scispace - formally typeset
Search or ask a question
Journal ArticleDOI

Kink motion in the barrier crossing of a chain molecule

01 Mar 2000-Physical Review E (American Institute of Physics)-Vol. 61, Iss: 3, pp 3245-3248
TL;DR: In this article, the authors considered the activated escape of a chain molecule of N segments over a barrier, a generalization of the classic Kramers problem, and showed that the free energy of activation has a square root dependence on the temperature T, leading to a nonArrhenius form for the rate.
Abstract: We consider the activated escape of chain molecule of N segments over a barrier, a generalization of the classic Kramers problem. Using the Rouse model, we show that the free energy of activation has a square root dependence on the temperature T, leading to a non-Arrhenius form for the rate. We further show that there is a special time dependent solution of the model, which corresponds to a kink in the chain, confined to the region of the barrier. The polymer goes from one side to the other by the motion of the kink in the reverse direction.If there is no free energy difference between the two sides of the barrier, then the kink moves by diffusion and the time of crossing $t_{cross} ~ N^2 /T^{3/2}$. If there is a free energy difference, then the kink moves with a nonzero velocity from the lower free energy side to the other, leading to $t_{cross}~N/\sqrt{T}$.
Citations
More filters
Journal ArticleDOI
TL;DR: The current state of applications of pore-forming peptides and proteins in nanomedicine, sensing, and nanoelectronics is reviewed.

315 citations

Journal ArticleDOI
TL;DR: This review of nanometer-scale nanopores surveys this field of research and discusses the prospects for advances that could be made in the near future.
Abstract: There are thousands of different nanometer-scale pores in biology, many of which act as sensors for specific chemical agents. Recent work suggests that protein and solid-state nanopores have many potential uses in a wide variety of analytical applications. In this review we survey this field of research and discuss the prospects for advances that could be made in the near future.

292 citations

Journal ArticleDOI
TL;DR: It is found that for such a molecule, the transition state resembles a hook, and this is in agreement with presently accepted view in cell biology.
Abstract: We consider a long chain molecule, initially confined to the metastable side of a biased double well potential. It can escape from this side to the other by the motion of its N segments across the barrier. We assume that the length of the molecule is much larger than the width w of the barrier. The width w is taken to be sufficiently large that a continuum description is applicable to even the portion over the barrier. We use the Rouse model and analyze the mechanism of crossing the barrier. There can be two dominant mechanisms: end crossing and hairpin crossing. We find the free energy of activation for the hairpin crossing to be two times that for end crossing. The pre-exponential factor for hairpin crossing is proportional to N, while it is independent of N for end crossing. In both cases, the activation energy has a square root dependence on the temperature T, leading to a non-Arrhenius form for the rate. We also show that there is a special time dependent solution of the model, which corresponds to a kink in the chain, confined to the region of the barrier. The movement of the polymer from one side to the other is equivalent to the motion of the kink on the chain in the reverse direction. If there is no free energy difference between the two sides of the barrier, then the kink moves by diffusion and the time of crossing ${t}_{\mathrm{cross}}\ensuremath{\sim}{N}^{2}{/T}^{3/2}.$ If there is a free energy difference, then the kink moves with a nonzero velocity from the lower free energy side to the other, leading to ${t}_{\mathrm{cross}}\ensuremath{\sim}N/\sqrt{T}.$ We also discuss the applicability of the mechanism to the recent experiments of Kasianowicz [Proc. Natl. Acad. Sci. USA 93, 13 770 (1996)], where DNA molecules were driven through a nanopore by the application of an electric field. The prediction that ${t}_{\mathrm{cross}}\ensuremath{\sim}N$ is in agreement with these experiments. Our results are in agreement with the recent experimental observations of Han, Turner, and Craighead [Phys. Rev. Lett. 83, 1688 (1999)]. We also consider the translocation of hydrophilic polypeptides across hydrophobic pores, a process that is quite common in biological systems. Biological systems accomplish this by having a hydrophobic signal sequence at the end that goes in first. We find that for such a molecule, the transition state resembles a hook, and this is in agreement with presently accepted view in cell biology.

85 citations

Journal ArticleDOI
TL;DR: This review takes a look at the progress of the field over the last 3 years using the glasses of the theoretical scientist and focusing mostly on new ideas and concepts, and sees a clear trend towards proteomics and microfluidic devices.
Abstract: Over the last two decades, the introduction of new methods such as pulsed-field gel electrophoresis and capillary array electrophoresis has made it possible to map and sequence entire genomes, including our own The development of these experimental methods has been helped by the progress of theoretical and computational sciences, and the interactions between these three modi operandi of modern science are still pushing the limits of our technologies We now see a clear trend towards proteomics and microfluidic (even nanofluidic!) devices In this review, we take a look at the progress of the field over the last 3 years using the glasses of the theoretical scientist and focusing mostly on new ideas and concepts About a dozen different subfields are discussed and reviewed We conclude by giving a commented list of some of the best review articles published over the last 2-3 years

66 citations

Journal ArticleDOI
TL;DR: Brownian dynamics simulations are used to characterize the time scales involved in polymer electrophoresis through narrow constrictions, where the polymer is modeled as a freely jointed bead−rod chain with a total charge distributed uniformly among the beads.
Abstract: Brownian dynamics simulations are used to characterize the time scales involved in polymer electrophoresis through narrow constrictions. The polymer is modeled as a freely jointed bead−rod chain with a total charge distributed uniformly among the beads. The narrow constriction is a thin channel with height hs < Rg which separates two thicker channels, both of height hl ∼ Rg where Rg is the polymer radius of gyration. The polymer is initially placed in a thick channel, and an applied electric field drives it into the next thick channel through the intervening narrow constriction. We find that the electrophoresis of the polymer is characterized by three time scales, each of which depends on the polymer chain length, N. An approach time, τapp, describes the motion of the polymer to the entrance of the thin channel. Upon reaching the entrance of the thin channel, the polymer is entropically trapped, and its escape from the trap is associated with an activation time, τact. After the activation event, the motio...

56 citations