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.     

Driven translocation dynamics of polynucleotides through a nanopore: off-lattice Monte-Carlo simulations

The driven translocation dynamics of a polynucleotide chain through a nanopore is studied using off-lattice Monte-Carlo simulations, which plays an important role in the nanopore sequencing of polynucleotides. We report a detailed study on the dependence of translocation dynamics on the chain length and the local geometry near the nanopore. In particular, we find that the length dependence of the infection time of the chain could exhibit very different behaviors for different geometries.     

纳米孔壁面作用对蛋白质过孔影响的粗粒化分子动力学模拟

基于粗粒化分子动力学方法模拟电驱动蛋白质过孔过程,研究纳米孔-水/纳米孔-蛋白质相互作用对电泳迁移率的影响;用操控式分子动力学模拟分析蛋白质在不同相互作用下过孔摩擦系数和摩擦阻力.研究发现：蛋白质黏附纳米孔壁面对其过孔特性影响并不明显,而纳米孔-水相互作用对蛋白质过孔电泳迁移率和摩擦系数影响较大.随纳米孔-水相互作用增强,纳米孔壁面与蛋白质附近水分子运动差异显现,蛋白质过孔摩擦阻力显著增大,过孔摩擦系数随之增大,进而影响蛋白质过孔电泳迁移率.所得结果可为纳米孔材料设计提供理论指导.     

Monte Carlo analysis of polymer translocation with deterministic and noisy electric fields

Polymer translocation through the nanochannel is studied by means of a Monte Carlo approach, in the presence of a static or oscillating external electric voltage. The polymer is described as a chain molecule according to the two-dimensional “bond fluctuation model”. It moves through a piecewise linear channel, which mimics a nanopore in a biological membrane. The monomers of the chain interact with the walls of the channel, modelled as a reflecting barrier. We analyze the polymer dynamics, concentrating on the translocation time through the channel, when an external electric field is applied. By introducing a source of coloured noise, we analyze the effect of correlated random fluctuations on the polymer translocation dynamics.     

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.     

Poisson-Fokker-Planck model for biomolecules translocation through nanopore driven by electroosmotic flow

A non-continuous electroosmotic flow model (PFP model) is built based on Poisson equation, Fokker-Planck equation and Navier-Stokse equation, and used to predict the DNA molecule translocation through nanopore. PFP model discards the continuum assumption of ion translocation and considers ions as discrete particles. In addition, this model includes the contributions of Coulomb electrostatic potential between ions, Brownian motion of ions and viscous friction to ion transportation. No ionic diffusion coefficient and other phenomenological parameters are needed in the PFP model. It is worth noting that the PFP model can describe non-equilibrium electroosmotic transportation of ions in a channel of a size comparable with the mean free path of ion. A modified clustering method is proposed for the numerical solution of PFP model, and ion current translocation through nanopore with a radius of 1 nm is simulated using the modified clustering method. The external electric field, wall charge density of nanopore, surface charge density of DNA, as well as ion average number density, influence the electroosmotic velocity profile of electrolyte solution, the velocity of DNA translocation through nanopore and ion current blockade. Results show that the ion average number density of electrolyte and surface charge density of nanopore have a significant effect on the translocation velocity of DNA and the ion current blockade. The translocation velocity of DNA is proportional to the surface charge density of nanopore, and is inversely proportional to ion average number density of electrolyte solution. Thus, the translocation velocity of DNAs can be controlled to improve the accuracy of sequencing by adjusting the external electric field, ion average number density of electrolyte and surface charge density of nanopore. Ion current decreases when the ion average number density is larger than the critical value and increases when the ion average number density is lower than the critical value. Our numerical simulation shows that the translocation velocity of DNA given by the PFP model agrees with the experimental, results better than that given by PNP model or PB model.     

Two-dimensional diffusion model for the biopolymers dynamics at nanometer scale

In this paper the driven transport of linear polymers through a nanopore is presented. Biopolymer physical behavior in an external electric field is modeled and its motion is simulated using the Langevin impulse integrator method. Within fairly large limits, the polymer translocation time is inversely proportional with the electric field intensity and directly proportional with the polymer chain length.      

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.     

Influence of polymer-pore interactions on translocation

We investigate the influence of polymer-pore interactions on the translocation dynamics using Langevin dynamics simulations. An attractive interaction can greatly improve the translocation probability. At the same time, it also increases the translocation time slowly for a weak attraction while an exponential dependence is observed for a strong attraction. For fixed driving force and chain length the histogram of translocation time has a transition from Gaussian distribution to long-tailed distribution with increasing attraction. Under a weak driving force and a strong attractive force, both the translocation time and the residence time in the pore show a nonmonotonic behavior as a function of the chain length. Our simulations results are in good agreement with recent experimental data.     

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.     

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 Single Polymer Chain from Nanopore on a Membrane： Solvent Effect

We investigate the translocation of single polymer chain through a nanopore located on a membrane with different solvents in the two sides of the membrane. For the case under study, the effect of solvents on the translocation dynamics is significant, and as a result, the mean first passage time shortens remarkably compared with that calculated in the case of good solvents on both the sides of the membrane. In addition, we also discuss the condition such that the present result holds true.     

Translocation of a confined polymer through a hole

Based on an analogy between polymer translocation across a free energy barrier associated with polymer worming through a hole and classical nucleation and growth process, the escape time tau is predicted asymptotically to be N(N/rho)(1/3nu). N is the polymer length, rho is the monomer density prior to escape, and nu is the radius of gyration exponent. Monte Carlo simulation data collected in the high salt limit (nu approximately 3/5) are in agreement with the asymptotic law and provide vivid details of the escape.     

