Morphogenetic action through flux-limited spreading

Physics of Life Reviews

Volumn 10, Issue 4, 2013, Pages 457-475

  Verbeni, M ^a   Sanchez O ^a   Mollica, E ^b   Siegl Cachedenier, I ^c   Carleton, A ^c   Guerrero, I ^b   Ruiz i Altaba, A ^c   Soler, J ^a  

^a UNIVERSITY OF GRANADA   (Spain)

^b CENTRO DE BIOLOGÍA MOLECULAR SEVERO OCHOA   (Spain)

^c UNIVERSITY OF GENEVA MEDICAL SCHOOL   (Switzerland)

Author keywords

Filopodia like structures; Flux limited; Hedgehog; Morphogenetic gradients

Indexed keywords

CONCENTRATION-DEPENDENT MANNERS; FLUX-LIMITED; HEDGEHOG; INFORMATION TRANSFERS; LINEAR DIFFUSION MODELS; MORPHOGENETIC GRADIENTS; MULTICELLULAR SYSTEMS; PROPAGATION VELOCITIES;

BROWNIAN MOVEMENT; CRACK PROPAGATION; DIFFUSION; MATHEMATICAL MODELS; MOLECULES;

BIOLOGY;

ERINACEIDAE; VERTEBRATA;

SONIC HEDGEHOG PROTEIN;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; CYTOLOGY; DROSOPHILA MELANOGASTER; EPITHELIUM; FILOPODIA-LIKE STRUCTURES; FLUX-LIMITED; FORELIMB; HEDGEHOG; METABOLISM; MORPHOGENESIS; MORPHOGENETIC GRADIENTS; MOVEMENT (PHYSIOLOGY); NEURAL TUBE; NONLINEAR SYSTEM; PRENATAL DEVELOPMENT; SIGNAL TRANSDUCTION;

FILOPODIA-LIKE STRUCTURES; FLUX-LIMITED; HEDGEHOG; MORPHOGENETIC GRADIENTS;

ANIMALS; DROSOPHILA MELANOGASTER; EPITHELIUM; HEDGEHOG PROTEINS; MODELS, BIOLOGICAL; MORPHOGENESIS; MOVEMENT; NEURAL TUBE; NONLINEAR DYNAMICS; SIGNAL TRANSDUCTION; WING;

EID: 84888035986     PISSN: 15710645     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.plrev.2013.06.004     Document Type: Review

References (90)

