Skip to main content
SpringerLink
Log in

Patterning of endocytic vesicles and its control by voltage-gated Na+ channel activity in rat prostate cancer cells: fractal analyses

  • Article
  • Published:
European Biophysics Journal Aims and scope Submit manuscript

Abstract

Fractal methods were used to analyze quantitative differences in secretory membrane activities of two rat prostate cancer cell lines (Mat-LyLu and AT-2) of strong and weak metastatic potential, respectively. Each cell’s endocytic activity was determined by horseradish peroxidase uptake. Digital images of the patterns of vesicular staining were evaluated by multifractal analyses: generalized fractal dimension (D q ) and its Legendre transform f(α), as well as partitioned iterated function system – semifractal (PIFS-SF) analysis. These approaches revealed consistently that, under control conditions, all multifractal parameters and PIFS-SF codes determined had values greater for Mat-LyLu compared with AT-2 cells. This would agree generally with the endocytic/vesicular activity of the strongly metastatic Mat-LyLu cells being more developed than the corresponding weakly metastatic AT-2 cells. All the parameters studied were sensitive to tetrodotoxin (TTX) pre-treatment of the cells, which blocked voltage-gated Na+ channels (VGSCs). Some of the parameters had a “simple” dependence on VGSC activity, whereby pre-treatment with TTX reduced the values for the MAT-LyLu cells and eliminated the differences between the two cell lines. For other parameters, however, there was a “complex” dependence on VGSC activity. The possible physical/physiological meaning of the mathematical parameters studied and the nature of involvement of VGSC activity in control of endocytosis/secretion are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2A–D
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  • Almqvist N (1996) Fractal analysis of scanning probe microscopy images. Surf Sci 355:221–228

    Article  CAS  Google Scholar 

  • Barnsley M (1988) Fractals everywhere. Academic Press, New York

  • Bashyam MD (2002) Understanding cancer metastasis: an urgent need for using differential gene expression analysis. Cancer 94:1821–1829

    Article  CAS  PubMed  Google Scholar 

  • Bottino DA, Kleen M, Kemming G, Meisner F, Habler O, Messmer K (2001) Three-dimensional visualization of lung blood flow heterogeneity based on fluorescent microsphere technique and fractal dimension: the blood flow analysis system – BFA system. Comput Methods Programs Biomed 65:79–87

    Article  CAS  PubMed  Google Scholar 

  • Conner SD, Schmid SL (2003) Regulated portals of entry into the cell. Nature 422:37–44

    Article  CAS  PubMed  Google Scholar 

  • Diss JKJ, Archer SN, Hirano J, Fraser SP, Djamgoz MBA (2001) Expression profiles of voltage-gated Na(+) channel alpha-subunit genes in rat and human prostate cancer cell lines. Prostate 48:165–178

    Google Scholar 

  • Djamgoz MBA (2001) Excitability of prostate cancer cells: a new concept in the pathophysiology of metastatic disease. Br J Cancer 85(suppl 1):8

    Google Scholar 

  • Djamgoz MBA, Krasowska M, Martinoli O, Sericano M, Vallerga S, Grzywna ZJ (2001) Structure–function correlation in transient amacrine cells of goldfish retina: basic and multifractal analyses of dendritic trees in distinct synaptic layers. J Neurosci Res 66:1208–1216

    Article  CAS  PubMed  Google Scholar 

  • Evans CP, Walsh DS, Kohn EC (1991) An autocrine motility factor secreted by the Dunning R-3327 rat prostatic adenocarcinoma cell subtype AT2.1. Int J Cancer 49:109–113

    CAS  PubMed  Google Scholar 

  • Foster CS, Cornford P, Forsyth L, Djamgoz MBA, Ke Y (1999) The cellular and molecular basis of prostate cancer. Br J Urol Int 83:171–194

    Article  CAS  Google Scholar 

  • Fraser SP, Grimes JA, Djamgoz MBA (2000) Effects of voltage-gated ion channel modulators on rat prostatic cancer cell proliferation: comparison of strongly and weakly metastatic cell lines. Prostate 44: 61–76

    Article  CAS  PubMed  Google Scholar 

  • Grimes JA, Fraser SP, Stephens GJ, Downing JE, Laniado ME, Foster CS, Abel PD, Djamgoz MBA (1995) Differential expression of voltage-activated Na+ currents in two prostatic tumour cell lines: contribution to invasiveness in vitro. FEBS Lett 369:290–294

    Article  CAS  PubMed  Google Scholar 

  • Gromada J, Hoy M, Renstrom E, Bokvist K, Eliasson L, Gopel S, Rorsman P (1999) CaM kinase II-dependent mobilization of secretory granules underlies acetylcholine-induced stimulation of exocytosis in mouse pancreatic B-cells. J Physiol (London) 518:745–759

