A mechanical perspective on vertebral segmentation

International Journal of Engineering Science

Volumn 83, Issue , 2014, Pages 124-137

  Truskinovsky, L ^a   Vitale, G ^a,b   Smit, T H ^c  

^a LABORATOIRE DE MÉCANIQUE DES SOLIDES   (France)

^b LIPHY   (France)

^c VU UNIVERSITY MEDICAL CENTER   (Netherlands)

Author keywords

Gradient elasticity; Mechanical signaling; Morphogenesis; Multiple cracking; Somitogenesis

Indexed keywords

CELL ADHESION;

GRADIENT ELASTICITY; INTERNAL LENGTH SCALE; MECHANICAL INSTABILITIES; MOLECULAR OSCILLATIONS; MORPHOGENESIS; MULTIPLE CRACKING; SOMITOGENESIS; VERTEBRAL SEGMENTATION;

CLOCKS;

EID: 84906704392     PISSN: 00207225     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijengsci.2014.05.003     Document Type: Article

References (142)

1. D.S. Adams, R. Keller, and M.A. Koehl The mechanics of notochord elongation, straightening and stiffening in the embryo of Xenopus laevis Development 110 1990 115 130
2. F. Ahimou, L.P. Mok, B. Bardot, and C. Wesley The adhesion force of Notch with Delta and the rate of Notch signaling Journal of Cell Biology 167 6 2004 1217 1229 (Pubitemid 40066635)
3. H. Alarcón, O. Ramos, L. Vanel, F. Vittoz, F. Melo, and J.-C. Géminard Softening induced instability of a stretched cohesive granular layer Physical Review Letters 105 20 2010 1 4
4. R. Bainer, and V. Weaver Cell biology. Strength under tension Science 341 6149 2013 965 966
5. R.E. Baker, and S. Schnell How can mathematics help us explore vertebrate segmentation? HFSP Journal 3 2009 1 5
6. R.E. Baker, S. Schnell, and P.K. Maini Mathematical models for somite formation Current Topics in Developmental Biology 81 2008 183 203
7. J.B.L. Bard A traction-based mechanism for somitogenesis in the chick Roux's Archives of Developmental Biology 197 1988 513 517 (Pubitemid 19068677)
8. J. Bard, and I. Lauder How well does Turing's theory of morphogenesis work? Journal of Theoretical Biology 45 2 1974 501 531
9. B. Belintsev, L. Beloussov, and A. Zaraisky Model of pattern formation in epithelial morphogenesis Journal of Theoretical Biology 129 4 1987 369 394 (Pubitemid 18040073)
10. R. Bellairs The mechanism of somite segmentation in the chick embryo Journal of Embryology and Experimental Morphology 51 1979 227 243 (Pubitemid 9210997)
11. Beloussov, L. V. (2001). Somitogenesis in vertebrate embryos as a robust macromorphological process. In NATO science series: Subseries I, life and behavioural sciences (Vol. 329, pp. 97-106).
12. L.V. Beloussov Mechanically based generative laws of morphogenesis Physical Biology 5 1 2008 015009
13. L.V. Beloussov Morphogenesis as a macroscopic self-organizing process Biosystems 109 3 2012 262 279
14. L.V. Beloussov Morphogenesis can be driven by properly parametrised mechanical feedback The European Physical Journal E 36 11 2013 1 16
15. B. Bénazéraf, P. Francois, R.E. Baker, N. Denans, C.D. Little, and O. Pourquié A random cell motility gradient downstream of FGF controls elongation of an amniote embryo Nature 466 7303 2010 248 252
16. B. Bénazéraf, and O. Pourquié Formation and segmentation of the vertebrate body axis Annual Review of Cell and Developmental Biology 29 2013 1 26
17. M. Benoit, and H.E. Gaub Measuring cell adhesion forces with the atomic force microscope at the molecular level Cells Tissues Organs 172 3 2002 174 189 (Pubitemid 36005556)
18. R. Bhat, and S.a. Newman Snakes and ladders: The ups and downs of animal segmentation Journal of Biosciences 34 2 2009 163 166
