Skip to main content

Spatial Modeling and Simulation of Diffusion in Nuclei of Living Cells

  • Conference paper
Computational Methods in Systems Biology (CMSB 2004)

Abstract

The mobility of fluorescently labelled molecules in the interphase nucleus has been increasingly employed to investigate the spatial organization of the interchromosomal space. We suggest an improved two-dimensional anisotropic diffusion model to address the inhomogeneous nature of nuclear organization, which is at odds with the generally applied ’well-mixed’ compartmental assumption. To consider the transfer function of the imaging system, we derived a modified fundamental solution of the two-dimensional, time-dependent diffusion equation. The model was validated through comparison of the forward simulation results with fluorescence recovery after photobleaching experiments using nuclear localization signal (NLS) – tagged YFP recorded by confocal laser scanning microscopy. To improve the fit error in the vicinity of the nuclear boundary, we suggest an isotropic diffusion model with Neumann boundary condition accounting for the exact shape of the nuclear boundary. The suggested approach is a first step towards diffusion tomography of the cell nucleus.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Monneron, A., Bernhard, W.: Fine structural organization of the interphase nucleus in some mammalian cells. J. Ultrastruct. Res. 27, 266–288 (1969)

    Article  Google Scholar 

  2. Cremer, T., Cremer, C.: Chromosome territories, nuclear architechture and gene regulation in mammalian cells. Nat. Rev. Genet. 2, 292–301 (2001)

    Article  Google Scholar 

  3. Cremer, T., Kurz, A., Zirbel, R., Dietzel, S., Rinke, B., Schröck, E., Speicher, M.R., Mathieu, U., Jauch, A., Emmerich, P., Scherthan, H., Ried, T., Cremer, C., Lichter, P.: Role of chromosome territories in the functional compartmentalization of the cell nucleus. In: Cold Spring Harbour Symposia on Quantitative Biology LVIII, pp. 777–792 (1993)

    Google Scholar 

  4. Lamond, A.I., Earnshaw, W.C.: Structure and function in the nucleus. Science 280, 547–553 (1998)

    Article  Google Scholar 

  5. Misteli, T.: Cell biology of transcription and pre-mRNA splicing: nuclear architecture meets nuclear function. J. Cell Sci. 113, 1841–1849 (2000)

    Google Scholar 

  6. Dundr, M., Misteli, T.: Functional architecture in the cell nucleus. Biochem. J. 163, 509–517 (2001)

    Google Scholar 

  7. Barboro, P., D’Arrigo, C., Mormino, M., Coradeghini, R., Parodi, S., Patrone, E., Balbi, C.: An intranuclear frame for chromatin compartmentalization and higher-order folding. J. Cell Biochem. 88, 113–120 (2003)

    Article  Google Scholar 

  8. Chalfie, M., Tu, Y., Euskirchen, G., Ward, W.W., Prasher, D.C.: Green fluorescent protein as a marker for gene expression. Science 263, 802–805 (1994)

    Article  Google Scholar 

  9. Misteli, T.: Protein dynamics: implications for nuclear architecture and gene expression. Science 291, 843–847 (2001)

    Article  Google Scholar 

  10. Phair, R.D., Misteli, T.: Kinetic modeling approaches in in vivo imaging. Nat. Rev. Mol. Cell Biol. 2, 898–907 (2001)

    Article  Google Scholar 

  11. Phair, R.D., Misteli, T.: High mobility of proteins in the mammalian cell nucleus. Nature 404, 604–609 (2000)

    Article  Google Scholar 

  12. Axelrod, D., Koppel, D.E., Schlessinger, J., Elson, E., Webb, W.W.: Mobility Measurement by Analysis of Fluorescence Photobleaching Recovery Kinetics. Biophys. J. 16, 1055–1069 (1976)

    Article  Google Scholar 

  13. Crank, J.: The Mathematics of Diffusion. Oxford University Press, Oxford (1976)

    MATH  Google Scholar 

  14. Weickert, J.: Anisotropic Diffusion in Image Processing, Teubner, Stuttgart (1997)

    Google Scholar 

  15. Hedberg, K.K., Chen, L.B.: Absence of intermediate filaments in a human adrenal cortex carcinoma-derived cell line. Exp. Cell Res. 163, 509–517 (1986)

    Article  Google Scholar 

  16. Reits, E.A., Neefjes, J.J.: From fixed to FRAP: measuring protein mobility and activity in living cells. Nat. Cell Biol. 3, E145–E147 (2001)

    Article  Google Scholar 

  17. Bastian, P., Birken, K., Lang, S., Johannsen, K., Neuß, N., Rentz-Reichert, H., Wieners, C.: UG: A flexible software toolbox for solving partial differential equations. Computing and Visualization in Science 1, 27 (1997)

    Article  MATH  Google Scholar 

  18. Nagorni, M., Hell, S.W.: 4Pi-confocal microscopy provides three-dimensional images of the microtubule network with 100- to 150-nm resolution. J. Struct. Biol. 123, 236–247 (1998)

    Article  Google Scholar 

  19. Siggia, E.D., Lippincott-Schwartz, J., Bekiranov, S.: Diffusion in Inhomogenous Media: Theory and Simulation Applied to Whole Cell Photobleach Recovery. Biophys. J. 79, 1761–1770 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Volz, D. et al. (2005). Spatial Modeling and Simulation of Diffusion in Nuclei of Living Cells. In: Danos, V., Schachter, V. (eds) Computational Methods in Systems Biology. CMSB 2004. Lecture Notes in Computer Science(), vol 3082. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25974-9_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-25974-9_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25375-4

  • Online ISBN: 978-3-540-25974-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics