Computational and mathematical models of chondrogenesis in vertebrate limbs

Birth Defects Research Part C - Embryo Today: Reviews

Volumn 96, Issue 2, 2012, Pages 176-192

  Glimm, T ^a   Headon, D ^b   Kiskowski, M A ^c  

^a WESTERN WASHINGTON UNIVERSITY   (United States)

^b UNIVERSITY OF EDINBURGH   (United Kingdom)

^c UNIVERSITY OF SOUTH ALABAMA   (United States)

Author keywords

Limb chondrogenesis; Mathematical models

Indexed keywords

SONIC HEDGEHOG PROTEIN;

BODY BUILD; BODY SIZE; CARTILAGE CELL; CELL ADHESION; CELL DIFFERENTIATION; CELL MOTION; CELL PROLIFERATION; CELL SURVIVAL; CHEMICAL INTERACTION; CHEMICAL REACTION; CHONDROGENESIS; DIFFUSION; EXTRACELLULAR MATRIX; LIMB DEVELOPMENT; MATHEMATICAL MODEL; MESENCHYME CELL; MOLECULAR BIOLOGY; NONHUMAN; PRIORITY JOURNAL; REVIEW; VERTEBRATE;

ANIMALS; CHONDROGENESIS; COMPUTER SIMULATION; EXTREMITIES; HUMANS; MICE; MODELS, BIOLOGICAL; VERTEBRATES;

EID: 84862248175     PISSN: 1542975X     EISSN: 15429768     Source Type: Journal    
DOI: 10.1002/bdrc.21014     Document Type: Review

References (99)