19. I.B. Bischofs, and U.S. Schwarz Cell organization in soft media due to active mechanosensing Proceedings of the National Academy of Sciences 16 100 2003 9274 9279 (Pubitemid 37033919)
20. B. Bourdin, G.A. Francfort, and J.-J. Marigo Variational approach to fracture 2009 Springer
21. B. Bourdin, J.-J. Marigo, C. Maurini, and P. Sicsic Morphogenesis and propagation of complex cracks induced by thermal shocks Physical Review Letters 112 1 2014 014301
22. A.E. Brent, and C.J. Tabin Developmental regulation of somite derivatives: Muscle, cartilage and tendon Current Opinion in Genetics and Development 12 2002 548 557 (Pubitemid 35013537)
23. M. Charlotte, and L. Truskinovsky Towards multi-scale continuum elasticity theory Continuum Mechanics and Thermodynamics 20 3 2008 133 161
24. B. Christ, R. Huang, and M. Scaal Amniote somite derivatives Developmental Dynamics 236 2007 2382 2396 (Pubitemid 47450929)
25. J. Cooke A note on segmentation and the scale of pattern formation in insects and in vertebrates Development 104 Supplement 1988 245 248
26. J. Cooke, and E.C. Zeeman A clock and wavefront model for control of the number of repeated structures during animal morphogenesis Journal of Theoretical Biology 58 2 1976 455 476
27. K.M. Correia, and R. Conlon Surface ectoderm is necessary for the morphogenesis of somites Mechanisms of Development 91 1-2 2000 19 30 (Pubitemid 30125901)
28. F. Corson, H. Henry, and M. Adda-Bedia A model for hierarchical patterns under mechanical stresses Philosophical Magazine 90 1-4 2010 357 373
29. L.a. Davidson, S.D. Joshi, H.Y. Kim, M. von Dassow, L. Zhang, and J. Zhou Emergent morphogenesis: Elastic mechanics of a self-deforming tissue Journal of Biomechanics 43 1 2010 63 70
30. A.S. Dias, I. de Almeida, J.M. Belmonte, J.A. Glazier, and C.D. Stern Somites without a clock Science 343 6172 2014 791 795
31. N. Dray, A. Lawton, A. Nandi, D. Jülich, T. Emonet, and S.a. Holley Cell-fibronectin interactions propel vertebrate trunk elongation via tissue mechanics Current Biology 23 14 2013 1335 1341
32. J.L. Duband, S. Dufour, K. Hatta, M. Takeichi, G.M. Edelman, and J.P. Thiery Adhesion molecules during somitogenesis in the avian embryo The Journal of cell biology 104 5 1987 1361 1374 (Pubitemid 17084495)
33. J. Dubrulle, and O. Pourquié From head to tail: Links between the segmentation clock and antero-posterior patterning of the embryo Current Opinion in Genetics and Development 12 2002 519 523 (Pubitemid 35013533)
34. Z. Ferjentsik, S. Hayashi, J.K. Dale, Y. Bessho, A. Herreman, and B. De Strooper et al. Notch is a critical component of the mouse somitogenesis oscillator and is essential for the formation of the somites PLoS Genetics 5 9 2009 e1000662
35. R. Foty, C. Pfleger, G. Forgacs, and M. Steinberg Surface tensions of embryonic tissues predict their mutual envelopment behavior Development 122 5 1996 1611 1620 (Pubitemid 26159647)
36. R. Fujimaki, Y. Toyama, and N. Hozumi Involvement of Notch signaling in initiation of prechondrogenic condensation and nodule formation in limb bud micromass cultures Journal of Bone and Mineral Metabolism 24 2006 191 198
37. F. Gallego-Gómez, V. Morales-Flórez, A. Blanco, N. de la Rosa-Fox, and C. López Water-dependent micromechanical and rheological properties of silica colloidal crystals studied by nanoindentation Nano Letters 12 9 2012 4920 4924
38. E. Gentleman, A.N. Lay, D.A. Dickerson, E.A. Nauman, G.A. Livesay, and K.C. Dee Mechanical characterization of collagen fibers and scaffolds for tissue engineering Biomaterials 24 21 2003 3805 3813 (Pubitemid 36773614)
