We discuss a macroscopical growth model which can be used to simulate growth forms of complex-shaped branching organisms with radiate accretive growth. This type of growth processes can be found in many different marine sessile organisms. We use scleractinian corals and a branching sponge as an example. With the radiate accretive growth model a wide range of morphologies and the influence of the physical environment (light and nutrient distribution by advection-diffusion) can be modelled. We show an (preliminary) example of how the accretive growth model can be coupled with a model of gene regulation and body plan formation in a branching sponge. 1. Introduction Many marine sessile organisms from very different taxonomical groups show a strong morphological plasticity, which is in many cases related to the impact of the physical environment. Two dominant parameters influencing morphological plasticity are water movement and the availability of light in photosynthetic organisms. Environmental parameters, closely linked to water movement, are the supply of suspended material in filter-feeding organisms and sedimentation. Sedimentation may also strongly influence the availability of light. Examples of studies in which the morphological plasticity and the relation to physical environment have been investigated are growth forms of the scleractinian Montastrea annularis and local light intensities [1, 2]; growth forms of the hydrozoan Millepora and the exposure to water movement [3, 4]; variations in morphology due to differences in exposure to water movement in the scleractinians Pocillopora [5, 6], Madracis [7, 8], and Agaricia agaricites [9]; colony forms of the bryozoan Electra pilosa and the influence of nutrient supply [10]; shape of coralline algae and the effect of exposure to water movement [11]; growth forms of the sponge Haliclona oculata [12, 13] and exposure to water movement. A detailed review on the morphological plasticity in corals and the influence of the environment can be found in a recent paper by Todd [14]. There are a large number of studies [14] where scleractinian coral colonies have been transplanted from one environment to a different one to identify the impact of the physical environment on the growth form of the colony. In [4] hydrozoan colonies (Millepora) and in [13] sponges (Haliclona oculata) were transplanted from sheltered to exposed environment and vice versa. There are a number of problematic issues in these experiments. The first issue is that many transplantation experiments were done with organisms or colonies which
References
[1]
D. J. Barnes, “Growth in colonial scleractinians,” Bulletin of Marine Science, vol. 23, pp. 280–298, 1973.
[2]
R. R. Graus and I. G. Macintyre, “Variation in growth forms of the reef coral Montastrea annularis (Ellis and Solander): a quantitative evaluation of growth response to light distribution using computer simulation,” Smithsonian Contributions to the Marine Sciences, vol. 12, pp. 441–464, 1982.
[3]
C. W. Stearn and R. Riding, “Forms of the hydrozoan Millepora on a recent coral reef,” Lethaia, vol. 6, pp. 187–200, 1973.
[4]
W. H. de Weerdt, “Transplantation experiments with Caribbean Millepora species (Hydrozoa, Coelenterata), including some ecological observations on growth forms,” Bijdr Dierk, vol. 51, no. 1, pp. 1–19, 1981.
[5]
M. P. Lesser, V. M. Weis, M. R. Patterson, and P. L. Jokiel, “Effects of morphology and water motion on carbon delivery and productivity in the reef coral, Pocillopora damicornis (Linnaeus): diffusion barriers, inorganic carbon limitation, and biochemical plasticity,” Journal of Experimental Marine Biology and Ecology, vol. 178, no. 2, pp. 153–179, 1994.
[6]
N. Chindapol, J. A. Kaandorp, C. Cronemberger, T. Mass, and A. Genin, “Modelling growth and form of the scleractinian coral Pocillopora verrucosa and the influence of hydrodynamics,” Plos Computational Biology, vol. 9, no. 1, Article ID 100284, 2013.
[7]
K. P. Sebens, J. Witting, and B. Helmuth, “Effects of water flow and branch spacing on particle capture by the reef coral Madracis mirabills (Duchassaing and Michelotti),” Journal of Experimental Marine Biology and Ecology, vol. 211, no. 1, pp. 1–28, 1997.
[8]
M. V. Filatov, J. A. Kaandorp, M. Postma, et al., “A comparison between coral colonies from the Madracis genus and simulated forms,” Proceedings of the Royal Society B, vol. 277, pp. 3555–3561, 2010.
[9]
B. Helmuth and K. Sebens, “The influence of colony morphology and orientation to flow on particle capture by the scleractinian coral Agaricia agaricites (Linnaeus),” Journal of Experimental Marine Biology and Ecology, vol. 165, no. 2, pp. 251–278, 1993.
