Modelling Time-Dependent Acquisition of Positional Information

  • Laurent Jutras-Dubé
  • Adrien Henry
  • Paul François
Part of the Methods in Molecular Biology book series (MIMB, volume 1863)


Theoretical and computational modelling are crucial to understand dynamics of embryonic development. In this tutorial chapter, we describe two models of gene networks performing time-dependent acquisition of positional information under control of a dynamic morphogen: a toy-model of a bistable gene under control of a morphogen, allowing for the numerical computation of a simple Waddington’s epigenetic landscape, and a recently published model of gap genes in Tribolium under control of multiple enhancers. We present detailed commented implementations of the models using python and jupyter notebooks.

Key words

Modelling Ordinary differential equations Positional information Multistability Seg-mentation Python 



We thank Ezzat El-Sherif for sharing the MATLAB code used in [17] and the referee for useful comments.

Supplementary material

427781_1_En_16_MOESM1_ESM.ipynb (146 kb)
Notebook_3.1 (IPYNB 146 KB)
427781_1_En_16_MOESM2_ESM.ipynb (295 kb)
Notebook_3.2 (IPYNB 296 KB)


  1. 1.
    Turing AM (1952) The chemical basis of morphogenesis. Philos Trans R Soc Lond Ser B Biol Sci 237(641):37–72CrossRefGoogle Scholar
  2. 2.
    Wolpert L (2006) Principles of development. Oxford University Press, OxfordGoogle Scholar
  3. 3.
    Cooke J, Zeeman EC (1976) A clock and wavefront model for control of the number of repeated structures during animal morphogenesis. J Theor Biol 58(2), 455–476CrossRefPubMedGoogle Scholar
  4. 4.
    Meinhardt H (1982) Models of biological pattern formation. Academic, New YorkGoogle Scholar
  5. 5.
    Palmeirim I, Henrique D, Ish-Horowicz D, Pourquié O (1997) Avian hairy gene expression identifies a molecular clock linked to vertebrate segmentation and somitogenesis. Cell 91(5):639–648CrossRefPubMedGoogle Scholar
  6. 6.
    Aulehla A, Wiegraebe W, Baubet V, Wahl MB (2008) Deng C, Taketo M, Lewandoski M, Pourquié O. A beta-catenin gradient links the clock and wavefront systems in mouse embryo segmentation. Nat Cell Biol 10(2):186–193Google Scholar
  7. 7.
    Hubaud A, Pourquié O (2013) Making the clock tick: right time, right pace. Dev Cell 24(2):115–116CrossRefPubMedGoogle Scholar
  8. 8.
    Lauschke VM, Tsiairis CD, François P, Aulehla A (2013) Scaling of embryonic patterning based on phase-gradient encoding. Nature 493(7430):101–105CrossRefPubMedGoogle Scholar
  9. 9.
    Raspopovic J, Marcon L, Russo L, Sharpe J (2014) Modeling digits. Digit patterning is controlled by a Bmp-Sox9-Wnt Turing network modulated by morphogen gradients. Science 345(6196):566–570CrossRefPubMedGoogle Scholar
  10. 10.
    Jaeger J, Surkova S, Blagov M, Janssens H, Kosman D, Kozlov KN, Manu, Myasnikova E, Vanario-Alonso CE, Samsonova M, Sharp DH, Reinitz J (2004) Dynamic control of positional information in the early Drosophila embryo. Nature 430(6997):368–371CrossRefPubMedGoogle Scholar
  11. 11.
    Crombach A, Wotton KR, Jiménez-Guri E, Jaeger J (2016) Gap gene regulatory dynamics evolve along a genotype network. Mol Biol Evol 33:1293–1307CrossRefPubMedPubMedCentralGoogle Scholar
  12. 12.
    Balaskas N, Ribeiro A, Panovska J, Dessaud E, Sasai N, Page KM, Briscoe J, Ribes V (2012) Gene regulatory logic for reading the sonic hedgehog signaling gradient in the vertebrate neural tube. Cell 148(1–2):273–284CrossRefPubMedPubMedCentralGoogle Scholar
  13. 13.
    Wotton KR, Jiménez-Guri E, Crombach A, Janssens H, Alcaine-Colet A, Lemke S, Schmidt-Ott U, Jaeger J (2015) Quantitative system drift compensates for altered maternal inputs to the gap gene network of the scuttle fly Megaselia abdita. eLife 4:e04785Google Scholar
  14. 14.
    Corson F, Siggia ED (2017) Gene free methodology for cell fate dynamics during development. eLife 6:e30743CrossRefPubMedPubMedCentralGoogle Scholar
  15. 15.
    Rothschild JB, Tsimiklis P, Siggia ED, François P (2016) Predicting ancestral segmentation phenotypes from drosophila to anopheles using in silico evolution. PLoS Gen 12(5):e1006052–19CrossRefGoogle Scholar
  16. 16.
    Peel A, Akam M (2003) Evolution of segmentation: rolling back the clock. Curr Biol 13(18):R708–10CrossRefPubMedGoogle Scholar
  17. 17.
    Zhu X, Rudolf H, Healey L, François P, Brown SJ, Klingler M, El-Sherif E (2017) Speed regulation of genetic cascades allows for evolvability in the body plan specification of insects. Proc Natl Acad Sci USA 128(41):E8646–E8655CrossRefGoogle Scholar
  18. 18.
    François P, Hakim V, Siggia ED (2007) Deriving structure from evolution: metazoan segmentation. Mol Syst Biol 3:9CrossRefGoogle Scholar
  19. 19.
    Hobert O (2008) Regulatory logic of neuronal diversity: terminal selector genes and selector motifs. Proc Natl Acad Sci USA 105(51):20067–20071CrossRefPubMedGoogle Scholar
  20. 20.
    Waddington CH (2014) The strategy of the genes. Routledge, LondonCrossRefGoogle Scholar
  21. 21.
    Gillespie DT (2007) Stochastic simulation of chemical kinetics. Annu Rev Phys Chem 58:35–55CrossRefPubMedGoogle Scholar
  22. 22.
    Perez-Carrasco R, Guerrero P, Briscoe J, Page KM (2016) Intrinsic noise profoundly alters the dynamics and steady state of morphogen-controlled bistable genetic switches. PLoS Comput Biol 12(10):e1005154CrossRefPubMedPubMedCentralGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Laurent Jutras-Dubé
    • 1
  • Adrien Henry
    • 1
  • Paul François
    • 1
  1. 1.McGill UniversityMontrealCanada

Personalised recommendations