39. E.L. George, E.N. Georges-Labouesse, R.S. Patel-King, H. Rayburn, and R.O. Hynes Defects in mesoderm, neural tube and vascular development in mouse embryos lacking fibronectin Development 119 4 1993 1079 1091 (Pubitemid 23358578)
40. E.N. Georges-Labouesse, E.L. George, H. Rayburn, and R.O. Hynes Mesodermal development in mouse embryos mutant for fibronectin Developmental Dynamics 207 2 1996 145 156 (Pubitemid 26362206)
41. S. Gibb, M. Maroto, and J.K. Dale Trends in cell biology the segmentation clock mechanism moves up a notch Trends in Cell Biology 20 2010 593 600
42. A. Girós, K. Grgur, A. Gossler, and M. Costell 51 integrin-mediated adhesion to fibronectin is required for axis elongation and somitogenesis in mice PloS One 6 7 2011 e22002
43. A. Goldbeter, and O. Pourquié Modeling the segmentation clock as a network of coupled oscillations in the Notch, Wnt and FGF signaling pathways Journal of Theoretical Biology 252 2008 574 585
44. C. Gomez, E.M. Ozbudak, J. Wunderlich, D. Baumann, J. Lewis, and O. Pourquié Control of segment number in vertebrate embryos Nature 454 2008 335 339
45. D. Gonzalez-Rodriguez, L. Bonnemay, J. Elgeti, S. Dufour, D. Cuvelier, and F. Brochard-Wyart Detachment and fracture of cellular aggregates Soft Matter 9 7 2013 2282
46. A. Gossler, and P.P. Tam Somitogenesis: Segmentation of the paraxial mesoderm and the delineation of tissue compartments J. Rossant, P.P. Tam, Mouse development 2002 Academic Press San Diego 127 149
47. Y. Grabovsky, and L. Truskinovsky The flip side of buckling Continuum Mechanics and Thermodynamics 19 3-4 2007 211 243 (Pubitemid 47241072)
48. R. Grima, and S. Schnell Can tissue surface tension drive somite formation? Developmental Biology 307 2 2007 248 257 (Pubitemid 47007684)
49. S. Grotmol, H. Kryvi, R. Keynes, C. Krossoy, K. Nordvik, and G.K. Totland Stepwise enforcement of the notochord and its intersection with the myoseptum: An evolutionary path leading to development of the vertebra? Journal of Anatomy 209 2006 339 357 (Pubitemid 44269824)
50. U. Handge, Y. Leterrier, G. Rochat, I. Sokolov, and A. Blumen Two scaling domains in multiple cracking phenomena Physical Review E 62 6 2000 7807 7810
51. Y. Harima, Y. Takashima, Y. Ueda, T. Ohtsuka, R. Kageyama, and H. Gene Report accelerating the tempo of the segmentation clock by reducing the number of introns in the hes7 gene Cell Reports 3 1 2013 1 7
52. A.K. Harris Cell traction and the generation of anatomical structure W. Jger, J. Murray, Modelling of patterns in space and time Lecture notes in biomathematics Vol. 55 1984 Springer 103 122
53. A.K. Harris Cell motility and the problem of anatomical homeostasis Journal of Cell Science 8 1987 121 140 (Pubitemid 18041162)
54. A. Harris Multicellular mechanics in the creation of anatomical structures N. Akka, Biomechanics of active movement and division of cells NATO ASI series Vol. 84 1994 Springer 87 129
55. A.K. Harris Direct physical formation of anatomical structures by cell traction forces The International Journal of Developmental Biology 2.3 50 2005 93 101
56. A.K. Harris, D. Stopak, and P. Warner Generation of spatially periodic patterns by a mechanical instability: A mechanical alternative to the Turing model Journal of Embryology and Experimental Morphology 80 1984 1 20 (Pubitemid 14149307)
57. A.K. Harris, D. Stopak, and P. Wild Fibroblast traction as a mechanism for collagen morphogenesis Nature 290 1981 249 251 (Pubitemid 11149655)
