title: Emerging of fractal geometry on surface of human cervical epithelial cells during progression towards cancer.
abstract: Despite considerable advances in understanding the molecular nature of cancer, many biophysical aspects of malignant development are still unclear. Here we study physical alterations of the surface of human cervical epithelial cells during stepwise in vitro development of cancer (from normal to immortal (premalignant), to malignant). We use atomic force microscopy to demonstrate that development of cancer is associated with emergence of simple fractal geometry on the cell surface. Contrary to the previously expected correlation between cancer and fractals, we find that fractal geometry occurs only at a limited period of development when immortal cells become cancerous; further cancer progression demonstrates deviation from fractal. Because of the connection between fractal behaviour and chaos (or far from equilibrium behaviour), these results suggest that chaotic behaviour coincides with the cancer transformation of the immortalization stage of cancer development, whereas further cancer progression recovers determinism of processes responsible for cell surface formation.
authors.affiliation: Department of Mechanical Engineering, Tufts University, Medford, MA 02155, USA.
authors.forename: M E
authors.initials: ME
authors.lastname: Dokukin
authors.affiliation: Department of Physics, Clarkson University, Potsdam, New York 13699-5820, USA.
authors.forename: N V
authors.initials: NV
authors.lastname: Guz
authors.affiliation: Department of Biology, Clarkson University, Potsdam, New York 13699-5820, USA.
authors.forename: C D
authors.initials: CD
authors.lastname: Woodworth
authors.affiliation: Department of Physics, Clarkson University, Potsdam, New York 13699-5820, USA ; Department of Biomedical Engineering, Tufts University, Medford, MA 02155, USA ; Department of Physics, Tufts University, Medford, MA 02155, USA.
authors.forename: I
authors.initials: I
authors.lastname: Sokolov
keywords: cell biophysics; fractals; physics of cancer
references.citation: Gynecol Oncol. 1999 Oct;75(1):78-83
references.pmid: 10502430
references.citation: Cancer Res. 2000 Jul 15;60(14):3683-8
references.pmid: 10919633
references.citation: Nat Struct Biol. 2000 Sep;7(9):719-24
references.pmid: 10966637
references.citation: Clin Cancer Res. 2001 Dec;7(12):4280-7
references.pmid: 11751530
references.citation: J Invest Dermatol. 2002 May;118(5):800-5
references.pmid: 11982756
references.citation: Cancer Res. 2003 Jul 1;63(13):3556-9
references.pmid: 12839941
references.citation: Diagn Cytopathol. 2005 Oct;33(4):244-5
references.pmid: 16138367
references.citation: Cancer Res. 1990 Jun 15;50(12):3709-15
references.pmid: 1692766
references.citation: J Colloid Interface Sci. 2007 Jun 15;310(2):385-90
references.pmid: 17335839
references.citation: Gynecol Oncol. 2007 Jul;106(1):170-6
references.pmid: 17481701
references.citation: Acta Haematol. 2008;119(3):142-50
references.pmid: 18417956
references.citation: Diagn Cytopathol. 2009 Jan;37(1):61-7
references.pmid: 18973127
references.citation: Small. 2009 Oct;5(20):2277-84
references.pmid: 19415648
references.citation: Nat Nanotechnol. 2009 Jun;4(6):389-93
references.pmid: 19498402
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2009 May;79(5 Pt 1):051920
references.pmid: 19518493
references.citation: Cancer Res. 1991 Jan 1;51(1):265-73
references.pmid: 1988088
references.citation: Analyst. 2011 Apr 7;136(7):1502-6
references.pmid: 21305062
references.citation: Phys Rev Lett. 2011 Jul 8;107(2):028101
references.pmid: 21797643
references.citation: Cell Biochem Biophys. 2012 Jun;63(2):109-16
references.pmid: 22351422
references.citation: Cancer Res. 1988 Aug 15;48(16):4620-8
references.pmid: 2456144
references.citation: J Virol. 1989 Jan;63(1):159-64
references.pmid: 2462058
references.citation: Cell. 2014 Mar 27;157(1):267-71
references.pmid: 24679541
references.citation: Skin Res Technol. 1995 Nov;1(4):177-9
references.pmid: 27326719
references.citation: Med Hypotheses. 1994 Jun;42(6):400
references.pmid: 7935089
references.citation: Cancer Invest. 1997;15(6):601-7
references.pmid: 9412666
references.citation: Phys Rev A. 1991 Aug 15;44(4):2730-2733
references.pmid: 9906256
references.citation: Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996 Jun;53(6):5749-5763
references.pmid: 9964931