Abstract
Mathematical models serve to explain complex biological phenomena and provide predictions that can be tested experimentally. They can provide plausible scenarios of a complex biological behavior when intuition is not sufficient anymore. The process from a biological hypothesis to a mathematical model might be challenging for biologists that are not familiar with mathematical modeling.
In this chapter we discuss a possible workflow that describes the steps to be taken starting from a biological hypothesis on a biochemical cellular mechanism to the construction of a mathematical model using the appropriate formalism. An important part of this workflow is formalization of biological knowledge, which can be facilitated by existing tools and standards developed by the systems biology community.
This chapter aims at introducing modeling to experts in molecular biology that would like to convert their hypotheses into mathematical models.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Hoffmann R, Valencia A (2004) A gene network for navigating the literature. Nat Genet 36:664.
Larkin JH, Simon HA (1987) Why a diagram is (sometimes) worth ten thousand words. Cogn Sci 11(1):65–100
Le Novère N, Hucka M, Mi H et al (2009) The systems biology graphical notation. Nat Biotechnol 27(8):735–741. doi:10.1038/nbt.1558
Wang PI, Marcotte EM (2010) It’s the machine that matters: predicting gene function and phenotype from protein networks. J Proteomics 73(11):2277–2289
Dixon SJ, Costanzo M, Baryshnikova A et al (2009) Systematic mapping of genetic interaction networks. Annu Rev Genet 43(1):601–625. doi:10.1146/annurev.genet.39.073003.114751
Ideker T, Krogan NJ (2012) Differential network biology. Mol Syst Biol 8:565. doi:10.1038/msb.2011.99
Przulj N (2011) Protein-protein interactions: making sense of networks via graph-theoretic modeling. Bioessays 33(2):115–123. doi:10.1002/bies.201000044
Schmeier S, Schaefer U, Essack M et al (2011) Network analysis of microRNAs and their regulation in human ovarian cancer. BMC Syst Biol 5:183. doi:10.1186/1752-0509-5-183
Pratt CH, Vadigepalli R, Chakravarthula P et al (2008) Transcriptional regulatory network analysis during epithelial-mesenchymal transformation of retinal pigment epithelium. Mol Vis 14:1414–1428
Cheng C, Yan K-K, Hwang W et al (2011) Construction and analysis of an integrated regulatory network derived from high-throughput sequencing data. PLoS Comput Biol 7(11):e1002190
Calzone L, Gelay A, Zinovyev A et al (2008) A comprehensive modular map of molecular interactions in RB/E2F pathway. Mol Syst Biol 4:174. doi:10.1038/msb.2008.7
Caron E, Ghosh S, Matsuoka Y et al (2010) A comprehensive map of the mTOR signaling network. Mol Syst Biol 6:453. doi:10.1038/msb.2010.108
Patil S, Pincas H, Seto J et al (2010) Signaling network of dendritic cells in response to pathogens: a community-input supported knowledgebase. BMC Syst Biol 4(1):137
Kohn KW (1999) Molecular interaction map of the mammalian cell cycle control and DNA repair systems. Mol Biol Cell 10(8):2703–2734
Joshi-Tope G, Gillespie M, Vastrik I et al (2005) Reactome: a knowledgebase of biological pathways. Nucleic Acids Res 33(Database issue):D428–D432. doi:10.1093/nar/gki072
Kanehisa M (2002) The KEGG database. Novartis Found Symp 247:91–101; discussion 101–103, 119–128, 244–252
Kitano H, Funahashi A, Matsuoka Y et al (2005) Using process diagrams for the graphical representation of biological networks. Nat Biotechnol 23(8):961–966. doi:10.1038/nbt1111
Czauderna T, Klukas C, Schreiber F (2010) Editing, validating and translating of SBGN maps. Bioinformatics 26(18):2340–2341. doi:10.1093/bioinformatics/btq407
Florez LA, Lammers CR, Michna R et al (2010) Cell Publisher: a web platform for the intuitive visualization and sharing of metabolic, signalling and regulatory pathways. Bioinformatics 26(23):2997–2999. doi:10.1093/bioinformatics/btq585
Kono N, Arakawa K, Ogawa R et al (2009) Pathway projector: web-based zoomable pathway browser using KEGG atlas and Google Maps API. PLoS One 4(11):e7710. doi:10.1371/journal.pone.0007710
Smoot ME, Ono K, Ruscheinski J et al (2011) Cytoscape 2.8: new features for data integration and network visualization. Bioinformatics 27(3):431–432. doi:10.1093/bioinformatics/btq675
Zinovyev A, Viara E, Calzone L et al (2008) BiNoM: a Cytoscape plugin for manipulating and analyzing biological networks. Bioinformatics 24(6):876–877. doi:10.1093/bioinformatics/btm553
Bonnet E, Calzone L, Rovera D, Stoll G, Barillot E, Zinovyev A (2013) BiNoM 2.0, a Cytoscape plugin for accessing and analyzing pathways using standard systems biology formats. BMC Syst Biol 7:18
Bachmann J, Raue A, Schilling M et al (2012) Predictive mathematical models of cancer signalling pathways. J Intern Med 271(2):155–165