58. C.a. Henry, L.a. Hall, M. Burr Hille, L. Solnica-Krezel, and M.S. Cooper Somites in zebrafish doubly mutant for knypek and trilobite form without internal mesenchymal cells or compaction Current Biology 10 17 2000 1063 1066
59. L. Herrgen, S. Ares, L.G. Morelli, C. Schröter, F. Jülicher, and A.C. Oates Intercellular coupling regulates the period of the segmentation clock Current Biology 20 14 2010 1244 1253
60. S.D. Hester, J.M. Belmonte, J.S. Gens, S.G. Clendenon, and J.a. Glazier A multi-cell, multi-scale model of vertebrate segmentation and somite formation PLoS Computational Biology 7 10 2011 e1002155
61. T. Hornig, I.M. Sokolov, and A. Blumen Patterns and scaling in surface fragmentation processes Physical Review E 54 4239 1996
62. J. Howard, S. Grill, and J. Bois Turings next steps: The mechanochemical basis of morphogenesis Nature Reviews. Molecular Cell Biology 6 12 2011 392 398
63. J.W. Hutchinson, and Z. Suo Mixed mode cracking in layered materials Advances in Applied Mechanics 29 1992 63 191
64. S. Kawai, Y. Nitta, and K. Nishinari Model study for large deformation of physical polymeric gels The Journal of Chemical Physics 128 13 2008 134903
65. A. Kicheva, T. Bollenbach, O. Wartlick, F. Jülicher, and M. Gonzalez-Gaitan Investigating the principles of morphogen gradient formation: From tissues to cells Current Opinion in Genetics & Development 22 6 2012 527 532
66. W. Kim, T. Matsui, M. Yamao, M. Ishibashi, K. Tamada, and T. Takumi et al. The period of the somite segmentation clock is sensitive to Notch activity Molecular Biology of the Cell 22 18 2011 3541 3549
67. S. Kondo Self-organizing somites Science 343 6172 2014 736 737
68. E.S. Kornikova, T. Troshina, S.V. Kremnyov, and L.V. Beloussov Neuromesodermal patterns in artificially deformed embryonic explants: A role for mechanogeometry in tissue differentiation Developmental Dynamics 239 3 2010 885 896
69. E. Kritikou Mechanotransduction: Under tension Nature Reviews Molecular Cell Biology 10 1 2008 3
70. P.M. Kulesa, and S.E. Fraser Cell dynamics during somite boundary formation revealed by time-lapse analysis Science 298 5595 2002 991 995 (Pubitemid 35247300)
71. M.F. Laguna, S. Bohn, and E.A. Jagla The role of elastic stresses on leaf venation morphogenesis PLoS Computational Biology 4 4 2008
72. Leocmach, M., Perge, C., Divoux, T., & Manneville, S. (2014). Creep and brittle failure of a protein gel under stress. arXiv:1401.8234 [cond-mat.soft].
73. H. Liang, and L. Mahadevan The shape of a long leaf Proceedings of the National Academy of Sciences U.S.A 106 2009 22049 22054
74. Y. Li, U. Fenger, C. Niehrs, and N. Pollet Cyclic expression of esr9 gene in Xenopus presomitic mesoderm Differentiation 71 2003 83 89 (Pubitemid 38230422)
75. C. Liguore, and S. Mora Fractures in complex fluids: The case of transient networks Rheologica Acta 2 52 2013 91 114
76. B.H. Lipton, and A.G. Jacobson Experimental analysis of the mechanisms of somite morphogenesis Developmental Biology 38 1 1974 91 103
77. T. Mammoto, and D.E. Ingber Mechanical control of tissue and organ development Development 137 2010 1407 1420
78. A.N. Mansurov, A. Stein, and L. Beloussov A simple model for estimating the active reactions of embryonic tissues to a deforming mechanical force Biomechanics and Modeling in Mechanobiology 8 11 2012 1123 1136
79. P. Meakin Fractal scaling in thin film condensation and material surfaces Critical Reviews in Solid State and Material Sciences 13 1986 143 189
80. S. Meier Development of the chick embryo mesoblast. Formation of the embryonic axis and establishment of the metameric pattern Developmental Biology 73 1979 24 45
