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Gene expression time delays & Turing pattern formation systems

By E. A. Gaffney and N. A. M. Monk

Abstract

The incorporation of time delays can greatly affect the behaviour of partial differential equations and dynamical systems. In addition, there is evidence that time delays in gene expression due to transcription and translation play an important role in the dynamics of cellular systems. In this paper, we investigate the effects of incorporating gene expression time delays into a one-dimensional putative reaction diffusion pattern formation mechanism on both stationary domains and domains with spatially uniform exponential growth. While oscillatory behaviour is rare, we find that the time taken to initiate and stabilise patterns increases dramatically as the time delay is increased. In addition, we observe that on rapidly growing domains the time delay can induce a failure of the Turing instability which cannot be predicted by a naive linear analysis of the underlying equations about the homogeneous steady state. The dramatic lag in the induction of patterning, or even its complete absence on occasions, highlights the importance of considering explicit gene expression time delays in models for cellular reaction diffusion patterning

Topics: Biology and other natural sciences
Publisher: Springer
Year: 2006
DOI identifier: 10.1007/s11538-006-9066-z
OAI identifier: oai:generic.eprints.org:885/core69

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Citations

  1. (2006). 68: 99–130 Crampin,
  2. (1983). A mechanical model for mesenchymal morphogenesis.
  3. (1981). A pre-pattern formation mechanism for animal coat markings.
  4. (1995). A reaction-diffusion wave on the skin of Pomacanthus, the marine Angelfish.
  5. (2003). Autoinhibition with transcriptional delay: A simple mechanism for the Zebrafish somitogenesis oscillator.
  6. (1984). Belgian Nuclear Centre,
  7. (1985). Calcium: The elusive morphogen in Acetabularia.
  8. (2005). Complex pattern formation in reaction diffusion systems with spatially-varying parameters. doi
  9. (2004). Control of Turing pattern formation by delayed feedback.
  10. (2004). Dynamical mechanisms for skeletal pattern formation in the vertebrate limb,
  11. (2005). Effect of time delay on pattern formation: Competition between homogenisation and patterning. doi
  12. (2000). Extracellular matrix environment influences chondrogenic pattern formation in limb bud micromass culture: Experimental verification of theoretical models.
  13. (1988). Genetic control models with diffusion and delays.
  14. (1974). How well does Turing’s theory of morphogenesis work?
  15. (2001). Instability in diffusive ecological models with non-local delay effects.
  16. (2002). Lefty proteins are long-range inhibitors of Squint-mediated Nodal signalling.
  17. (2002). Lefty-dependent antagonism of the Nodal and Wnt signalling pathways is essential for normal gastrulation.
  18. (1998). Local inhibitory action of BMPs and their relationships with activators in feather formation: Implications for periodic patterning.
  19. (1993). Mathematical Biology.
  20. (1983). Mechanical aspects of mesenchymal morphogenesis.
  21. (2002). Mode-doubling and tripling in reaction-diffusion patterns on growing domains: A piecewise linear model.
  22. (1982). Models of Biological Pattern Formations.
  23. (1984). Models of genetic control by repression with time delays and spatial effects.
  24. (2004). Morphogens, their identification and regulation. doi
  25. (2004). Nodal signalling: Cryptic lefty mechanism of antagonism decoded.
  26. (2003). Oscillatory expression of Hes1, p53, and NF-kappa B driven by transcriptional time delays.
  27. (1980). Pattern formation by reaction-diffusion instabilities: Applications to morphogenesis in Drosophila.
  28. (1986). Pattern sensitivity to boundary and initial conditions in reaction diffusion models.
  29. (2002). Spatio-temporal delays in a nutrient-plankton model on a finite domain: Linear stability and bifurcations.
  30. (2004). Speed of pattern appearance in reaction-diffusion models: Implications in the pattern formation of limb bud mesenchyme cells.
  31. (1995). Stages of embryonic development of the zebrafish.
  32. (1952). The chemical basis of morphogenesis. doi
  33. (1995). The human dystrophin gene requires 16 h to be transcribed and is cotranscriptionally spliced. doi
  34. (2001). The zebrafish Nodal signal Squint functions as a morphogen.
  35. (1998). Turing instability and travelling waves in diffusive plankton models with delayed nutrient recycling. doi
  36. (2004). Two modes by which lefty proteins inhibit nodal signalling.
  37. (2003). Vertebrate development: Taming the nodal waves. doi

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