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Modeling Procedures

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Modeling Methods for Medical Systems Biology

Part of the book series: Advances in Experimental Medicine and Biology ((AEMB,volume 1069))

Abstract

Being concerned by the understanding of the mechanism underlying chronic degenerative diseases , we presented in the previous chapter the medical systems biology conceptual framework that we present for that purpose in this volume. More specifically, we argued there the clear advantages offered by a state-space perspective when applied to the systems-level description of the biomolecular machinery that regulates complex degenerative diseases. We also discussed the importance of the dynamical interplay between the risk factors and the network of interdependencies that characterizes the biochemical, cellular, and tissue-level biomolecular reactions that underlie the physiological processes in health and disease. As we pointed out in the previous chapter, the understanding of this interplay (articulated around cellular phenotypic plasticity properties, regulated by specific kinds of gene regulatory networks) is necessary if prevention is chosen as the human-health improvement strategy (potentially involving the modulation of the patient’s lifestyle). In this chapter we provide the medical systems biology mathematical and computational modeling tools required for this task.

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References

  1. Adler, M., & Alon, U. (2018). Fold-change detection in biological systems. Current Opinion in Systems Biology, 8, 81–89.

    Article  Google Scholar 

  2. Albert, I., Thakar, J., Li, S., Zhang, R., & Albert, R. (2008). Boolean network simulations for life scientists. Source Code for Biology and Medicine, 3(1), 16.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  3. Albert, R., & Barabási, A. L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74(1), 47.

    Article  Google Scholar 

  4. Al-Hashmi, S., Ekanayake, M., & Martin, C. (2009). Type II diabetes and obesity: A control theoretic model. Emergent Problems in Nonlinear Systems and Control, 393, 1–19.

    Article  Google Scholar 

  5. Alon, U., Surette, M. G., Barkai, N., & Leibler, S. (1999). Robustness in bacterial chemotaxis. Nature, 397(6715), 168–171.

    Article  PubMed  CAS  Google Scholar 

  6. Álvarez-Buylla, E. R., Benítez, M., Davila, E. B., Chaos, A., Espinosa-Soto, C., & Padilla-Longoria, P. (2007). Gene regulatory network models for plant development. Current Opinion in Plant Biology, 10(1), 83–91.

    Article  PubMed  CAS  Google Scholar 

  7. Álvarez-Buylla, E. R., Chaos, Á., Aldana, M., Benítez, M., Cortes-Poza, Y., Espinosa-Soto, C., et al. (2008). Floral morphogenesis: Stochastic explorations of a gene network epigenetic landscape. PLoS One, 3(11), e3626.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  8. Álvarez-Buylla, E. R., Dávila-Velderrain, J., & Martínez-García, J. C. (2016). Systems biology approaches to development beyond bioinformatics: Nonlinear mechanistic models using plant systems. BioScience, 66(5), 371–383.

    Article  Google Scholar 

  9. Angeli, D., Ferrell, J. E., & Sontag, E. D. (2004). Detection of multistability, bifurcations, and hysteresis in a large class of biological positive-feedback systems. Proceedings of the National Academy of Sciences of the United States of America, 101(7), 1822–1827.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  10. Arellano, G., Argil, J., Azpeitia, E., Benítez, M., Carrillo, M., Góngora, P., et al. (2011). “Antelope”: A hybrid-logic model checker for branching-time Boolean GRN analysis. BMC Bioinformatics, 12(1), 490.

    Article  PubMed  PubMed Central  Google Scholar 

  11. Azpeitia, E., Benítez, M., Vega, I., Villarreal, C., & Álvarez-buylla, E. R. (2010). Single-cell and coupled GRN models of cell patterning in the Arabidopsis thaliana root stem cell niche. BMC Systems Biology, 4, 134.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  12. Azpeitia, E., Davila-Velderrain, J., Villarreal, C., & Álvarez-Buylla, E. R. (2014). Gene regulatory network models for floral organ determination. In Flower development: Methods and protocols (pp. 441–469). New York: Humana Press.

    Chapter  Google Scholar 

  13. Azpeitia, E., Muñoz, S., González-Tokman, D., Martínez-Sánchez, M. E., Weinstein, N., Naldi, A., et al. (2017). The combination of the functionalities of feedback circuits is determinant for the attractors’ number and size in pathway-like Boolean networks. Scientific Reports, 7, 42023.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  14. Bak, P., & Paczuski, M. (1995). Complexity, contingency, and criticality. Proceedings of the National Academy of Sciences of the United States of America, 92(15), 6689–6696.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  15. Balázsi, G., van Oudenaarden, A., & Collins, J. J. (2011). Cellular decision making and biological noise: From microbes to mammals. Cell, 144(6), 910–925.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  16. Baldwin, G., Bayer, T., Dickinson, R., Ellis, T., Freemont, P. S., Kitney, R. I., et al. (2015). Synthetic biology—A primer. Singapore: World Scientific. Revised edition.

    Book  Google Scholar 

  17. Bargaje, R., Trachana, K., Shelton, M. N., McGinnis, C. S., Zhou, J. X., Chadick, C., et al. (2017). Cell population structure prior to bifurcation predicts efficiency of directed differentiation in human induced pluripotent cells. Proceedings of the National Academy of Sciences of the United States of America, 114(9), 2271–2276.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  18. Batchelor, E., Loewer, A., Mock, C., & Lahav, G. (2011). Stimulus-dependent dynamics of p53 in single cells. Molecular Systems Biology, 7(1), 488.