81. S. Meier Somite formation and its relationship to metameric patterning of the mesoderm Cell Differentiation 14 1984 235 243 (Pubitemid 15176995)
82. H. Meinhardt Models of biological pattern formation 1982 Academic Press London
83. H. Meinhardt Models of biological pattern formation: From elementary steps to the organization of embryonic axes Current Topics in Developmental Biology 81 2008 1 63
84. B. Menkes, and S. Sandor Somitogenesis: Regulation potencies, sequence determination and primordial interactions D. Ede, J.R. Hinchcliffe, M. Balls, Vertebrate limb and somite mophogenesis 1977 Cambridge University Press 405 419
85. P. Milani, S.A. Braybrook, and A. Boudaoud Shrinking the hammer: Micromechanical approaches to morphogenesis Journal of Experimental Botany 64 15 2013 4651 4662
86. M. Milinkovitch, L. Manukyan, A. Debry, N. Di-Poï, S. Martin, and D. Singh et al. Crocodile head scales are not developmental units but emerge from physical cracking Science 339 6115 2013 78 81
87. V. Mirabet, P. Das, A. Boudaoud, and O. Hamant The role of mechanical forces in plant morphogenesis Annual Review of Plant Biology 62 1 2011 365 385
88. O. Morgenstern, I. Sokolov, and A. Blumen Analysis of a one-dimensional fracture model Journal of Physics A: Mathematical and General 26 4521 1993
89. K.R. Mosaliganti, R.R. Noche, F. Xiong, I.a. Swinburne, and S.G. Megason ACME: Automated cell morphology extractor for comprehensive reconstruction of cell membranes PLoS Computational Biology 8 12 2012 e1002780
90. J.D. Murray Mechanical theory for generating pattern and form in development J.D. Murray, Mathematical biology Vol. 18 2003 Springer 311 395
91. P.J. Murray, P.K. Maini, and R.E. Baker The clock and wavefront model revisited Journal of Theoretical Biology 283 1 2011 227 238
92. J.D. Murray, G.F. Oster, and A.K. Harris A mechanical model for mesenchymal morphogenesis Journal of Mathematical Biology 17 1983 125 129 (Pubitemid 13027651)
93. N. Nakayama, R. Smith, T. Mandel, S. Robinson, S. Kimura, and A. Boudaoud et al. Mechanical regulation of auxin-mediated growth Current Biology 22 16 2012 1468 1476
94. C.M. Nelson, R.P. Jean, J.L. Tan, W.F. Liu, N.J. Sniadecki, and A.A. Spector et al. Emergent patterns of growth controlled by multicellular form and mechanics Proceedings of the National Academy of Sciences U.S.A 102 2005 11594 11599 (Pubitemid 41170771)
95. D. New The adhesive properties and expansion of the chick blastoderm Journal of Embryology & Experimental Morphology 7 June 1959 146 164
96. G. Odell, G. Oster, P. Alberch, and B. Burnside The mechanical basis of morphogenesis: Epithelial folding and invagination Developmental Biology 85 2 1981 446 462 (Pubitemid 13142518)
97. J. Osborn A model simulating tooth morphogenesis without morphogenes Journal of Theoretical Biology 165 1993 429 445 (Pubitemid 24035919)
98. I. Palmeirim, J. Dubrulle, D. Henrique, D. Ish-Horowicz, and O. Pourquié Uncoupling segmentation and somitogenesis in the chick presomitic mesoderm Developmental Genetics 23 1998 77 85 (Pubitemid 28368160)
99. I. Palmeirim, D. Henrique, D. Ish-Horowicz, and O. Pourquié Avian hairy gene expression identifies a molecular clock linked to vertebrate segmentation and somitogenesis Cell 91 1997 639 648 (Pubitemid 27513655)
100. O. Pourquié Segmentation of the paraxial mesoderm and vertebrate somitogenesis Current Topics in Developmental Biology 47 1999 81 105