Ay A, Arnosti DN (2011) Mathematical modeling of gene expression: a guide for the perplexed biologist. Crit Rev Biochem Mol Biol 46(2):137–151. doi:10.3109/10409238.2011.556597
Morris MK, Saez-Rodriguez J, Sorger PK et al (2010) Logic-based models for the analysis of cell signaling networks. Biochemistry 49(15):3216–3224
Karlebach G, Shamir R (2008) Modeling and analysis of regulatory networks. Nat Rev Mol Cell Biol 9:771–780. doi:10.1038/nrm2503
Calzone L, Tournier L, Fourquet S et al (2010) Mathematical modelling of cell-fate decision in response to death receptor engagement. PLoS Comput Biol 6(3):e1000702
Philippi N, Walter D, Schlatter R et al (2009) Modeling system states in liver cells: survival, apoptosis and their modifications in response to viral infection. BMC Syst Biol 3:97. doi:10.1186/1752-0509-3-97
Saez-Rodriguez J, Alexopoulos LG, Zhang M et al (2011) Comparing signaling networks between normal and transformed hepatocytes using discrete logical models. Cancer Res 71(16):5400–5411. doi:10.1158/0008-5472.CAN-10-4453
Schlatter R, Schmich K, Avalos Vizcarra I et al (2009) ON/OFF and beyond–a Boolean model of apoptosis. PLoS Comput Biol 5(12):e1000595. doi:10.1371/journal.pcbi.1000595
Britton NF (1986) Reaction–diffusion equations and their applications to biology. Academic, London
Hegland M, Burden C, Santoso L et al (2007) A solver for the stochastic master equation applied to gene regulatory networks. J Comput Appl Math 205(2):708–724. doi:10.1016/j.cam.2006.02.053
Sherr CJ, McCormick F (2002) The RB and p53 pathways in cancer. Cancer Cell 2(2):103–112. doi:10.1016/S1535-6108(02)00102-2
Polager S, Ginsberg D (2008) E2F at the crossroads of life and death. Trends Cell Biol 18(11):528–535. doi:10.1016/j.tcb.2008.08.003
Calzone L, Fages F, Soliman S (2006) BIOCHAM: an environment for modeling biological systems and formalizing experimental knowledge. Bioinformatics 22(14):1805–1807. doi:10.1093/bioinformatics/btl172
Vass M, Allen N, Shaffer CA, Ramakrishnan N, Watson LT, Tyson JJ (2004) The JigCell model builder and run manager. Bioinformatics 20(18):3680–3681
Funahashi A, Matsuoka Y, Jouraku A et al (2008) Cell Designer 3.5: a versatile modeling tool for biochemical networks. Proc IEEE 96(8):1254–1265
Schmidt H, Jirstrand M (2006) Systems Biology Toolbox for MATLAB: a computational platform for research in systems biology. Bioinformatics 22(4):514–515. doi:10.1093/bioinformatics/bti799
Aguda BD, Tang Y (1999) The kinetic origins of the restriction point in the mammalian cell cycle. Cell Prolif 32(5):321–335
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. doi:10.1152/ajpcell.00066.2002
Novak B, Tyson JJ (2004) A model for restriction point control of the mammalian cell cycle. J Theor Biol 230(4):563–579. doi:10.1016/j.jtbi.2004.04.039
Gonzalez AG, Naldi A, Sanchez L et al (2006) GINsim: a software suite for the qualitative modelling, simulation and analysis of regulatory networks. Biosystems 84(2):91–100. doi:10.1016/j.biosystems.2005.10.003
Mussel C, Hopfensitz M, Kestler HA (2010) BoolNet–an R package for generation, reconstruction and analysis of Boolean networks. Bioinformatics 26(10):1378–1380. doi:10.1093/bioinformatics/btq124
Klamt S, Saez-Rodriguez J, Gilles E (2007) Structural and functional analysis of cellular networks with Cell NetAnalyzer. BMC Syst Biol 1(1):2
Stoll G, Viara E, Barillot E et al (2012) Continuous time Boolean modeling for biological signaling: application of Gillespie algorithm. BMC Syst Biol 6:116. doi:10.1186/1752-0509-6-116
Faure A, Naldi A, Chaouiya C et al (2006) Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle. Bioinformatics 22(14):e124–e131. doi:10.1093/bioinformatics/btl210
Barillot E, Calzone L, Hupe P, Vert J-P, Zinovyev A (2012) Computational systems biology of cancer. Chapman & Hall, CRC Mathematical & Computational Biology 452 p.
Acknowledgements
We are grateful for receiving funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement n°259348. DC, IK, EB, AZ, and LC are members of the team “Computational Systems Biology of Cancer” Equipe labellisée par la Ligue Nationale Contre le Cancer. We would also like to thank Nicolas Le Novère for discussions on different types of diagrams and for providing Fig. 1.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media, LLC
About this protocol
Cite this protocol
Cohen, D., Kuperstein, I., Barillot, E., Zinovyev, A., Calzone, L. (2013). From a Biological Hypothesis to the Construction of a Mathematical Model. In: Schneider, M. (eds) In Silico Systems Biology. Methods in Molecular Biology, vol 1021. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-62703-450-0_6
Download citation
DOI: https://doi.org/10.1007/978-1-62703-450-0_6
Published:
Publisher Name: Humana Press, Totowa, NJ
Print ISBN: 978-1-62703-449-4
Online ISBN: 978-1-62703-450-0
eBook Packages: Springer Protocols