Markovian description of unbiased polymer translocation

We perform, with the help of cloud computing resources, extensive Langevin simulations which provide compelling evidence in favor of a general Markovian framework for unbiased three-dimensional polymer translocation. Our statistical analysis consists of careful evaluations of (i) two-point correlation functions of the translocation coordinate and (ii) the empirical probabilities of complete polymer translocation (taken as a function of the initial number of monomers on a given side of the membrane). We find good agreement with predictions derived from the Markov chain approach recently addressed in the literature by the present authors.     

Single long-polymer translocation through a long pore

This paper theoretically studies the free energy and conformational entropy of a long polymer threading a long nanopore (n₀/N \ge 0.1) on external electric field. The polymer expanded model is built in this paper, that is, a single long polymer chain with N monomers (each of size a) threading a pore with n₀ monomers can be regarded as polymer with N+n_{0} monomers translocating a 2-dimension hole embedded in membrane. A theoretical approach is presented which explicitly takes into account the nucleation theory. Our calculations imply that, the structure of polymer changes more acutely than other situation, while its leading monomer reaches the second vacuum and its end monomer escapes the first vacuum. And it is also shown that the length scale of polymer and pore play a very important role for polymer translocation dynamics. The present model predicts that the translocation time depends on the chemical potential gradient and the property of the solvent on sides of pore to some extent.     

打结高分子链穿孔行为的研究

以三叶草型结(即3₁结)为例,采用分子动力学(MD)方法,研究打结高分子链在外场力作用下穿越微孔的动力学过程.模拟发现,在拉动打结高分子链的过程中,结的大小呈涨落变化,直至最后散结.定性讨论了结的存在对高分子链穿孔速率的影响.在外场力作用下,打结高分子链平均穿孔时间(τ)与链长(N)满足标度关系τ～N ^α,其中标度系数α随外场力f增大而增大.对于短链,外场力越大,平均穿孔时间越短     

Active polymer translocation through flickering pores

Single file translocation of a homopolymer through an active channel under the presence of a driving force is studied using Langevin dynamics simulation. It is shown that a channel with sticky walls and oscillating width could lead to significantly more efficient translocation as compared to a static channel that has a width equal to the mean width of the oscillating pore. The gain in translocation exhibits a strong dependence on the stickiness of the pore, which could allow the polymer translocation process to be highly selective.     

Scaling exponents of forced polymer translocation through a nanopore

We investigate several properties of a translocating homopolymer through a thin pore driven by an external field present inside the pore only using Langevin Dynamics (LD) simulations in three dimensions (3D). Motivated by several recent theoretical and numerical studies that are apparently at odds with each other, we estimate the exponents describing the scaling with chain length (Nof the average translocation time \(\ensuremath \langle\tau\rangle\) , the average velocity of the center of mass \(\ensuremath \langle v_{{\rm CM}}\rangle\) , and the effective radius of gyration \(\ensuremath \langle {R}_g\rangle\) during the translocation process defined as \(\ensuremath \langle\tau\rangle \sim N^{\alpha}\) , \(\ensuremath \langle v_{{\rm CM}} \rangle \sim N^{-\delta}\) , and \(\ensuremath {R}_g \sim N^{\bar{\nu}}\) respectively, and the exponent of the translocation coordinate (s -coordinate) as a function of the translocation time \(\ensuremath \langle s^2(t)\rangle\sim t^{\beta}\) . We find \(\ensuremath \alpha=1.36 \pm 0.01\) , \(\ensuremath \beta=1.60 \pm 0.01\) for \(\ensuremath \langle s^2(t)\rangle\sim \tau^{\beta}\) and \(\ensuremath \bar{\beta}=1.44 \pm 0.02\) for \(\ensuremath \langle\Delta s^2(t)\rangle\sim\tau^{\bar{\beta}}\) , \(\ensuremath \delta=0.81 \pm 0.04\) , and \(\ensuremath \bar{\nu}\simeq\nu=0.59 \pm 0.01\) , where \( \nu\) is the equilibrium Flory exponent in 3D. Therefore, we find that \(\ensuremath \langle\tau\rangle\sim N^{1.36}\) is consistent with the estimate of \(\ensuremath \langle\tau\rangle\sim\langle R_g \rangle/\langle v_{{\rm CM}} \rangle\) . However, as observed previously in Monte Carlo (MC) calculations by Kantor and Kardar (Y. Kantor, M. Kardar, Phys. Rev. E 69, 021806 (2004)) we also find the exponent α = 1.36 ± 0.01 < 1 + ν. Further, we find that the parallel and perpendicular components of the gyration radii, where one considers the “cis” and “trans” parts of the chain separately, exhibit distinct out-of-equilibrium effects. We also discuss the dependence of the effective exponents on the pore geometry for the range of N studied here.     

Molecular Dynamics simulation of a polymer chain translocating through a nanoscopic pore

The detection of linear polymers translocating through a nanoscopic pore is a promising idea for the development of new DNA analysis techniques. However, the physics of constrained macromolecules and the fluid that surrounds them at the nanoscopic scale is still not well understood. In fact, many theoretical models of polymer translocation neglect both excluded-volume and hydrodynamic effects. We use Molecular Dynamics simulations with explicit solvent to study the impact of hydrodynamic interactions on the translocation time of a polymer. The translocation time τ that we examine is the unbiased (no charge on the chain and no driving force) escape time of a polymer that is initially placed halfway through a pore perforated in a monolayer wall. In particular, we look at the effect of increasing the pore radius when only a small number of fluid particles can be located in the pore as the polymer undergoes translocation, and we compare our results to the theoretical predictions of Chuang et al. (Phys. Rev. E 65, 011802 (2001)). We observe that the scaling of the translocation time varies from τ ∼ N ^11/5 to τ ∼ N ^9/5 as the pore size increases (N is the number of monomers that goes up to 31 monomers). However, the scaling of the polymer relaxation time remains consistent with the 9/5 power law for all pore radii.     

