S.A., Gerstein, M.: Genomic analysis of regulatory network dynamics reveals large topological changes. Nature 431, 308–312 (2004)

    Article  Google Scholar 

  55. Monk, N.A.M.: Oscillatory expression of Hes1, p53, and NF-\(\kappa \)B driven by transcriptional time delayes. Curr. Biol. 13, 1409–1413 (2003)

    Article  Google Scholar 

  56. Morohashi, M., Winn, A.E., Borisuk, M.T., Bolouri, H., Doyle, J., Kitano, H.: Robustness as a measure of plausibility in models of biochemical networks. J. Theor. Biol. 216, 19–30 (2002)

    Article  MathSciNet  Google Scholar 

  57. Novak, B., Pataki, Z., Ciliberto, A., Tyson, J.J.: Mathematical model of the cell division cycle of fission yeast. Chaos 11, 277–286 (2001)

    Article  MATH  Google Scholar 

  58. Okino, M.S., Mavrovouniotis, M.L.: Simplification of mathematical models of chemical reaction systems. Chem. Rev. 98, 391–408 (1998)

    Article  Google Scholar 

  59. Raue, A., Kreutz, C., Maiwald, T., Bachmann, J., Schilling, M., Klingmüller, U., Timmer, J.: Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics 25, 1923–1929 (2009)

    Article  Google Scholar 

  60. Saez-Rodriguez, J., Kremling, A., Conzelmann, H., Bettenbrock, K., Gilles, E.D.: Modular analysis of signal transduction networks. IEEE Control Syst. Mag. 24, 35–52 (2004)

    Article  MathSciNet  Google Scholar 

  61. Saez-Rodriguez, J., Kremling, A., Gilles, E.D.: Dissecting the puzzle of life: modularization of signal transduction networks. Comput. Chem. Eng. 29, 619–629 (2005)

    Article  Google Scholar 

  62. Sanghvi, J.C., Regot, S., Carrasco, S., Karr, J.R., Gutschow, M.V., Bolival Jr, B., Covert, M.W.: Accelerated discovery via a whole-cell model. Nat. Methods 10, 1192–1195 (2013)

    Article  Google Scholar 

  63. Schena, M., Shalon, D., Davis, R., Brown, P.: Quantitative monitoring of gene expression patterns with a complementary dna microarray. Science 270, 467–470 (1995)

    Article  Google Scholar 

  64. Schliemann-Bullinger, M., Fey, D., Bastogne, T., Findeisen, R., Scheurich, P., Bullinger, E.: The experimental side of parameter estimation. In: Uncertainty in Biology, A Computational Modeling Approach. Springer, Chem (2016, this volume)

    Google Scholar 

  65. Schmidt, H., Madsen, M.F., Danø, S., Cedersund, G.: ‘Complexity reduction of biochemical rate expressions’. Bioinformatics 24, 848–854 (2008)

    Google Scholar 

  66. Smallbone, K., et al.: A model of yeast glycolysis based on a consistent kinetic characterisation of all its enzymes. FEBS Lett. 587, 2832–2841 (2013)

    Article  Google Scholar 

  67. Smolen, P., Baxter, A.D., Byrne, J.H.: A reduced model clarifies the role of feedback loops and time delays in the Drosophila circadian oscillator. Biophys. J. 83, 2349–2359 (2002)

    Article  Google Scholar 

  68. Sorensen, M.E., DeWeerth, S.P.: An algorithmic method for reducing conductance-based neuron models. Biol. Cybern. 95, 185–192 (2006)

    Article  MATH  Google Scholar 

  69. Srividhya, J., Gopinathan, M.S., Schnell, S.: The effects of time delays in a phosphorylation-dephosphorylation pathway. Biophys. Chem. 125, 286–297 (2007)

    Article  Google Scholar 

  70. Sunnåker, M., Stelling, J.: Model extension and model selection. In: Uncertainty in Biology, A Computational Modeling Approach. Springer, Chem (2016, this volume)

    Google Scholar 

  71. Sunnåker, M., Zamora-Sillero, E., Dechant, R., Ludwig, C., Busetto, A. G., Wagner, A., and Stelling, J.: Automatic generation of predictive dynamic models reveals nuclear phosphorylation as the key Msn2 control mechanism. Sci. Signal. 6, ra41 (2013)

