Abstract
We present a theoretical description of the dynamics of a semi-flexible polymer being pulled through a nanopore by an external force acting at the pore. Our theory is based on the tensile blob picture of Pincus in which the front of the tensile force propagates through the backbone of the polymer, as suggested by Sakaue and recently applied to study a completely flexible polymer with self-avoidance, by Dubbledam et al. For a semi-flexible polymer with a persistence length P, its statistics is self-avoiding for a very long chain. As the local force increases, the blob size starts to decrease. At the blob size \(P^{2}/a\), where a is the size of a monomer, the statistics becomes that of an ideal chain. As the blob size further decreases to below the persistence length P, the statistics is that of a rigid rod. We argue that semi-flexible polymer in translocation should include the three regions: a self-avoiding region, an ideal chain region and a rigid rod region, under uneven tension propagation, instead of a uniform scaling picture as in the case of a completely flexible polymer. In various regimes under the effect of weak, intermediate and strong driving forces we derive equations from which we can calculate the translocation time of the polymer. The translocation exponent is given by \(\alpha =1+\mu \), where \(\mu \) is an effective exponent for the end-to-end distance of the semi-flexible polymer, having a value between 1/2 and 3/5, depending on the total contour length of the polymer. Our results are of relevance for forced translocation of biological polymers such as DNA through a nanopore.
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Ikonen, T., Bhattacharya, A., Ala-Nissila, T., Sung, W.: Unifying model of driven polymer translocation. Phys. Rev. E 85, 051803 (2012)
Palyulin, V.V., Ala-Nissila, T., Metzler, Ralf: Polymer translocation: the first two decades and the recent diversification. Soft Matter 10, 9016 (2014)
Panja, D., Barkema, G.T., Kolomeisky, A.B.: Through the eye of the needle: recent advances in understanding biopolymer translocation. J. Phys. Condens. Matter 25, 413101 (2013)
Luo, K., Ala-Nissila, T., Ying, S.-C., Metzler, R.: Driven polymer translocation through nanopores: slow-vs.-fast dynamics. Europhys. Lett. 88, 68006 (2009)
Dreiseikelmann, B.: Translocation of DNA across bacterial membranes. Microbiol. Rev. 58, 293–316 (1994)
Hanss, B., Leal-Pinto, E., Bruggeman, L.A., Copeland, T.D., Klotman, P.E.: Identification and characterization of a cell membrane nucleic acid channel. Proc. Natl. Acad. Sci. USA 95, 1921–1926 (1998)
Citovsky, V., Zambryski, P.: Transport of nucleic acids through membrane channels: snaking through small holes. Annu. Rev. Microbiol. 47, 167–197 (1993)
Kasianowicz, J., Brandin, E., Branton, D., Deamer, D.W.: Characterization of individual polynucleotide molecules using a membrane channel. Proc. Natl. Acad. Sci. USA 93, 13770–13773 (1996)
Kasianowicz, J., Bezrukov, S.M.: Protonation dynamics of the alpha-Toxin ion channel from spectral analysis of pH-dependent current fluctuations. Biophys. J. 69, 94–105 (1995)
Szabo, I., Bathori, G., Tombola, F., Brini, M., Coppola, A., Zoratti, M.: DNA translocation across planar bilayers containing Bacillus subtilis ion channels. J. Biol. Chem. 272, 25275–25282 (1997)
Szabo, I., Bathori, G., Tombola, F., Coppola, A., Schmehl, I., Brini, M., Ghazi, A., De Pinto, V., Zoratti, M.: Double-stranded DNA can be translocated across a planar membrane containing purified itochondrial porin. FASEB J. 12, 495–502 (1998)
Lubensky, D.K., Nelson, D.R.: Driven polymer translocation through a narrow pore. Biophys. J. 77, 1824–1838 (1999)
Kantor, Y., Kardar, M.: Anomalous dynamics of forced translocation. Phys. Rev. E 69, 021806 (2004)
de Gennes, P.G.: Scaling Concepts in Polymer Physics. Cornell University Press, Ithaca (1979)
Doi, M., Edwards, S.F.: The Theory of Polymer Dynamics. Clarendon, Oxford (1986)
Dubbeldam, J.L.A., Rostiashvili, V.G., Milchev, A., Vilgis, T.A.: Driven translocation of a polymer: role of pore friction and crowding. J. Chem. Phys. 141, 124112 (2014)
Sakaue, T.: Sucking genes into pores: insight into driven translocation. Phys. Rev. E 81, 041808 (2010)
Saito, T., Sakaue, T.: Dynamical diagram and scaling in polymer driven translocation. Eur. Phys. J. E 34, 135 (2011)
Saito, T., Sakaue, T.: Process time distribution of driven polymer transport. Phys. Rev. E 85, 061803 (2012)
Dubbeldam, J.L.A., Rostiashvili, V.G., Milchev, A., Vilgis, T.A.: Forced translocation of a polymer: dynamical scaling versus molecular dynamics simulation. Phys. Rev. E 85, 041801 (2012)
Rowghanian, P., Grosberg, A.Y.: Force-driven polymer translocation through a nanopore: an old problem revisited. J. Phys. Chem. B 115, 14127 (2011)
Hsu, H.-P., Paul, W., Binder, K.: Scattering function of semiflexible polymer chains under good solvent conditions. J. Chem. Phys. 137, 174902 (2012)
Hsu, H.-P., Binder, K.: Stretching semiflexible polymer chains: evidence for the importance of excluded volume effets from Monte Carlo simulation. J. Chem. Phys. 136, 024901 (2012)
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Lam, PM., Zhen, Y. Dynamic Scaling Theory of the Forced Translocation of a Semi-flexible Polymer Through a Nanopore. J Stat Phys 161, 197–209 (2015). https://doi.org/10.1007/s10955-015-1322-x
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DOI: https://doi.org/10.1007/s10955-015-1322-x