# From a Biological Hypothesis to the Construction of a Mathematical Model

• David Cohen
• Inna Kuperstein
• Emmanuel Barillot
• Andrei Zinovyev
• Laurence Calzone
Protocol
Part of the Methods in Molecular Biology book series (MIMB, volume 1021)

## 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.

## Key words

Network diagram Mathematical model ODE Boolean Formalism

## Notes

### 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.

## References

1. 1.
Hoffmann R, Valencia A (2004) A gene network for navigating the literature. Nat Genet 36:664.
2. 2.
Larkin JH, Simon HA (1987) Why a diagram is (sometimes) worth ten thousand words. Cogn Sci 11(1):65–100
3. 3.
Le Novère N, Hucka M, Mi H et al (2009) The systems biology graphical notation. Nat Biotechnol 27(8):735–741. doi:
4. 4.
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
5. 5.
Dixon SJ, Costanzo M, Baryshnikova A et al (2009) Systematic mapping of genetic interaction networks. Annu Rev Genet 43(1):601–625. doi:
6. 6.
Ideker T, Krogan NJ (2012) Differential network biology. Mol Syst Biol 8:565. doi:
7. 7.
Przulj N (2011) Protein-protein interactions: making sense of networks via graph-theoretic modeling. Bioessays 33(2):115–123. doi:
8. 8.
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:
9. 9.
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
10. 10.
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
11. 11.
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:
12. 12.
Caron E, Ghosh S, Matsuoka Y et al (2010) A comprehensive map of the mTOR signaling network. Mol Syst Biol 6:453. doi:
13. 13.
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
14. 14.
Kohn KW (1999) Molecular interaction map of the mammalian cell cycle control and DNA repair systems. Mol Biol Cell 10(8):2703–2734
15. 15.
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:
16. 16.
Kanehisa M (2002) The KEGG database. Novartis Found Symp 247:91–101; discussion 101–103, 119–128, 244–252Google Scholar
17. 17.
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:
18. 18.
Czauderna T, Klukas C, Schreiber F (2010) Editing, validating and translating of SBGN maps. Bioinformatics 26(18):2340–2341. doi:
19. 19.
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:
20. 20.
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:
21. 21.
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:
22. 22.
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:
23. 23.
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 7:18Google Scholar
24. 24.
Bachmann J, Raue A, Schilling M et al (2012) Predictive mathematical models of cancer signalling pathways. J Intern Med 271(2):155–165
25. 25.
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:
26. 26.
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
27. 27.
Karlebach G, Shamir R (2008) Modeling and analysis of regulatory networks. Nat Rev Mol Cell Biol 9:771–780. doi:
28. 28.
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
29. 29.
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:
30. 30.
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:
31. 31.
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:
32. 32.
Britton NF (1986) Reaction–diffusion equations and their applications to biology. Academic, LondonGoogle Scholar
33. 33.
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:
34. 34.
Sherr CJ, McCormick F (2002) The RB and p53 pathways in cancer. Cancer Cell 2(2):103–112. doi:
35. 35.
Polager S, Ginsberg D (2008) E2F at the crossroads of life and death. Trends Cell Biol 18(11):528–535. doi:
36. 36.
Calzone L, Fages F, Soliman S (2006) BIOCHAM: an environment for modeling biological systems and formalizing experimental knowledge. Bioinformatics 22(14):1805–1807. doi:
37. 37.
Vass M, Allen N, Shaffer CA, Ramakrishnan N, Watson LT, Tyson JJ (2004) The JigCell model builder and run manager. Bioinformatics 20(18):3680–3681Google Scholar
38. 38.
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
39. 39.
Schmidt H, Jirstrand M (2006) Systems Biology Toolbox for MATLAB: a computational platform for research in systems biology. Bioinformatics 22(4):514–515. doi:
40. 40.
Aguda BD, Tang Y (1999) The kinetic origins of the restriction point in the mammalian cell cycle. Cell Prolif 32(5):321–335
41. 41.
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:
42. 42.
Novak B, Tyson JJ (2004) A model for restriction point control of the mammalian cell cycle. J Theor Biol 230(4):563–579. doi:
43. 43.
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:
44. 44.
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:
45. 45.
Klamt S, Saez-Rodriguez J, Gilles E (2007) Structural and functional analysis of cellular networks with Cell NetAnalyzer. BMC Syst Biol 1(1):2
46. 46.
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:
47. 47.
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:
48. 48.
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.Google Scholar

## Authors and Affiliations

• David Cohen
• 1
• 2
• 3
• Inna Kuperstein
• 1
• 2
• 3
• Emmanuel Barillot
• 1
• 2
• 3
• Andrei Zinovyev
• 1
• 2
• 3
• Laurence Calzone
• 1
• 2
• 3
1. 1.Institut CurieParisFrance
2. 2.INSERM, U900ParisFrance
3. 3.Mines ParisTechFontainebleauFrance