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Mathematical Tools in Cancer Signalling Systems Biology

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Cancer Systems Biology, Bioinformatics and Medicine

Abstract

Rather than a strictly formalized methodological framework, we here describe systems biology as a flexible approach in which the modelling strategy used depends on a trade-off between the nature of the biochemical network investigated, the biomedical question to be elucidated, and the quantity (and quality) of the experimental data available. To further substantiate this idea, we chose a number of recent scientific publications in which systems biology was used in the context of cancer cell signalling . Fundamental aspects of the strategy used to set up the mathematical models , integrate available biomedical knowledge, and specifically to generate quantitative data and analyse the system using theoretical and computational tools, are compared and discussed, but new avenues are also suggested.

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References

  • Albeck JG, Burke JM, Aldridge BB, Zhang M, Lauffenburger DA, Sorger PK (2008a) Quantitative analysis of pathways controlling extrinsic apoptosis in single cells. Mol Cell 30(1):11–27

    Google Scholar 

  • Albeck JG, Burke JM, Spencer SL, Lauffenburger DA, Sorger PK (2008b) Modeling a snap-action, variable-delay switch controlling extrinsic cell death. PLoS Biol 6(12):2831–2852

    Google Scholar 

  • Aldridge BB, Burke JM, Lauffenburger DA, Sorger PK (2006) Physicochemical modelling of cell signalling pathways. Nat Cell Biol 8(11):1195–1203

    Article  PubMed  CAS  Google Scholar 

  • Aldridge BB, Saez-Rodriguez J, Muhlich JL, Sorger PK, Lauffenburger DA (2009) Fuzzy logic analysis of kinase pathway crosstalk in TNF/EGF/insulin-induced signaling. PLoS Comput Biol 5(4):e1000340

    Article  Google Scholar 

  • Ashall L, Horton CA, Nelson DE, Paszek P, Harper CV, Sillitoe K, Ryan S, Spiller DG, Unitt JF, Broomhead DS, Kell DB, Rand DA, Sée V, White MR (2009) Pulsatile stimulation determines timing and specificity of NF-kappaB-dependent transcription. Science 324(5924):242–246

    Article  PubMed  CAS  Google Scholar 

  • Banga JR, Balsa-Canto E (2008) Parameter estimation and optimal experimental design. Essays Biochem 45:195–209

    Article  PubMed  CAS  Google Scholar 

  • Bhalla US, Ram PT, Iyengar R (2002) MAP kinase phosphatase as a locus of flexibility in a mitogen-activated protein kinase signaling network. Science 297(5583):1018–1023

    Article  PubMed  CAS  Google Scholar 

  • Birkemeyer C, Luedemann A, Wagner C, Erban A, Kopka J (2005) Metabolome analysis: the potential of in vivo labeling with stable isotopes for metabolite profiling. Trends Biotechnol 23(1):28–33

    Article  PubMed  CAS  Google Scholar 

  • Blüthgen N, Legewie S, Kielbasa SM, Schramme A, Tchernitsa O, Keil J, Solf A, Vingron M, Schäfer R, Herzel H, Sers C (2009) A systems biological approach suggests that transcriptional feedback regulation by dual-specificity phosphatase 6 shapes extracellular signal-related kinase activity in RAS-transformed fibroblasts. FEBS J 276(4):1024–1037

    Article  PubMed  Google Scholar 

  • Bollard ME, Stanley EG, Lindon JC, Nicholson JK, Holmes E (2005) NMR-based metabonomic approaches for evaluating physiological influences on biofluid composition. NMR Biomed 18:143–162

    Article  PubMed  CAS  Google Scholar 

  • Borisov N, Aksamitiene E, Kiyatkin A, Legewie S, Berkhout J, Maiwald T, Kaimachnikov NP, Timmer J, Hoek JB, Kholodenko BN (2009) Systems-level interactions between insulin-EGF networks amplify mitogenic signaling. Mol Syst Biol 5:256

    Article  PubMed  Google Scholar 

  • Chaouiya C (2007) Petri net modelling of biological networks. Brief Bioinform 8(4):210–219

    Article  PubMed  CAS  Google Scholar 

  • Chen WW, Schoeberl B, Jasper PJ, Niepel M, Nielsen UB, Lauffenburger DA, Sorger PK (2009) Input-output behavior of ErbB signaling pathways as revealed by a mass action model trained against dynamic data. Mol Syst Biol 5:239