    Article  PubMed  PubMed Central  Google Scholar 

  19. Batchelor, E., Mock, C. S., Bhan, I., Loewer, A., & Lahav, G. (2008). Recurrent initiation: A mechanism for triggering p53 pulses in response to DNA damage. Molecular Cell, 30(3), 277–289.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  20. Becskei, A., & Serrano, L. (2000). Engineering stability in gene networks by autoregulation. Nature, 405(6786), 590–593.

    Article  PubMed  CAS  Google Scholar 

  21. Benítez, M., Espinosa-Soto, C., Padilla-Longoria, P., & Álvarez-Buylla, E. R. (2008). Interlinked nonlinear subnetworks underlie the formation of robust cellular patterns in Arabidopsis epidermis: A dynamic spatial model. BMC Systems Biology, 2(1), 98.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  22. Bratus, A., Samokhin, I., Yegorov, I., & Yurchenko, D. (2017). Maximization of viability time in a mathematical model of cancer therapy. Mathematical Biosciences, 294, 110–119.

    Article  PubMed  Google Scholar 

  23. Briggs, G. E., & Haldane, J. B. S. (1925). A note on the kinetics of enzyme action. Biochemical Journal, 19(2), 338.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  24. Caligaris, C., Vázquez-Victorio, G., Sosa-Garrocho, M., Ríos-López, D. G., Marín-Hernández, A., & Macías-Silva, M. (2015). Actin-cytoskeleton polymerization differentially controls the stability of Ski and SnoN co-repressors in normal but not in transformed hepatocytes. Biochimica et Biophysica Acta (BBA)-General Subjects, 1850(9), 1832–1841.

    Article  CAS  Google Scholar 

  25. Calzone, L., Fages, F., & Soliman, S. (2006). BIOCHAM: An environment for modeling biological systems and formalizing experimental knowledge. Bioinformatics, 22(14), 1805–1807.

    Article  PubMed  CAS  Google Scholar 

  26. Cannavó, F. (2012). Sensitivity analysis for volcanic source modeling quality assessment and model selection. Computers & Geosciences, 44, 52–59.

    Article  Google Scholar 

  27. Cellier, F. E. (1991). Continuous system modeling. New York: Springer.

    Book  Google Scholar 

  28. Chalmers, D. J. (2006). Strong and weak emergence. In The reemergence of emergence (pp. 244–256). Oxford: Oxford University Press.

    Google Scholar 

  29. Chaos, A., Aldana, M., Espinosa-Soto, C., de León, B. G. P., Arroyo, A. G., & Alvarez-Buylla, E. R. (2006). From genes to flower patterns and evolution: Dynamic models of gene regulatory networks. Journal of Plant Growth Regulation, 25(4), 278–289.

    Article  CAS  Google Scholar 

  30. Chaves, M., & Tournier, L. (2011). Predicting the asymptotic dynamics of large biological networks by interconnections of Boolean modules. In 2011 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC) (pp. 3026–3031). New York: IEEE.

    Chapter  Google Scholar 

  31. Chen, L., Liu, R., Liu, Z. P., Li, M., & Aihara, K. (2012). Detecting early-warning signals for sudden deterioration of complex diseases by dynamical network biomarkers. Scientific Reports, 2, 342.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  32. Cheng, D., Qi, H., & Li, Z. (2010). Analysis and control of Boolean networks: A semi-tensor product approach. Berlin: Springer Science & Business Media.

    Google Scholar 

  33. Chickarmane, V., Troein, C., Nuber, U. A., Sauro, H. M., & Peterson, C. (2006). Transcriptional dynamics of the embryonic stem cell switch. PLoS Computational Biology, 2(9), e123.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  34. Christodoulides, P., Hirata, Y., Domínguez-Hüttinger, E., Danby, S. G., Cork, M. J., Williams, H. C., et al. (2017). Computational design of treatment strategies for proactive therapy on atopic dermatitis using optimal control theory. Philosophical Transactions of the Royal Society A, 375(2096), 20160285.

    Article  CAS  Google Scholar 

  35. Clausznitzer, D., Oleksiuk, O., Løvdok, L., Sourjik, V., & Endres, R. G. (2010). Chemotactic response and adaptation dynamics in Escherichia coli. PLoS Computational Biology, 6(5), e1000784.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  36. Clune, J., Mouret, J. B., & Lipson, H. (2013). The evolutionary origins of modularity. Proceedings of the Royal Society B, 280(1755), 20122863.

    Article  PubMed  PubMed Central  Google Scholar 

  37. Colman-Lerner, A., Gordon, A., Serra, E., Chin, T., Resnekov, O., Endy, D., et al. (2005). Regulated cell-to-cell variation in a cell-fate decision system. Nature, 437(7059), 699–706.

    Article  PubMed  CAS  Google Scholar 

  38. Corblin, F., Fanchon, E., & Trilling, L. (2010). Applications of a formal approach to decipher discrete genetic networks. BMC Bioinformatics, 11(1), 385.

    Article  PubMed  PubMed Central  Google Scholar 

  39. Cosentino, C., & Bates, D. (2011). Feedback control in systems biology. Boca Raton: CRC Press.

    Google Scholar 

  40. Craciun, G., & Feinberg, M. (2005). Multiple equilibria in complex chemical reaction networks: I. The injectivity property. SIAM Journal on Applied Mathematics, 65(5), 1526–1546.

    Article  CAS  Google Scholar 

  41. Davila-Velderrain, J., Juarez-Ramiro, L., Martinez-Garcia, J. C., Alvarez-Buylla, E. R. (2015). Methods for characterizing the epigenetic attractors landscape associated with Boolean gene regulatory networks. arXiv preprint. arXiv:1510.04230.

