A MATHEMATICAL MODEL FOR THE ENHANCED CYTOPLASMIC TRANSPORT - How to Get (Faster) to the Nucleus

Luna Dimitrio, Roberto Natalini, Luciano Milanesi

2011

Abstract

We consider a simple model for signal transport in the cytoplasm. Following some recent experimental evidences, the standard diffusion model is supplemented by advection operated through an attachement/detachement mechanism along microtubules. This model is given by a system of partial differential equations which are cast in different dimensions and connected by suitable exchange rules. A numerical scheme is introduced and some simulations are presented and discussed to show the performances of our model.

References

  1. Agutter, P. S., Malone, P. C., and Wheatley, D. N. (1995). Intracellular transport mechanisms: a critique of diffusion theory. J Theor Biol, 176(2):261-272.
  2. Briani, M., Natalini, R., and Russo, G. (2007). Implicitexplicit numerical schemes for jump-diffusion processes. Calcolo, 44:33-57.
  3. Campbell, E. M. and Hope, T. J. (2003). Role of the cytoskeleton in nuclear import. Adv Drug Deliv Rev, 55(6):761-771.
  4. Cangiani, A. and Natalini, R. (2010). A spatial model of cellular molecular trafficking including active transport along microtubules. J Theor Biol.
  5. Dinh, A.-T., Theofanous, T., and Mitragotri, S. (2007). Modeling of pattern regulation in melanophores. J Theor Biol, 244(1):141-153.
  6. Giannakakou, P., Nakano, M., Nicolaou, K. C., O'Brate, A., Yu, J., Blagosklonny, M. V., Greber, U. F., and Fojo, T. (2002). Enhanced microtubule-dependent trafficking and p53 nuclear accumulation by suppression of microtubule dynamics. Proc Natl Acad Sci U S A, 99(16):10855-10860.
  7. Gong, X., Ming, X., Deng, P., and Jiang, Y. (2010). Mechanisms regulating the nuclear translocation of p38 map kinase. J Cell Biochem.
  8. Kholodenko, B. N. (2009). Spatially distributed cell signalling. FEBS Lett, 583(24):4006-4012.
  9. Lam, M. H. C., Thomas, R. J., Loveland, K. L., Schilders, S., Gu, M., Martin, T. J., Gillespie, M. T., and Jans, D. A. (2002). Nuclear transport of parathyroid hormone (pth)-related protein is dependent on microtubules. Mol Endocrinol, 16(2):390-401.
  10. Mallik, R., Petrov, D., Lex, S. A., King, S. J., and Gross, S. P. (2005). Building complexity: an in vitro study of cytoplasmic dynein with in vivo implications. Curr Biol, 15(23):2075-2085.
  11. Nan, X., Sims, P. A., Chen, P., and Xie, X. S. (2005). Observation of individual microtubule motor steps in living cells with endocytosed quantum dots. J Phys Chem B, 109(51):24220-24224.
  12. Nédélec, F., Surrey, T., and Maggs, A. C. (2001). Dynamic concentration of motors in microtubule arrays. Phys. Rev. Lett., 86(14):3192-3195.
  13. Passerini, T., Luca, M. D., Formaggia, L., Quarteroni, A., and Veneziani, A. (2009). A 3d/1d geometrical multiscale model of cerebral vasculature. Journal of Engineering Mathematics, 64:319-330.
  14. Roe, P. (1981). Approximate riemann solver, parameter vectors, and difference schemes. J. Comp. Phys., 43:357-372.
  15. Roth, D. M., Moseley, G. W., Glover, D., Pouton, C. W., and Jans, D. A. (2007). A microtubule-facilitated nuclear import pathway for cancer regulatory proteins. Traffic, 8(6):673-686.
  16. Salman, H., Abu-Arish, A., Oliel, S., Loyter, A., Klafter, J., Granek, R., and Elbaum, M. (2005). Nuclear localization signal peptides induce molecular delivery along microtubules. Biophys J, 89(3):2134-2145.
  17. Smith, D. A. and Simmons, R. M. (2001). Models of motorassisted transport of intracellular particles. Biophys J, 80(1):45-68.
  18. Sweby, P. K. (1984). High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal., 21(5):995-1011.
  19. Sweeby, P. (1984). High resolution schemes using fluxlimiters for hyperbolic conservation laws. SIAM J. Num. Anal., 21:995-1011.
  20. Wagstaff, K. M. and Jans, D. A. (2009). Importins and beyond: non-conventional nuclear transport mechanisms. Traffic, 10(9):1188-1198.
Download


Paper Citation


in Harvard Style

Dimitrio L., Natalini R. and Milanesi L. (2011). A MATHEMATICAL MODEL FOR THE ENHANCED CYTOPLASMIC TRANSPORT - How to Get (Faster) to the Nucleus . In Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms - Volume 1: BIOINFORMATICS, (BIOSTEC 2011) ISBN 978-989-8425-36-2, pages 39-46. DOI: 10.5220/0003135700390046


in Bibtex Style

@conference{bioinformatics11,
author={Luna Dimitrio and Roberto Natalini and Luciano Milanesi},
title={A MATHEMATICAL MODEL FOR THE ENHANCED CYTOPLASMIC TRANSPORT - How to Get (Faster) to the Nucleus},
booktitle={Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms - Volume 1: BIOINFORMATICS, (BIOSTEC 2011)},
year={2011},
pages={39-46},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0003135700390046},
isbn={978-989-8425-36-2},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Bioinformatics Models, Methods and Algorithms - Volume 1: BIOINFORMATICS, (BIOSTEC 2011)
TI - A MATHEMATICAL MODEL FOR THE ENHANCED CYTOPLASMIC TRANSPORT - How to Get (Faster) to the Nucleus
SN - 978-989-8425-36-2
AU - Dimitrio L.
AU - Natalini R.
AU - Milanesi L.
PY - 2011
SP - 39
EP - 46
DO - 10.5220/0003135700390046