[10]
D. Jebram, “Influences of the food on the colony forms of Electra pilosa (Bryozoa, Cheilostomata),” Zoologische Jahrbücher. Abteilung für Systematik, vol. 108, pp. 1–14, 1980.
[11]
D. W. J. Bosence, “Ecological studies on two unattached coralline algae from western Ireland,” Palaeontology, vol. 19, no. 2, pp. 365–395, 1976.
[12]
J. A. Kaandorp, “Modelling growth forms of the sponge Haliclona oculata (Porifera, Demospongiae) using fractal techniques,” Marine Biology, vol. 110, no. 2, pp. 203–215, 1991.
[13]
J. A. Kaandorp and M. J. de Kluijver, “Verification of fractal growth models of the sponge Haliclona oculata (Porifera) with transplantation experiments,” Marine Biology, vol. 113, no. 1, pp. 133–143, 1992.
[14]
P. A. Todd, “Morphological plasticity in scleractinian corals,” Biological Reviews, vol. 83, no. 3, pp. 315–337, 2008.
[15]
K. J. Kruszyński, J. A. Kaandorp, and R. van Liere, “A computational method for quantifying morphological variation in scleractinian corals,” Coral Reefs, vol. 26, no. 4, pp. 831–840, 2007.
[16]
F. L. Bookstein, Morphometric Tools for Landmark Data: Geometry and Biology, Cambridge University Press, New York, NY, USA, 1991.
[17]
D. Stoyan and F. L. Bookstein, Morphometric Tools for Landmark Data. Geometry and Biology, Cambridge University Press, Cambridge, UK, 1993.
[18]
J. L. Harper, B. R. Rosen, and J. White, The Growth and Form of Modular Organisms, The Royal Society London, London, UK, 1986.
[19]
J. B. C. Jackson, L. W. Bass, and R. E. Cock, Population Biology and Evolution of Clonal Organisms, Yale University Press, London, UK, 1985.
[20]
J. A. Sánchez and H. R. Lasker, “Patterns of morphological integration in marine modular organisms: supra-module organization in branching octocoral colonies,” Proceedings of the Royal Society B, vol. 270, no. 1528, pp. 2039–2044, 2003.
[21]
J. A. Sánchez, H. R. Lasker, E. G. Nepomuceno, J. D. Sánchez, and M. J. Woldenberg, “Branching and self-organization in marine modular colonial organisms: a model,” The American Naturalist, vol. 163, no. 3, pp. E24–E39, 2004.
[22]
T. Vuorisalo and J. Tuomi, “Unitary and modular organisms: criteria for ecological division,” Oikos, vol. 47, no. 3, pp. 382–385, 1986.
[23]
K. Kim and H. R. Lasker, “Allometry of resource capture in colonial cnidarians and constraints on modular growth,” Functional Ecology, vol. 12, no. 4, pp. 646–654, 1998.
[24]
J. E. N. Veron and M. Pichon, Scleractinia of Eastern Australia Part Families Thamnasteriidae, Astrocoeniidae, Pocilloporidae, Australian Government Publishing Service, Canberra, Australia, 1976.
[25]
J. A. Kaandorp, E. A. Koopman, P. M. A. Sloot, R. P. M. Bak, M. J. A. Vermeij, and L. E. H. Lampmann, “Simulation and analysis of flow patterns around the scleractinian coral Madracis mirabilis (Duchassaing and Michelotti),” Philosophical Transactions of the Royal Society B, vol. 358, no. 1437, pp. 1551–1557, 2003.
[26]
J. A. Chamberlain and R. R. Graus, “Water flow and hydromechanical adaptations of branched reef corals,” Bulletin of Marine Science, vol. 25, pp. 112–125, 1977.
[27]
K. R. N. Anthony, “Coral suspension feeding on fine particulate matter,” Journal of Experimental Marine Biology and Ecology, vol. 232, pp. 85–106, 1999.
[28]
M. J. Atkinson and R. W. Bilger, “Effects of water velocity on phosphate uptake in coral reef-flat communities,” Limnology and Oceanography, vol. 37, no. 2, pp. 273–279, 1992.
[29]
F. I. M. Thomas and M. J. Atkinson, “Ammonium uptake by coral reefs: effects of water velocity and surface roughness on mass transfer,” Limnology and Oceanography, vol. 42, no. 1, pp. 81–88, 1997.
[30]
B. D. Badgley, F. Lipschultz, and K. P. Sebens, “Nitrate uptake by the reef coral Diploria strigosa: effects of concentration, water flow, and irradiance,” Marine Biology, vol. 149, no. 2, pp. 327–338, 2006.
