Skip to main content
SpringerLink
Log in

Applications of Mathematical Modelling to Biological Pattern Formation

  • Conference paper
  • First Online:
Coherent Structures in Complex Systems

Part of the book series: Lecture Notes in Physics ((LNP,volume 567))

Abstract

The formation of spatiotemporal patterning in biology has intrigued experimentalists and theoreticians for many generations. Here we present a brief review of some mathematical models for pattern formation and then focus on three models which use the phenomenon of chemotaxis to generate pattern.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. B.R. Johnson, S.K. Scott: Chemical Soc. Reviews, 25, 265 (1996)

    Article  Google Scholar 

  2. J.D. Murray: Mathematical Biology, 2nd edn. (Springer-Verlag 1993)

    Google Scholar 

  3. A.V. Panfilov, A.V. Holden (eds): Computational Biology of the Heart, (John Wiley & Sons, Chichester 1997)

    MATH  Google Scholar 

  4. A.M. Turing: Phil. Trans. Roy. Soc. Lond. B 327, 37–72 (1952)

    Article  ADS  Google Scholar 

  5. L.G. Harrison: Kinetic Theory of Pattern Formation, (Cambridge University Press, 1993)

    Google Scholar 

  6. V. Castets, E. Dulos, J. Boissonade, P. De Kepper: Phys. Rev. Lett., 64, 2953 (1990)

    Article  ADS  Google Scholar 

  7. Q. Ouyang, H. L. Swinney: Nature (London) 352, 610 (1991)

    Article  ADS  Google Scholar 

  8. J. P. Armitage, J.M. Lackie: Biology of the Chemotactic Response, (Cambridge University Press 1990)

    Google Scholar 

  9. W. Alt, A. Deutsch, G. Dunn (eds): Dynamics of Cell and Tissue Motion, (Birkhäuser 1997)

    Google Scholar 

  10. L. Wolpert: J. theor. Biol., 25, 1 (1969)

    Article  Google Scholar 

  11. J.B.L. Bard: J. theor. Biol., 93, 363 (1981)

    Article  MathSciNet  Google Scholar 

  12. E.F. Keller, L.A. Segel: J. theor. Biol., 30, 235 (1971)

    Article  Google Scholar 

  13. P.K. Maini, M.R. Myerscough, K.H. Winters, J.D. Murray: Bull. Math. Biol., 53, 701 (1991)

    MATH  Google Scholar 

  14. G.F. Oster, J.D. Murray, A.K. Harris: J. Embryol.exp. Morph., 78, 83 (1983)

    Google Scholar 

  15. M.S. Steinberg: J. exp. Zool., 173, 395 (1970)

    Article  Google Scholar 

  16. D. Sulsky, S. Childress, J.K. Percus: J. theor. Biol., 106, 275 (1984)

    Article  Google Scholar 

  17. G. Cocho, R. Pérez-Pascual, J.L. Rius: J. theor. Biol., 125, 419 (1987)

    Article  Google Scholar 

  18. G. Cocho, R. Pérez-Pascual, J.L. Rius, F. Soto: J. theor. Biol., 125, 437 (1987)

    Article  Google Scholar 

  19. P.K. Maini: ‘Mathematical models for biological pattern formation’. In: On Growth and Form:Sp atio-temporal Patterning in Biology. ed. by M.A.J. Chaplain, G.D. Singh, J.C. McLachlan (John Wiley & Sons, Chichester 1999) pp. 111–128

    Google Scholar 

  20. P.K. Maini, M. Solursh: Int. Rev. Cytology, 129, 91 (1991)

    Article  Google Scholar 

  21. G.F. Oster, J.D. Murray: Zool., 251, 186 (1989)

    Google Scholar 

  22. J.R. Collier, N.A.M. Monk, P.K. Maini, J.H. Lewis: J. theor. Biol., 183, 429 (1996)

    Article  Google Scholar 

  23. P.D. Dale, P.K. Maini, J.A. Sherratt: Math. Biosciences 124, 127 (1994)

    Article  MATH  Google Scholar 

  24. K.J. Painter, P.K. Maini, H.G. Othmer: Bull. Math. Biol. 62, 501 (2000)

    Article  Google Scholar 

  25. H.G. Othmer, A. Stevens: SIAM J. Appl. Math. 57, 1044 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  26. T. Höfer, J.A. Sherratt, P.K. Maini: Proc. Roy. Soc. Lond. B 259, 249 (1995)

    Article  ADS  Google Scholar 

  27. T. Höfer, J.A. Sherratt, P.K. Maini: Physica D 85, 425 (1995)

    Google Scholar 

  28. T. Höfer, P.K. Maini: Phys. Rev. E 56, 2074 (1997)

    ADS  Google Scholar 

  29. J.A. Sherratt, J.C. Dallon, T. Höfer, P.K. Maini: ‘Mathematical modelling of signalling in Dictyostelium discoideum’. In Microbial Signalling and Communication. ed. by R. England, G. Hobbs, N. Bainton, D. McL. Roberts (Cambridge University Press 1999) pp. 241–254

    Google Scholar 

  30. J.-L. Martiel, A. Goldbeter: Biohys. J. 52, 807 (1987)

    Article  Google Scholar 

  31. S. Kondo, R. Asai: Nature 376, 765 (1995)

    Article  ADS  Google Scholar 

  32. K.J. Painter, P.K. Maini, H.G. Othmer: Proc. Natl. Acad. Sci. 96, 5549 (1999)

    Article  ADS  Google Scholar 

  33. E.J. Crampin, E.A. Gaffney, P.K. Maini: Bull. Math. Biol. 61, 1093 (1999)

    Article  Google Scholar 

  34. K.J. Painter, P.K. Maini, H.G. Othmer: J. Math. Biol. (accepted)

    Google Scholar 

  35. R. Dillon, H.G. Othmer: J. theor. Biol. 197, 295 (1999)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Mathematical Biology, Mathematical Institute, OX1 3LB, Oxford, UK

    Philip K. Maini

Authors
  1. Philip K. Maini
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028, Barcelona, Spain

    David Reguera  & José Miguel Rubí  & 

  2. Departamento de Matemáticas Escuela Politécnica Superior, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911, Leganés, Spain

    Luis López Bonilla

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Maini, P.K. (2001). Applications of Mathematical Modelling to Biological Pattern Formation. In: Reguera, D., Rubí, J.M., Bonilla, L.L. (eds) Coherent Structures in Complex Systems. Lecture Notes in Physics, vol 567. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44698-2_13

Download citation

  • DOI: https://doi.org/10.1007/3-540-44698-2_13

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41705-7

  • Online ISBN: 978-3-540-44698-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation