Translocation of a proteinlike chain through a finite channel

We use the pruned-enriched-Rosenbluth method and the modified orientation-dependent monomer-monomer interaction model to study the translocation of a proteinlike chain through a finite channel. The mean-square radius of gyration per bond /N and shape factor of proteinlike chains with different secondary structures transporting through a finite channel with different channel radii R=1, 2, 3, 4, and 20 are investigated in the translocation. The average Helmholtz free energy per bond A/N and the mechanical force f are also presented. A/N remains unchanged when X(0)<0 and X(0)>1, and decreases monotonously when 0.5/N is also calculated in the process of translocation. An energy barrier is shown. The proteinlike chains must cross this energy barrier when they escape from the channel. The position of the maximum of /N depends on the secondary structures and the channel radius. We also discuss the average contact energy per bond c/N, the average alpha-helical energy per bond h/N, and the average beta-sheet energy per bond b/N.     

Simulation study on the translocation of a partially charged polymer through a nanopore

The translocation of a partially charged polymer through a neutral nanopore under external electrical field is studied by using dynamic Monte Carlo method on a simple cubic lattice. One monomer in the polymer is charged and it suffers a driving force when it locates inside the pore. Two time scales, mean first passage time τ(FP) with the first monomer restricted to never draw back into cis side and translocation time τ for polymer continuously threading through nanopore, are calculated. The first passage time τ(FP) decreases with the increase in the driving force f, and the dependence of τ(FP) on the position of charged monomer M is in agreement with the theoretical results using Fokker-Planck equation [A. Mohan, A. B. Kolomeisky, and M. Pasquali, J. Chem. Phys. 128, 125104 (2008)]. But the dependence of τ on M shows a different behavior: It increases with f for M < N/2 with N the polymer length. The novel behavior of τ is explained qualitatively from dynamics of polymer during the translocation process and from the free energy landscape.     

拉伸分子动力学方法研究聚乙烯单链的力学行为

采用拉伸分子动力学方法(steered molecular dynamics,SMD)研究一端固定的聚乙烯单链(singlepolyethylene chain)在被拉伸过程中的力学性质.在拉伸过程中发现平均拉力〈f〉受拉伸速度v的影响,当v<0.05 nm/ps时,〈f〉在250 pN附近会出现一个拉力平台.聚乙烯单链各部分的形状因子在拉伸过程中表现出一定的规律性,总是头部和尾部的形状因子〈δh〉、〈tδ〉先增加然后才是中间部分〈δm〉增加.如果按顺序再释放被拉开的聚乙烯单链,就会出现力学回滞现象,这与Kellermayer等的力学回滞曲线实验是一致的.力学回滞曲线面积表示耗散能〈Ed〉,与速度v满足方程〈Ed〉=a+b×e-cv,而且在v<0.005 nm/ps和v>0.005 nm/ps两个速度区域有不同的特性.〈Ed〉在不同的分子热运动温度区域,也表现出不同的规律性,当温度T>220 K时,〈Ed〉随着温度T的升高而减小,这与Pegoretti等的实验一致,当T<220 K时〈Ed〉随着温度T的升高而增加.     

Elastic Behaviors of Adsorbed Protein-like Chains

Elastic behaviors of protein-like chains are investigated by Pruned-Enriched-Rosenbluth method and modified orientation-dependent monomer-monomer interactions model. The protein-like chain is pulled away from the attractive surface slowly with elastic force acting on it. Strong adsorption interaction and no adsorption interaction are both considered. We calculate the characteristic ratio and shape factor of protein-like chains in the process of elongation. The conformation change of the protein-like chain is well depicted. The shape of chain changes from “rod” to “sphere” at the beginning of elongation. Then, the shape changes from “sphere” to “rod”. In the end, the shape becomes a “sphere” as the chain leaves away from the surface. In the meantime, we discuss average Helmoholtz free energy per bond, average energy per bond, average adsorbed energy per bond, average α-helical energy per bond, average β-sheet energy per bond and average contact energy per bond.On the other hand, elastic force is also studied. It is found that elastic force has a long plateau during the tensile elongation when there exists adsorption interaction. This result is consistent with SMFS experiment of general polymers. Energy contribution to elastic force and contact energy contribution to elastic force are both discussed. These investigations can provide some insights into the elastic behaviors of adsorbed protein chains.     

Escape of polymer chains from an attractive channel under electrical force

The escape of polymer chains from an attractive channel under external electrical field is studied using dynamical Monte Carlo method. Though the escaping process is nonequilibrium in nature, results show that the one-dimensional diffusion theoretical model based on the equilibrium assumption can describe the dependence of the average escaping time (τ(0)) on the polymer-channel interaction (?), the electrical field (E), the chain length (n), and the channel length (L), qualitatively. Results indicate that both ? and E play very important roles in the escaping dynamics. For small ?, the polymer chain moves out of the channel continuously and quickly. While for large ?, the polymer chain is difficult to move out of long channels as it is trapped for a long time (τ(trap)) when the end segment is near the critical point x(C). These results are consistent with the theoretical results for the free energy profiles at small ? and large ?, respectively. The dependence of x(C) and τ(trap) on ? and E are discussed, and specific relations are obtained. The configurational properties of polymer chain are also investigated during the escaping process.     

Langevin dynamics simulations of polymer translocation through nanopores

We investigate the dynamics of polymer translocation through a nanopore using two-dimensional Langevin dynamics simulations. In the absence of an external driving force, we consider a polymer which is initially placed in the middle of the pore and study the escape time tau(e) required for the polymer to completely exit the pore on either side. The distribution of the escape times is wide and has a long tail. We find that tau(e) scales with the chain length N as tau(e) approximately N(1+2nu), where nu is the Flory exponent. For driven translocation, we concentrate on the influence of the friction coefficient xi, the driving force E, and the length of the chain N on the translocation time tau, which is defined as the time duration between the first monomer entering the pore and the last monomer leaving the pore. For strong driving forces, the distribution of translocation times is symmetric and narrow without a long tail and tau approximately E(-1). The influence of xi depends on the ratio between the driving and frictional forces. For intermediate xi, we find a crossover scaling for tau with N from tau approximately N(2nu) for relatively short chains to tau approximately N(1+nu) for longer chains. However, for higher xi, only tau approximately N(1+nu) is observed even for short chains, and there is no crossover behavior. This result can be explained by the fact that increasing xi increases the Rouse relaxation time of the chain, in which case even relatively short chains have no time to relax during translocation. Our results are in good agreement with previous simulations based on the fluctuating bond lattice model of polymers at intermediate friction values, but reveal additional features of dependency on friction.     

The chain sucker: translocation dynamics of a polymer chain into a long narrow channel driven by longitudinal flow

Using analytical techniques and Langevin dynamics simulations, we investigate the dynamics of polymer translocation into a narrow channel of width R embedded in two dimensions, driven by a force proportional to the number of monomers in the channel. Such a setup mimics typical experimental situations in nano/microfluidics. During the translocation process if the monomers in the channel can sufficiently quickly assume steady state motion, we observe the scaling τ ～ N∕F of the translocation time τ with the driving force F per bead and the number N of monomers per chain. With smaller channel width R, steady state motion cannot be achieved, effecting a nonuniversal dependence of τ on N and F. From the simulations we also deduce the waiting time distributions under various conditions for the single segment passage through the channel entrance. For different chain lengths but the same driving force, the curves of the waiting time as a function of the translocation coordinate s feature a maximum located at identical s(max), while with increasing the driving force or the channel width the value of s(max) decreases.     

