Translocation of closed polymers through a nanopore under an applied external field

The dynamic behaviours of the translocations of closed circular polymers and closed knotted polymers through a nanopore, under the driving of an applied field, are studied by three-dimensional Langevin dynamics simulations. The power-law scaling of the translocation time τ with the chain length N and the distribution of translocation time are investigated separately. For closed circular polymers, a crossover scaling of translocation time with chain length is found to be τ～ N α , with the exponent α varying from α = 0.71 for relatively short chains to α = 1.29 for longer chains under driving force F = 5. The scaling behaviour for longer chains is in good agreement with experimental results, in which the exponent α = 1.27 for the translocation of double-strand DNA. The distribution of translocation time D(τ) is close to a Gaussian function for duration time τ < τ p and follows a falling exponential function for duration time τ > τ p . For closed knotted polymers, the scaling exponent α is 1.27 for small field force (F = 5) and 1.38 for large field force (F = 10). The distribution of translocation time D(τ) remarkably features two peaks appearing in the case of large driving force. The interesting result of multiple peaks can conduce to the understanding of the influence of the number of strands of polymers in the pore at the same time on translocation dynamic process and scaling property.     

Translocation of polymers in a lattice model

Voltage-driven polymer translocation is studied by means of a stochastic lattice model. The model incorporates voltage drop over the membrane as a bias in the hopping rate through the pore and exhibits the two main ingredients of the translocation process: driven motion through the pore and diffusive supply of chain length towards the pore on the cis-side and the drift away from the pore on the trans-side. The translocation time is either bias limited or diffusion limited. In the bias-limited regime the translocation time is inversely proportional to the voltage drop over the membrane. In the diffusion-limited regime the translocation time is independent of the applied voltage, but it is rather sensitive to the motion rules of the model. We find that the whole regime is well described by a single curve determined by the initial slope and the saturation value. The dependence of these parameters on the length of the chain, the motion rules and the repton statistics are established. Repulsion of reptons as well as the increase of chain length decrease the throughput of the polymer through the pore. As for free polymers, the inclusion of a mechanism for hernia creations/annihilations leads to the cross-over from Rouse-like behaviour to reptation. For the experimentally most relevant case (Rouse dynamics) the bimodal power law dependence of the translocation time on the chain length is found.     

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.     

Theory of transport of long polymer molecules through carbon nanotube channels

A theory of transport of long chain polymer molecules through carbon nanotube (CNT) channels is developed using the Fokker-Planck equation and direct molecular dynamics simulations. The mean transport or translocation time tau is found to depend on the chemical potential energy, the entropy, and the diffusion coefficient. A power law dependence tau approximately N2 is found, where N is the number of monomers in a molecule. For 10(5)-unit long polyethylene molecules, tau is estimated to be approximately 1 micros. The diffusion coefficient of long polymer molecules inside CNTs, like that of short ones, is found to be a few orders of magnitude larger than in ordinary silicate based zeolite systems.     

Polymer translocation in crowded environments

We study the effect of the crowded environments on the translocation of a polymer through a pore in a membrane. By systematically treating the entropic penalty due to crowding, we show that the translocation dynamics are significantly altered, leading to novel scaling behaviors of the translocation time. We also observe new and qualitatively different translocation regimes depending upon the extent of crowding, transmembrane chemical potential asymmetry, and polymer length.     

Polymer translocation in the presence of excluded volume and explicit hydrodynamic interactions

Molecular Dynamics simulations of polymer translocation are hereby reported. No external force was applied to the polymer during translocation, and the dynamics was dominated by polymer–pore interactions. It was found that hydrodynamic interactions play an important role in the relaxation of the polymer on each side of the membrane but have a negligible impact on the translocation process itself. Also, the scaling laws obtained for the relaxation and translocation times indicate that long translocating polymers may be considered to be following a quasi-equilibrium anomalous diffusion process in the absence of external forces.     

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.     

