A mathematical model for outgrowth and spatial patterning of the vertebrate limb bud

Journal of Theoretical Biology

Volumn 197, Issue 3, 1999, Pages 295-330

  Dillon, Robert ^a   Othmer, Hans G ^b  

^a WASHINGTON STATE UNIVERSITY   (United States)

^b UNIVERSITY OF UTAH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MORPHOGEN;

GENETIC STRUCTURE; GROWTH; MATHEMATICAL METHOD; SPATIAL ANALYSIS;

ALGORITHM; ARTICLE; CELL DIVISION; CELL GROWTH; EMBRYO PATTERN FORMATION; GENE EXPRESSION; LIMB BUD; LIMB DEVELOPMENT; MATHEMATICAL MODEL; PRIORITY JOURNAL;

VERTEBRATA;

EID: 0033531784     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.1998.0876     Document Type: Article

References (73)

1. Allen, F., Tickle, C. & Warner, A. (1990). The role of gap junctions in patterning of the chick limb bud. Development 108, 623-634.
2. Batchelor, G. K. (1973). An Introduction to Fluid Mechanics. Cambridge: Cambridge University Press.
3. Bellaiche, Y., The, I. & Perrimon, N. (1998). Tout-velu is a Drosophila homologue of the putative tumour suppressor EXT-1 and is needed for Hh diffusion. Nature 394, 85-88.
4. Bowen, J., Hinchliffe, J. R., Horder, T. J. & Reeve, A. M. F. (1989). The fate map of the chick forelimb-bud and its bearing on hypothesized developmental control mechanisms. Anat. Embryol. 179, 269-283.
5. Cohn, M. J., Izpisúa-Belmonte, J. C., Abud, H. & Heath, J. K. (1995). Fibroblast growth factors induce additional limb development from the flank of chick embryos. Cell 80(5), 739-746.
6. Crossley, P. H. & Martin, G. R. (1995). The mouse gene Fgf-8 encodes a family of polypeptides and is expressed in regions that direct outgrowth and patterning in the developing embryo. Development 121, 439-451.
7. Crossley, P. H., Minowada, G., Macarthur, C. A. & Martin, G. R. (1996). Roles for FGF8 in the induction, initiation, and maintenance of chick limb development. Cell 84(1), 127-136.
8. Duprez, D. M., Kostakopoulos, K., Francis-West, P. H., Tickle, C. & Brickell, P. M. (1996). Activation of Fgf-4 and HoxD gene expression by BMP-2 expressing cells in the developing chick limb. Development 122, 1821-1828.
9. Fung, Y. C. (1993). Biomechanics: Mechanical Properties of Living Tissues. Berlin: Springer-Verlag.
10. Grieshammer, U., Minowada, G., Pisenti, J. M., Abbott, U. K. & Martin, G. R. (1996). The chick limbless mutation causes abnormalities in limb bud dorsal-ventral patterning: Implications for the mechanism of apical ridge formation. Development 122, 3851-3861.
11. Haramis, A. G., Brown, J. M. & Zeller, R. (1995). The limb deformity mutation disrupts the SHH/FGF-4 feedback loop and regulation of 5′ HoxD genes during limb pattern formation. Development 121, 4237-4245.
12. Helms, J., Thaller, C. & Eichele, G. (1994). Relationship between retinoic acid and sonic hedgehog, two polarizing signals in the chick wing bud. Development 120, 3267-3274.
13. Hinchliffe, J. R. & Griffiths, P. J. (1984). Experimental analysis of the control of cell death in chick limb bud development. In: Society for Experimental Biology Seminar Series, Vol. 25. Cell Ageing and Cell Death; Meeting (Davies I. & Sigee, D. C., eds) pp. 223-242. Cambridge, England, New York: Cambridge University Press.
14. Honig, L. S. & Summerbell, D. (1985). Maps of strength of positional signaling activity in the developing chick wing bud. J. Embryol. Exp. Morphol. 87, 163-174.
15. Hornbruch, A. & Wolpert, L. (1991). The spatial and temporal distribution of polarizing activity in the flank of the pre-limb-bud stages in the chick embryo. Development 111, 725-731.
16. Izpisúa-Belmonte, J. C., Tickle, C., Dollé, P., Wolpert, L. & Duboule, D. (1991). Expression of the homeobox Hox-4 genes and specification of position in chick wing development. Nature 350, 585-589.
17. Javois, L. C. & Iten, L. E. (1981). Position of origin of donor posterior chick wing bud tissue transplanted to an anterior host site determines the extra structures formed. Dev. Biol. 82(2), 329-342.
18. Javois, L. C. & Iten, L. E. (1986). The handedness and origin of supernumerary limb structures following 180 degree rotation of the chick wing bud on its stump. J. Embryol. Exp. Morphol. 91, 135-152.
19. Johnson, R. L. & Tabin, C. J. (1997). Molecular models for vertebrate limb development. Cell 90, 979-990.