  • Grzywna ZJ, Stolarczyk J (2002) On some structure-morphology problems by the extended partioned iterated function system (PIFS-SF). Chaos Solitons Fractals 13:897–905

    Article  CAS  Google Scholar 

  • Grzywna ZJ, Krasowska M, Ostrowski Ł, Stolarczyk J (2001) Can generalized dimension (D q ) and f(α) be used in structure–morphology analysis? Acta Phys Polon B 32:1561–1577

    CAS  Google Scholar 

  • Grzywna ZJ, Krasowska M, Stolarczyk J (2003) On the application of PIFS-SF and D q (f(α)) to dendrites analysis. Acta Phys Polon B 34:3681–3693

    CAS  Google Scholar 

  • Gundelfinger ED, Kessels MM, Qualmann B (2003) Temporal and spatial coordination of exocytosis and endocytosis. Nat Rev Mol Cell Biol 4:127–139

    Article  CAS  PubMed  Google Scholar 

  • Herzog RI, Liu C, Waxman SG, Cummins TR (2003) Calmodulin binds to the C terminus of sodium channels Nav1.4 and Nav1.6 and differentially modulates their functional properties. J Neurosci 23:8261–8270

    CAS  PubMed  Google Scholar 

  • Hilfiker S, Czernik AJ, Greengard P, Augustine GJ (2001) Tonically active protein kinase A regulates neurotransmitter release at the squid giant synapse. J Physiol (London) 531:141-146

  • Isaacs JT, Isaacs WB, Feitz WF, Scheres J (1986) Establishment and characterization of seven Dunning rat prostatic cancer cell lines and their use in developing method for predicting metastatic abilities of prostatic cancers. Prostate 9:261–281

    CAS  PubMed  Google Scholar 

  • Jaquin AE (1993) Fractal image coding – a review. Proc IEEE 81:1451–1465

    Article  Google Scholar 

  • Jelinek HF, Fernandez E (1998) Neurons and fractals: how reliable and useful are calculations of fractal dimension? J Neurosci Methods 81:9-18

    Article  CAS  PubMed  Google Scholar 

  • Kurbel S, Kurbel B, Kovacic D, Sulava D, Krajina Z, Dimitrovic B, Sokcevic M (1999) Endothelin-secreting tumors and the idea of the pseudoectopic hormone secretion in tumors. Med Hypoth 52:329–233

    Article  CAS  Google Scholar 

  • Laniado ME, Lalani E-N, Fraser SP, Grimes JA, Bhangal G, Djamgoz MBA, Abel PD (1997) Expression and functional analysis of voltage-activated Na+ channels in human prostate cancer cell lines and their contribution to invasion in vitro. Am J Pathol 150:1213–1221

    CAS  PubMed  Google Scholar 

  • Latka M, Glaubic-Latka M, Latka D, West BJ (2004) Fractal rigidity in migraine. Chaos Solitons Fractals 20:165–170

    Article  Google Scholar 

  • Lasota A, Myjak J (1996) Semifractals. Bull Pol Acad Sci Math 44:5–21

    Google Scholar 

  • Lee AK, Tse A (1997) Mechanism underlying corticotropin-releasing hormone (CRH) triggered cytosolic Ca2+ rise in identified rat corticotrophs. J Physiol (London) 504:367–378

  • Lin SW, Lee MT, Ke FC, Lee PP, Huang CJ, Ip MM, Chen L, Hwang JJ (2000) TGFbeta1 stimulates the secretion of matrix metalloproteinase 2 (MMP2) and the invasive behavior in human ovarian cancer cells, which is suppressed by MMP inhibitor BB3103. Clin Exp Metastasis 18:493–439

    Article  CAS  PubMed  Google Scholar 

  • Liotta LA (1986) Molecular biology of metastases: a review of recent approaches. Eur J Cancer Clin Oncol 22:345–348

    CAS  PubMed  Google Scholar 

  • Llorente A, van Deurs B, Garred O, Eker P, Sandvig K (2000) Apical endocytosis of ricin in MDCK cells is regulated by the cyclooxygenase pathway. J Cell Sci 113:1213–1221

    CAS  PubMed  Google Scholar 

  • Minami N, Berglund K, Sakaba T, Kohmoto H, Tachibana M (1998) Potentiation of transmitter release by protein kinase C in goldfish retinal bipolar cells. J Physiol (London) 512:219–225

  • Murakami Y, Tanaka J, Koshimura K, Kato Y (1998) Involvement of tetrodoxin-sensitive sodium channels in rat growth hormone secretion induced by pituitary adenylate cyclase-activating polypeptide (PACAP). Regul Pept 73:119–121

