Skip to main content

Mathematical Modeling in the Study of Organisms and Their Parts

  • Protocol
  • First Online:
Systems Biology

Part of the book series: Methods in Molecular Biology ((MIMB,volume 2745))

  • 372 Accesses

Abstract

Mathematical modeling is a very powerful tool to understand natural phenomena. Such a tool carries its own assumptions and should always be used critically. In this chapter we highlight the key ingredients and steps of modeling and focus on their biological interpretation. Particularly, we discuss the role of theoretical principles in writing models. We also highlight the meaning and interpretation of equations. The main aim of this chapter is to facilitate the interaction between biologists and mathematical modelers. We focus on the case of cell proliferation and motility in the context of multicellular organisms.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Protocol
USD 49.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Beeman D (2013) Hodgkin-Huxley model. In: Encyclopedia of computational neuroscience. Springer New York, New York, p 1–13. https://doi.org/10.1007/978-1-4614-7320-6_127-3

    Chapter  Google Scholar 

  2. Descartes R (2016) Discours de la méthode. Flammarion

    Google Scholar 

  3. Montévil M, Mossio M, Pocheville A, Longo G (2016a) Theoretical principles for biology: variation. Prog Biophys Mol Biol 122(1):36–50. https://doi.org/10.1016/j.pbiomolbio.2016.08.005

    Article  PubMed  Google Scholar 

  4. Mossio M, Montévil M, Longo G (2016) Theoretical principles for biology: organization. Prog Biophys Mol Biol 122(1):24–35. https://doi.org/10.1016/j.pbiomolbio.2016.07.005

    Article  PubMed  Google Scholar 

  5. Noble D (2010) Biophysics and systems biology. Philos Trans R Soc A Math Phys Eng Sci 368(1914):1125. https://doi.org/10.1098/rsta.2009.0245

    Article  CAS  Google Scholar 

  6. Sonnenschein C, Soto A (1999) The society of cells: cancer and control of cell proliferation. Springer Verlag, New York

    Google Scholar 

  7. Soto AM, Longo G, Montévil M, Sonnenschein C (2016) The biological default state of cell proliferation with variation and motility, a fundamental principle for a theory of organisms. Prog Biophys Mol Biol 122(1):16–23. https://doi.org/10.1016/j.pbiomolbio.2016.06.006

    Article  PubMed  PubMed Central  Google Scholar 

  8. Montévil M, Speroni L, Sonnenschein C, Soto AM (2016b) Modeling mammary organogenesis from biological first principles: cells and their physical constraints. Prog Biophys Mol Biol 122(1):58–69. https://doi.org/10.1016/j.pbiomolbio.2016.08.004

    Article  PubMed  PubMed Central  Google Scholar 

  9. D’Anselmi F, Valerio M, Cucina A, Galli L, Proietti S, Dinicola S, Pasqualato A, Manetti C, Ricci G, Giuliani A, Bizzarri M (2011) Metabolism and cell shape in cancer: a fractal analysis. Int J Biochem Cell Biol 43(7):1052–1058. Metabolic Pathways in Cancer. https://doi.org/10.1016/j.biocel.2010.05.002

    Article  CAS  PubMed  Google Scholar 

  10. Longo G, Montévil M (2014) Perspectives on organisms: biological time, symmetries and singularities. In: Lecture notes in morphogenesis. Springer, Dordrecht. https://doi.org/10.1007/978-3-642-35938-5

    Chapter  Google Scholar 

  11. Tjørve E (2003) Shapes and functions of species–area curves: a review of possible models. J Biogeogr 30(6):827–835. https://doi.org/10.1046/j.1365-2699.2003.00877.x

    Article  Google Scholar 

  12. Hoehler TM, Jorgensen BB (2013) Microbial life under extreme energy limitation. Nat Rev Microl 11(2):83–94. https://doi.org/10.1038/nrmicro2939

    Article  CAS  Google Scholar 

  13. Camalet S, Duke T, Julicher F, Prost J (2000) Auditory sensitivity provided by self-tuned critical oscillations of hair cells. Proc Natl Acad Sci:3183–3188. https://doi.org/10.1073/pnas.97.7.3183

  14. Lesne A, Victor J-M (2006) Chromatin fiber functional organization: some plausible models. Eur Phys J E Soft Matter 19(3):279–290. https://doi.org/10.1140/epje/i2005-10050-6

    Article  CAS  PubMed  Google Scholar 

  15. Montévil M, Mossio M (2015) Biological organisation as closure of constraints. J Theor Biol 372(0):179–191. https://doi.org/10.1016/j.jtbi.2015.02.029

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2024 The Author(s), under exclusive license to Springer Science+Business Media, LLC, part of Springer Nature

About this protocol

Check for updates. Verify currency and authenticity via CrossMark

Cite this protocol

Montévil, M. (2024). Mathematical Modeling in the Study of Organisms and Their Parts. In: Bizzarri, M. (eds) Systems Biology. Methods in Molecular Biology, vol 2745. Humana, New York, NY. https://doi.org/10.1007/978-1-0716-3577-3_7

Download citation

  • DOI: https://doi.org/10.1007/978-1-0716-3577-3_7

  • Published:

  • Publisher Name: Humana, New York, NY

  • Print ISBN: 978-1-0716-3576-6

  • Online ISBN: 978-1-0716-3577-3

  • eBook Packages: Springer Protocols

Publish with us

Policies and ethics