Skip to main content
Log in

Effects of Non-Uniform Occupancy on Selective Transport Through Nanochannels

  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

By using an exclusion model, in this work we address how the non-uniform occupancy of a nanochannel, for a limited set of conditions, is related to the transport of specific molecules through it. The results show that the shape of a channel greatly influences its transporting behavior and therefore, it can be used as a tunable parameter to achieve a desired set of transporting conditions. In particular, we have found that for applications which require a highly selective channel that is able to handle large input fluxes of specific particles in both directions, a double-funnel architecture is the best suited. As the obtained results mainly arise from the competition of particles for limited space, we expect them to be applicable to a great variety of transporting phenomena where the channel has a limited number of interacting sites with the transported particles.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Zilman, A., Pearson, J., Bel, G.: Effects of jamming on nonequilibrium transport times in nanochannels. Phys. Rev. Lett. 103(12), 128103 (2009)

    Article  ADS  Google Scholar 

  2. Martin, C.R.: Nanomaterials: a membrane-based synthetic approach science. Science 266, 1961–1966 (1994)

    Article  ADS  Google Scholar 

  3. Kohli, P., Harrell, C.C., Cao, Z., Gasparac, R., Tan, W., Martin, C.R.: DNA functionalized nanotube membranes with single-base mismatch selectivity. Science 305, 984–986 (2004)

    Article  ADS  Google Scholar 

  4. Jovanovic-Talisman, T., Tetenbaum-Novatt, J., McKenney, A.S., Zilman, A., Peters, R., Rout, M.P., Chait, B.T.: Artificial nanopores that mimic the transport selectivity of the nuclear pore complex. Nature 457(7232), 1023–7 (2009)

    Article  ADS  Google Scholar 

  5. Huh, D., Mills, K.L., Zhu, X., Burns, M.A., Thouless, M.D., Takayama, S.: Tuneable elastomeric nanochannels for nanofluidic manipulation. Nat Mater 6(6), 424–428 (2007)

    Article  ADS  Google Scholar 

  6. Li, W., Bell, N.A.W., Hernández-Aisa, S., Thacker, V.V., Thacray, A.M., Bujdoso, R., Keyser, U.F.: Single protein molecule detection by glass nanopores. ACS Nano 7(5), 4129–4134 (2013)

    Article  Google Scholar 

  7. Alberts, B., Johnson, A., Lewis, J., Raff, M., Roberts, K., Walter, P.: Molecular biology of the cell, 5th edn. Garland Science, New York (2008)

    Google Scholar 

  8. Zilman, A., Di Talia, S., Chait, B.T., Rout, M.P., Magnasco, M.O.: Efficiency, selectivity, and robustness of nucleocytoplasmic transport. PLoS Comput. Biol. 3(7), 1281–1290 (2007)

    Article  Google Scholar 

  9. Berezhkovskii, A.M., Pustovoit, M.A., Bezrukov, S.M.: Channel-facilitated membrane transport: transit probability and interaction with the channel. J. Chem. Phys. 116(22), 9952–9956 (2002)

    Article  ADS  Google Scholar 

  10. Dagdug, L., Berezhkovskii, A.M., Bezrukov, S.M.: Particle lifetime in cylindrical cavity with absorbing spot on the wall: going beyond the narrow escape problem. J. Chem. Phys. 137(23), 234108 (2012)

    Article  ADS  Google Scholar 

  11. Kolomeisky, A.B., Uppulury, K.: How interactions control molecular transport in channels. J. Stat. Phys. 142, 1268–1276 (2011)

    Article  ADS  MATH  Google Scholar 

  12. Kolomeisky, A.B., Kotsev, S.: Effect of interactions on molecular fluxes and fluctuations in the transport across membrane channels. J. Chem. Phys. 128(8), 085101 (2008)

    Article  ADS  Google Scholar 

  13. Klumpp, S., Hwa, T.: Stochasticity and traffic jams in the transcription of ribosomal RNA: Intriguing role of termination and antitermination. Proc. Natl. Acad. Sci. 105(47), 18159–18164 (2008)