20. Kuhlman, J. & Niswander, L. (1997). Limb deformity proteins: Role in mesodermal induction of the apical ectodermal ridge. Development 124(1), 133-139.
21. Laufer, E., Nelson, C. E., Johnson, R. L., Morgan, B. A. & Tabin, C. (1994). Sonic hedgehog and Fgf-4 act through a signaling cascade and feedback loop to integrate growth and patterning in the developing limb bud. Cell 79, 993-1003.
22. Leveque, R. J. & Li, Z. (1994). The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31, 1019-1944.
23. Lu, H.-C., Revelli, J.-P., Goering, L., Thaller, C. & Eichele, G. (1997). Retinoid signaling is required for the establishment of a ZPA and for the expression of Hoxb-8, a mediator of ZPA formation. Development 124(9), 1643-1651.
24. 4: A polydactylous mutation in the chicken. J. Exp. Zool. 191, 383-392.
25. Maden, M., Ong, D. E., Summerbell, D. & Chytil, F. (1988). Spatial distribution of cellular protein binding to retinoic acid in the chick limb bud. Nature 335, 733-735.
26. Maini, P. K. & Solursh, M. (1991). Cellular mechanisms of pattern formation in the developing limb. Int. Rev. Cytol. 129, 91-133.
27. Marigo, V., Johnson, R. L., Vortkamp, A. & Tabin, C. J. (1996). Sonic hedgehog differentially regulates expression of GL1 and GLI3 during limb development. Dev. Biol. 180(1), 273-283.
28. Mehta, P., Bertram, J. S. & Loewenstein, W. R. (1989). The actions of retinoids on cellular growth correlate with their actions on gap junctional communication. J. Cell Biol. 108, 1053-1065.
29. Meinhardt, H. (1982). Models of Biological Pattern Formation. London: Academic Press.
30. Meinhardt, H. (1983). A boundary model for pattern formation in vertebrate limbs. J. Embryol. Exp. Morphol. 76, 115-137.
31. Michaud, J. L., Lapointe, F. & Le Douarin, N. M. (1997). The dorsoventral polarity of the presumptive limb is determined by signals produced by the somites and by the lateral somatopleure. Development 124(8), 1453-1463.
32. Morton, K. W. & Mayers, D. F. (1994). Numerical Solution of Partial Differential Equations. Cambridge: Cambridge University Press.
33. Nelson, C. E., Morgan, B. A., Burke, A. C., Laufer, E., Dimambro, E., Murtaugh, L. C., Gonzales, E., Tessarollo, L., Parada, L. F. & Tabin, C. (1996). Analysis of Hox gene expression in the chick limb bud. Development 122, 1449-1466.
34. Niswander, L. (1997). Limb mutants: What can they tell us about normal limb development? Curr. Opin. Gen. Dev. 7, 530-536.
35. Niswander, L. & Martin, G. R. (1993). Mixed signals from the AER: FGF-4 and BMP-2 have opposite effects on limb outgrowth. In: Limb Development and Regeneration pp. 625-633. New York: Wiley-Liss.
36. Ogura, T., Alvarez, I. S., Vogel, A., Rodriguez, C., Evans, R. M. & Belmonte, J. C. I. (1996). Evidence that shh cooperates with a retinoic acid inducible co-factor to establish ZPA-like activity. Development 122, 537-542.
37. Ohuchi, H., Nakagawa, T., Yamamoto, A., Araga, A., Ohata, T., Ishimaru, Y., Yoshioka, H., Kuwana, T., Nohno,t.,Yamasaki,m., Itoh, N. & Noji, S. (1997). The mesenchymal factor, FGF10, initiates and maintains the outgrowth of the chick limb bud through interaction with FGF8, an apical ectodermal factor. Development 124(11), 2235-2244.
38. Oster, G. F., Murray, J. D. & Harris, A. K. (1983). Mechanical aspects of mesenchymal morphogenesis. J. Embryol. Exp. Morph. 78, 83-125.
39. Pautou, M. P. (1973). Analyse de la morphogenese du pied des oiseaux a l'aide de melange cellulaires interspecifiques. I. Etude morphologique. J. Embryol. Exp. Morphol. 29, 175-196.
40. Peskin, C. S. (1977). Numerical analysis of blood flow in the heart. J. Comp. Phys., 25, 220-252.
41. Peskin, C. S. & McQueen, D. M. (1995). A general method for the computer simulation of biological systems interacting with fluids. In: Biological Fluid Dynamics (Ellington, C. P. & Pedley, T. J., eds). Company of Biologists, Ltd.
42. Philips, H. M. & Steinberg, M. S. (1969). Equilibrium measurements of embryonic chick cell adhesiveness. I. Shape equilibrium in centrifugal fields. Proc. Nat. Acad. Sci. U.S.A., 64, 121-127.
43. Philips, H. M. & Steinberg, M. S. (1978). Embryonic tissues as elasticoviscous liquids. I. Rapid and slow shape changes in centrifuged cell aggregates. J. Cell Sci. 30, 1-20.