Translocation of Polymer Chains Through a Channel with Complex Geometries

采用nPERMis (new pruned-enriched rosenbluth method with importance sampling) 算法,研究了高分子链在通道中穿行的力学行为. 在管道穿行的过程中,计算了其作用力,发现进入中间通道的过程其对应的作用力f和第一个单体在x轴方向的位置关系曲线有一个平台(f>0). 由于高分子链的受限减少了高分子链的构象数目和熵,从而增加了其自由能, 因此只有在外力的作用下,高分子链才可以进入中间管道. 当高分子运动到某一位置后,第二个平台开始形成(f<0),这时高分子链自发进入右通道. 这是因为在右通道中高分子链的自由能降低的比左通道中高分子链的自由能升高的快. 右通道中的高分子链自发地拉动左通道中的高分子链. 研究了链长、左、右通道宽度对穿孔有很大影响. 通过这些研究可以详细解释各部分穿行时间不同的原因.     

Free energy change of crystallisation in single copolymers

ABSTRACT

We performed dynamic Monte Carlo simulations to calculate the free energy change of crystallisation in single linear and ring polymers containing one or more non-crystallisable sequence defects (comonomers) along the chain. We found that, similar to chain ends, the numbers of comonomers bring only a thermodynamic effect to the free energy barrier and shift down the melting points of single copolymers by following Flory’s thermodynamic equation. Furthermore, there exists a critical comonomer number (or sequence length) for the success of crystallisation, which explains the segregation of sequence lengths upon crystallisation in statistical copolymers. Our observations shed light onto the kinetic suppression of crystallinity for polymers containing various chemical, geometrical or stereo-optical sequence defects, as well as for protein molecules containing specific sequences.     

Effects of an attractive wall on the translocation of polymer under driving

The effects of an attractive wall at the trans side on the translocation of an eight-site bond-fluctuation model (BFM) polymer through a pore in a membrane under driving are simulated by the dynamic Monte Carlo method. The attractive wall shows two contrary effects: its excluded volume effect reduces configuration entropy and thus hinders the translocation of the polymer, while its attraction decreases the energy and thus accelerates the translocation. At a critical polymer-wall interaction ε*?≈-?1, we find that the two effects compensate each other and the translocation time τ is roughly independent of the separation distance between the wall and the pore. The value ε*?≈-?1 is roughly equal to the critical adsorption point for the BFM polymer. Moreover, the value of the critical attraction is roughly independent of chain length N and chemical potential difference Δμ. At last, a scaling relation τ?～?N(α) is observed for polymer translocation at a high value of NΔμ. Though the translocation time is highly dependent on the polymer-wall interaction and pore-wall separation distance, the exponent α is always about 1.30?±?0.05 so long as NΔμ is large enough.     

Optical detection of DNA translocation through silicon nanopore by ultraviolet light

In this paper, we propose a new optical detection scheme for nanopore-based DNA sequencing with high resolution towards eventual base identification. We use ultraviolet light for excitation of a fluorescent probe attached to DNA and a nanopore in the silicon membrane that has a significantly large refractive index and an extinction coefficient at ultraviolet wavelengths. In this study, numerical electromagnetic simulation revealed that the z-polarization component (perpendicular to the membrane plane) of the electric field was dominant near the nanopore and generated a large electric field gradient at the nanopore exit, typically with a decay length of 2 nm for a nanopore with diameter of 7 nm. The large extinction coefficient contributed to reduction in background noise coming from fluorophore-labeled DNA strands that remain behind the membrane (the cis side of the membrane). We observed a high signal-to-noise ratio of single DNA translocation events under the application of an electric field.     

脱氧核糖核酸单链序列的预测

利用Langevin动力学方法模拟了脱氧核糖核酸(DNA)单链在电场力作用下穿越纳米孔道的动力学过程.研究表明,不同种类的单体对应着不同的居留时间,相邻单体的居留时间随着孔道长度的增大而减小.在简化模型的基础上,可以从居留时间图中一次性地推测出一条DNA链的嘌呤和嘧啶的分布.应用该方法对17条不同序列的DNA链进行了预测,平均准确率为951%.在此方法的基础上做一些改进,可以为DNA链的测序提供一种高效的低成本方法. 关键词： Langevin动力学 脱氧核糖核酸单链 序列预测     

Thermodynamic Free Energy Behavior of Diblock Copolymer Chains Confined Between Planar Surfaces Having End-Tethered Flexible Polymer Molecules

A molecular model for the free energy of a confined system of diblock copolymer chains within a 2D slit with the interior surfaces having end-tethered chains is presented, based on a combined lattice and scaling theory approach. The thermodynamics of a model system, based on a constrained minimization of free energy, is explored as a function of the intermolecular energy parameters for interaction between the segments of block copolymer chains, end-tethered chains, and the surfaces. The effects of chain length and the block length ratio are investigated over a wide range of values. The results obtained are qualitative in nature; however, the model can be implemented to real systems provided appropriate parameterization of the model parameters to real systems can be performed. The phase diagrams obtained here provide ways for designing thermodynamically stable systems within the physical parametric variable space.     

Concentration polarization in translocation of DNA through nanopores and nanochannels

In this Letter we provide a theory to show that high-field electrokinetic translocation of DNA through nanopores or nanochannels causes large transient variations of the ionic concentrations in front and at the back of the DNA due to concentration polarization (CP). The CP causes strong local conductivity variations, which can successfully explain the nontrivial current transients and ionic distributions observed in molecular dynamics simulations of nanopore DNA translocations as well as the transient current dips and spikes measured for translocating hairpin DNA. Most importantly, as the future of sequencing of DNA by nanopore translocation will be based on time-varying electrical conductance, CP, must be considered in experimental design and interpretation--currently these studies are mostly based on the incomplete pore conductance models that ignore CP and transients in the electrical conductance.