    Article  ADS  Google Scholar 

  14. Kosinska, I.D., Goychuk, I.: Rectification in synthetic conical nanopores: a one-dimensional Poisson–Nernst–Planck model. Phy. Rev. E 77(3), 031131 (2008)

    Article  ADS  Google Scholar 

  15. Berezhkovskii, A.M., Pustovoit, M.A., Bezrukov, S.M.: Diffusion in a tube of varying cross section: numerical study of reduction to effective one-dimensional description. J. Chem. Phys. 126(13), 134706 (2007)

    Article  ADS  Google Scholar 

  16. Berezhkovskii, A.M., Pustovoit, M.A., Bezrukov, S.M.: Fluxes of non-interacting and strongly repelling particles through a single conical channel: analytical results and their numerical tests. Chem. Phys. 375(2–3), 523–528 (2010)

    Article  ADS  Google Scholar 

  17. Dagdug, L., Berezhkovskii, A.M., Makhnovskii, Y.A., Zitserman, VYu., Bezrukov, S.M.: Force-dependent mobility and entropic rectification in tubes of periodically varying geometry. J. Chem. Phys. 136(21), 214110 (2012)

    Article  ADS  Google Scholar 

  18. Carrillo-Tripp, M., Saint-Martin, H., Ortega-Blake, I.: Minimalist molecular model for nanopore selectivity. Phys. Rev. Lett. 93(16), 1–4 (2004)

    Article  Google Scholar 

  19. Carrillo-Tripp, M., San-Román, M.L., Hernández-Cobos, J., Saint-Martin, H., Ortega-Blake, I.: Ion hydration in nanopores and the molecular basis of selectivity. Biophys. Chem. 124(3), 243–50 (2006)

    Article  Google Scholar 

  20. Gouaux, E., Mackinnon, R.: Principles of selective ion transport in channels and pumps. Science 310(5753), 1461–1465 (2005)

    Article  ADS  Google Scholar 

  21. Zilman, A., Bel, G.: Crowding effects in non-equilibrium transport through nano-channels. J. Phys. Condens. Mater. 22(45), 454130 (2010)

    Article  ADS  Google Scholar 

  22. Chou, T.: How fast do fluids squeeze through microscopic single-file pores? Phy. Rev. Lett. 80(1), 85–88 (1998)

    Article  ADS  Google Scholar 

  23. Derrida, B., Domany, E., Mukamel, D.: An exact solution of a one-dimensional asymmetric exclusion model with open boundaries. J. Stat. Phys. 69(3–4), 667–687 (1992)

    Article  ADS  MATH  MathSciNet  Google Scholar 

  24. Schadschneider, A., Chowdhury, D., Nishinari, K.: Stochastic Transport in Complex Systems. Elsevier, Amsterdam (2011)

    MATH  Google Scholar 

  25. Hanggi, P., Marchesoni, F.: Artificial Brownian motors: controlling transport on the nanoscale. Rev. Mod. Phys. 81, 387 (2009)

    Article  ADS  Google Scholar 

  26. Zilman, A.: Effects of multiple occupancy and interparticle interactions on selective transport through narrow channels: theory versus experiment. Biophys. J. 96(4), 1235–48 (2009)

    Article  ADS  Google Scholar 

  27. Zilman, A., Di Talia, S., Jovanovic-Talisman, T., Chait, B.T., Rout, M.P., Magnasco, M.O.: Enhancement of transport selectivity through nano-channels by non-specific competition. PLoS Comput. Biol. 6(6), e1000804 (2010)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work was supported by UNAM-DGAPA-PAPIIT IN106714. H.T. acknowledges the scholarship from CONACyT (Mexico). Computing resources from the Supercomputing Department of DGTIC-UNAM were given through project SC14-1-I-49.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Luis A. Pérez.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Terborg, H., Pérez, L.A. Effects of Non-Uniform Occupancy on Selective Transport Through Nanochannels. J Stat Phys 158, 494–512 (2015). https://doi.org/10.1007/s10955-014-1132-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10955-014-1132-6

Keywords

Navigation