Dynamics of polymer translocation through nanopores: theory meets experiment

The dynamics of translocation of polymer molecules through nanopores is investigated via molecular dynamics. We find that an off-lattice minimalist model of the system is sufficient to reproduce quantitatively all the experimentally observed trends and scaling behavior. Specifically, simulations show (i) two translocation regimes depending on the ratio of pore and polymer length, (ii) two different regimes for the probability of translocation depending on applied voltage, (iii) an exponential dependence of translocation velocity upon applied voltage, and (iv) an exponential decrease of the translocation time with temperature. We also propose a simple theoretical explanation of each of the observed trends within a free energy landscape framework.     

Confinement-driven translocation of a flexible polymer

We consider the escape of a flexible, self-avoiding polymer chain out of a confined geometry. By means of simulations, we demonstrate that the translocation time can be described by a simple scaling law that exhibits a nonlinear dependence on the degree of polymerization and that is sensitive to the nature of the confining geometry. These results contradict earlier predictions but are in agreement with recently confirmed geometry-dependent expressions for the free energy of confinement.     

Passage of particle through a cylindrical structure

Phenomena arising during the passage of a particle through a cylindrical structure are considered. The pore formation in a very thin film by the moving of highly charged ions, as well as the enhanced probability of the particle passage through a porous structure, is discussed.     

Passage of a Gaussian Beam through a Gradient Medium

The problem of the passage of a Gaussian laser beam of light through a layer of gradient medium, whose dielectric permeability changes linearly in a direction approximately perpendicular to that of the propagation of the beam, is solved in the paraxial–optics approximation. The center of the beam in this medium propagates along a parabola, its divergence is independent of the parameter of the medium inhomogeneity, while the phase front remains approximately spherical.     

Free energy and scalings for polymer translocation through a nanopore: A molecular dynamics simulation study combined with milestoning

Coarse-grained molecular dynamics simulations combined with milestoning method are used to study the stochastic process of polymer chain translocation though a nanopore. We find that the scalings for polymer translocation process (the chain is initialized with the first monomer in the nanopore) and for polymer escape process (the chain is initialized with the middle monomer in the nanopore) are different. The translocation process is mainly controlled by the entropic barrier, while the polymer escape process is driven by the effective force due to free energy difference.     

Translocation of knotted proteins through a pore

We report the results of molecular dynamics simulations of translocation of knotted proteins through pores. The protein is pulled into the pore with a constant force, which in many cases leads to the tightening of the knot. Since the radius of tightened knot is larger than that of the pore opening, the tight knot can block the pore thus preventing further translocation of the chain. Analyzing six different proteins, we show that the stuck probability increases with the applied force and that final positions of the tightened knot along the protein backbone are not random but are usually associated with sharp turns in the polypeptide chain. The combined effect of the confining geometry of the pore and the inhomogeneous character of the protein chain leads thus to the appearance of topological traps, which can immobilize the knot and lead to the jamming of the pore.     

Passage of a high-current relativistic electron beam through matter

A solution is presented for the problem of passage of a high-current relativistic electron beam through matter in the stationary case with one-dimensional geometry. The system of equations describing the passage of the beam consists of the kinetic equation for fast electrons, which considers the effect of the electric field on the magnitude and direction of particle momentum, the equations for the field produced by the space charge generated by thermalized electrons, and relations connecting the conductivity of the medium to the radiation field. Higher-order perturbation theory is used for the solution. The solutions reveal that the distribution of expended energy, thermalized electrons, and other properties of the flow are highly dependent on the density of the incident flux and the conductivity of the medium. It will be shown that linear transfer theory may be applied to calculation of the passage of high-current beams through matter over a wide range of currents and conductivities, if the barrier thickness does not exceed one-half the path length, but cannot be used for calculation of passage through large-thickness barriers, i.e., with thickness comparable to the electron free path length.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 67–74, September, 1979.The author thanks A. N. Didenko and A. M. Kol'chuzhkin for their evaluation of the study.     

Non-equilibrium effects in chaperone-assisted translocation of a stiff polymer

Chaperone-assisted biopolymer translocation is the main model proposed for translocation in vivo. A dynamical Monte Carlo method is used to simulate the translocation of a stiff homopolymer through a nanopore driven by chaperones. Chaperones are proteins that bind to the polymer near the wall and prevent its backsliding through Cis side. The important parameters include binding energy, size and the local concentration of the chaperones. The profile of these local concentrations, build up the chaperones distribution. Here we investigate the effects of binding energy, size and the exponential distribution of chaperones in their equilibration in each step of the polymer translocation needed for stable translocation time. The simulation results show that in case of chaperones with the size of a monomer ($\lambda =1$) and/or positive effective binding energy and/or uniform distribution, the chaperones binding equilibration rate/frequency is less than 5 times per monomer. However, in some special cases in the exponential distribution of chaperones with size $\lambda >1$ and negative effective binding energy the equilibration rate will diverge to more than 20 times per monomer. We show that this non-equilibrium effect results in supper diffusion, seen before. Moreover, we confirm the equilibration process theoretically.