[31]
R. Riedl, “Water movement-animal,” in Marine Ecology, O. Kinne, Ed., vol. 1, pp. 1123–1156, John Wiley & Sons, New York, NY, USA, 1971.
[32]
K. P. Sebens and A. S. Johnson, “Effects of water movement on prey capture and distribution of reef corals,” Hydrobiologia, vol. 226, no. 2, pp. 91–101, 1991.
[33]
W. C. Dennison and D. J. Barnes, “Effect of water motion on coral photosynthesis and calcification,” Journal of Experimental Marine Biology and Ecology, vol. 115, pp. 67–77, 1988.
[34]
M. R. Patterson, K. P. Sebens, and R. R. Olson, “In situ measurements of flow effects on primary production and dark respiration in reef corals,” Limnology and Oceanography, vol. 36, no. 5, pp. 936–948, 1991.
[35]
Y. I. Sorokin, Coral Reef Ecology, Springer, Heidelberg, Germany, 1993.
[36]
F. Marubini and B. Thake, “Bicarbonate addition promotes coral growth,” Limnology and Oceanography, vol. 44, no. 3 I, pp. 716–720, 1999.
[37]
F. Marubini, C. Ferrier-Pages, and J. P. Cuif, “Suppression of skeletal growth in scleractinian corals by decreasing ambient carbonate-ion concentration: a cross-family comparison,” Proceedings of the Royal Society B, vol. 270, no. 1511, pp. 179–184, 2003.
[38]
M. A. Reidenbach, J. R. Koseff, S. G. Monismith, J. V. Steinbuck, and A. Genin, “The effects of waves and morphology on mass transfer within branched reef corals,” Limnology and Oceanography, vol. 51, no. 2, pp. 1134–1141, 2006.
[39]
S. Chang, C. Elkins, M. Alley, J. Eaton, and S. Monismith, “Flow inside a coral colony measured using magnetic resonance velocimetry,” Limnology and Oceanography, vol. 54, no. 5, pp. 1819–1827, 2009.
[40]
S. G. Monismith, “Hydrodynamics of coral reefs,” Annual Review of Fluid Mechanics, vol. 39, pp. 37–55, 2007.
[41]
P. L. Jokiel, “Ocean acidification and control of reef coral calcification by boundary layer limitation of proton flux,” Bulletin of Marine Science, vol. 87, no. 3, pp. 639–657, 2011.
[42]
P. L. Jokiel, “The reef coral two compartment proton flux model: a new approach relating tissue-level physiological processes to gross corallum morphology,” Journal of Experimental Marine Biology and Ecology, vol. 409, pp. 1–12, 2011.
[43]
T. A. McConnaughey, J. Burdett, J. F. Whelan, and C. K. Paull, “Carbon isotopes in biological carbonates: respiration and photosynthesis,” Geochimica et Cosmochimica Acta, vol. 61, no. 3, pp. 611–622, 1997.
[44]
J. M. Heikoop, J. J. Dunn, M. J. Risk, H. P. Schwarcz, T. A. McConnaughey, and I. M. Sandeman, “Separation of kinetic and metabolic isotope effects in carbon-13 records preserved in reef coral skeletons,” Geochimica et Cosmochimica Acta, vol. 64, no. 6, pp. 975–987, 2000.
[45]
C. Maier, J. P？tzold, and R. P. M. Bak, “The skeletal isotopic composition as an indicator of ecological and physiological plasticity in the coral genus Madracis,” Coral Reefs, vol. 22, no. 4, pp. 370–380, 2003.
[46]
T. Mass and A. Genin, “Environmental versus intrinsic determination of colony symmetry in the coral Pocillopora verrucosa,” Marine Ecology Progress Series, vol. 369, pp. 131–137, 2008.
[47]
T. Mass, A. Genin, U. Shavit, M. Grinstein, and D. Tchernov, “Flow enhances photosynthesis in marine benthic autotrophs by increasing the efflux of oxygen from the organism to the water,” Proceedings of the National Academy of Sciences of the United States of America, vol. 107, no. 6, pp. 2527–2531, 2010.
[48]
T. Mass, I. Brickner, E. Hendy, and A. Genin, “Enduring physiological and reproductive benefits of enhanced flow for a stony coral,” Limnology and Oceanography, vol. 56, pp. 2176–2188, 2011.
