| Passage Times for Polymer Translocation Pulled through a Narrow Pore Biophysical Journal, Volume 94, Issue 5, 1 March 2008, Pages 1630-1637 Debabrata Panja and Gerard T. Barkema Abstract We study the passage times of a translocating polymer of length in three dimensions, while it is pulled through a narrow pore with a constant force applied to one end of the polymer. At small to moderate forces, satisfying the condition /≲1, where ≈0.588 is the Flory exponent for the polymer, we find that , the mean time the polymer takes to leave the pore, scales as independent of , in agreement with our earlier result for =0. At strong forces, i.e., for, /≫1, the behavior of the passage time crosses over to ∼/. We show here that these behaviors stem from the polymer dynamics at the immediate vicinity of the pore—in particular, the memory effects in the polymer chain tension imbalance across the pore. Abstract | Full Text | PDF (196 kb) |
| Scaling Theory of Polymer Translocation into Confined Regions Biophysical Journal, Volume 95, Issue 8, 15 October 2008, Pages 3619-3627 Chiu Tai Andrew Wong and Murugappan Muthukumar Abstract We examine the voltage-driven polymer translocation from a spacious region into a confined region imposed by two parallel planes, so that the entry is impeded by the entropic confinement but aided by the electric field inside the confined region. Two modes of entry are examined: linear translocation where a chain enters the confined region with chain ends, and hairpin translocation where a chain enters the confined region by forming a hairpin. Our calculation shows that translocation time increases with polymer length for linear entries but decreases with polymer length for hairpin entries. Applying to electrophoresis of DNA molecules through periodic spacious and confined regions, our theory shows that the dominance of hairpin translocations leads to the experimentally observed faster migration of longer DNA molecules. Our theory predicts experimental conditions for the validity of this law in terms of polymer length, size of the confined region, and solution conditions. Abstract | Full Text | PDF (212 kb) |
| Nonexponential Kinetics of DNA Escape from α-Hemolysin Nanopores Biophysical Journal, Volume 95, Issue 11, 1 December 2008, Pages 5317-5323 Matthew Wiggin, Carolina Tropini, Vincent Tabard-Cossa, Nahid N. Jetha and Andre Marziali Abstract Throughput and resolution of DNA sequence detection technologies employing nanometer scale pores hinge on accurate kinetic descriptions of DNA motion in nanopores. We present the first detailed experimental study of DNA escape kinetics from -hemolysin nanopores and show that anomalously long escape times for some events result in nonexponential kinetics. From the distribution of first-passage times, we determine that the energy barrier to escape follows a Poisson-like distribution, most likely due to stochastic weak binding events between the DNA and amino acid residues in the pore. Abstract | Full Text | PDF (282 kb) |
Copyright © 2008 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 94, Issue 5, 1547-1548, 1 March 2008
doi:10.1529/biophysj.107.122770
New and Notable
Department of Chemistry, Rice University, Houston, Texas
Address reprint requests to Anatoly B. Kolomeisky, Tel.: 713-348-5672.Many biological processes, such as DNA and RNA transport across nuclear pores, injections of viral DNA, gene swapping, and protein transport across cellular membranes, involve the motion of polymer molecules across narrow channels 1. Translocation through nanopores is also one of the most important and powerful methods for analyzing properties of single biopolymer molecules and for investigating different biophysical phenomena 2,3. The polymer translocation is generally viewed as an effective one-dimensionally activated process that involves overcoming the entropic barriers. These barriers appear due to the decrease in the number of available polymer configurations in the translocating molecule in comparison with the free polymers. External fields and chemical interactions significantly accelerate transport across the channels. In biological systems, the motion of DNA, RNA, and proteins through the pores is assisted by specific chemical interactions with membranes or other molecules 1. In experiments, charged polymer molecules are driven through nanopores with the help of electric fields 2,4.