44. Philips, H. M., Steinberg, M. S. & Lipton, B. H. (1977). Embryonic tissues as elasticoviscous liquids. II. Direct evidence for cell slippage in centrifuged aggregates. Dev. Biol. 59, 124-134.
45. Riddle, R. D., Johnson, R. L., Laufer, E. & Tabin, C. (1993). Sonic hedgehog mediates polarizing activity of the ZPA. Cell 75, 1401-1416.
46. Robertson, K. E. & Tickle, C. (1997). Recent molecular advances in understanding vertebrate limb development. Br. J. Plastic Surgery 50(2), 109-115.
47. Ruiz I Altaba, A. (1994). Later. Trends Neurosci. 17, 233-243.
48. Searls, R. L. & Janners, M. Y. (1971). The initiation of limb bud outgrowth in the embryonic chick. Dev. Biol. 24, 198-213.
49. Smith, S. M., Pang, K., Sundin, O., Wedden, S. E., Thaller, C. & Eichele, G. (1989). Molecular approaches to vertebrate limb morphogenesis. Development (Suppl), 121-131.
50. Solursh, M. & Jensen, K. L. (1988). The accumulation of basement membrane components during the onset of chondrogenesis and myogenesis in the chick wing bud. Development 104(1), 41-50.
51. Stark, R. J. & Searls, R. L. (1973). A description of chick wing bud development and a model of limb morphogenesis. Dev. Biol. 33, 138-153.
52. Summerbell, D. (1974a). Interaction between the proximodistal and antero-posterior coordinates of positional value during the specification of positional information in the early development of the chick limb-bud. J. Embryol. Exp. Morphol. 32, 227-237.
53. Summerbell, D. (1974b). A quantitative analysis of the effect of excision of the AER from the chick limb-bud. J. Embryol. Exp. Morphol. 32, 651-660.
54. Summerbell, D. (1977). Regulation of deficiencies along the proximal distal axis of the chick wing-bud: A quantitative analysis. J. Embryol. Exp. Morphol. 41, 137-159.
55. Summerbell, D. (1979). The zone of polarizing activity: Evidence for a role in normal chick morphogenesis. J. Embryol. Exp. Morph. 50, 217-233.
56. Summerbell, D. (1981). Control of growth and the development of pattern across the anteroposterior axis of the chick limb bud. J. Embryol. Exp. Morphol. 63, 161-180.
57. Summerbell, D. & Lewis, J. H. (1975). Time, place and positional value in the chick limb-bud. J. Embryol. Exp. Morph. 33, 621-643.
58. Summerbell, D., Lewis, J. H. & Wolpert, L. (1973). Positional information in chick limb morphogenesis. Nature 244, 492-496.
59. Thaller, C. & Eichele, G. (1987). Identification and spatial distribution of retinoids in the developing chick limb bud. Nature 327, 625-628.
60. Tickle, C. (1980). The polarizing region and limb development. In: Development in Mammals (Johnson, M. H., ed.), vol. 4, pp. 101-136. Amsterdam: Elsevier/North-Holland Biomedical Press.
61. Tickle, C. & Eichele, G. (1994). Vertebrate limb development. In: Annual Review of Cell Biology pp. 121-152. Annual Reviews, Inc.
62. 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.
63. Tickle, C., Summerbell, D. & Wolpert, L. (1975). Positional signalling and specification of digits in chick limb morphogenesis. Nature 254, 199-202.
64. Vargesson, N., Clarke, J. D., Vincent, K., Coles, C., Wolpert, L. & Tickle, C. (1997). Cell fate in the chick limb bud and relationship to gene expression. Development 124(10), 1909-1918.
65. Vogel, A. & Tickle, C. (1993). FGF-4 maintains polarizing activity of posterior limb bud cells in vivo and in vitro. Development 119, 199-206.
66. Vogel, A., Rodriguez, C. & Izpisúa-Belmonte, J.-C. (1996). Involvement of FGF-8 in initiation, outgrowth and patterning of the vertebrate limb. Development 122, 1737-1750.
67. Wilby, O. K. & Ede, D. A. (1975). A model for generating the pattern of cartilage skeletal elements in the embryonic chick limb. J. Theor. Biol. 52, 199-217.
68. Wolpert, L. (1969). Positional information and the spatial pattern of cellular differentiation. J. Theor. Biol. 25, 1-47.
69. Wolpert, L. (1976). Mechanisms of limb development and malformation. Br. Med. J. 32, 65-70.
70. Wolpert, L. (1987). An introduction to cells. Br. Med. J. 295(6604), 987-988.
71. Wolpert, L. & Hornbruch, A. (1990). Double anterior chick limb buds and models for cartilage rudiment specification. Development 109, 961-966.
72. Wolpert, L., Lewis, J. & Summerbell, d. (1975). Morphogenesis of the vertebrate limb. Ciba Symp. 29, 95-130.
73. Zwilling, E. (1961). Limb morphogenesis. Adv. Morphogen. 1, 301-330.