    Google Scholar 

  42. Davila-Velderrain, J., Villarreal, C., & Álvarez-Buylla, E. R. (2015). Reshaping the epigenetic landscape during early flower development: Induction of attractor transitions by relative differences in gene decay rates. BMC Systems Biology, 9(1), 20.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  43. De Jong, H., Geiselmann, J., Hernandez, C., & Page, M. (2003). Genetic network analyzer: Qualitative simulation of genetic regulatory networks. Bioinformatics, 19(3), 336–344.

    Article  PubMed  CAS  Google Scholar 

  44. Domínguez Hüttinger, E. (2014). Mathematical modelling of epithelium homeostasis (Doctoral dissertation, Imperial College London).

    Google Scholar 

  45. Dominguez-Hüttinger, E., Boon, N. J., Clarke, T. B., & Tanaka, R. J. (2017). Mathematical modelling of colonization, invasive infection and treatment of Streptococcus pneumoniae. Frontiers in Physiology, 8, 115.

    Article  PubMed  PubMed Central  Google Scholar 

  46. Domínguez-Hüttinger, E., Christodoulides, P., Miyauchi, K., Irvine, A. D., Okada-Hatakeyama, M., Kubo, M., et al. (2017). Mathematical modeling of atopic dermatitis reveals “double-switch” mechanisms underlying 4 common disease phenotypes. Journal of Allergy and Clinical Immunology, 139(6), 1861–1872.

    Article  PubMed  Google Scholar 

  47. Domínguez-Hüttinger, E., Ono, M., Barahona, M., & Tanaka, R. J. (2013). Risk factor-dependent dynamics of atopic dermatitis: Modelling multi-scale regulation of epithelium homeostasis. Interface Focus, 3(2), 20120090.

    Article  PubMed  PubMed Central  Google Scholar 

  48. Doncic, A., Atay, O., Valk, E., Grande, A., Bush, A., Vasen, G., et al. (2015). Compartmentalization of a bistable switch enables memory to cross a feedback-driven transition. Cell, 160(6), 1182–1195.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  49. Eissing, T., Conzelmann, H., Gilles, E. D., Allgöwer, F., Bullinger, E., & Scheurich, P. (2004). Bistability analyses of a caspase activation model for receptor-induced apoptosis. Journal of Biological Chemistry, 279(35), 36892–36897.

    Article  PubMed  CAS  Google Scholar 

  50. Ellner, S. P., & Guckenheimer, J. (2011). Dynamic models in biology. Princeton: Princeton University Press.

    Google Scholar 

  51. Elnashaie, S. S., & Uhlig, F. (2007). Numerical techniques for chemical and biological engineers using MATLAB: A simple bifurcation approach. Berlin: Springer Science & Business Media.

    Google Scholar 

  52. Espinosa-Soto, C., Padilla-Longoria, P., & Álvarez-Buylla, E. R. (2004). A gene regulatory network model for cell–fate determination during Arabidopsis thaliana flower development that is robust and recovers experimental gene expression profiles. Plant Cell, 16, 2923–2939.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  53. Fauré, A., Naldi, A., Chaouiya, C., & Thieffry, D. (2006). Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle. Bioinformatics, 22(14), e124–e131.

    Article  PubMed  Google Scholar 

  54. Ferrell, J. E. (2012). Bistability, bifurcations, and Waddington’s epigenetic landscape. Current Biology, 22(11), R458–R466.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  55. Ferrell, J. E., & Machleder, E. M. (1998). The biochemical basis of an all-or-none cell fate switch in Xenopus oocytes. Science, 280(5365), 895–898.

    Article  PubMed  CAS  Google Scholar 

  56. Ferrell, J. E., Pomerening, J. R., Kim, S. Y., Trunnell, N. B., Xiong, W., Huang, C. Y. F., et al. (2009). Simple, realistic models of complex biological processes: Positive feedback and bistability in a cell fate switch and a cell cycle oscillator. FEBS Letters, 583(24), 3999–4005.

    Article  PubMed  CAS  Google Scholar 

  57. Fey, D., Halasz, M., Dreidax, D., Kennedy, S. P., Hastings, J. F., Rauch, N., et al. (2015). Signaling pathway models as biomarkers: Patient-specific simulations of JNK activity predict the survival of neuroblastoma patients. Science Signaling, 8(408), 1–16.

    Article  CAS  Google Scholar 

  58. Fox, R. F. (1993). Review of Stuart Kauffman, The origins of order: Self-organization and selection in evolution. Biophysical Journal, 65(6), 2698.

    Article  PubMed Central  Google Scholar 

  59. Fuchs, A. (2014). Nonlinear dynamics in complex systems. Berlin: Springer.

    Google Scholar 

  60. Garg, A., Mohanram, K., De Micheli, G., & Xenarios, I. (2012). Implicit methods for qualitative modeling of gene regulatory networks. In Gene regulatory networks: Methods and protocols (Vol. 786, pp. 397–443). New York: Humana Press.

    Google Scholar 

  61. Gershenfeld, N. (1998). The nature of mathematical modeling. Cambridge: Cambridge University Press.

    Google Scholar 

  62. Glass, L., & Kauffman, S. A. (1973). The logical analysis of continuous, non-linear biochemical control networks. Journal of Theoretical Biology, 39(1), 103–129.