Noise effects in two different biological systems

We investigate the role of the colored noise in two biological systems: (i) adults of Nezara viridula (L.) (Heteroptera: Pentatomidae), and (ii) polymer translocation. In the first system we analyze, by directionality tests, the response of N. viridula individuals to subthreshold signals plus noise in their mating behaviour. The percentage of insects that react to the subthreshold signal shows a nonmonotonic behaviour, characterized by the presence of a maximum, as a function of the noise intensity. This is the signature of the non-dynamical stochastic resonance phenomenon. By using a “soft” threshold model we find that the maximum of the input-output cross correlation occurs in the same range of noise intensity values for which the behavioural activation of the insects has a maximum. Moreover this maximum value is lowered and shifted towards higher noise intensities, compared to the case of white noise. In the second biological system the noise driven translocation of short polymers in crowded solutions is analyzed. An improved version of the Rouse model for a flexible polymer is adopted to mimic the molecular dynamics by taking into account both the interactions between adjacent monomers and the effects of a Lennard-Jones potential between all beads. The polymer dynamics is simulated in a two-dimensional domain by numerically solving the Langevin equations of motion in the presence of thermal fluctuations and a colored noise source. At low temperatures or for strong colored noise intensities the translocation process of the polymer chain is delayed. At low noise intensity, as the polymer length increases, we find a nonmonotonic behaviour for the mean first translocation time of the polymer centre of inertia. We show how colored noise influences the motion of short polymers, by inducing two different regimes of translocation in the dynamics of molecule transport.     

Sequence dependence of DNA translocation through a nanopore

We investigate the dynamics of DNA translocation through a nanopore using 2D Langevin dynamics simulations, focusing on the dependence of the translocation dynamics on the details of DNA sequences. The DNA molecules studied in this work are built from two types of bases A and C, which have been shown previously to have different interactions with the pore. We study DNA with repeating blocks A(n)C(n) for various values of n and find that the translocation time depends strongly on the block length 2n as well as on the orientation of which base enters the pore first. Thus, we demonstrate that the measurement of translocation dynamics of DNA through a nanopore can yield detailed information about its structure. We have also found that the periodicity of the block sequences is contained in the periodicity of the residence time of the individual nucleotides inside the pore.     

Polymer translocation in a double-force arrangement

Using Langevin dynamics simulations, we investigate the translocation dynamics of an externally driven polymer chain through a nanopore, where a pulling force F is exerted on the first monomer whilst there is an opposing force F _E < F within the pore. Such a double-force arrangement has been proposed recently to allow better dynamical control of the translocation process in order to sequence biopolymers. We find that in the double-force arrangement translocation becomes slower as compared to the case under a single monomer pulling force of magnitude F - F _E , but scaling of the translocation time as a function of the chain length ∼ N ² does not change. The waiting time (m) for monomer m to exit the pore is found to be a monotonically increasing function of the bead number almost until m N , which indicates relatively well-defined slowing down and control of the chain velocity during translocation. We also study the waiting time distributions for the beads in the chain, and characterize in detail fluctuations in the bead positions and their transverse position coordinates during translocation. These data should be useful in estimating position-dependent sequencing errors in double-force experiments.     

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.     

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.     

非均匀外力对粗粒化DNA穿孔行为影响的模拟研究

通过建立DNA高分子的粗粒化模型,采用分子动力学方法模拟其穿孔行为,研究了不同的孔内非均匀外力对DNA高分子穿孔的影响.外力及高分子链内部势能在分子水平下对单体的综合作用很复杂,某些条件穿孔过程会产生后面粒子超过前面粒子而使高分子链堵塞在孔内的情况.研究还发现,穿孔行为是否成功与孔口力的大小有关,在成功穿孔的情况下,非均匀外力相比于恒力情况穿孔时间至少减少了1/2.这些结果对理解DNA复杂的穿孔机理提供了新的视角.     

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.     

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     

Turbulent dynamics of polymer solutions

We study properties of dilute polymer solutions. The probability density function (PDF) of polymer end-to-end extensions R in turbulent flows is examined. We show that if the value of the Lyapunov exponent lambda is smaller than the inverse molecular relaxation time 1/tau then the PDF has a strong peak at the equilibrium size R0 and a power tail at R>R0. This confirms and extends the results of J. L. Lumley [Symp. Math. 9, 315 (1972)]. There is no essential influence of polymers on the flow in this regime. At lambdatau>1 the majority of molecules is stretched to the linear size R(op)>R0, which can be much smaller than the maximal length of the molecules due to their back reaction.     

Exponential sensitivity to dephasing of electrical conduction through a quantum dot

According to random-matrix theory, interference effects in the conductance of a ballistic chaotic quantum dot should vanish proportional to (tau(phi)/tau(D))(p) when the dephasing time tau(phi) becomes small compared to the mean dwell time tau(D). Aleiner and Larkin have predicted that the power law crosses over to an exponential suppression proportional to exp((-tau(E)/tau(phi)) when tau(phi) drops below the Ehrenfest time tau(E). We report the first observation of this crossover in a computer simulation of universal conductance fluctuations. Their theory also predicts an exponential suppression proportional to exp((-tau(E)/tau(D)) in the absence of dephasing--which is not observed. We show that the effective random-matrix theory proposed previously for quantum dots without dephasing explains both observations.     