    Article  CAS  PubMed  Google Scholar 

  • Mycielska ME, Szatkowski M, Djamgoz MBA (2003) Contribution of functional voltage-gated Na+ channel expression to cell behaviours in the matastatic cascade in rat prostate cancer. II. Secretory membrane activity. J Cell Physiol 195:461–469

    Article  CAS  PubMed  Google Scholar 

  • Nicholson B, Schaefer G, Theodorescu D (2001) Angiogenesis in prostate cancer: biology and therapeutic opportunities. Cancer Metastasis Rev 20:297–319

    Article  CAS  PubMed  Google Scholar 

  • Philippe JM, Dubois JM, Rouzaire-Dubois B, Cartron PF, Vallette F, Morel N (2002) Functional expression of V-ATPases in the plasma membrane of glial cells. Glia 37:365–373

    Article  PubMed  Google Scholar 

  • Renstrom E, Eliasson L, Bokvist K, Rorsman P (1996) Cooling inhibits exocytosis in single mouse pancreatic B-cells by suppression of granule mobilization J Physiol (London) 494:41–52

  • Sampo B, Tricaud N, Leveque C, Seagar M, Couraud F, Dargent B (2000) Direct interaction between synaptotagamin and intracellular loop I–II of neuronal voltage-gated sodium channels. Proc Natl Acad Sci USA 28:3666–3671

    Article  Google Scholar 

  • Schroeder M (1991) Fractals, chaos, power laws. Freeman, New York

  • Shtiegman K, Yarden Y (2003) The role of ubiquitylation in signaling by growth factors: implications to cancer. Semin Cancer Biol 13:29–40

    Article  CAS  PubMed  Google Scholar 

  • Siwy Z, Mycielska M, Djamgoz MBA (2003) Statistical and fractal analyses of rat prostate cancer cell motility in direct-current electric field: comparison of strongly and weakly metastatic cells. Eur Biophys J 32:12–21

    PubMed  Google Scholar 

  • Song JC, Hrnjez BJ, Farokhzad OC, Matthews JB (1999) PKC-epsilon regulates basolateral endocytosis in human T84 intestinal epithelia: role of F-actin and MARCKS. Am J Physiol 277:C1239–C1249

    CAS  PubMed  Google Scholar 

  • Stanley HG (1996) Fractals and multifractals: the interplay of physics and geometry. In: Bunde A, Havlin S (eds) Fractals and disordered systems. Springer, Berlin Heidelberg New York

  • Trifaro J, Rose SD, Lejen T, Elzagallaai A (2000) Two pathways control chromaffin cell cortical F-actin dynamics during exocytosis. Biochimie 82:339–352

    Article  CAS  PubMed  Google Scholar 

  • Turiel A (2003) Relevance of multifractal textures in static images. Electron Lett Comput Vision Image Anal 1:35–49

    Google Scholar 

  • Vico PG, Boyer H, Carlier LH (1994) New concept in the study of tissue vascularization. Plast Reconstr Surg 94:174–179

    CAS  PubMed  Google Scholar 

  • Yang PC, Berin MC, Yu LC, Conrad DH, Perdue MH (2000) Enhanced intestinal transepithelial antigen transport in allergic rats is mediated by IgE and CD23 (FcepsilonRII). J Clin Invest 106:879–886

    CAS  PubMed  Google Scholar 

Download references

Acknowledgements

This study was supported by the Pro Cancer Research Fund (PCRF), and collaboration grants from NATO (Scientific Division) and the British Council (Warsaw). Z.J.G. would like to acknowledge the generous hospitality of Ealing Abbey during stays in London.

Author information

Authors and Affiliations

  1. Neuroscience Solutions to Cancer Research Group, Department of Biological Sciences, Imperial College London, Sir Alexander Fleming Building, South Kensington Campus, London , SW7 2AZ, UK

    Monika Krasowska, Maria E. Mycielska & Mustafa B. A. Djamgoz

  2. Section of Physics and Applied Mathematics, Department of Physical Chemistry and Polymer Technology, Silesian University of Technology, Strzody 9, 44-100 , Gliwice, Poland

    Monika Krasowska & Zbigniew J. Grzywna

Authors
  1. Monika Krasowska
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zbigniew J. Grzywna
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Maria E. Mycielska
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mustafa B. A. Djamgoz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mustafa B. A. Djamgoz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Krasowska, M., Grzywna, Z.J., Mycielska, M.E. et al. Patterning of endocytic vesicles and its control by voltage-gated Na+ channel activity in rat prostate cancer cells: fractal analyses. Eur Biophys J 33, 535–542 (2004). https://doi.org/10.1007/s00249-004-0394-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00249-004-0394-3

Keywords

Search

Navigation