Theoretical study on the translocation of partially charged polymers through nanopore

The translocation time τ of partially charged polymers through a neutral nanopore is calculated using Fokker–Planck equation with adsorbing–adsorbing boundary conditions. For the polymer with one charged monomer, we find that τ is dependent on the position of the charged monomer and on the magnitude of the driving force f inside the nanopore. When the charge is located at the front half of the polymer chain, τ is larger than that of neutral polymer and increases with f. When the charge is located at the back half, it is smaller than that of the neutral polymer and decreases with increasing f. We have also studied the behavior of a symmetrical polymer with two like charges located symmetrically in the chain and that of an asymmetrical polymer with two unlike charges. Moreover, we have calculated the translocation time for a general condition of polymer with two randomly distributed charges. All results show that τ is dependent on the positions of charges in the polymer chain and on the magnitude of the driving force. The results can be explained qualitatively by the free‐energy landscape of polymer translocation. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2017 , 55, 1017–1025     

流场驱动高分子链迁移穿过微通道的耗散粒子动力学模拟

利用耗散粒子动力学模拟方法研究了高分子链在流场驱动作用下迁移穿过微通道过程中的链构象变化和动力学行为.在足够大的流场力驱动作用下,高分子链在沿着流场方向逐渐被拉伸,从而能够穿过管径小于其自身尺寸的微通道.耗散粒子动力学模拟结果表明高分子链的迁移过程主要分为3个步骤:(1)在流场驱动作用下,高分子链漂移并逐渐靠近微通道入口;(2)高分子链逐渐调整自身构象,并使其部分进入微通道;(3)高分子链成功穿过微通道.同时,模拟还发现当高分子链尺寸大于微通道细管道管径时,高分子链穿过微通道所需的平均迁移时间随着流量的增加而逐渐减小.此外,为了研究高分子链刚性对高分子链穿过微通道的影响,模型中还引入了蠕虫状高分子链模型.模拟结果发现,高分子链的链刚性越强,其迁移穿过微通道的时间越长.     

EFFECTS OF SECONDARY STRUCTURE ON ELASTIC BEHAVIOR OF PROTEIN-LIKE CHAINS

The elastic behavior of protein-like chains was investigated by using the Pruned-Enriched-Rosenbluth Method (PERM).Three typical protein-like chains such as all-α,all-β,and α+β(α/β) proteins were studied in our modified orientation dependent monomer-monomer interaction (ODI) model.We calculated the ratio of /N and shape factor <δ*> of protein-like chains in the process of elongation.In the meantime,we discussed the average energy per bond ＜U＞/N,average contact energy per bond ＜U＞c/N,average helical energy per bond ＜U＞h/N and average sheet energy per bond ＜U＞b/N.Three maps of contact formation,α-helix formation,β-sheet formation were depicted.All the results educe a view that the helix structure is the most stable structure,while the other two structures are easy to be destroyed.Besides,the average Helmholtz free energy per bond ＜A＞/Nis was presented.The force f obtained from the free energy was also discussed.It was shown that the chain extended itself spontaneously first.The force was studied in the process of elongation.Lastly,the energy contribution to elastic force fu was calculated too.It was noted that fu for all-β chains increased first,and then decreased with x0 increasing.     

Permeation of particle through a four-helix-bundle model channel

By using molecular dynamics simulation, the dynamic behaviors of particle permeation through a four-helix-bundle model channel are studied. The interior cavity of the four-helix-bundle provides the "routes" for particle permeation. The main structural properties of the model channel are similar to those that appear in natural four-helix-bundle proteins. It is found that the interior structure of the model channel may greatly influence the permeation process. At the narrow necks of the model channel, the particle would be trapped during the permeation. There is a threshold value for the driving force. When the driving force is larger than this threshold value, the mean first permeation time decreases sharply and tends to be saturated. Increasing the temperature of either the model channel or the particle reservoir can also facilitate the permeation. Enhancing the interaction strength between the particle and monomer on the four-helix-bundle model chain will hinder the permeation. Hence, the electrical current which is induced by the particle permeation is a function of the driving force and temperature. It is found that this current increases monotonically as the strength of the driving force or the temperature increases, but decreases as the interaction strength between the particle and monomer increases. It is also found that the larger the friction coefficient, the slower the permeation is. In addition, the multiparticle (or multi-ion) permeation process is also studied. The permeation of multiparticle is usually quicker than that of the single particle. The permeation of particle through a five-helix-bundle shows similar properties as that through a four-helix-bundle.     

