Mathematical modelling of digit specification by a sonic hedgehog gradient

Developmental Dynamics

Volumn 243, Issue 2, 2014, Pages 290-298

  Woolley, Thomas E ^a   Baker, Ruth E ^a   Tickle, Cheryll ^b   Maini, Philip K ^a   Towers, Matthew ^c  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b University of Bath   (United Kingdom)

^c UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Chick wing; Diffusion; Digits; Gradient; Growth; Limb; Mathematical modelling; Morphogen; Shh

Indexed keywords

MORPHOGEN; SONIC HEDGEHOG PROTEIN;

ANIMAL CELL; ARTICLE; CHICK; FINGER; FORELIMB; LIMB; MATHEMATICAL MODEL; MOUSE; NONHUMAN; PRIORITY JOURNAL;

ERINACEIDAE;

CHICK WING; DIFFUSION; DIGITS; GRADIENT; GROWTH; LIMB; MATHEMATICAL MODELLING; MORPHOGEN; SHH;

ANIMALS; BODY PATTERNING; CHICK EMBRYO; DIFFUSION; HEDGEHOG PROTEINS; MICE; MODELS, THEORETICAL; SPECIES SPECIFICITY; WING;

EID: 84892674543     PISSN: 10588388     EISSN: 10970177     Source Type: Journal    
DOI: 10.1002/dvdy.24068     Document Type: Article

References (53)

