NS  Vol.3 No.10 , October 2011
Evidence for pentagonal symmetry in living and model cellular systems
Abstract: Microscope observations of normal human ke- ratinocytes (NHK) propagated in a serum-free medium reveal a high frequency (>70%) of pentagonally-shaped colonies over a wide range of colony sizes that persist over many sequential cell generations. NHK colonies derived from sin- gle cell isolates also display pentagonal symme- try as confirmed by a photographic technique known as “Markham Rotation”. The generality of pentagonal cellular morphology was extended to observations in situ of pentagonally-shaped basal layer epidermal cells of normal human epidermis, monolayer cultures of normal and immortalized keratinocytes, several different ch- ick embryo cells, and in previously published photographs. Statistical methods were applied that differentiate planar close-packing of polygonal configurations observed in living cellular system from several examples of non-living cellular aggregates that were produced spontaneously in nature or in the laboratory under defined physico-chemical conditions.
Cite this paper: Wille, J. (2011) Evidence for pentagonal symmetry in living and model cellular systems. Natural Science, 3, 866-883. doi: 10.4236/ns.2011.310112.

[1]   Weyl, H. (1952) Symmetry. Princeton University Press, Princeton.

[2]   Goddard, T., Huang, C. and Ferrin, T. (2004) New approaches for visualizing virus capsids. Poster for NCRR Principle Investigator Meeting, 1-7.

[3]   Hickman, C.P.Sr., Hickman, C.P.Jr. and Hickman, F.M. (1974) Integrated principles of zoology. 5th Edition, The CV Mosby Company, St. Louis.

[4]   Romer, A.S. (1974) The vertebrate body: A shorter version of the second edition. W.B. Saunders Company, Philadelphia.

[5]   Breder, C.M.Jr. (1955) Observations on the occurrence and attributes of pentagonal symmetry. Bulletin of American Museum of Natural History, 106, 173-220.

[6]   Frankel, J. (1984) Pattern formation in ciliated protozoa. In: Malacinski, G.M. and Bryant, S.V., Eds., Pattern Formation: A Primer in Developmental Biology, Macmillan Publishing Company, New York, 163-196.

[7]   Thompson, D.W. (1943) On growth and form. New Edition, Cambridge University Press, The Macmillan Company, Cambridge.

[8]   Honda H. (1983) Geometrical models for cells and tissues. International Review of Cytology, 83, 191-246. doi:10.1016/S0074-7696(08)62339-6

[9]   Ehret, C.F. (1967) Paratene theory of the shapes of cells. Journal of Theoretical Biology, 15, 263-272. doi:10.1016/0022-5193(67)90207-X

[10]   Othmer. H.G. and Scriven, L.E. (1971) Instability and dynamic pattern in cellular networks. Journal of Theoretical Biology, 32, 507-537. doi:10.1016/0022-5193(71)90154-8

[11]   Chen, C.S. Mrksich, M., Huang, S., Whitesides. G.M. and Ingebar, D.E. (1997) Geometric control of cell life and death. Science, 276, 1425-1428. doi:10.1126/science.276.5317.1425 PMid:9162012

[12]   Li, R. and Bowerman, B. (2010) Symmetry breaking in biology. In: Symmetry Breaking in Biology. Cold Spring Harbor Perspect Biology, Cold Spring Harbor Laboratory Press, Cold Spring Harbor, 2, 1-6.

[13]   Aoyama, Y. and Kitajima, Y. (1999) Pemphigus vulgaris-IgG causes a rapid depletion of desmoglein 3 (Dsg 3) from the Triton-X-100 soluble pools, leading to the formation of Dsg 3-depleted desmosomes in a human squamous carcinoma cell line, DJM-1 cells. Journal of Investigative Dermatology, 112, 67-71. doi:10.1046/j.1523-1747.1999.00463.x PMid:9886266

[14]   Penas, P.F., Gomez, M., Buezo, G.F., Rios, L., Yanez-Mo, M., Cabanas, C., Sanchez-Madrid, F. and Garcia-Diez, A. (1998) Differentiation expression of activation epitopes of beta-1 integrins in psoriasis and normal skin. Journal of Investigative Dermatology, 111, 19-24. doi:10.1046/j.1523-1747.1998.00232.x PMid:9665381