1. Turing A.M. The chemical basis of morphogenesis. Philos Trans R Soc Lond B, Biol Sci 1952, 237:37-72.
2. Crick F. Diffusion in embryogenesis. Nature 1970, 40:561-563.
3. Meinhardt H. Space-dependent cell determination under the control of a morphogen gradient. J Theor Biol 1978, 74:307-321.
4. Wolpert L. Positional information and the spatial pattern of cellular differentiation. J Theor Biol 1969, 25:1-47.
5. Lander A.D., Nie Q., Wan F.Y.-M. Do morphogen gradients arise by diffusion?. Dev Cell 2002, 2:785-796.
6. Lai K., Robertson M.J., Schaffer D.V. The Sonic Hedgehog signaling system as a bistable genetic switch. Biophys J 2004, 86:2748.
7. Saha K., Schaffer D.V. Signaling dynamics in Sonic Hedgehog tissue patterning. Development 2006, 133:889-900.
8. Kicheva K., Pantazis P., Bollenbach T., Kalaidzidis Y., Bittig T., Julicher F., et al. Science 2007, 315:521.
9. Neugebauer J.M., Amack J.D., Peterson A.G., Bisgrove B.W., Yost H.J. FGF signaling during embryo development regulates cilia length in diverse epithelia. Nature 2009, 458:651-654.
10. Schwank G., Restrepo S., Basler K. Growth regulation by Dpp: an essential role for Brinker and a non-essential role for graded signaling levels. Development 2008, 135:4003-4013.
11. Müller P., Rogers K.W., Jordan B.M., Lee J.S., Robson D., Ramanathan S., et al. Differential diffusivity of nodal and lefty underlies a reaction-diffusion patterning system. Science 2012, 336:721-724.
12. Harvey S.A., Smith J.C. Visualisation and quantification of morphogen gradient formation in the Zebrafish. PLoS Biol 2009, 7(5):e1000101.
13. Smith J.C. Forming and interpreting gradients in the early xenopus embryo. Cold Spring Harb Perspect Biol 2009, 1-12.
14. Kondo S., Miura T. Reaction-Diffusion model as a framework for understanding biological pattern formation. Science 2010, 329:1616-1620.
15. Roth S. Mathematics and biology: a Kantian view on the history of pattern formation theory. Dev Genes Evol 2011, 221(5-6):255-279.
16. John F. Partial differential equations 1971, Springer.
17. Einstein A. Zür Theorie der Brownschen Bewegung. Ann Phys 1906, 19:371-381.
18. Dessaud E., Yang L.L., Hill K., Cox B., Ulloa F., Ribeiro A., et al. Interpretation of the Sonic Hedgehog morphogen gradient by a temporal adaptation mechanism. Nature 2007, 450:717-720.
19. Scherz P.J., McGlinn E., Nissim S., Tabin C.J. Extended exposure to Sonic Hedgehog is required for patterning the posterior digits of the vertebrate limb. Dev Biol 2007, 308(2):343-354.
20. Harfe B.D., Scherz P.J., Nissim S., Tian H., McMahon A.P., Tabin C.J. Evidence for an expansion-based temporal Shh gradient in specifying vertebrate digit identities. Cell 2004, 118(4):517-528.
21. Kornberg T.B. The imperatives of context and contour for morphogen dispersion. Biophys J 2012, 103:2252-2256.
22. Jessell T.M. Neuronal specification in the spinal cord: inductive signals and transcriptional codes. Nat Rev Genet 2000, 1:20-29.
23. Stecca B., Ruiz i Altaba A. Context-dependent regulation of the GLI code in cancer by Hedgehog and non-Hedgehog signals. J Mol Cell Biol 2010, 2(2):84-95.
24. Gritli-Linde A., Lewis P., McMahon A.P., Linde A. The whereabouts of a morphogen: direct evidence for short- and graded long-range activity of Hedgehog signaling peptides. Dev Biol 2001, 236(2):364-386.
25. Lek M., Dias J.M., Marklund U., Uhde C.W., Kurdija S., Lei Q., et al. A homeodomain feedback circuit underlies step-function interpretation of a Shh morphogen gradient during ventral neural patterning. Development 2010, 137:4051-4060.
26. Parker D.S., White M.A., Ramos A.I., Cohen B.A., Barolo S. The cis-regulatory logic of Hedgehog gradient responses: key roles for gli binding affinity, competition, and cooperativity. Sci Signal 2011, 4(176):ra38.
27. Litingtung Y., Dahn R.D., Li Y., Fallon J.F., Chiang C. Shh and Gli3 are dispensable for limb skeleton formation but regulate digit number and identity. Nature 2002, 418:979-983.
28. te Welscher P., Fernandez-Teran M., Ros M.A., Zeller R. Mutual genetic antagonism involving GLI3 and dHAND prepatterns the vertebrate limb bud mesenchyme prior to Shh signaling. Genes Dev 2002, 16:421-426.
29. Guerrero I., Chiang C. A conserved mechanism of Hedgehog gradient formation by lipid modifications. Trends Cell Biol 2007, 17:1-5.
30. Vyas N., Goswami D., Manonmani A., Sharma P., Ranganath H., VijayRaghavan K., et al. Nanoscale organization of Hedgehog is essential for long-range signaling. Cell 2008, 133:1214-1227.
31. Zeng X., Goetz J.A., Suber L.M., Scott W.J., Schreiner C.M., Robbins D.J. A freely diffusible form of Sonic Hedgehog mediates long-range signalling. Nature 2011, 411:716-720.