    Article  PubMed  CAS  Google Scholar 

  63. Goldbeter, A., & Koshland, D. E. (1984). Ultrasensitivity in biochemical systems controlled by covalent modification. Interplay between zero-order and multistep effects. Journal of Biological Chemistry, 259(23), 14441–14447.

    PubMed  CAS  Google Scholar 

  64. Goodwin, B. C. (2009). Beyond the Darwinian paradigm: Understanding biological forms. In Evolution: The first four billion years (pp. 299–312). Cambridge: Harvard University Press.

    Google Scholar 

  65. Grabe, N., & Neuber, K. (2005). A multicellular systems biology model predicts epidermal morphology, kinetics and Ca2+ flow. Bioinformatics, 21(17), 3541–3547.

    Article  PubMed  CAS  Google Scholar 

  66. Green, E. D., Rubin, E. M., & Olson, M. V. (2017). The future of DNA sequencing. Nature News, 550(7675), 179.

    Article  Google Scholar 

  67. Guevara, M. R. (2003). Bifurcations involving fixed points and limit cycles in biological systems. In Dynamics in physiology and medicine (pp. 41–85). New York: Springer.

    Chapter  Google Scholar 

  68. Halasz, M., Kholodenko, B. N., Kolch, W., & Santra, T. (2016). Integrating network reconstruction with mechanistic modeling to predict cancer therapies. Science Signaling, 9(455), ra114.

    Google Scholar 

  69. Harrington, H. A., Ho, K. L., Ghosh, S., & Tung, K. C. (2008). Construction and analysis of a modular model of caspase activation in apoptosis. Theoretical Biology and Medical Modelling, 5(1), 26.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  70. Hijmans, B. S., Tiemann, C. A., Grefhorst, A., Boesjes, M., van Dijk, T. H., Tietge, U. J., et al. (2015). A systems biology approach reveals the physiological origin of hepatic steatosis induced by liver X receptor activation. The FASEB Journal, 29(4), 1153–1164.

    Article  PubMed  CAS  Google Scholar 

  71. Hinrichsen, D., & Pritchard, A. J. (2005). Mathematical Systems Theory I - Modelling, State Space Analysis, Stability and Robustness. Texts in applied mathematics (Vol. 48). Berlin: Springer.

    Google Scholar 

  72. Höfer, T., Nathansen, H., Löhning, M., Radbruch, A., & Heinrich, R. (2002). GATA-3 transcriptional imprinting in Th2 lymphocytes: A mathematical model. Proceedings of the National Academy of Sciences, 99(14), 9364–9368.

    Article  CAS  Google Scholar 

  73. Hong, T., Watanabe, K., Ta, C. H., Villarreal-Ponce, A., Nie, Q., & Dai, X. (2015). An Ovol2-Zeb1 mutual inhibitory circuit governs bidirectional and multi-step transition between epithelial and mesenchymal states. PLoS Computational Biology, 11(11), e1004569.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  74. Huang, S., & Kauffman, S. A. (2009). Complex GRN regulatory networks: From structure to biological observables: Cell fate determination. In Encyclopedia of complexity and systems science (pp. 1180–1213). New York: Springer.

    Chapter  Google Scholar 

  75. Hucka, M., Finney, A., Sauro, H. M., Bolouri, H., Doyle, J. C., Kitano, H., et al. (2003). The systems biology markup language (SBML). A medium for representation and exchange of biochemical network models. Bioinformatics, 19(4), 524–531.

    Article  PubMed  CAS  Google Scholar 

  76. Ideta, A. M., Tanaka, G., Takeuchi, T., & Aihara, K. (2008). A mathematical model of intermittent androgen suppression for prostate cancer. Journal of Nonlinear Science, 18(6), 593–614.

    Article  CAS  Google Scholar 

  77. Inoue, K., Shinohara, H., Behar, M., Yumoto, N., Tanaka, G., Hoffmann, A., et al. (2016). Oscillation dynamics underlie functional switching of NF-κB for B-cell activation. NPJ Systems Biology and Applications, 2, 16024.

    Article  PubMed  PubMed Central  Google Scholar 

  78. Izhikevich, E. M. (2007). Dynamical systems in neuroscience. Cambridge: MIT Press.

    Google Scholar 

  79. Jeanquartier, F., Jean-Quartier, C., Kotlyar, M., Tokar, T., Hauschild, A. C., Jurisica, I., et al. (2016). Machine learning for in silico modeling of tumor growth. In Machine learning for health informatics (pp. 415–434). Berlin: Springer International Publishing.

    Chapter  Google Scholar 

  80. Juárez-Ramiro, L. (2015). Modelado de patrones de interconexión de módulos de regulación transcripcional: aplicación a la interacción entre la transición epitelio-mesénquima y el ciclo celular. Tesis de Maestría en Ciencias, Agosto, Departamento de Control Automático, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional.

    Google Scholar 

  81. Jurtz, V. I., Johansen, A. R., Nielsen, M., Almagro Armenteros, J. J., Nielsen, H., Sønderby, C. K., et al. (2017). An introduction to deep learning on biological sequence data: Examples and solutions. Bioinformatics, 33(22), 3685–3690.

    Article  PubMed  PubMed Central  Google Scholar 

  82. Kaneko, K. (2011). Characterization of stem cells and cancer cells on the basis of gene expression profile stability, plasticity, and robustness. Bioessays, 33(6), 403–413.

    Article  PubMed  CAS  Google Scholar 

  83. Kaplan, D., & Glass, L. (2012). Understanding nonlinear dynamics. Berlin: Springer Science & Business Media.

    Google Scholar 

  84. Kauffman, S. A. (1969). Metabolic stability and epigenesis in randomly constructed genetic nets. Journal of Theoretical Biology, 22(3), 437–467.