    PubMed  Google Scholar 

  • Chou IC, Voit EO (2009) Recent developments in parameter estimation and structure identification of biochemical and genomic systems. Math Biosci 219(2):57–83

    Article  PubMed  CAS  Google Scholar 

  • Ciliberto A, Novak B, Tyson JJ (2005) Steady states and oscillations in the p53/Mdm2 network. Cell Cycle 4(3):488–493

    Article  PubMed  CAS  Google Scholar 

  • Csikász-Nagy A, Battogtokh D, Chen KC, Novák B, Tyson JJ (2006) Analysis of a generic model of eukaryotic cell-cycle regulation. Biophys J 90(12):4361–4379

    Article  PubMed  Google Scholar 

  • Dakna M, He Z, Yu WC, Mischak H, Kolch W (2009) Technical, bioinformatical and statistical aspects of liquid chromatography-mass spectrometry (LC-MS) and capillary electrophoresis-mass spectrometry (CE-MS) based clinical proteomics: a critical assessment. J Chromatogr B Analyt Technol Biomed Life Sci 877(13):1250–1258

    Google Scholar 

  • Fall CP, Marland ES, Wagner JM, Tyson JJ (2002) Computational cell biology. Springer Science & Business Media, New York

    Google Scholar 

  • Frieboes HB, Edgerton ME, Fruehauf JP, Rose FR, Worrall LK, Gatenby RA, Ferrari M, Cristini V (2009) Prediction of drug response in breast cancer using integrative experimental/computational modeling. Cancer Res 69(10):4484–4492

    Article  PubMed  CAS  Google Scholar 

  • Funahashi A, Tanimura N, Morohashi M, Kitano H (2003) CellDesigner: a process diagram editor for gene-regulatory and biochemical networks. BIOSILICO 1:159–162

    Article  Google Scholar 

  • Gerber SA, Rush J, Stemman O, Kirschner MW, Gygi SP (2003) Absolute quantification of proteins and phosphoproteins from cell lysates by tandem MS. Proc Natl Acad Sci U S A 100(12):6940–6947

    Article  PubMed  CAS  Google Scholar 

  • Geva-Zatorsky N, Rosenfeld N, Itzkovitz S, Milo R, Sigal A, Dekel E, Yarnitzky T, Liron Y, Polak P, Lahav G, Alon U (2006) Oscillations and variability in the p53 system. Mol Syst Biol 2:2006.0033

    Google Scholar 

  • Gutenkunst RN, Waterfall JJ, Casey FP, Brown KS, Myers CR, Sethna JP (2007) Universally sloppy parameter sensitivities in systems biology models. PLoS Comput Biol 3(10):1871–1878

    Article  PubMed  CAS  Google Scholar 

  • Hanahan D, Weinberg RA (2000) The hallmarks of cancer. Cell 100(1):57–70

    Article  PubMed  CAS  Google Scholar 

  • Heiner M, Koch I, Will J (2004) Model validation of biological pathways using Petri nets—demonstrated for apoptosis. Biosystems 75(1–3):15–28

    Article  PubMed  Google Scholar 

  • Heyman H (2006) Quantification of activated signal transduction proteins using fast activated cell-based ELISAs (FACETM). Nat Appl Notes. doi:10.1038/an1562

    Google Scholar 

  • Hoffmann A, Levchenko A, Scott ML, Baltimore D (2002) The IkappaB-NF-kappaB signaling module: temporal control and selective gene activation. Science 298(5596):1241–1247

    Article  PubMed  CAS  Google Scholar 

  • Huang CY, Ferrell JE Jr (1996) Ultrasensitivity in the mitogen-activated protein kinase cascade. Proc Natl Acad Sci U S A 93(19):10078–10083

    Article  PubMed  CAS  Google Scholar 

  • Jeffrey A (1993) Linear algebra and ordinary differential equations. CRC press, Boca Raton

    Google Scholar 

  • Kholodenko BN (2000) Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades. Eur J Biochem 267(6):1583–1588

    Article  PubMed  CAS  Google Scholar 

  • Kholodenko BN, Demin OV, Moehren G, Hoek JB (1999) Quantification of short term signaling by the epidermal growth factor receptor. J Biol Chem 274(42):30169–30181

    Article  PubMed  CAS  Google Scholar 

  • Kim D, Rath O, Kolch W, Cho KH (2007) A hidden oncogenic positive feedback loop caused by crosstalk between Wnt and ERK pathways. Oncogene 26(31):4571–4579