Initially linear echo-spacing dependence of 1/T2 measurements in many porous media with pore-scale inhomogeneous fields

For a liquid sample with unrestricted diffusion in a constant magnetic field gradient g, the increase R in R2=1/T2 for CPMG measurements is 1/3(taugammag)2D, where gamma is magnetogyric ratio, tau is the half the echo spacing TE, and D is the diffusion constant. For measurements on samples of porous media with pore fluids and without externally applied gradients there may still be significant pore-scale local inhomogeneous fields due to susceptibility differences, whose contributions to R2 depend on tau. Here, diffusion is not unrestricted nor is the field gradient constant. One class of approaches to this problem is to use an "effective gradient" or some kind of average gradient. Then, R2 is often plotted against tau2, with the effective gradient determined from the slope of some of the early points. In many cases, a replot of R2 against tau instead of tau2 shows a substantial straight-line interval, often including the earliest available points. In earlier work [G.C. Borgia, R.J.S. Brown, P. Fantazzini, Phys. Rev. E 51 (1995) 2104; R.J.S. Brown, P. Fantazzini, Phys. Rev. B 47 (1993) 14823] these features were noted, and attention was called to the fact that very large changes in field and gradient are likely for a small part of the pore fluid over distances very much smaller than pore dimensions. A truncated Cauchy-Lorentz (C-L) distribution of local fields in the pore space was used to explain observations, giving reduced effects of diffusion because of the averaging properties of the C-L distribution, the truncation being at approximately +/-1/2chiB0, where chi is the susceptibility difference. It was also noted that, when there is a narrow range of pore size a, over a range of about 40 of the parameter xi=1/3chinua2/D, where nu is the frequency, R2 does not depend much on pore size a nor on diffusion constant D. Examples are shown where plots of R2 vs tau show better linear fits to the data for small tau values than do plots vs tau2. The present work shows that, if both grain-scale and sample-scale gradients are present for samples with narrow ranges of T2, it may be possible to identify the separate effects with the linear and quadratic coefficients in a second-order polynomial fit to the early data points. Of course, many porous media have wide pore size and T2 distributions and hence wide ranges of xi. For some of these wide distributions we have plotted R2 vs tau for signal percentiles, normalized to total signal for shortest tau, again showing initially linear tau-dependence even when available data do not cover the longest and/or shortest T2 values for alltau values. For the examples presented, both the intercepts and the initial slopes of the plots of R2 vs tau increase systematically with signal percentile, starting at smallest R2.     

Molecular mobility in polymer thin films

Fluorescence recovery after photobleaching was used to measure in-plane dye-probe diffusion coefficients, D, in thin films of monodisperse polystyrene supported on fused quartz substrates. The substrates were prepared with a high density of surface hydroxyl groups which interact favorably with repeat units of the polymer. The effects of temperature and film thickness were investigated, at temperatures above the bulk glass transition of the polymer, T(g), and in the range of film thicknesses from 1-10(2) times the radius of gyration (R(g)) of individual polymer molecules. As the film thickness decreases towards R(g) the value of D increases above the bulk values, with significant effects first appearing in films approximately 20R(g). In the thinnest films studied, about 4R(g), the values of D lie as much as two orders over bulk values. At the same time, the temperature dependence of D becomes much weaker than in bulk. Analysis by free volume theory indicates that apparent values of both T(g) and the thermal expansion coefficient for liquid state, alpha(L), decrease as the film thickness decreases. The possible effects of surface segregation of the dye probe are discussed.     

Density-fluctuation-induced swelling of polymer thin films in carbon dioxide

We report an anomalous swelling of polymer thin films in carbon dioxide (CO(2)) which is associated (in both locus and form) with the density fluctuation ridge that forms along the extension of the coexistence curve of gas and liquid in the P-T phase diagram. Neutron reflectivity results showed that CO(2) could be sorbed to a large extent ( approximately 60%) in thin polymer films even when the bulk miscibility of the polymer with CO(2) is very poor. The anomalous swelling is found to scale with the polymer radius of gyration (R(g)) and extends to a distance approximately 10 R(g).