    Article  PubMed  CAS  Google Scholar 

  85. Keller, A. D. (1995). Model genetic circuits encoding autoregulatory transcription factors. Journal of Theoretical Biology, 172(2), 169–185.

    Article  PubMed  CAS  Google Scholar 

  86. Kirkpatrick, S., Gelatt, C. D., Jr., & Vecchi, M. P. (1987). Optimization by simulated annealing. In Spin glass theory and beyond: An introduction to the replica method and its applications, World scientific lecture notes in physics (Vol. 9, pp. 339–348). Singapore: World Scientific.

    Google Scholar 

  87. Kuznetsov, Y. A. (2013). Elements of applied bifurcation theory (Vol. 112). Berlin: Springer Science & Business Media.

    Google Scholar 

  88. Lanczos, C. (2012). The variational principles of mechanics. North Chelmsford: Courier Corporation.

    Google Scholar 

  89. Le Novere, N., Hucka, M., Mi, H., Moodie, S., Schreiber, F., Sorokin, A., et al. (2009). The systems biology graphical notation. Nature Biotechnology, 27(8), 735–741.

    Article  PubMed  CAS  Google Scholar 

  90. Lee, T. I., & Young, R. A. (2013). Transcriptional regulation and its misregulation in disease. Cell, 152(6), 1237–1251.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  91. Lillacci, G., & Khammash, M. (2010). Parameter estimation and model selection in computational biology. PLoS Computational Biology, 6(3), e1000696.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  92. Lipniacki, T., Hat, B., Faeder, J. R., & Hlavacek, W. S. (2008). Stochastic effects and bistability in T cell receptor signaling. Journal of Theoretical Biology, 254(1), 110–122.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  93. Lobo, D., & Levin, M. (2015). Inferring regulatory networks from experimental morphological phenotypes: A computational method reverse-engineers planarian regeneration. PLoS Computational Biology, 11(6), e1004295.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  94. Louis, M., & Becskei, A. (2002). Binary and graded responses in gene networks. Science STKE, 2002(143), pe33.

    Google Scholar 

  95. Margueron, R., & Reinberg, D. (2010). Chromatin structure and the inheritance of epigenetic information. Nature Reviews Genetics, 11(4), 285.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  96. Marino, S., Hogue, I. B., Ray, C. J., & Kirschner, D. E. (2008). A methodology for performing global uncertainty and sensitivity analysis in systems biology. Journal of Theoretical Biology, 254(1), 178–196.

    Article  PubMed  PubMed Central  Google Scholar 

  97. Martinez-Sanchez, M. E., Mendoza, L., Villarreal, C., & Álvarez-Buylla, E. R. (2015). A minimal regulatory network of extrinsic and intrinsic factors recovers observed patterns of CD4+ T cell differentiation and plasticity. PLoS Computational Biology, 11(6), e1004324.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  98. Mayo, A. E., Setty, Y., Shavit, S., Zaslaver, A., & Alon, U. (2006). Plasticity of the cis-regulatory input function of a gene. PLoS Biology, 4(4), e45.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  99. Melmed, S., & Conn, P. M. (Eds.). (2007). Endocrinology: Basic and clinical principles. Berlin: Springer Science & Business Media.

    Google Scholar 

  100. Mendes, N. D., Lang, F., Le Cornec, Y. S., Mateescu, R., Batt, G., & Chaouiya, C. (2013). Composition and abstraction of logical regulatory modules: Application to multicellular systems. Bioinformatics, 29(6), 749–757.

    Article  PubMed  CAS  Google Scholar 

  101. Mendes, P., Hoops, S., Sahle, S., Gauges, R., Dada, J., & Kummer, U. (2009). Computational modeling of biochemical networks using COPASI. In Methods in Molecular Biology, Systems Biology (Vol. 500, pp. 17–59). New York: Humana Press.

    Google Scholar 

  102. Méndez-López, L. F., Davila-Velderrain, J., Domínguez-Hüttinger, E., Enríquez-Olguín, C., Martínez-García, J. C., & Álvarez-Buylla, E. R. (2017). Gene regulatory network underlying the immortalization of epithelial cells. BMC Systems Biology, 11(1), 24.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  103. Mendoza, L., & Álvarez-Buylla, E. R. (1998). Dynamics of the genetic regulatory network for arabidopsis thaliana flower morphogenesis. Journal of Theoretical Biology, 193(2), 307–319.

    Article  PubMed  CAS  Google Scholar 

  104. Milo, R. (2013). What is the total number of protein molecules per cell volume? A call to rethink some published values. Bioessays, 35(12), 1050–1055.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  105. Monk, N. A. (2003). Oscillatory expression of Hes1, p53, and NF-κB driven by transcriptional time delays. Current Biology, 13(16), 1409–1413.

    Article  PubMed  CAS  Google Scholar 

  106. Moris, N., Pina, C., & Arias, A. M. (2016). Transition states and cell fate decisions in epigenetic landscapes. Nature Reviews Genetics, 17(11), 693–703.

    Article  PubMed  CAS  Google Scholar 

  107. Müller, J., & Tjardes, T. (2003). Modeling the cytokine network in vitro and in vivo. Computational and Mathematical Methods in Medicine, 5(2), 93–110.

    Google Scholar 

  108. Murray, J. D. (2003). Mathematical biology: II: Spatial models and biomedical applications. Interdisciplinary applied mathematics (3rd ed., Vol. 18). New York: Springer.