三维吸附紧密高分子单链的力学性质研究

采用PERM(pruned-enriched Rosenbluth method)算法,研究了吸附在界面附近的紧密高分子链力学行为.发现当界面的吸附能比较大时,紧密高分子链从紧贴于吸附界面到逐渐远离的过程中,其外形会经历4种典型的变化.同时紧密高分子链的尺寸大小如/N、xy/N、z/N,形状参数<δ*>,热力学性质如每个键的平均自由能A/N,平均相互作用能/N等,甚至所受外力的大小都会同时做出相应的变化,其出现变化的位置也一致.特别是随着紧密高分子链离开吸附界面的过程中,作用于高分子链上的外力明显出现几个力学平台,这与实验得到的结果完全一致.同时还研究了弱吸附能的情况,在这种情况下实验是很难进行的.     

On the cycle index of point groups

In this brief work we express the cycle index of the molecular point groups as a function of a limited number of initial geometrical parameters. Such parameters are the number of elements composing the domain D of sites of substitutions in the molecule belonging to the point group G, and the numbers of sites of D lying on the symmetry elements for G.     

Effect of Hydrodynamic Interaction on Flow-induced Polymer Translocation Through a Nanotube

We investigated the effect of hydrodynamic interaction(HI) on flow-induced polymer translocation through a nanotube by Brownian dynamics simulations. Whether there is HI in the simulation system is separately controlled by using different diffusion tensors. It is found that HI has no effect on critical velocity flux for long polymer chains due to the competition between more drag force and the hindrance of chain stretching from HI, however, HI broadens the transition interval. In addition, for flow-induced polymer translocation with HI, the critical velocity flux firstly slowly decreases with the increase of chain length and then becomes identical to that of it without HI, that is, the critical velocity flux is independent of chain length. At the same time, HI also accelerates the translocation process and makes the relative variation amplitude of single bead translocation time smaller. In fact, HI can enhance the intrachain cooperativity to make the whole chain obtain more drag force from fluid field and hinder chain stretching, both of which play an important role in translocation process.     

On some multiplicative product of kth derivative of Dirac's delta in x0+|x| and x0−|x|

In this paper we give a sense to the products $${{\left| x \right|^{(n - 2)/2} }} \cdot \frac{{\delta ^{(k - 1)} (x_0 + \left| x \right|)}} {{\left| x \right|^{(n - 2)/2} }}$$ and $\delta ^{(k - 1)} (x_0 - \left| x \right|) \cdot \delta ^{(k - 1)} (x_0 + \left| x \right|)$ . The first of them is a generalization of the product $${{\left| x \right|^{(n - 2)/2} }} \cdot \frac{{\delta (x_0 + \left| x \right|)}} {{\left| x \right|^{(n - 2)/2} }}{\text{ }}$$ given in [1, p. 158].     

Polymer translocation through a cylindrical channel

A formalism of polymer translocation through a cylindrical channel of finite diameter and length between two spherical compartments is developed. Unlike previous simplified systems, the finite diameter of the channel allows the number of polymer segments inside the channel to be adjusted during translocation according to the free energy of possible conformations. The translocation process of a Gaussian chain without excluded volume and hydrodynamic interactions is studied using exact formulas of confinement free energy under this formalism. The free energy landscape for the translocation process, the distribution of the translocation time, and the average translocation time are presented. The complex dependencies of the average translocation time on the length and diameter of the channel, the sizes of the donor and receptor compartments, and the chain length are illustrated.     