32. Greco V., Hannus M., Eaton S. Argosomes: a potential vehicle for the spread of morphogens through epithelia. Cell 2001, 106:633-645.
33. Panáková D., Sprong H., Marois E., Thiele C., Eaton S. Lipoprotein particles are required for Hedgehog and Wingless signalling. Nature 2005, 435:58-65.
34. Callejo A., Culi J., Guerrero I. Patched, the receptor of Hedgehog, is a lipoprotein receptor. Proc Natl Acad Sci USA 2008, 105:912-917.
35. Ruiz i Altaba A. Coexpression of HNF-3β and Isl-1/2 and mixed distribution of ventral cell types in the early neural tube. Int J Dev Biol 1996, 40:1081-1088.
36. Gurdon J.B., Mitchell A., Mahony D. Direct and continuous assessment by cells of their position in a morphogen gradient. Nature 1995, 376:520-521.
37. Meinhardt H., Prusinkiewicz P., Fowler D.R. The algorithmic beauty of sea shells 1998, Springer-Verlag, Berlin.
38. Ramirez-Weber F.A., Kornberg T.B. Cytonemes: cellular processes that project to the principal signaling center in Drosophila imaginal discs. Cell 1999, 97(5):599-607.
39. Roy S., Hsiung F., Kornberg T.B. Specificity of Drosophila cytonemes for distinct signaling pathways. Science 2011, 15:354-358.
40. Gradilla A.C., Guerrero I. Cytoneme-mediated cell-cell signaling during development. Cell Tissue Res 2013.
41. Sanders T.A., Llagostera E., Barna M. Specialized filopodia direct long-range transport of Shh during vertebrate tissue patterning. Nature 2013, 497:628-632.
42. Rosenau P. Tempered diffusion: a transport process with propagating front and inertial delay. Phys Rev A 1992, 46:7371-7374.
43. Chertock A., Kurganov A., Rosenau P. Formation of discontinuities in flux-saturated degenerate parabolic equations. Nonlinearity 2003, 16:1875-1898.
44. Kurganov A., Rosenau P. On reaction processes with saturating diffusion. Nonlinearity 2006, 19:171-193.
45. Brenier Y. Extended Monge-Kantorovich theory. Lect Notes Math 2003, vol. 1813:91-122. Springer-Verlag. L.A. Caffarelli, S. Salsa (Eds.).
46. McCann R., Puel M. Constructing a relativistic heat flow by transport time steps. Ann Inst Henri Poincaré, Anal Non Linéaire 2009, 26:2539-2580.
47. Bellomo N., Bellouquid A., Nieto J., Soler J. Multiscale biological tissue models and flux-limited chemotaxis for multicellular growing systems. Math Models Methods Appl Sci 2010, 20(7):1179-1207.
48. Andreu F., Caselles V., Mazón J.M., Moll S. The Dirichlet problem associated to the relativistic heat equation. Math Ann 2010, 347:135-199.
49. Calvo J., Mazón J., Soler J., Verbeni M. Qualitative properties of the solutions of a nonlinear flux-limited equation arising in the transport of morphogens. Math Models Methods Appl Sci 2011, 21:893-937.
50. Caselles V. On the entropy conditions for some flux limited diffusion equations. J Differ Equ 2011, 250:3311-3348.
51. Campos J., Guerrero P., Sánchez O., Soler J. On the analysis of traveling waves to a nonlinear flux limited reaction-diffusion equation. Ann Inst Henri Poincaré, Anal Non Linéaire 2013, 30(1):141-155.
52. Bellomo N., Soler J. On the mathematical theory of the dynamics of swarms viewed as complex systems. Math Models Methods Appl Sci 2012, 22:1140006.
53. Bellomo N., Dogbè C. On the modelling of traffic and crowds - a survey of models, speculations, and perspectives. SIAM Rev 2011, 53(3):409-463.
54. Schwank G., Dalessi S., Yang S.F., Yagi R., de Lachapelle A.M., Affolter M., et al. Formation of the long range Dpp morphogen gradient. PLoS Biol 2011, 9(7):e1001111.
55. Kerszberg M., Wolpert L. Mechanisms for positional signalling by morphogen transport: a theoretical study. J Theor Biol 1998, 191:103-114.
56. Su V.F., Jones K.A., Brodsky M., The I. Quantitative analysis of Hedgehog gradient formation using an inducible expression system. BMC Dev Biol 2007, 7(43):1-15.
57. Chamberlain Ch.E., Jeong J., Guo Ch., Allen B.L., McMahon A.P. 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 2008, 135:1097-1106.
58. Ingham P.W., Fietz M.J. Quantitative effects of Hedgehog and decapentaplegic activity on the patterning of the Drosophila wing. Curr Biol 1995, 5(4):432-440.
59. Torroja C., Gorfinkiel N., Guerrero I. Patched controls the Hedgehog gradient by endocytosis in a dynamin-dependent manner, but this internalization does not play a major role in signal transduction. Development 2004, 131:2395-2408.
60. Casali A. Self-Induced Patched receptor down-regulation modulates cell sensitivity to the Hedgehog morphogen gradient. Sci Signal 2010, 3(136):1-8.
61. Chen Y., Struhl G. Dual roles for patched in sequestering and transducing Hedgehog. Cell 1996, 87(3):553-563.