    Google Scholar 

  109. Müssel, C., Hopfensitz, M., & Kestler, H. A. (2010). BoolNet–An R package for generation, reconstruction and analysis of Boolean networks. Bioinformatics, 26(10), 1378–1380.

    Article  PubMed  CAS  Google Scholar 

  110. Naldi, A., Berenguier, D., Fauré, A., Lopez, F., Thieffry, D., & Chaouiya, C. (2009). Logical modelling of regulatory networks with GINsim 2.3. Biosystems, 97(2), 134–139.

    Article  PubMed  CAS  Google Scholar 

  111. Nam, J., Aguda, B. D., Rath, B., & Agarwal, S. (2009). Biomechanical thresholds regulate inflammation through the NF-κB pathway: Experiments and modeling. PLoS One, 4(4), e5262.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  112. Nevozhay, D., Adams, R. M., Murphy, K. F., Josić, K., & Balázsi, G. (2009). Negative autoregulation linearizes the dose-response and suppresses the heterogeneity of gene expression. Proceedings of the National Academy of Sciences, 106(13), 5123–5128.

    Article  Google Scholar 

  113. Nieto, M. A., Huang, R. Y. J., Jackson, R. A., & Thiery, J. P. (2016). EMT: 2016. Cell, 166(1), 21–45.

    Article  PubMed  CAS  Google Scholar 

  114. Olsen, L., Sherratt, J. A., & Maini, P. K. (1996). A mathematical model for fibro-proliferative wound healing disorders. Bulletin of Mathematical Biology, 58(4), 787–808.

    Article  PubMed  CAS  Google Scholar 

  115. Oyarzún, D. A., Chaves, M., & Hoff-Hoffmeyer-Zlotnik, M. (2012). Multistability and oscillations in genetic control of metabolism. Journal of Theoretical Biology, 295, 139–153.

    Article  PubMed  CAS  Google Scholar 

  116. Ozbudak, E. M., Thattai, M., Lim, H. N., Shraiman, B. I., & Van Oudenaarden, A. (2004). Multistability in the lactose utilization network of Escherichia coli. Nature, 427(6976), 737–740.

    Article  PubMed  CAS  Google Scholar 

  117. Pantoja-Hernández, L., & Martínez-García, J. C. (2015). Retroactivity in the context of modularly structured biomolecular systems. Frontiers in Bioengineering and Biotechnology, 3, 85.

    Article  PubMed  PubMed Central  Google Scholar 

  118. Paulsen, M., Legewie, S., Eils, R., Karaulanov, E., & Niehrs, C. (2011). Negative feedback in the bone morphogenetic protein 4 (BMP4) synexpression group governs its dynamic signaling range and canalizes development. Proceedings of the National Academy of Sciences, 108(25), 10202–10207.

    Article  Google Scholar 

  119. Pedersen, E., & Bongo, L. A. (2017). Large-scale biological meta-database management. Future Generation Computer Systems, 67, 481–489.

    Article  Google Scholar 

  120. Pérez-Ruiz, R. V., García-Ponce, B., Marsch-Martínez, N., Ugartechea-Chirino, Y., Villajuana-Bonequi, M., de Folter, S., et al. (2015). XAANTAL2 (AGL14) is an important component of the complex gene regulatory network that underlies Arabidopsis shoot apical meristem transitions. Molecular Plant, 8(5), 796–813.

    Article  PubMed  CAS  Google Scholar 

  121. Plsek, P., & Greenhalgh, T. (2001). The challenge of complexity in health care: An introduction. BMJ, 323(7314), 625–628.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  122. Podtschaske, M., Benary, U., Zwinger, S., Höfer, T., Radbruch, A., & Baumgrass, R. (2007). Digital NFATc2 activation per cell transforms graded T cell receptor activation into an all-or-none IL-2 expression. PLoS One, 2(9), e935.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  123. Pujadas, E., & Feinberg, A. P. (2012). Regulated noise in the epigenetic landscape of development and disease. Cell, 148(6), 1123–1131.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  124. Purvis, J. E., Karhohs, K. W., Mock, C., Batchelor, E., Loewer, A., & Lahav, G. (2012). p53 dynamics control cell fate. Science, 336(6087), 1440–1444.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  125. Purvis, J. E., & Lahav, G. (2013). Encoding and decoding cellular information through signaling dynamics. Cell, 152(5), 945–956.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  126. Richard, C. Y., Pesce, C. G., Colman-Lerner, A., Lok, L., Pincus, D., Serra, E., et al. (2008). Negative feedback that improves information transmission in yeast signalling. Nature, 456(7223), 755–761.

    Article  CAS  Google Scholar 

  127. Ryu, H., Chung, M., Dobrzyński, M., Fey, D., Blum, Y., Lee, S. S., et al. (2015). Frequency modulation of ERK activation dynamics rewires cell fate. Molecular Systems Biology, 11(11), 838.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  128. Schilstra, M. J., & Nehaniv, C. L. (2008). Bio-logic: Gene expression and the laws of combinatorial logic. Artificial Life, 14(1), 121–133.

    Article  PubMed  Google Scholar 

  129. Schmidt, H., & Jirstrand, M. (2005). Systems biology toolbox for MATLAB: A computational platform for research in systems biology. Bioinformatics, 22(4), 514–515.

    Article  PubMed  CAS  Google Scholar 

  130. Setty, Y., Mayo, A. E., Surette, M. G., & Alon, U. (2003). Detailed map of a cis-regulatory input function. Proceedings of the National Academy of Sciences, 100(13), 7702–7707.