    Article  PubMed  CAS  Google Scholar 

  • Kim SY, Ferrell JE Jr (2007) Substrate competition as a source of ultrasensitivity in the inactivation of Wee1. Cell 128(6):1133–1147

    Article  PubMed  CAS  Google Scholar 

  • Kitano H (2007) Towards a theory of biological robustness. Mol Syst Biol 3:137

    Article  PubMed  Google Scholar 

  • Klamt S, Saez-Rodriguez J, Lindquist JA, Simeoni L, Gilles ED (2006) A methodology for the structural and functional analysis of signaling and regulatory networks. BMC Bioinformatics 7:56

    Article  PubMed  Google Scholar 

  • Krüger R, Heinrich R (2004) Model reduction and analysis of robustness for the Wnt/beta-catenin signal transduction pathway. Genome Inform 15(1):138–148

    PubMed  Google Scholar 

  • Lai X, Nikolov S, Wolkenhauer O, Vera J (2009) A multi-scale model accounting for the effects of JAK2-STAT5 signal modulation in Erythropoiesis. Comput Biol Chem 30:312–324

    Article  Google Scholar 

  • Le Novère N, Hucka M, Mi H, Moodie S, Schreiber F, Sorokin A, Demir E, Wegner K, Aladjem MI, Wimalaratne SM, Bergman FT, Gauges R, Ghazal P, Kawaji H, Li L, Matsuoka Y, Villéger A, Boyd SE, Calzone L, Courtot M, Dogrusoz U, Freeman TC, Funahashi A, Ghosh S, Jouraku A, Kim S, Kolpakov F, Luna A, Sahle S, Schmidt E, Watterson S, Wu G, Goryanin I, Kell DB, Sander C, Sauro H, Snoep JL, Kohn K, Kitano H (2009) The systems biology graphical notation. Nat Biotechnol 27(8):735–741

    Article  PubMed  Google Scholar 

  • van Leeuwen IMM, Byrne HM, Jensen OE, King JR (2007) Elucidating the interactions between the adhesive and transcriptional functions of b-catenin in normal and cancerous cells. J Theor Biol 247(1):77–102

    Article  PubMed  CAS  Google Scholar 

  • van Leeuwen IM, Mirams GR, Walter A, Fletcher A, Murray P, Osborne J, Varma S, Young SJ, Cooper J, Doyle B, Pitt-Francis J, Momtahan L, Pathmanathan P, Whiteley JP, Chapman SJ, Gavaghan DJ, Jensen OE, King JR, Maini PK, Waters SL, Byrne HM (2009) An integrative computational model for intestinal tissue renewal. Cell Prolif 42(5):617–636

    Article  PubMed  CAS  Google Scholar 

  • Lévi F, Altinok A, Clairambault J, Goldbeter A (2008) Implications of circadian clocks for the rhythmic delivery of cancer therapeutics. Philos Transact A Math Phys Eng Sci 366(1880):3575–3598

    Article  PubMed  Google Scholar 

  • Mullassery D, Horton CA, Wood CD, White MR (2008) Single live-cell imaging for systems biology. Essays Biochem 45:121–133

    Article  PubMed  CAS  Google Scholar 

  • Nelson DE, Ihekwaba AE, Elliott M, Johnson JR, Gibney CA, Foreman BE, Nelson G, See V, Horton CA, Spiller DG, Edwards SW, McDowell HP, Unitt JF, Sullivan E, Grimley R, Benson N, Broomhead D, Kell DB, White MR (2004) Oscillations in NF-kappaB signaling control the dynamics of gene expression. Science 306(5696):704–708

    Article  PubMed  CAS  Google Scholar 

  • Neves SR, Tsokas P, Sarkar A, Grace EA, Rangamani P, Taubenfeld SM, Alberini CM, Schaff JC, Blitzer RD, Moraru II, Iyengar R (2008) Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks. Cell 133(4):666–680

    Article  PubMed  CAS  Google Scholar 

  • Nikolov S, Lai X, Liebal UW, Wolkenhauer O, Vera J (2010) Integration of sensitivity and bifurcation analysis to detect critical processes in a model combining signalling and cell population dynamics. Int J Syst 41(1):81–105

    Google Scholar 

  • Papin JA, Hunter T, Palsson BO, Subramaniam S (2005) Reconstruction of cellular signalling networks and analysis of their properties. Nat Rev Mol Cell Biol 6(2):99–111