1. Alber M, Glimm T, Hentschel HG, et al. 2008. The morphostatic limit for a model of skeletal pattern formation in the vertebrate limb. Bull Math Biol 70: 460-483.
2. Bhat R, Lerea KM, Peng H, et al. 2011. A regulatory network of two galectins mediates the earliest steps of avian limb skeletal morphogenesis. BMC Dev Biol 11: 16.
3. Boehm B, Westerberg H, Lesnicar-Pucko G, et al. 2010. The role of spatially controlled cell proliferation in limb bud morphogenesis. PLoS Biol 8: e1000420.
4. Chaturvedi RC, et al. 2004. A hybrid discrete-continuum model for 3-D skeletogenesis of vertebrate limb. Lecture Notes Comput Sci 3305: 543-552.
5. Chaturvedi RI, et al. 2003. Multi-model simulations of chicken limb morphogenesis. Lecture Notes Comput Sci 2659:39-49.
6. Chimal-Monroy J, Rodriguez-Leon J, Montero JA, et al. 2003. Analysis of the molecular cascade responsible for mesodermal limb chondrogenesis: sox genes and BMP signaling. Dev Biol 257: 292-301.
7. Christley S, Alber MS, Newman SA. 2007. Patterns of mesenchymal condensation in a multiscale, discrete stochastic model. PLoS Comput Biol 3: e76.
8. Cickovski TM, Huang C, Chaturvedi R, et al. 2005. A framework for three-dimensional simulation of morphogenesis. IEEE/ACM Trans Comput Biol Bioinform 2: 273-288.
9. Crick AP, Babbs C, Brown JM, Morriss-Kay GM. 2003. Developmental mechanisms underlying polydactyly in the mouse mutant Doublefoot. J Anat 202: 21-26.
10. Cui C. 2005. Dynamics of cell movement and tissue motion in gastrulation and micromass cell culture. Bloomington (Indiana): Indiana University.
11. Delise AM, Tuan RS. 2002. Analysis of N-cadherin function in limb mesenchymal chondrogenesis in vitro. Dev Dyn 225: 195-204.
12. Dillon R, Othmer HG. 1999. A mathematical model for outgrowth and spatial patterning of the vertebrate limb bud. J Theor Biol 197: 295-330.
13. 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.
14. Downie SA, Newman SA. 1994. Morphogenetic differences between fore and hind limb precartilage mesenchyme: relation to mechanisms of skeletal pattern formation. Dev Biol 162: 195-208.
15. Downie SA, Newman SA. 1995. Different roles for fibronectin in the generation of fore and hind limb precartilage condensations. Dev Biol 172: 519-530.
16. Dudley AT, Ros MA, Tabin CJ. 2002. A re-examination of proximodistal patterning during vertebrate limb development. Nature 418: 539-544.
17. Ede DA, Flint OP, Wilby 0K, Colquhoun P. 1977. The development of precartilage condensations in limb bud mesenchyme in vivo and in vitro. In: Ede DA, Hinchliffe JR, Balls M, editors. Vertebrate limb and somite morphogenesis. Cambridge University Press, Cambridge, pp. 161-179.
18. Ede DA, Law JT. 1969. Computer simulation of vertebrate limb morphogenesis. Nature 221: 244-248.
19. Forgacs G, Newman SA. 2005. Biological Physics of the Developing Embryo. Cambridge University Press.
20. Frenz DA, Jaikaria NS, Newman SA. 1989a. The mechanism of precartilage mesenchymal condensation: a major role for interaction of the cell surface with the amino-terminal heparin-binding domain of fibronectin. Dev Biol 136: 97-103.
21. Frenz DA, Akiyama SK, Paulsen DF, Newman SA. 1989b. Latex beads as probes of cell surface-extracellular matrix interactions during chondrogenesis: evidence for a role for amino-terminal heparin-binding domain of fibronectin. Dev Biol 136: 87-96.
22. Gierer A, Meinhardt H. 1972. A theory of biological pattern formation. Kybernetik 12: 30-39.
23. Glazier JA, Graner F. 1993. Simulation of the differential adhesion driven rearrangement of biological cells. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 47: 2128-2154.
24. Glimm T, Zhang J, Shen Y.-Q. 2009. Interaction of Turing patterns with an external linear morphogen gradient. Nonlinearity, 22: 2541-2560.
25. Glimm T, Zhang J, Shen YQ, Newman SA. 2012. Reaction-diffusion systems and external morphogen gradients: the two-dimensional case, with an application to skeletal pattern formation. Bull Math Biol 74: 666-687.
26. Goldring MB, Tsuchimochi K, Ijiri K. 2006. The control of chondrogenesis. J Cell Biochem 97: 33-44.
27. Graner F, Glazier JA. 1992. Simulation of biological cell sorting using a two-dimensional extended Potts model. Phys Rev Lett 69: 2013-2016.
28. Gregor T, Tank DW, Wieschaus EF, Bialek W. 2007. Probing the limits to positional information. Cell 130: 153-164.
29. Hall BK, Miyake T. 1995. Divide, accumulate, differentiate: cell condensation in skeletal development revisited. Int J Dev Biol 39: 881-893.
30. Hall BK, Miyake T. 2000. All for one and one for all: condensations and the initiation of skeletal development. Bioessays 22: 138-147.
31. Hardy A, Richardson MK, Francis-West PH, et al. 1995. Gene expression, polarising activity and skeletal patterning in reaggregated hind limb mesenchyme. Development 121: 4329-4337.
32. Harfe BD, Scherz PJ, Nissim S, et al. ( 2004). Evidence for an expansion-based temporal Shh gradient in specifying vertebrate digit identities. Cell 118: 517-528.