    Article  CAS  Google Scholar 

  131. Shah, N. A., & Sarkar, C. A. (2011). Robust network topologies for generating switch-like cellular responses. PLoS Computational Biology, 7(6), e1002085.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  132. Shalek, A. K., Satija, R., Adiconis, X., Gertner, R. S., Gaublomme, J. T., Raychowdhury, R., et al. (2013). Single-cell transcriptomics reveals bimodality in expression and splicing in immune cells. Nature, 498(7453), 236–240.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  133. Shin, S., Seong, J. K., & Bae, Y. S. (2016). Ahnak stimulates BMP2-mediated adipocyte differentiation through Smad1 activation. Obesity, 24(2), 398–407.

    Article  PubMed  CAS  Google Scholar 

  134. Soetaert, K. E. R., Petzoldt, T., & Setzer, R. W. (2010). Solving differential equations in R: Package deSolve. Journal of Statistical Software, 33, 1–25. ISSN: 1548-7660.

    Google Scholar 

  135. Steinway, S. N., Zañudo, J. G. T., Michel, P. J., Feith, D. J., Loughran, T. P., & Albert, R. (2015). Combinatorial interventions inhibit TGF β-driven epithelial-to-mesenchymal transition and support hybrid cellular phenotypes. NPJ Systems Biology and Applications, 1, 15014.

    Article  PubMed  PubMed Central  Google Scholar 

  136. Stelling, J., Sauer, U., Szallasi, Z., Doyle, F. J., & Doyle, J. (2004). Robustness of cellular functions. Cell, 118(6), 675–685.

    Article  PubMed  CAS  Google Scholar 

  137. Strogatz, S. H. (2014). Nonlinear dynamics and chaos with applications to physics, biology, chemistry, and engineering (2nd ed.). Boulder: Westview Press.

    Google Scholar 

  138. Sung, M. H., Li, N., Lao, Q., Gottschalk, R. A., Hager, G. L., & Fraser, I. D. (2014). Switching of the relative dominance between feedback mechanisms in lipopolysaccharide-induced NF-κB signaling. Science Signaling, 7(308), ra6.

    Google Scholar 

  139. Sütterlin, T., Huber, S., Dickhaus, H., & Grabe, N. (2009). Modeling multi-cellular behavior in epidermal tissue homeostasis via finite state machines in multi-agent systems. Bioinformatics, 25(16), 2057–2063.

    Article  PubMed  CAS  Google Scholar 

  140. Sütterlin, T., Kolb, C., Dickhaus, H., Jäger, D., & Grabe, N. (2012). Bridging the scales: Semantic integration of quantitative SBML in graphical multi-cellular models and simulations with EPISIM and COPASI. Bioinformatics, 29(2), 223–229.

    Article  PubMed  CAS  Google Scholar 

  141. Szallasi, Z., Periwal, V., & Stelling, J. (2006). System modeling in cellular biology: From concepts to nuts and bolts. Cambridge: The MIT Press.

    Book  Google Scholar 

  142. Tanaka, G., Christodoulides, P., Domínguez-Hüttinger, E., Aihara, K., & Tanaka, R. J. (2018). Bifurcation analysis of a mathematical model of atopic dermatitis to determine patient-specific effects of treatments on dynamic phenotypes. Journal of Theoretical Biology, 448, 66–79.

    Article  PubMed  CAS  Google Scholar 

  143. Tanaka, R. J., Ono, M., & Harrington, H. A. (2011). Skin barrier homeostasis in atopic dermatitis: Feedback regulation of kallikrein activity. PloS One, 6(5), e19895.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  144. Tay, S., Hughey, J. J., Lee, T. K., Lipniacki, T., Quake, S. R., & Covert, M. W. (2010). Single-cell NF-κB dynamics reveal digital activation and analogue information processing. Nature, 466(7303), 267–271.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  145. Thorén, H., & Gerlee, P. (2010). Weak emergence and complexity. In Artificial Life XII Proceedings of the Twelfth International Conference on the Synthesis and Simulation of Living Systems (pp. 879–886). Cambridge: MIT Press.

    Google Scholar 

  146. Tiemann, C. A., Vanlier, J., Hilbers, P. A., & van Riel, N. A. (2011). Parameter adaptations during phenotype transitions in progressive diseases. BMC Systems Biology, 5(1), 174.

    Article  PubMed  PubMed Central  Google Scholar 

  147. Tiemann, C. A., Vanlier, J., Oosterveer, M. H., Groen, A. K., Hilbers, P. A., & van Riel, N. A. (2013). Parameter trajectory analysis to identify treatment effects of pharmacological interventions. PLoS Computational Biology, 9(8), e1003166.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  148. Tiwari, A., Ray, J. C. J., Narula, J., & Igoshin, O. A. (2011). Bistable responses in bacterial genetic networks: Designs and dynamical consequences. Mathematical Biosciences, 231(1), 76–89.

    Article  PubMed  PubMed Central  Google Scholar 

  149. Toni, T., & Stumpf, M. P. (2009). Simulation-based model selection for dynamical systems in systems and population biology. Bioinformatics, 26(1), 104–110.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  150. Transtrum, M. K., & Qiu, P. (2016). Bridging mechanistic and phenomenological models of complex biological systems. PLoS Computational Biology, 12(5), e1004915.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  151. Tyson, J. J., Chen, K. C., & Novak, B. (2003). Sniffers, buzzers, toggles and blinkers: Dynamics of regulatory and signaling pathways in the cell. Current Opinion in Cell Biology, 15(2), 221–231.