101. O. Pourquié Vertebrate segmentation: From cyclic gene networks to scoliosis Cell 145 5 2011 650 663
102. D. Primmett, W. Norris, G. Carlson, R. Keynes, and C. Stern Periodic segmental anomalies induced by heat shock in the chick embryo are associated with the cell cycle Development 105 1 1989 119 130 (Pubitemid 19046656)
103. P.-H. Puech, K. Poole, D. Knebel, and D.J. Muller A new technical approach to quantify cell-cell adhesion forces by AFM Ultramicroscopy 106 8-9 2006 637 644 (Pubitemid 43994307)
104. X. Ren, and L. Truskinovsky Finite scale microstructures in nonlocal elasticity Journal of Elasticity 59 2000 319 355 (Pubitemid 32432075)
105. J. Rice The Localization of Plastic Deformation W. Koiter, 14th international congress on theoretical and applied mechanics 1976 North-Holland Publishing Delft 207 220
106. P. Rifes, L. Carvalho, C. Lopes, R.P. Andrade, G. Rodrigues, and I. Palmeirim et al. Redefining the role of ectoderm in somitogenesis: A player in the formation of the fibronectin matrix of presomitic mesoderm Development 134 17 2007 3155 3165 (Pubitemid 47506154)
107. P. Rifes, and S. Thorsteinsdóttir Extracellular matrix assembly and 3D organization during paraxial mesoderm development in the chick embryo Developmental Biology 368 2 2012 370 381
108. O. Ronsin, C. Caroli, and T. Baumberger Microstructuration stages during gelation of gelatin under shear The European Physical Journal E 6 34 2011 1 7
109. J. Rowlinson, and B. Widom Molecular theory of capillarity 1982 Dover
110. P. Rué, and J. Garcia-Ojalvo Modeling gene expression in time and space Annual Review of Biophysics 42 2013 605 627
111. T. Savin, N.A. Kurpios, A.E. Shyer, P. Florescu, H. Liang, and L. Mahadevan et al. On the growth and form of the gut Nature 476 2011 57 62
112. C. Schröter, S. Ares, L.G. Morelli, A. Isakova, K. Hens, and D. Soroldoni et al. Topology and dynamics of the zebrafish segmentation clock core circuit PLoS Biology 10 7 2012 e1001364
113. U.S. Schwarz, and S.A. Safran Physics of adherent cells Reviews of Modern Physics 85 3 2013 1327 1381
114. L.J. Sluys, and R. DeBorst Concrete - an analysis of crack width and spacing International Journal of Solids and Structures 33 1996 3257 3276
115. M.S. Steinberg Does differential adhesion govern self-assembly processes in histogenesis? equilibrium configurations and the emergence of a hierarchy among populations of embryonic cells Journal of Experimental Zoology 4 173 1970 395 433
116. M.S. Steinberg Differential adhesion in morphogenesis: A modern view Current Opinion in Genetics and Development 4 17 2007 281 286 (Pubitemid 47238601)
117. C.D. Stern, and R. Bellairs The roles of node regression and elongation of the area pellucida in the formation of somites in avian embryos Journal of Embryology and Experimental Morphology 81 1984 75 92 (Pubitemid 14122305)
118. C.D. Stern, and D. Vasiliauskas Segmentation: A view from the border Current Topics in Developmental Biology 47 1999 107 129
119. D. Stopak, and A.K. Harris Connective tissue morphogenesis by fibroblast traction. I. Tissue culture observations Developmental Biology 90 1982 383 398 (Pubitemid 12126154)
120. L.A. Taber Towards a unified theory for morphomechanics Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367 1902 2009 3555 3583
121. P. Tam, S. Meier, and A. Jacobson Differentiation of the metameric pattern in the embryonic axis of the mouse ii. somitomeric organization of the presodtic mesoderm Differentiation 109-122 1-3 1982 183 224