33. 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.
34. Hirashima T, Iwasa Y, Morishita Y. 2008. Distance between AER and ZPA is defined by feed-forward loop and is stabilized by their feedback loop in vertebrate limb bud. Bull Math Biol 70: 438-459.
35. Hopyan S, Sharpe J, Yang Y. 2011. Budding behaviors: growth of the limb as a model of morphogenesis. Dev Dyn 240: 1054-1062.
36. Hurle JM, Ganan Y, Macias D. 1989. Experimental analysis of the in vivo chondrogenic potential of the interdigital mesenchyme of the chick leg bud subjected to local ectodermal removal. Dev Biol 132: 368-374.
37. Izaguirre JA, Chaturvedi R, Huang C, et al. 2004. CompuCell, a multi-model framework for simulation of morphogenesis. Bioinformatics 20: 1129-1137.
38. Karsenty G, Kronenberg HM, Settembre C. 2009. Genetic control of bone formation. Annu Rev Cell Dev Biol 25: 629-648.
39. Kauffman SA. 1993. The origins of order: self-organization and selection in evolution. Oxford University Press, USA.
40. Kerszberg M, Wolpert L. 2007. Specifying positional information in the embryo: looking beyond morphogens. Cell 130: 205-209.
41. Kiskowski MA, Alber MS, Thomas GL, et al. 2004. Interplay between activator-inhibitor coupling and cell-matrix adhesion in a cellular automaton model for chondrogenic patterning. Dev Biol 271: 372-387.
42. Klopocki E, Ott CE, Benatar N, et al. 2008. A microduplication of the long range SHH limb regulator (ZRS) is associated with triphalangeal thumb-polysyndactyly syndrome. J Med Genet 45: 370-375.
43. Kondo S, Miura T. 2010. Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329: 1616-1620.
44. Leonard CM, Fuld HM, Frenz DA, et al. 1991. Role of transforming growth factor-beta in chondrogenic pattern formation in the embryonic limb: stimulation of mesenchymal condensation and fibronectin gene expression by exogenenous TGF-beta and evidence for endogenous TGF-beta-like activity. Dev Biol 145: 99-109.
45. Maini PK, Solursh M. 1991. Cellular mechanisms of pattern formation in the developing limb. Int Rev Cytol 129: 91-133.
46. Mariani FV, Martin GR. 2003. Deciphering skeletal patterning: clues from the limb. Nature 423: 319-325.
47. Mariani FV, Ahn CP, Martin GR. 2008. Genetic evidence that FGFs have an instructive role in limb proximal-distal patterning. Nature 453: 401-405.
48. Meinhardt H, Gierer A. 1974. Applications of a theory of biological pattern formation based on lateral inhibition. J Cell Sci 15: 321-346.
49. Merino R, Ganan Y, Macias D, et al. 1998. Morphogenesis of digits in the avian limb is controlled by FGFs, TGFbetas, and noggin through BMP signaling. Dev Biol 200: 35-45.
50. Miura T, Maini PK. 2004. Speed of pattern appearance in reaction-diffusion models: implications in the pattern formation of limb bud mesenchyme cells. Bull Math Biol 66: 627-649.
51. Miura T, Shiota K. 2000a. TGFbeta2 acts as an activator molecule in reaction-diffusion model and is involved in cell sorting phenomenon in mouse limb micromass culture. Dev Dyn 217: 241-249.
52. Miura T, Shiota K. 2000b. Extracellular matrix environment influences chondrogenic pattern formation in limb bud micromass culture: experimental verification of theoretical models. Anat Rec 258: 100-107.
53. Miura T, Komori M, Shiota K. 2000. A novel method for analysis of the periodicity of chondrogenic patterns in limb bud cell culture: correlation of in vitro pattern formation with theoretical models. Anat Embryol 201: 419-428.
54. 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.
55. Moftah MZ, Downie SA, Bronstein NB, et al. 2002. Ectodermal FGFs induce perinodular inhibition of limb chondrogenesis in vitro and in vivo via FGF receptor 2. Dev Biol 249: 270-282.
56. Montero JA, Hurlé JM. 2007. Deconstructing digit chondrogenesis. Bioessays 29: 725-737.
57. Morishita Y, Iwasa Y. 2009. Estimating the spatiotemporal pattern of volumetric growth rate from fate maps in chick limb development. Dev Dyn 238: 415-422.
58. Murray JD, Oster GF. 1984. Cell traction models for generating pattern and form in morphogenesis. J Math Biol 19: 265-279.
59. Murray JD, Oster GF, Harris AK. 1983. A mechanical model for mesenchymal morphogenesis. J Math Biol 17: 125-129.
60. Newman S. 1977. Lineage and pattern in the developing wing bud. In: Ede DA, Hinchliffe JR, Balls M, editors. Vertebrate limb and somite morphogenesi. pp. 181-197.
61. Newman SA. 1996. Sticky fingers: hox genes and cell adhesion in vertebrate limb development. Bioessays 18: 171-174.
62. Newman SA, Frisch HL. 1979. Dynamics of skeletal pattern formation in developing chick limb. Science 205: 662-668.
63. Newman SA, Frisch HL, Percus JK. 1988. On the stationary state analysis of reaction-diffusion mechanisms for biological pattern formation. J Theor Biol 134: 183-197.
64. Newman SA, Tomasek JJ. 1996. Morphogenesis of connective tissues Extracellular Matrix (Molecular Components and Interactions, Vol. 2, Comper, WD, editor. Amsterdam: Harwood Academic; pp. 335-369.