[49]
D. R. Webster and M. J. Weissburg, “The hydrodynamics of chemical cues among aquatic organisms,” Annual Review of Fluid Mechanics, vol. 41, pp. 73–90, 2009.
[50]
J. F. Bruno and P. J. Edmunds, “Metabolic consequences of phenotypic plasticity in the coral Madracis mirabilis (Duchassaing and Michelotti): the effect of morphology and water flow on aggregate respiration,” Journal of Experimental Marine Biology and Ecology, vol. 229, no. 2, pp. 187–195, 1998.
[51]
S. Muko, K. Kawasaki, K. Sakai, F. Takasu, and N. Shigesada, “Morphological plasticity in the coral Porites sillimaniani and its adaptive significance,” Bulletin of Marine Science, vol. 66, no. 1, pp. 225–239, 2000.
[52]
J. A. Kaandorp, “A formal description of radiate accretive growth,” Journal of Theoretical Biology, vol. 166, no. 2, pp. 149–161, 1994.
[53]
J. A. Kaandorp, Fractal Modelling: Growth and Form in Biology, Springer, Berlin, Germany, 1994.
[54]
J. A. Kaandorp, “Morphological analysis of growth forms of branching marine sessile organisms along environmental gradients,” Marine Biology, vol. 134, no. 2, pp. 295–306, 1999.
[55]
P. Brien, C. Lévi, M. Sara, O. Tuzet, and J. Vacelet, Traité de Zoologie: Anatomie, Systématique, Biologie, Tome III Spongiares, chapter 1, Paris, France, 1973.
[56]
J. A. Kaandorp and J. E. Kuebler, The Algorithmic Beauty of Seaweeds, Sponges and Corals, Springer, Heidelberg, Germany, 2001.
[57]
W. H. de Weerdt, “A systematic revision of the north-eastern Atlantic shallow-water Haplosclerida (Porifera, Demospongiae), part II: Chalinidae,” Beaufortia, vol. 36, pp. 81–165, 1986.
[58]
S. Vogel, “Current-induced flow through the sponge, Halichondria,” Biological Bulletin, vol. 147, no. 2, pp. 443–456, 1974.
[59]
J. P. Grotzinger and D. H. Rothman, “An abiotic model for stromatolite morphogenesis,” Nature, vol. 383, no. 6599, pp. 423–425, 1996.
[60]
M. R. Walter, Stromatolites, Elsevier, Amsterdam, The Netherlands, 1976.
[61]
J. A. Kaandorp, J. G. Blom, J. Verhoef, M. Filatov, M. Postma, and W. E. G. Müller, “Modelling genetic regulation of growth and form in a branching sponge,” Proceedings of the Royal Society B, vol. 275, pp. 2569–2577, 2008.
[62]
J. A. Kaandorp, C. P. Lowe, D. Frenkel, and P. M. A. Sloot, “Effect of nutrient diffusion and flow on coral morphology,” Physical Review Letters, vol. 77, no. 11, pp. 2328–2331, 1996.
[63]
J. A. Kaandorp, P. M. A. Sloot, R. M. H. Merks, R. P. M. Bak, M. J. A. Vermeij, and C. Maier, “Morphogenesis of the branching reef coral Madracis mirabilis,” Proceedings of the Royal Society B, vol. 272, pp. 127–133, 2005.
[64]
R. M. H. Merks, A. G. Hoekstra, J. A. Kaandorp, and P. M. A. Sloot, “Polyp oriented modelling of coral growth,” Journal of Theoretical Biology, vol. 228, no. 4, pp. 559–576, 2004.
[65]
W. E. Lorensen and H. E. Cline, “Marching cubes: a high resolution 3D surface construction algorithm,” ACM Computer Graphics, vol. 21, no. 4, pp. 163–169, 1987.
[66]
J. A. Kaandorp and P. M. A. Sloot, “Morphological models of radiate accretive growth and the influence of hydrodynamics,” Journal of Theoretical Biology, vol. 209, no. 3, pp. 257–274, 2001.
[67]
J. A. Kaandorp, M. Filatov, and N. Chindapol, “Simulating and quantifying the environmental influence on coral growth and form,” in Coral Reefs: An Ecosystem in Transition, Z. Dubinsky and N. Stambler, Eds., part 3, pp. 177–185, 2011.
[68]
W. M. Darke and D. J. Barnes, “Growth trajectories of corallites and ages of polyps in massive colonies of reef-building corals of the genus Porites,” Marine Biology, vol. 117, no. 2, pp. 321–326, 1993.