    Google Scholar 

  72. Sunnåker, M., Schmidt, H., Jirstrand, M., Cedersund, G.: Zooming of states and parameters using a lumping approach including back-translation. BMC Syst. Biol. 4, 28 (2010)

    Article  Google Scholar 

  73. Sunnåker, M., Cedersund, G., Jirstrand, M.: A method for zooming of nonlinear models of biochemical systems. BMC Syst. Biol. 5, 140 (2011)

    Article  Google Scholar 

  74. The 1000 Genomes Project Consortium: An integrated map of genetic variation from 1,092 human genomes. Nature 491, 56–65 (2012)

    Google Scholar 

  75. The ENCODE Project Consortium: An integrated encyclopedia of DNA elements in the human genome. Nature 489, 57–74 (2012)

    Article  Google Scholar 

  76. The International Human Genome Mapping Consortium: A physical map of the human genome. Nature 409, 934–941 (2001)

    Article  Google Scholar 

  77. Tyson, J.J., Chen, K., Novak, B.: Network dynamics and cell physiology. Nat. Rev. Mol. Cell. Biol. 2, 908–916 (2001)

    Article  Google Scholar 

  78. Tyson, J.J., Chen, J.C., Novak, B.: Sniffers, buffers, toggles and blinkers: dynamics of regulatory and signaling pathways in the cell. Curr. Opin. Cell. Biol. 15, 221–231 (2003)

    Article  Google Scholar 

  79. Uetz, P., et al.: A comprehensive analysis of protein-protein interactions in Saccharomyces cerevisiae. Nature 403, 623–627 (2000)

    Article  Google Scholar 

  80. Van Schepdael, A., Carlier, A., Geris, L.: Sensitivity analysis by design of experiments. In: Uncertainty in Biology, A Computational Modeling Approach. Springer, Chem (2016, this volume)

    Google Scholar 

  81. Venter, J., et al.: The sequence of the human genome. Science 291, 1304–1351 (2001)

    Article  Google Scholar 

  82. von Dassov, G., Meir, E., Munro, E.M., Odell, M.O.: The segment polarity network is a robust developmental module. Nature 406, 188–192 (2000)

    Article  Google Scholar 

  83. Willems, J.C.: Paradigm and puzzles in the theory of dynamical systems. IEEE Trans. Automatic Control 36, 259–294 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  84. Yasuda, R.: Imaging intracellular signaling using two-photon fluorescent lifetime imaging microscopy. Cold Spring Harb. Protoc. 2012, 1121–1128 (2012)

    Article  Google Scholar 

  85. Yildirim, N., Santillan, M., Horike, D., Mackey, M.C.: Dynamics and bistability in a reduced model of the lac operon. Chaos 14, 279–292 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  86. Zamora-Sillero, E., Hafner, M., Ibig, A., Stelling, J., Wagner, A.: Efficient characterization of high-dimensional parameter spaces for systems biology. BMC Syst. Biol. 5, 142 (2011)

    Article  Google Scholar 

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Acknowledgments

We would like to thank Yishao Zhou and Omar Gutierrez-Arenas for valuable discussions and important input, Sara Maad Sasane for commenting on the manuscript and the Swedish e-Science Research Center (SeRC) and the the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no 604102 (HBP) for financial support.

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Authors and Affiliations

  1. Department of Numerical Analysis and Computer Science, Stockholm University, Stockholm, Sweden

    Olivia Eriksson

  2. Unit of Computational Medicine, Department of Medicine, Center for Molecular Medicine, Karolinska Institutet, Karolinska University Hospital, Stockholm, Sweden

    Jesper Tegnér

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  1. Olivia Eriksson
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Correspondence to Olivia Eriksson .

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  1. Biomechanics Research Unit, University of Liège, Liège 1, Belgium

    Liesbet Geris

  2. Center for Molecular Medicine, Karolinska University Hospital, Stockholm, Sweden

    David Gomez-Cabrero

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Eriksson, O., Tegnér, J. (2016). Modeling and Model Simplification to Facilitate Biological Insights and Predictions. In: Geris, L., Gomez-Cabrero, D. (eds) Uncertainty in Biology. Studies in Mechanobiology, Tissue Engineering and Biomaterials, vol 17. Springer, Cham. https://doi.org/10.1007/978-3-319-21296-8_12

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