65. Newman SA, Bhat R. 2007. Activator-inhibitor dynamics of vertebrate limb pattern formation. Birth Defects Res C Embryo Today 81: 305-319.
66. Niswander L, Tickle C, Vogel A, et al. 1993. FGF-4 replaces the apical ectodermal ridge and directs outgrowth and patterning of the limb. Cell 75: 579-587.
67. Oberlender SA, Tuan RS. 1994a. Expression and functional involvement of N-cadherin in embryonic limb chondrogenesis. Development 120: 177-187.
68. Oberlender SA, Tuan RS. 1994b. Spatiotemporal profile of N-cadherin expression in the developing limb mesenchyme. Cell Adhes Commun 2: 521-537.
69. Oster GF, Murray JD. 1989. Pattern formation models and developmental constraints. J Exp Zool 251: 186-202.
70. Oster GF, Murray JD, Harris AK. 1983. Mechanical aspects of mesenchymal morphogenesis. J Embryol Exp Morphol 78: 83-125.
71. Oster GF, Murray JD, Maini PK. 1985. A model for chondrogenic condensations in the developing limb: the role of extracellular matrix and cell tractions. J Embryol Exp Morphol 89: 93-112.
72. Othmer HG. 1986. On the Newman-Frisch model of limb chondrogenesis. J Theor Biol 121: 505-508.
73. Poplawski NJ, Swat M, Gens JS, Glazier JA. 2007. Adhesion between cells, diffusion of growth factors, and elasticity of the AER produce the paddle shape of the chick limb. Physica A 373: 521-532.
74. Riddle RD, Johnson RL, Laufer E, Tabin C. 1993. Sonic hedgehog mediates the polarizing activity of the ZPA. Cell 75: 1401-1416.
75. Ros MA, Lyons GE, Mackem S, Fallon JF. 1994. Recombinant limbs as a model to study homeobox gene regulation during limb development. Dev Biol 166: 59-72.
76. Salazar-Ciudad I, Jernvall J, Newman SA. 2003. Mechanisms of pattern formation in development and evolution. Development 130: 2027-2037.
77. 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.
78. Seo S, Na K. 2011. Mesenchymal Stem Cell-Based Tissue Engineering for Chondrogenesis. J of Biomed Biotechnol 2011, Article ID 806891, 8 pages.
79. Summerbell D, Lewis JH, Wolpert L. 1973. Positional information in chick limb morphogenesis. Nature 244: 492-496.
80. Sun M, Ma F, Zeng X, et al. 2008. Triphalangeal thumb-polysyndactyly syndrome and syndactyly type IV are caused by genomic duplications involving the long range, limb-specific SHH enhancer. J Med Genet 45: 589-595.
81. Sun X, Mariani FV, Martin GR. 2002. Functions of FGF signalling from the apical ectodermal ridge in limb development. Nature 418: 501-508.
82. Tabin C, Wolpert L. 2007. Rethinking the proximodistal axis of the vertebrate limb in the molecular era. Genes Dev 21: 1433-1442.
83. Temtamy SA, McKusick VA. 1978. The genetics of hand malformations. Birth Defects Orig Artic Ser 14: 1-619.
84. Tickle C, Munsterberg A. 2001. Vertebrate limb development-the early stages in chick and mouse. Curr Opin Genet Dev 11: 476-481.
85. Tickle C, Wolpert L. 2002. The progress zone-alive or dead? Nat Cell Biol 4: E216-E217.
86. Towers M, Tickle C. 2009a. Growing models of vertebrate limb development. Development 136: 179-190.
87. Towers M, Tickle C. 2009b. Generation of pattern and form in the developing limb. Int J Dev Biol 53: 805-812.
88. Towers M, Mahood R, Yin Y, Tickle C. 2008. Integration of growth and specification in chick wing digit-patterning. Nature 452: 882-886.
89. Turing AM. 1952. The chemical basis of morphogenesis. Philos Trans R Soc London Ser B 237: 37-72.
90. Wieczorek D, Pawlik B, Li Y, et al. 2010. A specific mutation in the distant sonic hedgehog (SHH) cis-regulator (ZRS) causes Werner mesomelic syndrome (WMS) while complete ZRS duplications underlie Haas type polysyndactyly and preaxial polydactyly (PPD) with or without triphalangeal thumb. Hum Mutat 31: 81-89.
91. 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.
92. Wolpert L. 1969. Positional information and the spatial pattern of cellular differentiation. J Theor Biol 25: 1-47.
93. Wolpert L. 2002. Limb patterning: reports of models death exaggerated. Curr Biol 12: R628-630.
94. Wolpert L, Hornbruch A. 1990. Double anterior chick limb buds and models for cartilage rudiment specification. Development 109: 961-966.
95. Yang Y, Guillot P, Boyd Y, et al. 1998. Evidence that preaxial polydactyly in the Doublefoot mutant is due to ectopic Indian Hedgehog signaling. Development 125: 3123-3132.
96. Zeng W, Thomas GL, Newman SA, Glazier JA. 2003. A novel mechanism for mesenchymal condensation during limb chondrogenesis in vitro. Mathematical modelling and computing in biology and medicine, 5th ESMTB Conference, 2002. In: Capasso V, editor. Società Editrice Esculapio, Bologna; pp 80-86.
97. Zeng W, Thomas GL, Glazier JA. 2004. Non-Turing stripes and spots: a novel mechanism for biological cell clustering. Phys A: Stat Mech Appl 341: 482-494.
98. Zhu J, Zhang YT, Alber MS, Newman SA. 2010. Bare bones pattern formation: a core regulatory network in varying geometries reproduces major features of vertebrate limb development and evolution. PLoS ONE 5: e10892.
99. Zwilling E. 1964. Development of fragmented and of dissociated limb bud mesoderm. Dev Biol 89: 20-37.