    Article  PubMed  CAS  Google Scholar 

  • Ptitsyn AA, Weil MM, Thamm DH (2008) Systems biology approach to identification of biomarkers for metastatic progression in cancer. BMC Bioinformatics 9(Suppl 9):S8

    Article  PubMed  Google Scholar 

  • Qu Z, Weiss JN, MacLellan WR (2003) Regulation of the mammalian cell cycle: a model of the G1-to-S transition. Am J Physiol Cell Physiol 284(2):C349–C364

    PubMed  CAS  Google Scholar 

  • Ramalingam S, Honkanen P, Young L, Shimura T, Austin J, Steeg PS, Nishizuka S (2007) Quantitative assessment of the p53-Mdm2 feedback loop using protein lysate microarrays. Cancer Res 67(13):6247–6252

    Article  PubMed  CAS  Google Scholar 

  • Raue A, Kreutz C, Maiwald T, Bachmann J, Schilling M, Klingmüller U, Timmer J (2009) Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics 25(15):1923–1929

    Article  PubMed  CAS  Google Scholar 

  • Rautio J, Barken KB, Lahdenperä J, Breitenstein A, Molin S, Neubauer P (2003) Sandwich hybridisation assay for quantitative detection of yeast RNAs in crude cell lysates. Microb Cell Fact 2(1):4

    Article  PubMed  Google Scholar 

  • Rehm M, Huber HJ, Dussmann H, Prehn JH (2006) Systems analysis of effector caspase activation and its control by X-linked inhibitor of apoptosis protein. EMBO J 25(18):4338–4349

    Article  PubMed  CAS  Google Scholar 

  • Reynolds AR, Tischer C, Verveer PJ, Rocks O, Bastiaens PI (2003) EGFR activation coupled to inhibition of tyrosine phosphatases causes lateral signal propagation. Nat Cell Biol 5(5):447–453

    Article  PubMed  CAS  Google Scholar 

  • Ribba B, Colin T, Schnell S (2006) A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies. Theor Biol Med Model 3:7

    Article  PubMed  Google Scholar 

  • Rizk A, Batt G, Fages F, Soliman S (2009) A general computational method for robustness analysis with application to synthetic gene networks. Bioinformatics 25(12):i169–i178

    Article  PubMed  CAS  Google Scholar 

  • Roth CM (2002) Quantifying gene expression. Curr Issues Mol Biol 4(3):93–100

    PubMed  CAS  Google Scholar 

  • Saez-Rodriguez J, Simeoni L, Lindquist JA, Hemenway R, Bommhardt U, Arndt B, Haus UU, Weismantel R, Gilles ED, Klamt S, Schraven B (2007) A logical model provides insights into T cell receptor signaling. PLoS Comput Biol 3(8):e163

    Article  PubMed  Google Scholar 

  • Sahin O, Löbke C, Korf U, Appelhans H, Sültmann H, Poustka A, Wiemann S, Arlt D (2007) Combinatorial RNAi for quantitative protein network analysis. Proc Natl Acad Sci U S A 104(16):6579–6584

    Article  PubMed  CAS  Google Scholar 

  • Saltelli A, Chan K, Scott E (200) Sensitivity analysis. Wiley, New York

    Google Scholar 

  • Schauer N, Steinhauser D, Strelkov S et al (2005) GC-MS libraries for the rapid identification of metabolites in complex biological samples. FEBS Lett 579:1332–1337

    Article  PubMed  CAS  Google Scholar 

  • Schefe JH, Lehmann KE, Buschmann IR, Unger T, Funke-Kaiser H (2006) Quantitative real-time RT-PCR data analysis: current concepts and the novel “gene expression’s CT difference” formula. J Mol Med 84(11):901–910

    Article  PubMed  CAS  Google Scholar 

  • Schilling M, Maiwald T, Bohl S, Kollmann M, Kreutz C, Timmer J, Klingmüller U (2005) Computational processing and error reduction strategies for standardized quantitative data in biological networks. FEBS J 272:6400–6411

    Article  PubMed  CAS  Google Scholar 

  • Schmidt H, Madsen M, Dano S, Cedersund G (2008) Complexity reduction of biochemical rate expressions. Bioinformatics 24(6):848–854