62. Aza-Blanc P., Ramírez-Webber F.A., Laget M.P., Schwartz C., Kornberg T.B. Proteolysis that is inhibited by Hedgehog targets Cubitus interruptus protein to the nucleus and converts it to a repressor. Cell 1997, 89:1043-1053.
63. Alvarez-Medina R., Cayuso J., Okubo T., Takada S., Martí E. Wnt canonical pathway restricts graded Shh/Gli patterning activity through the regulation of Gli3 expression. Development 2008, 135:237.
64. Lee J., Platt K.A., Censullo P., Ruiz i Altaba A. Gli1 is a target of Sonic Hedgehog that induces ventral neural tube development. Development 1997, 124:2537-2552.
65. Ruiz i Altaba A. Combinatorial Gli gene function in floor plate and neuronal inductions by Sonic Hedgehog. Development 1998, 125:2203-2212.
66. Yao S., Lum L., Beachy Ph.A. The ihog cell-surface proteins bind Hedgehog and mediate pathway activation. Cell 2006, 125:343-357.
67. Aza-Blanc P., Lin H.Y., Ruiz i Altaba A., Kornberg T.B. Expression of the vertebrate Gli proteins in Drosophila reveals a distribution of activator and repressor activities. Development 2000, 127(19):4293-4301.
68. Casali A., Struhl G. Reading the Hedgehog morphogen gradient by measuring the ratio of bound to unbound Patched protein. Nature 2004, 431:76-80.
69. Taipale J., Cooper M.K., Maiti T., Beachy P.A. Patched acts catalytically to suppress the activity of Smoothened. Nature 2002, 418:892-897.
70. Jiang G.S., Shu C.W. Efficient implementation of weighted ENO schemes. J Comput Phys 1996, 126:202-228.
71. Dessaud E., McMahon A.P., Briscoe J. Pattern formation in the vertebrate neural tube: a Sonic Hedgehog morphogen-regulated transcriptional network. Development 2008, 135:2489-2503.
72. Sherer N.M., Mothes W. Cytonemes and tunneling nanotubules in cell-cell communication and viral pathogenesis. Trends Cell Biol 2008, 18(9):414-420.
73. Bilioni A., Sánchez-Hernández D., Callejo A., Gradilla A.C., Ibáñez C., Mollica E., et al. Balancing Hedgehog, a retention and release equilibrium given by Dally, Ihog, Boi and shifted/DmWif. Dev Biol 2013, 376(2):198-212.
74. Gerdes H.H., Carvalho R.N. Intercellular transfer mediated by tunneling nanotubes. Curr Opin Cell Biol 2008, 20(4):470-475.
75. Rojas-Ríos P., Guerrero I., González-Reyes A. Cytoneme-mediated delivery of Hedgehog regulates the expression of bone morphogenetic proteins to maintain germline stem cells in Drosophila. PLoS Biol 2012, 10(4):e1001298.
76. Beachy Ph.A., Hymowitz S.G., Lazarus R.A., Leahy D.J., Siebold C. Interactions between Hedgehog proteins and their binding partners come into view. Genes Dev 2010, 24:2001-2012.
77. Clement V., Sanchez P., De Tribolet N., Radovanovic I., Ruiz i Altaba A. Hedgehog-GLI signaling regulates human glioma growth, cancer stem cell self-renewal and tumorigenicity. Curr Biol 2007, 17:165-172.
78. Zbinden M., Duquet A., Lorente-Trigos A., Ngwabyt S.N., Borges I., Ruiz i Altaba A. NANOG regulates glioma stem cells and is essential in vivo acting in a cross-functional network with GLI1 and p53. EMBO J 2010, 29:2659-2674.
79. Ochs S. Fast transport of materials in mammalian nerve fibers. Science 1972, 176(4032):252-260.
80. Meinhardt H. Models for the generation and interpretation of gradients. Cold Spring Harb Perspect Biol 2009, 1:a001362.
81. Ruiz i Altaba A. Catching a Gli-mpse of Hedgehog. Cell 1997, 90:193-196.
82. Callejo A., Bilioni A., Mollica E., Gorfinkiel N., Andrés G., Ibáñez C., et al. Dispatched mediates Hedgehog basolateral release to form the long-range morphogenetic gradient in the Drosophila wing disk epithelium. Proc Natl Acad Sci USA 2011, 108(31):12591-12598.
83. Udolph G., Luer K., Bossing T., Technau G.M. Commitment of cns progenitors along the dorsoventral axis of Drosophila neuroectoderm. Science 1995, 269:1278-1281.
84. Spiteri R.J., Ruuth S.J. A new class of optimal high-order strong-stability-preserving time discretization methods. SIAM J Numer Anal 2002, 40:469-491.
85. Scorcioni R., Polavaram S., Ascoli G.A. L-Measure: a web-accessible tool for the analysis, comparison and search of digital reconstructions of neuronal morphologies. Nat Protoc 2008, 3:866-876.
86. Lauffenburger D.A., Linderman J.J. Receptors: models for binding, trafficking, and signaling 1993, Oxford University Press, New York.
87. Rubin M.B. Hyperbolic heat conduction and the second law. Int J Engng Sci 1992, 30:1665-1676.
88. Levermore C.D., Pomraning G.C. A flux-limited diffusion theory. Astrophys J 1981, 248:321-334.
89. Coulombel J.-F., Golse F., Goudon Th. Diffusion approximation and entropy based moment closure for kinetic equations. Asymptot Anal 2005, 45(1-2):1-39.
90. Agueh M. Existence of solutions to degenerate parabolic equations via the Monge-Kantorovich theory 2001, PhD thesis, Georgia Tech, Atlanta.