[69]
M. Le Tissier, B. Clayton, B. E. Brown, and P. Spencer Davies, “Skeletal correlates of coral density banding and an evaluation of radiography as used in scelerochronology,” Marine Ecology Progress Series, vol. 110, pp. 29–44, 1994.
[70]
W. Schroeder, K. Martin, and B. Lorensen, The Visualization Toolkit: An Object-Oriented Approach To 3D Graphics, Prentice Hall, New Jersey, NJ, USA, 2nd edition, 1997.
[71]
O. V. Kaluzhnaya, S. I. Belikov, H. C. Schr？der, et al., “Dynamics of skeletal formation in the Lake Baikal sponge Lubomirskia baicalensis. Part I. Biological and biochemical studies,” Naturwissenschaften, vol. 92, pp. 128–133, 2005.
[72]
O. V. Kaluzhnaya, S. I. Belikov, H. C. Schr ？der, et al., “Dynamics of skeletal formation in the Lake Baikal sponge Lubomirskia baicalensis. Part II. Molecular biological studies,” Naturwissenschaften, vol. 92, pp. 134–138, 2005.
[73]
F. Wiedenmayer, Shallow-Water Sponges of the Western Bahamas, Birkh？user, Basel, Switzerland, 1977.
[74]
C. P. Lowe and D. Frenkel, “The super long-time decay of velocity fluctuations in a two-dimensional fluid,” Physica A, vol. 220, no. 3-4, pp. 251–260, 1995.
[75]
R. M. H. Merks, A. G. Hoekstra, and P. M. A. Sloot, “The moment propagation method for advection-diffusion in the Lattice Boltzmann method: validation and Péclet number limits,” Journal of Computational Physics, vol. 183, no. 2, pp. 563–576, 2002.
[76]
A. J. C. Ladd, “Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation,” Journal of Fluid Mechanics, vol. 271, pp. 285–309, 1994.
[77]
A. J. C. Ladd, “Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 2. Numerical results,” Journal of Fluid Mechanics, vol. 271, pp. 311–339, 1994.
[78]
B. Chopard and M. Droz, Cellular Automata Modelling of Physical Systems, Cambridge Univerity Press, 1998.
[79]
S. Succi, The Lattice Boltzmann Equation: for Fluid Dynamics and Beyond, Oxford University Press, 2001.
[80]
A. Koponen, D. Kandhai, E. Hellén et al., “Permeability of three-dimensional random fiber webs,” Physical Review Letters, vol. 80, no. 4, pp. 716–719, 1998.
[81]
D. Kandhai, D. Hlushkou, A. G. Hoekstra, P. M. A. Sloot, H. Van As, and U. Tallarek, “Influence of stagnant zones on transient and asymptotic dispersion in macroscopically homogeneous porous media,” Physical Review Letters, vol. 88, no. 23, Article ID 234501, 4 pages, 2002.
R. Merks, A. Hoekstra, J. Kaandorp, and P. Sloot, “Models of coral growth: spontaneous branching, compactification and the Laplacian growth assumption,” Journal of Theoretical Biology, vol. 224, no. 2, pp. 153–166, 2003.
[84]
J. Verhoef, Morph space exploration of the accretive growth model [M.S. thesis], University of Amsterdam, 2006.
[85]
J. Huang, R. Yagel, V. Filippov, and Y. Kurzion, “An accurate method for voxelizing polygon meshes,” in Proceedings of the ACE/IEEE Symposium on Volume Visualization, pp. 119–126, 1998.
[86]
A. Kaufman, “Efficient algorithms for scan-converting 3D polygons,” Computers and Graphics, vol. 12, no. 2, pp. 213–219, 1988.
[87]
A. Kaufman, “Efficient algorithms for 3D scan-conversion of parametric curves, surfaces and volumes,” Computer Graphics, vol. 21, no. 4, pp. 269–277, 1987.
[88]
B. E. Chalker and D. L. Taylor, “Light-enhanced calcification, and the role of oxidative phosphorylation in calcification of the coral Acropora cervicornis,” Proceedings of the Royal Society of London B, vol. 190, no. 1100, pp. 323–331, 1975.
[89]
B. Rinkevich and Y. Loya, “Does light enhance calcification in hermatypic corals?” Marine Biology, vol. 80, no. 1, pp. 1–6, 1984.