    Article  PubMed  CAS  Google Scholar 

  • Schoeberl B, Eichler-Jonsson C, Gilles E, Müller G (2002) Computational modeling of the dynamics of the MAP kinase cascade activated by surface and internalized EGF receptors. Nat Biotechnol 20:370–377

    Article  PubMed  Google Scholar 

  • Schoeberl B, Pace EA, Fitzgerald JB, Harms BD, Xu L, Nie L, Linggi B, Kalra A, Paragas V, Bukhalid R, Grantcharova V, Kohli N, West KA, Leszczyniecka M, Feldhaus MJ, Kudla AJ, Nielsen UB (2009) Therapeutically targeting ErbB3: a key node in ligand-induced activation of the ErbB receptor-PI3K axis. Sci Signal 2(77):ra31

    Article  Google Scholar 

  • Stelling J, Sauer U, Szallasi Z, Doyle FJ, Doyle J (2004) Robustness of cellular functions. Cell 118(6):675–687

    Article  PubMed  CAS  Google Scholar 

  • Swameye I, Muller TG, Timmer J, Sandra O, Klingmuller U (2003) Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by databased modeling. Proc Natl Acad Sci U S A 100(3):1028–1033

    Article  PubMed  CAS  Google Scholar 

  • Turner TE, Schnell S, Burrage K (2004) Stochastic approaches for modelling in vivo reactions. Comput Biol Chem 28(3):165–178

    Article  PubMed  CAS  Google Scholar 

  • Ullah M, Wolkenhauer O (2009) Investigating the two-moment characterisation of subcellular biochemical networks. J Theor Biol 260(3):340–352

    Article  PubMed  Google Scholar 

  • Vera J, Bachmann J, Pfeifer AC, Becker V, Hormiga JA, Darias NV, Timmer J, Klingmüller U, Wolkenhauer O (2008) A systems biology approach to analyse amplification in the JAK2-STAT5 signalling pathway. BMC Syst Biol 2:38

    Article  PubMed  Google Scholar 

  • Vera J, Balsa-Canto E, Wellstead P, Banga JR, Wolkenhauer O (2007) Power-law models of signal transduction pathways. Cell Signal 19:1531–1541

    Article  PubMed  CAS  Google Scholar 

  • Vera J, Rath O, Balsa-Canto E, Banga JR, Kolch W, Wolkenhauer O (2010) Investigating dynamics of inhibitory and feedback loops in ERK signalling using power-law models. Mol Biosyst 6(11):2174–2191

    Google Scholar 

  • Vera J, Schultz J, Raatz Y, Ibrahim S, Wolkenhauer O, Kunz M (2010) Dynamical effects of epigenetic silencing of 14-3-3σ expression. Mol Biosyst 6(1):264–273

    Google Scholar 

  • Vera J, Wolkenhauer O (2008) A system biology approach to understand functional activity of cell communication systems. Methods Cell Biol 90:399–417

    Article  PubMed  CAS  Google Scholar 

  • Wilhelm BT, Landry JR (2009) RNA-Seq-quantitative measurement of expression through massively parallel RNA-sequencing. Methods 48(3):249–257

    Article  PubMed  CAS  Google Scholar 

  • Wolkenhauer et al (2010) Systems biologists seek fuller integration of systems biology approaches in new cancer research programs. Cancer Res 70(1):12–13

    Google Scholar 

  • Xiayan L, Legido-Quigley C (2008) Advances in separation science applied to metabonomics. Electrophoresis 29(18):3724–3736

    Article  PubMed  Google Scholar 

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Acknowledgements

We thank the collaboration of the following people in the discussions of the papers analysed in this book chapter: A. Bittig, S. Boldt, S. Frey, J. Isaeva, X. Lai, F. Lange, A. Lao, U. Liebal, T. Millat, S. Pauleweit, P. Raasch, K. Rateischak, Y. Schmidt, U. Schmitz, F. Winter. J.V. is funded by the German Federal Ministry of Education and Research (BMBF) as part of the project CALSYS-FORSYS under contract 0315264 (http://www.sbi.uni-rostock.de/calsys). O.W. acknowledges funding through the Helmholtz Association, as part of the Systems Biology Alliance and the Stellenbosch Institute for Advanced Study (STIAS).

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Vera, J., Wolkenhauer, O. (2011). Mathematical Tools in Cancer Signalling Systems Biology. In: Cesario, A., Marcus, F. (eds) Cancer Systems Biology, Bioinformatics and Medicine. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1567-7_7

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