[15]   Inamatsu, M., Matsizaki, T. Iwanari, H. and Yoshizatu, K. (1998) Establishment of rat dermal papilla cell lines that sustain the potency to induce hair follicles from afollicular skin. Journal of Investigative Dermatology, 111, 767-775. doi:10.1046/j.1523-1747.1998.00382.x PMid:9804336

[16]   Tateno, C. and Yoshizato, K. (1999) Growth potential and differentiation capacity of adult rat hepatocytes in vitro. Wound Repair and Regeneration, 7, 36-44. doi:10.1046/j.1524-475X.1999.00036.x PMid:10231504

[17]   Rambo, C.C. and Szego, C.M. (1983) Estrogen action at endometrial membranes: alterations in luminal surface detectable within seconds. Journal of Cell Biology, 97, 679-685. doi:10.1083/jcb.97.3.679 PMid:6885915

[18]   Markham, R., Frey, S. and Hills, G.J. (1963) A photographic image enhancement technique applied viral structures. Virology, 20, 88. doi:10.1016/0042-6822(63)90143-0

[19]   Ayoub, P. and Sklaar, G. (1983) A Modification of the Mallory connective tissue stain as a stain for keratin. Oral Surgery, 16, 80-581.

[20]   Wille, J., Pittelkow, M.R., Shipley, G.D. and Scott, R.E. (1984) Integrated control of growth and differentiation of normal human prokeratinocytes cultured in serum-free medium: clonal analyses, growth kinetics and cell cycle studies. Journal of Cellular Physiology, 121, 31-44. doi:10.1002/jcp.1041210106 PMid:6207187

[21]   Aroeti, B. (2007) Published image. Chroma Technology Corp. Institute for Life science, Hebrew University, Jerusalem.

[22]   Yang, C.N. (1962) Elementary particles. Princeton University Press, Princeton, 51.

[23]   Wille, J.J. and Ehret, C.F. (1968) Circadian rhythm of pattern formation in populations of free-swimming organism, Terahymena, Journal of Protozoology, 15, 789- 797.

[24]   Livio, M. (2002) The golden ratio. Broadway Book, New York, 110.

[25]   Penrose, R. (1999) The emperor’s new mind. Oxford University Press, Oxford, 172-173.

[26]   Urban, K.W. (1998) From tilings to coverings Nature, 396, 14-15. doi:10.1038/23806

[27]   Bagley, A. (1965) A dense packing of hard spheres with five-fold symmetry. Nature, 208, 674-675. doi:10.1038/208674a0

[28]   Penrose, R. (1974) The role of aesthetics in pure and applird mathematical research. Bulletin of the Institute of Mathematics and Its Applications, 10, 266-271.

[29]   Steinhardt, P.J., Jeong, H.-C., Saitoh, K., Tanaka, E., Abe, E. and Tsai, A.P. (1998) Experimental verification of the quasi-unit cell model of quasicrystal structure. Nature, 396, 55-57. doi:10.1038/23902

[30]   Steinberg, M. (1963) Reconstruction of tissues by dissociated cells. Some morphogenetic tissue movements and the sorting out of embryonic cells may have a common explanation. Science, 141, 401-408. doi:10.1126/science.141.3579.401 PMid:13983728

[31]   Beysens, D.A., Forgacs, G. and Glazier, J.A. (2000) Cell sorting is analogous to phase ordering in fluids. Proceedings of the National Academy of Sciences of the United States of America, 97, 9467-9471. doi:10.1073/pnas.97.17.9467

[32]   Forgacs, G. and Foty, R.A. (2004) Biological implications of tissue viscoelasticity. In: Deutsch, A., Folke, M., Howard, J. and Zimmermann, W., Eds., Function and Regulation of Cellular Systems: Experiments and Models. Biskhauser, Basel, 269-277. doi:10.1007/978-3-0348-7895-1_27

[33]   Arago’n, J.L., Torres, M., Gil, D., Barrio, R.A. and P.K. Maini, P.K. (2000) Turing patterns with pentagonal symmetry. Physical Review E, 65, 051913, 1-9.

[34]   Turing, A.M. (1952) The chemical basis of morphogenesis. Philosophical Transactions of the Royal Society B: Biological Sciences, 237, 37-72. doi:10.1098/rstb.1952.0012

[35]   Li, R. and Bowerman, B. (2010) Symmetry breaking in biology. Cold Spring Harbor Laboratory Perspectives in Biology, 2a003475, 1-18.