The polymer translocation is well-studied experimentally using biological channels (α-hemolysin proteins) and solid-state synthetic nanopores. However, theoretical understanding of the transport mechanism of polymer molecules is still limited. The situation is especially controversial when external fields are weak and the translocation dynamics is mainly controlled by entropic factors. Phenomenological theories, which assume that during the translocation, the polymer quickly relaxes to an equilibrium state 5,6, predict that in this regime, the mean translocation time τ is a function of the polymer's size N, which is τ ∝ Nα with α=2. However, this result s unphysical 7, since the translocating polymer chain cannot move faster than the free polymer, which has a relaxation time of ∼τ ∝ N1+2ν, where ν ≈ 0.59 is an exponent for real polymers in three-dimensional systems 7,8. It was suggested that the mean translocation time-scales exactly as τ ∝ N1+2ν, which corresponds to neglecting polymer-pore interactions 7. It was also argued that the polymer translocation shows anomalous dynamic behavior 9, although the origin of this phenomenon was not explained. Since the weak forces regime is not easily accessible experimentally, extensive Monte Carlo computer simulations have been performed 8,9. But the results of computer studies led to more confusion, yielding values of the exponent α that are between 2.18 and 2.59, and underscoring the complexity of polymer translocation processes. An article by Panja and Barkema in this issue of Biophysical Journal provides a comprehensive theoretical description of mechanisms of driven polymer translocation, and it is supported by high-precision, extensive Monte Carlo computer simulations.
A theoretical model by Panja and Barkema focuses on dynamics of polymer segments at the immediate vicinity of the pore. Entry of a monomer into the channel or moving out of the pore affects the chain tension, which leads to an adjustment of the translocation velocity as well. However, the change in the tension is not instantaneous, and there is some delay in the response for the translocation velocity. This leads to an important observation that memory effects are critical for polymer translocation. The delay is determined by the properties of a polymer chain near the hard wall, and it is shown that for weak forces, the Rouse time
and for large forces, the time
separates regimes of anomalous translocation dynamics and simple diffusive behavior. Theoretical calculations also show that the mean translocation times for weak forces scales as
as a function of the polymer length, while for large external forces F, the dependence is
.The most striking result of this work is the fact that translocation velocity is not a constant, and it generally depends on time as a direct consequence of the dynamics of polymer segments near the pore.
Although the theoretical picture of polymers threading through pores presented by Panja and Barkema provides a significant advancement in our understanding mechanisms of translocation, it still leaves many questions unanswered. The theoretical analysis has been performed for a local application of the external force at one of the polymer ends. In cells, chemical interactions that assist in the polymer moving across the channels are typically localized in or near the membrane pores. In experiments, the external fields influence many monomers inside and around the pore. External forces might also change significantly the distribution of polymer segments near the pore. Probably, the most important question is related to the effect of hydrodynamic forces and interactions during the polymer translocation. It is not at all clear how hydrodynamics might affect memory. Another question is what the mechanisms of translocation are when the polymer moves through the channel not like a single linear chain but in a folded configuration 10. The work by Panja and Barkema presents an excellent example of how complex biophysical processes can be analyzed via a combination of theoretical and computational approaches that provide guidance for future experiments.
1 (2000). Molecular Cell Biology. 4th Ed., (New York: W.H. Freeman and Company). PubMed
2 (2003). Dynamics of polynucleotide transport through nanometer-scale pores. J. Phys. Condens. Matter. 15, R581–R607. PubMed
3 (2007). Direct measurement of the dissociation kinetics of Escherichia coli exonuclease I from single stranded DNA using a nanopore. Nat. Methods. 4, 315–317. PubMed
4 (2005). Stretching DNA using the electric field in a synthetic nanopore. Nano Lett. 5, 1883. CrossRef | PubMed
5 (1999). Polymer translocation through a hole. J. Chem. Phys. 111, 10371–10374. CrossRef | PubMed
6 (2003). Polymer translocation through a long nanopore. J. Chem. Phys. 118, 7112–7118. CrossRef | PubMed
7 (2001). Anomalous dynamics of translocation. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65, 011802. PubMed
8 (2004). Polymer translocation through a nanopore induced by adsorption: Monte Carlo simulation of a coarse-grained model. J. Chem. Phys. 121, 6042–6051. CrossRef | PubMed
9 (2007). Driven polymer translocation through a nanopore: a manifestation of anomalous diffusion. Europhys. Lett. 79, 18002. PubMed
10 (2007). Langevin dynamics simulations of ds-DNA translocation through synthetic nanopores. J. Chem. Phys. 127, 015102. CrossRef | PubMed