1. Ahn S, Joyner AL. 2004. Dynamic changes in the response of cells to positive hedgehog signaling during mouse limb patterning. Cell 118:505-516.
2. Allen BL, Song JY, Izzi L, Althaus IW, Kang JS, Charron F, Krauss RS, McMahon AP. 2011. Overlapping roles and collective requirement for the coreceptors GAS1, CDO, and BOC in SHH pathway function. Dev Cell 14:775-787.
3. 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 148:273-284.
4. Benson DL, Maini PK, Sherratt JA. 1993. Diffusion driven instability in an inhomogeneous domain. Bull Math Biol 55:365-384.
5. Blair SS. 2007. Wing vein patterning in Drosophila and the analysis of intercellular signaling. Annu Rev Cell Dev Biol 23:293-19.
6. Chamberlain CE, Jeong J, Guo C, Allen BL, McMahon AP. 2008. Notochord-derived Shh concentrates in close association with the apically positioned basal body in neural target cells and forms a dynamic gradient during neural patterning. Development 135:1097-1106.
7. Chiang C, Litingtung Y, Lee E, Young KE, Corden JL, Westphal H, Beachy PA. 1996. Cyclopia and defective axial patterning in mice lacking sonic hedgehog function. Science 383:407-413
8. Cooke J, Summerbell D. 1980. Cell cycle and experimental pattern duplication in the chick wing during embryonic development. Nature 287:697-701.
9. Crampin EJ, Gaffney EA, Maini PK. 1999. Reaction and diffusion on growing domains: scenarios for robust pattern formation. Bull Math Biol 61:1093-1120.
10. Dessaud E, McMahon AP, Briscoe J. 2008. Pattern formation in the vertebrate neural tube: a sonic hedgehog morphogen-regulated transcriptional network. Development 135:2489-2503.
11. Dillon R, Gadgil C, Othmer HG. 2003. Short- and long-range effects of Sonic hedgehog in limb development. Proc Natl Acad Sci USA 100:10152-10157.
12. Drossopoulou G, Lewis KE, Sanz-Ezquerro JJ, Nikbakht N, McMahon AP, Hofmann C, Tickle C. 2000. A model for anteroposterior patterning of the vertebrate limb based on sequential long- and short-range Shh signalling and Bmp signalling. Development 127:1337-1348.
13. Eichele G, Tickle C, Alberts BM. 1985. Studies on the mechanism of retinoid-induced pattern duplications in the early chick limb bud: temporal and spatial aspects. J Cell Biol 101:1913-1920.
14. French, V, Bryant PJ, Bryant SV. 1976. Pattern regulation in epimorphic fields. Science 193:969-981.
15. Glimm T, Headon D, Kiskowski MA. 2012a. Computational and mathematical models of chondrogenesis in vertebrate limbs. Birth Defects Res C Embryo Today 96:176-192.
16. Glimm T, Zhang J, Shen YQ, Newman SA. 2012b. Reaction-diffusion systems and external morphogen gradients: the two-dimensional case, with an application to skeletal pattern formation. Bull Math Biol 74:666-687.
17. Hentschel HG, Glimm T, Glazier JA, Newman SA. 2004. Dynamical mechanisms for skeletal pattern formation in the vertebrate limb. Proc Biol Sci 271:1713-1722.
18. Honig LS. 1981. Positional signal transmission in the developing chick limb. Nature 291:72-73.
19. Izaguirre JA. 2004. Chaturvedi R, Huang C, Cickovski T, Coffland J, Thomas G, Forgacs G, Alber M, Hentschel G, Newman SA, Glazier JA. CompuCell, a multi-model framework for simulation of morphogenesis. Bioinformatics 20:1129-1137.
20. Marigo V, Scott MP, Johnson RL, Goodrich LV, Tabin CJ. 1996. Conservation in hedgehog signaling: induction of a chicken patched homolog by Sonic hedgehog in the developing limb. Development 122:1225-1233.
21. Meinhardt H. 1983. A boundary model for pattern formation in vertebrate limbs. J Embryol Exp Morphol 76:115-137.
22. Miura T, Shiota K, Morriss-Kay G, Maini PK. 2006. Mixed-mode pattern in Doublefoot mutant mouse limb: Turing reaction-diffusion model on a growing domain during limb development. J Theor Biol 240:562-573.
23. Newman SA, Frisch HL. 1979. Dynamics of skeletal pattern formation in developing chick limb. Science 205:662-668.
24. Newman SA, Christley S, Glimm T, Hentschel HG, Kazmierczak B, Zhang YT, Zhu J, Alber M. 2008. Multiscale models for vertebrate limb development. Curr Top Dev Biol 81:311-340.
25. Ribes V, Balaskas N, Sasai N, Cruz C, Dessaud E, Cayuso J, Tozer S, Yang LL, Novitch B, Marti E, Briscoe J. 2010. Distinct Sonic Hedgehog signaling dynamics specify floor plate and ventral neuronal progenitors in the vertebrate neural tube. Genes Dev 24:1186-1200.
26. Riddle RD, Johnson RL, Laufer E, Tabin C. 1993. Sonic hedgehog mediates the polarizing activity of the ZPA. Cell 75:1401-1416.
