Diffusible ligand and lateral inhibition dynamics for pattern formation

Journal of Statistical Mechanics: Theory and Experiment

Volumn 2009, Issue 3, 2009, Pages

  Formosa Jordan, Pau ^a   Ibães, Marta ^a  

^a UNIVERSITY OF BARCELONA   (Spain)

Author keywords

Cell cell signalling (theory); Diffusion; Pattern formation (theory); Stationary states

Indexed keywords

EID: 65449119587     PISSN: 17425468     EISSN: 17425468     Source Type: Journal    
DOI: 10.1088/1742-5468/2009/03/P03019     Document Type: Article

References (24)

1. Turing A M 1952 The chemical basis of morphogenesis Phil. Trans. R. Soc. B 237 37
2. Koch A J and Meinhardt H 1994 Biological pattern formation: from basic mechanisms to complex structures Rev. Mod. Phys. 66 4
3. Gilbert S F 2006 Developmental Biology (Sunderland, MA: Sinauer Associates)
4. Collier J R, Monk N A M, Maini P K and Lewis J H 1996 Pattern formation by lateral inhibition with feedback: a mathematical model of Delta-Notch intercellular signalling J. Theor. Biol. 183 429 (Pubitemid 27033749)
5. Owen M R and Sherratt J A 1998 Mathematical modelling of juxtacrine cell signalling Math. Biosci. 153 125
6. Plahte E 2001 Pattern formation in discrete cell lattices J. Math. Biol. 43 411 (Pubitemid 33772403)
7. Meir E, von Dassow G, Munro E and Odell G M 2002 Robustness, flexibility, and the role of lateral inhibition in the neurogenic network Curr. Biol. 12 778
8. Lewis J 2003 Autoinhibition with transcriptional delay: a simple mechanism for the zebrafish somitogenesis oscillator Curr. Biol. 13 1398 (Pubitemid 37029429)
9. Salazar-Ciudad I, Jernvall J and Newman S A 2003 Mechanisms of pattern formation in development and evolution Development 130 2027
10. Raya A, Kawakami Y, Rodriguez-Esteban C, Ibães M, Rasskin-Gutman D, Rodriguez-León J, Büscher D, Feijó J A and Izpisa Belmonte J C 2004 Notch activity acts as a sensor for extracellular calcium during vertebrate left-right determination Nature 427 121
11. Webb S D and Owen M R 2004 Oscillations and patterns in spatially discrete models for developmental intercellular signalling J. Math. Biol. 48 444 (Pubitemid 40876408)
12. Buceta J, Herranz H, Canela-Xandri O, Reigada R, Sagués F and Miln M 2007 Robustness and stability of the gene regulatory network involved in DV boundary formation in the Drosophila wing PLoS ONE 2 e602
13. Sternberg P W 1988 Lateral inhibition during vulval induction in Caenorhabditis elegans Nature 335 551
14. Greenwald I and Rubin G M 1992 Making a difference: the role of cell-cell interactions in establishing separate identities for equivalent cells Cell 68 271
15. Louvi A and Artavanis-Tsakonas S 2006 Notch signalling in vertebrate neural development Nat. Rev. Neurosci. 7 93
16. Qi H, Rand M D, Wu X, Sestan N, Wang W, Rakic P, Xu T and Artavanis-Tsakonas S 1999 Processing of the Notch ligand Delta by the metalloprotease Kuzbanian Science 283 91
17. Hicks C, Ladi E, Lindsell C, Hsieh J J, Hayward S D, Collazo A and Weinmaster G 2002 A secreted Delta1-Fc fusion protein functions both as an activator and inhibitor of Notch1 signaling J. Neurosci. Res. 68 655 (Pubitemid 34594983)
18. Mishra-Gorur K, Rand M D, Perez-Villamil B and Artavanis-Tsakonas S 2002 Downregulation of Delta by proteolytic processing J. Cell Biol. 159 313
19. Alon U 2006 An Introduction to Systems Biology: Design Principles of Biological Circuits vol 10 (Harvard Medical School, Boston, MA: Chapman and Hall/CRC Mathematical and Computational Biology)
20. Formosa-Jordan P and Ibães M 2008 Coupled positive and negative feedback loops for Notch signalling with cis-interactions in preparation
21. Ibães M, Garcia-Ojalvo J, Toral R and Sancho J M 2000 Dynamics and scaling of noise-induced domain growth Eur. Phys. J. B 18 663
22. Murray J D 2003 Mathematical Biology: I. An Introduction 3rd edn (Berlin: Springer)
23. Cross M C and Hohenberg P C 1993 Pattern formation outside of equilibrium Rev. Mod. Phys. 65 851 (Pubitemid 223000784)
24. Rudge T and Burrage K 2008 Effects of intrinsic and extrinsic noise can accelerate juxtacrine pattern formation Bull. Math. Biol. 70 971