    Article  PubMed  CAS  Google Scholar 

  152. Valeyev, N. V., Hundhausen, C., Umezawa, Y., Kotov, N. V., Williams, G., Clop, A., et al. (2010). A systems model for immune cell interactions unravels the mechanism of inflammation in human skin. PLoS Computational Biology, 6(12), e1001024.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  153. Van Kampen, N. G. (1992). Stochastic processes in physics and chemistry (revised and enlarged edition). Amsterdam: Elsevier.

    Google Scholar 

  154. van Riel, N. A., Tiemann, C. A., Vanlier, J., & Hilbers, P. A. (2013). Applications of analysis of dynamic adaptations in parameter trajectories. Interface Focus, 3(2), 20120084.

    Article  PubMed  PubMed Central  Google Scholar 

  155. Veening, J. W., Smits, W. K., & Kuipers, O. P. (2008). Bistability, epigenetics, and bet-hedging in bacteria. Annual Review of Microbiology, 62, 193–210.

    Article  PubMed  CAS  Google Scholar 

  156. Velderrain, J. D., Martínez-García, J. C., & Álvarez-Buylla, E. R. (2017). Boolean dynamic modeling approaches to study plant gene regulatory networks: Integration, validation, and prediction. In Methods in molecular biology (Clifton, NJ), (Vol. 629, pp. 297–315). New York: Humana Press.

    Google Scholar 

  157. Waddington, C. H. (1957). The strategy of the genes. A discussion of some aspects of theoretical biology; with an appendix by H. Kacser. London: George Allen & Unwin.

    Google Scholar 

  158. Wagner, A. (2013). Robustness and evolvability in living systems. Princeton: Princeton University Press.

    Book  Google Scholar 

  159. Wang, R. S., Saadatpour, A., & Albert, R. (2012). Boolean modeling in systems biology: An overview of methodology and applications. Physical Biology, 9(5), 055001.

    Article  PubMed  CAS  Google Scholar 

  160. Weber, M., & Buceta, J. (2013). Dynamics of the quorum sensing switch: Stochastic and non-stationary effects. BMC Systems Biology, 7(1), 6.

    Article  PubMed  PubMed Central  Google Scholar 

  161. Weiss, J. N. (1997). The Hill equation revisited: Uses and misuses. The FASEB Journal, 11(11), 835–841.

    Article  PubMed  CAS  Google Scholar 

  162. Wilhelm, T. (2009). The smallest chemical reaction system with bistability. BMC Systems Biology, 3(1), 90.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  163. Williams, J. W., Cui, X., Levchenko, A., & Stevens, A. M. (2008). Robust and sensitive control of a quorum-sensing circuit by two interlocked feedback loops. Molecular Systems Biology, 4(1), 234.

    PubMed  PubMed Central  Google Scholar 

  164. Wolkenhauer, O., Ullah, M., Wellstead, P., & Cho, K. H. (2005). The dynamic systems approach to control and regulation of intracellular networks. FEBS Letters, 579(8), 1846–1853.

    Article  PubMed  CAS  Google Scholar 

  165. Yi, T. M., Huang, Y., Simon, M. I., & Doyle, J. (2000). Robust perfect adaptation in bacterial chemotaxis through integral feedback control. Proceedings of the National Academy of Sciences, 97(9), 4649–4653.

    Article  CAS  Google Scholar 

  166. Zhang, Q., Bhattacharya, S., Kline, D. E., Crawford, R. B., Conolly, R. B., Thomas, R. S., et al. (2010). Stochastic modeling of B lymphocyte terminal differentiation and its suppression by dioxin. BMC Systems Biology, 4(1), 40.

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  167. Zhang, T., Schmierer, B., & Novák, B. (2011). Cell cycle commitment in budding yeast emerges from the cooperation of multiple bistable switches. Open Biology, 1(3), 110009.

    Article  PubMed  PubMed Central  Google Scholar 

  168. Zhao, Y., Ransom, J. F., Li, A., Vedantham, V., von Drehle, M., Muth, A. N., et al. (2007). Dysregulation of cardiogenesis, cardiac conduction, and cell cycle in mice lacking miRNA-1-2. Cell, 129(2), 303–317.

    Article  PubMed  CAS  Google Scholar 

  169. Zhou, J. X., Samal, A., d’Hérouël, A. F., Price, N. D., & Huang, S. (2016). Relative stability of network states in Boolean network models of gene regulation in development. Biosystems, 142, 15–24.

    Article  PubMed  Google Scholar 

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Authors and Affiliations

  1. Ciudad Universitaria, UNAM, Instituto de Ecología, Ciudad de México, Distrito Federal, Mexico

    María Elena Álvarez-Buylla Roces & Mariana Esther Martínez-Sánchez

  2. Departamento de Control Automático, CINVESTAV, Ciudad de México, Distrito Federal, Mexico

    Juan Carlos Martínez-García

  3. CSIL, Massachusetts Institute of Technology, Cambridge, MA, USA

    José Dávila-Velderrain

  4. Centro de Ciencias Matemáticas, UNAM, Morelia, México

    Elisa Domínguez-Hüttinger

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Álvarez-Buylla Roces, M.E., Martínez-García, J.C., Dávila-Velderrain, J., Domínguez-Hüttinger, E., Martínez-Sánchez, M.E. (2018). Modeling Procedures. In: Modeling Methods for Medical Systems Biology. Advances in Experimental Medicine and Biology, vol 1069. Springer, Cham. https://doi.org/10.1007/978-3-319-89354-9_2

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