27. Ros MA, Dahn RD, Fernandez-Teran M, Rashka K, Caruccio NC, Hasso SM, Bitgood JJ, Lancman JJ, Fallon JF. 2003. The chick oligozeugodactyly (ozd) mutant lacks sonic hedgehog function in the limb. Development 130:527-537.
28. Saha K, Schaffer DV. 2006. Signal dynamics in Sonic hedgehog tissue patterning. Development 133:889-900.
29. Sanz-Ezquerro JJ, Tickle C. 2000. Autoregulation of Shh expression and Shh induction of cell death suggest a mechanism for modulating polarising activity during chick limb development. Development 127:4811-4823.
30. Saunders JW, Gasseling MT. 1968. Ectodermal-mesenchymal interactions in the origin of limb symmetry. In: Fleischmeyer R, Billingham RE, editors. Mesenchymal-epithelial interactions. Baltimore: Williams and Wilkins, p 78-97.
31. Scherz PJ, McGlinn E, Nissim S, Tabin CJ. 2007. Extended exposure to Sonic hedgehog is required for patterning the posterior digits of the vertebrate limb. Dev Biol 308:343-354.
32. Sheth R, Marcon L, Bastida MF, Junco M, Quintana L, Dahn R, Kmita M, Sharpe J, Ros MA. 2012. Hox genes regulate digit patterning by controlling the wavelength of a Turing-type mechanism. Science 338:1476-1480.
33. Smith JC. 1980. The time required for positional signalling in the chick wing bud. J Embryol Exp Morphol 60:321-328.
34. Smith JC, Tickle C, Wolpert L. 1978. Attenuation of positional signalling in the chick limb by high doses of gamma-radiation. Nature 272:612-613.
35. Summerbell D, Tickle C. 1977. Pattern formation along the anterior- posterior axis of the chick limb bud. In: Ede DA, Hinchliffe JR, Balls M, editors. Vertebrate limb and somite morphogenesis. Cambridge: Cambridge University Press. p 41-53.
36. Tabin CJ, McMahon AP. 2008. Grasping limb patterning. Science 321:350-352.
37. Tamura K, Nomura N, Seki R, Yonei-Tamura S, Yokoyama H. 2011. Embryological evidence identifies wing digits in birds as digits 1, 2, and 3. Science 331:753-757.
38. Tickle C. 1981. The number of polarizing region cells required to specify additional digits in the developing chick wing. Nature 289:295-298.
39. Tickle C. 1995. Vertebrate limb development. Curr Opin Genet Dev 5:478-484.
40. Tickle C. 2006. Making digit patterns in the vertebrate limb. Nature Rev 7:45-53.
41. Tickle C, Summerbell D, Wolpert L. 1975. Positional signalling and specification of digits in chick limb morphogenesis. Nature 254:199-202.
42. Tickle C, Lee J, Eichele G. 1985. A quantitative analysis of the effect of all-trans-retinoic acid on the pattern of chick wing development. Dev Biol 109:82-95.
43. Towers M, Tickle C. 2009. Growing models of vertebrate limb development. Development 136:179-190.
44. Towers M, Manhood R, Yin Y, Tickle C. 2008. Integration of growth and specification in chick wing digit-patterning. Nature 452:882-886.
45. Towers M, Signolet J, Sherman A, Sang H, Tickle C. 2011. Insights into bird wing evolution and digit specification from polarizing region fate maps. Nat Commun 2:426.
46. Vargesson N, Clarke JD, Vincent K, Coles C, Wolpert L, Tickle C. 1997. Cell fate in the chick limb bud and relationship to gene expression. Development 124:1909-1918.
47. Wagner M, Thaller C, Jessell T, Eichele G. 1990. Polarizing activity and retinoid synthesis in the floor plate of the neural tube. Nature 345:819-822.
48. Wilby OK, Ede DA. 1975. A model generating the pattern of cartilage skeletal elements in the embryonic chick limb. J Theor Biol 52:199-217.
49. Wolpert L. 1969. Positional information and the spatial pattern of cellular formation. J Theor Biol 25:1-47.
50. Wolpert L, Hornbruch A. 1981. Positional signalling along the anteroposterior axis of the chick wing. The effect of multiple polarizing region grafts. J Embryol Exp Morphol 63:145-159.
51. Yang Y, Drossopoulou G, Chuang PT, Duprez D, Marti E, Bumcrot D, Vargesson N, Clarke J, Niswander L, McMahon A, Tickle C. 1997. Relationship between dose, distance and time in Sonic Hedgehog-mediated regulation of anteroposterior polarity in the chick limb. Development 124:4393-4404.
52. Zeng X, Goetz JA, Suber LM, Scott WJ Jr., Schreiner CM, Robbins DJ. 2001. A freely diffusible form of Sonic hedgehog mediates long-range signalling. Nature 411:716-720.
53. Zhu J, Nakamura E, Nguyen MT, Bao X, Akiyama H, Mackem S. 2008. Uncoupling Sonic hedgehog control of pattern and expansion of the developing limb bud. Dev Cell 14:624-632.