122. K.H.W.J. Ten Tusscher Mechanisms and constraints shaping the evolution of body plan segmentation The European Physical Journal E 36 5 2013 54
123. D. Thompson On growth and form 1963 Cambridge University Press
124. M.D. Thouless, Z. Li, N.J. Douville, and S. Takayama Periodic cracking of films supported on compliant substrates Journal of the Mechanics and Physics of Solids 59 9 2011 1927 1937
125. N. Triantafyllidis, and E.C. Aifantis A gradient approach to localization of deformation. i. Hyperelastic materials Journal of Elasticity 16 3 1986 225 237 (Pubitemid 17459967)
126. N. Triantafyllidis, and S. Bardenhagen On higher order gradient continuum theories in 1-d nonlinear elasticity. Derivation from and comparison to the corresponding discrete models Journal of Elasticity 33 3 1993 259 293
127. Truskinovsky, L. (1996). Fracture as a phase transition. In R. C. Batra, & M. F. Beatty (Eds.), Contemporary research in the mechanics and mathematics of materials. CIMNE (pp. 322-332).
128. L. Truskinovsky, and G. Zanzotto Ericksen's bar revisited: Energy wriggles Journal of the Mechanics and Physics of Solids 44 8 1996 1371 1408
129. A. Turing The chemical basis of morphogenesis Philosophical Transactions of the Royal Society of London Series B 237 1952 37 72
130. S. Urdy On the evolution of morphogenetic models: Mechano-chemical interactions and an integrated view of cell differentiation, growth, pattern formation and morphogenesis Biological Reviews of the Cambridge Philosophical Society 87 4 2012 786 803
131. A. Vainchtein Dynamics of phase transitions and hysteresis in a viscoelastic Ericksen's bar on an elastic foundation Journal of Elasticity 57 1999 243 280 (Pubitemid 32073315)
132. A. Vainchtein, T. Healey, and P. Rosakis Bifurcation and metastability in a new one-dimensional model for martensitic phase transitions Computer Methods in Applied Mechanics and Engineering 170 3 1999 407 421
133. A. Vainchtein, T. Healey, P. Rosakis, and L. Truskinovsky The role of the spinodal region in one-dimensional martensitic phase transitions Physica D: Nonlinear Phenomena 115 12 1998 29 48 (Pubitemid 128676545)
134. B.L. Vaughan, R.E. Baker, D. Kay, and P.K. Maini A modified Oster-Murray-Harris mechanical model of morphogenesis SIAM Journal on Applied Mathematics 73 6 2013 2124 2142
135. B. Vianay, J. Käfer, E. Planus, M. Block, F. Graner, and H. Guillou Single cells spreading on a protein lattice adopt an energy minimizing shape Physical Review Letters 105 12 2010 128101
136. C.H. Waddington, and E.M. Deuchar Studies on the mechanism of meristic segmentation: I. The dimensions of somites Journal of Embryology and Experimental Morphology 1 4 1953 349 356
137. C. Wiebe, and G.W. Brodland Tensile properties of embryonic epithelia measured using a novel instrument Journal of Biomechanics 38 10 2005 2087 2094 (Pubitemid 41111753)
138. P.A. Wilson, G. Oster, and R. Keller Cell rearrangement and segmentation in Xenopus: Direct observation of cultured explants Development 105 1989 155 166 (Pubitemid 19046660)
139. L. Wolpert Positional information and the spatial pattern of cellular differentiation Journal of Theoretical Biology 1 25 1969 1 47
140. L. Wolpert Positional information and pattern formation Current Topics in Developmental Biology 6 6 1971 183 224
141. L. Wolpert Positional information and patterning revisited Current Topics in Developmental Biology 1 269 2011 359 365
142. M.A. Wyczalkowski, Z. Chen, B.A. Filas, V.D. Varner, and L.A. Taber Computational models for mechanics of morphogenesis Birth Defects Research. Part C 96 2 2012 132 152