Barriers to ion translocation in cationic and anionic receptors from the Cys-loop family

Understanding the mechanisms of gating and ion permeation in biological channels and receptors has been a long-standing challenge in biophysics. Recent advances in structural biology have revealed the architecture of a number of transmembrane channels and allowed detailed, molecular-level insight into these systems. Herein, we have examined the barriers to ion conductance and origins of ion selectivity in models of the cationic human alpha7 nicotinic acetylcholine receptor (nAChR) and the anionic alpha1 glycine receptor (GlyR), based on the structure of Torpedo nAChR. Molecular dynamics simulations were used to determine water density profiles along the channel length, and they established that both receptor pores were fully hydrated. The very low water density in the middle of the nAChR pore indicated the existence of a hydrophobic constriction. By contrast, the pore of GlyR was lined with hydrophilic residues and remained well-hydrated throughout. Adaptive biasing force simulations allowed us to reconstruct potentials of mean force (PMFs) for chloride and sodium ions in the two receptors. For the nicotinic receptor we observed barriers to ion translocation associated with rings of hydrophobic residues-Val13' and Leu9'-in the middle of the transmembrane domain. This finding further substantiates the hydrophobic gating hypothesis for nAChR. The PMF revealed no significant hydrophobic barrier for chloride translocation in GlyR. For both receptors nonpermeant ions displayed considerable barriers. Thus, the overall electrostatics and the presence of rings of charged residues at the entrance and exit of the channels were sufficient to explain the experimentally observed anion and cation selectivity.     

First passage time distribution of chaperone driven polymer translocation through a nanopore: homopolymer and heteropolymer cases

Combining the advection-diffusion equation approach with Monte Carlo simulations we study chaperone driven polymer translocation of a stiff polymer through a nanopore. We demonstrate that the probability density function of first passage times across the pore depends solely on the Pe?clet number, a dimensionless parameter comparing drift strength and diffusivity. Moreover it is shown that the characteristic exponent in the power-law dependence of the translocation time on the chain length, a function of the chaperone-polymer binding energy, the chaperone concentration, and the chain length, is also effectively determined by the Pe?clet number. We investigate the effect of the chaperone size on the translocation process. In particular, for large chaperone size, the translocation progress and the mean waiting time as function of the reaction coordinate exhibit pronounced sawtooth-shapes. The effects of a heterogeneous polymer sequence on the translocation dynamics is studied in terms of the translocation velocity, the probability distribution for the translocation progress, and the monomer waiting times.     

Solvent‐Induced Length Variation of Cylindrical Brushes

Polymacromonomers with a main chain much larger than the side‐chain length adopt the form of cylindrical brush polymers the contour length per main‐chain monomer of which depends on the side‐chain length. In the present investigation it is demonstrated that the length per monomer also depends on the solvent quality, i.e., the cylinders are shorter in a poor solvent as compared to a good solvent. It is argued that the repulsion of the side chains represents the extension force, which acts against the entropic contraction force of the main chain. Thus, cylindrical brushes may be suitable as responsive materials for sensors, actuators or soft machines.     

Energy-driven asymmetric partitioning of a semiflexible polymer between interconnected cavities

The distribution of a semiflexible chain in the volume of two interconnected spherical cavities of equal size has been investigated by using Monte Carlo simulations. The chain possessed an extension exceeding that of the cavity, leading to large probabilities of translocated states despite the entropic penalty of passing the narrow passage. Furthermore, an asymmetric state with unequal subchain lengths in the two cavities was more favorable than the symmetric state. The preference for the asymmetric state is driven by the bending energy. Basically, in the symmetric state both subchains are forced to be bent, whereas in the asymmetric case only one of the subchains must bend, leading to an overall smaller bending penalty and overall smaller free energy of the asymmetric state. These results are in contrast to the entropy-controlled partitioning of polymers into confinement and the symmetric translocation state appearing for flexible polymers.