[90]
J. P. Gairuso, D. Allemand, and M. Frankignoulle, “Photosynthesis and calcification at cellular, organismal and community levels in coral reefs: a review on interactions and control by carbonate chemistry,” American Zoologist, vol. 39, no. 1, pp. 160–183, 1999.
[91]
D. Allemand, C. Ferrier-Pagès, C. Furla, et al., “Biomineralisation in reef-building corals: from molecular mechanisms to environmental control,” Comptes Rendus Palevol, vol. 3, no. 6-7, pp. 453–467, 2004.
[92]
F. A. Al-Horani, S. M. Al-Moghrabi, and D. de Beer, “The mechanism of calcification and its relation to photosynthesis and respiration in the scleractinian coral Galaxea fascicularis,” Marine Biology, vol. 142, no. 3, pp. 419–426, 2003.
[93]
F. A. Al-Horani, S. M. Al-Moghrabi, and D. de Beer, “Microsensor study of photosynthesis and calcification in the scleractinian coral, Galaxea fascicularis: active internal carbon cycle,” Journal of Experimental Marine Biology and Ecology, vol. 288, no. 1, pp. 1–15, 2003.
[94]
F. A. Al-Horani, E. Tambutte, and D. Allemand, “Dark calcification and the daily rhythm of calcification in the scleractinian coral, Galaxea fascicularis,” Coral Reefs, vol. 26, no. 3, pp. 531–538, 2007.
[95]
A. Moya, S. Tambutté, E. Tambutté, D. Zoccola, N. Caminiti, and D. Allemand, “Study of calcification during a daily cycle of the coral Stylophora pistillata: implications for ‘light-enhanced calcification’,” The Journal of Experimental Biology, vol. 209, no. 17, pp. 3413–3419, 2006.
[96]
G. Le Pennec, S. Perovic, M. S. A. Ammar et al., “Cultivation of primmorphs from the marine sponge Suberites domuncula: morphogenetic potential of silicon and iron,” Journal of Biotechnology, vol. 100, no. 2, pp. 93–108, 2003.
[97]
B. Rinkevich and Y. Loya, “Oriented translocation of energy in grafted reef corals,” Coral Reefs, vol. 1, no. 4, pp. 243–247, 1983.
[98]
T. Adell, I. Nefkens, and W. E. G. Müller, “Polarity factor “Frizzled” in the demosponge Suberites domuncula: identification, expression and localization of the receptor in the epithelium/pinacoderm,” FEBS Letters, vol. 554, pp. 363–368, 2003.
[99]
S. Perovic, H. C. Schr？der, S. Sudek, et al., “Expression of one sponge Iroquois homeobox gene in primmorphs from Suberites domuncula during canal formation,” Evolution & Development, vol. 5, pp. 240–250, 2003.
[100]
W. E. G. Müller, A. Krasko, G. Pennec, et al., “Molecular mechanism of spicule formation in the demosponge Suberites domuncula: silicatein-collagen- myotrophin,” Progress in Molecular and Subcellular Biology, vol. 33, pp. 195–231, 2003.
[101]
W. E. G. Müller, M. Wiens, T. Adell, V. Gamulin, H. C. Schr？der, and I. M. Müller, “Bauplan of urmetazoa: basis for genetic complexity of metazoa,” International Review of Cytology, vol. 235, pp. 53–92, 2004.
[102]
W. E. G. Müller, M. Binder, J. von Lintig, et al., “Interaction of the retinoic acid signaling pathway with spicule formation in the marine sponge Suberites domuncula through activation of bone morphogenetic protein’’,” Biochimica et Biophysica Acta, vol. 1810, pp. 1178–1194, 2011.
[103]
H. C. Schr？der, F. Natalio, I. Shukoor et al., “Apposition of silica lamellae during growth of spicules in the demosponge Suberites domuncula: biological/biochemical studies and chemical/biomimetical confirmation,” Journal of Structural Biology, vol. 159, no. 3, pp. 325–334, 2007.
[104]
M. Wiens, S. I. Belikov, O. V. Kaluzhnaya et al., “Regional and modular expression of morphogenetic factors in the demosponge Lubomirskia baicalensis,” Micron, vol. 39, no. 4, pp. 447–460, 2008.
[105]
A. Gierer and H. Meinhardt, “A theory of biological pattern formation,” Kybernetik, vol. 12, no. 1, pp. 30–39, 1972.
[106]
C. Zemlin, Rhytms and wave propogation in the heart [Ph.D. thesis], Humboldt-Universit？t zu Berlin, 2002.
