Translocation of Polymer Through a Nanopore Studied by Langevin Dynamics:Effect of the Friction Coefficient

The driven polymer translocation through a nanopore with unbiased initial configuration has been studied by using Langevin dynamics(LD) simulations.It is found that the scaling relationship between translocation time and the polymer chain length is strongly affected by the friction coefficient in LD and the driving force.However,there is no scaling relationship between the translocation time and the friction coefficient.The translocation time is almost inversely proportional to the driving force,which is in agreement with those obtained in biased translocation.The scaling relationship between gyration radius(R g) of subchain at the trans side with the subchain length(L) is R g ～L 0.33 that is in good agreement with the limiting value for molten globule state,while the curve of R g of subchain at the cis side has two distinct stages.During translocation,the subchain at the cis side is being stretched gradually,and the structure of the subchain transforms from sphere-like to rod-like.When the effect of stretching reaches the tail end,the subchain is at the most stretched state.Finally the subchain will rapidly restore to coil structure.According to the results of force analysis,the retarding force at the trans side is more crucial during the practical translocation.

Numerical Study of the Efficiency of Multi-Layer Membrane Filtration in Desalination Processes

Multi-layer membrane filtration is a widely used technology for separating and purifying different components ofa liquid mixture. This technique involves passing the liquid mixture through a series of membranes with decreasing pore sizes, which allows for the separation of different components according to their molecular size. Thisstudy investigates the filtration process of a fluid through a two-dimensional porous medium designed forseawater desalination. The focus is on understanding the impact of various parameters such as the coefficientof friction, velocity, and the number of layers on filtration efficiency. The results reveal that the number of layersplays a crucial role in desalination, with an increase in layers leading to enhanced filtration quality, following apower law relationship. The study explores the influence of the coefficient of friction on filtration performance,emphasizing its significant effect on the number of particles filtered over time. Additionally, the role of the initialvelocity in filtration efficiency is examined, showing distinct effects at both high and low velocities. Biofouling isidentified as a factor influencing filtration, with an initial increase in filtered particles followed by a decline due toparticle accumulation in pores.

Transition from isotropic to polar state of self-driven eccentric disks

Inspired by the eccentricity design of self-driven disks,we propose a computational model to study the remarkable behavior of this kind of active matter via Langevin dynamics simulations.We pay attention to the effect of rotational friction coefficient and rotational noise on the phase behavior.A homogeneous system without rotational noise exhibits a sharp discontinuous transition of orientational order from an isotropic to a polar state with the increase of rotational friction coefficient.When there is rotational noise,the transition becomes continuous.The formation of polar state originates from the effective alignment effect due to the mutual coupling of the positional and orientational degrees of freedom of each disk.The rotational noise could weaken the alignment effect and cause the large spatial density inhomogeneity,while the translational noise homogenizes the system.Our model makes further conceptual progress on how the microscopic interaction among self-driven agents yields effective alignment.

Superselective Adsorption of Multivalent Polymer Chains to a Surface with Receptors

Multivalent polymer chains exhibit excellent prospect in biomedical applications by serving as therapeutic agents. Using three-dimensional （3D） Langevin dynamics simulations, we investigate adsorption behaviors of multivalent polymer chains to a surface with receptors. Multivalent polymer chains display superselective adsorption. Furthermore, the range of density of surface receptors at which a multivalent polymer chain displays a superselective behavior, narrows down for chains with higher density of ligands. Meanwhile, the optimal density of surface receptors where the highest superselectivity is achieved, decreases with increasing the density of ligands. Then, the conformational properties of bound multivalent chains are studied systematically. Interestingly, we find that the equilibrium radius of gyration Rg and its horizontal component have a maximum as a function of the density of surface receptors. The scaling exponents of Rg with the length of chain suggest that with increasing the density of surface receptors., the conformations of a bound multivalent polymer chain first fall in between those of a two-dimensional （2D） and a 3D chain, while it is slightly collapsed subsequently.

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 sinmlations. The power-law scaling of the translocation time T 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 T - N^a with the exponent a varying from a = 0.71 for relatively short chains to a = 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 transloeation of double-strand DNA. The distribution of translocation time D（τ） is close to a Gaussian function for duration time τ 〈 τp and follows a falling exponential function for duration time T 〉 wp. For closed knotted polymers, the scaling exponent a 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.

Anomalous and Normal Diffusion of Tracers in Crowded Environments： Effect of Size Disparity between Tracer and Crowders

The dynamics of tracers in crowded matrix is of interest in various areas of physics, such as the diffusion of proteins in living cells. By using two-dimensional （2D） Langevin dynamics simulations, we investigate the diffusive properties of a tracer of a diameter in crowded environments caused by randomly distributed crowders of a diameter. Results show that the emergence of subdiffusion of a tracer at intermediate time scales depends on the size ratio of the tracer to crowders a. If a falls between a lower critical size ratio and a upper one, the anomalous diffusion occurs purely due to the molecular crowding, tqlrther analysis indicates that the physical origin of subdiffusion is the ＂cage effect＂. Moreover, the subdiffusion exponent α decreases with the increasing medium viscosity and the degree of crowding, and gets a minimum αmin=0.75 at δ=1. At long time scales, normal diffusion of a tracer is recovered. For δ≤1, the relative mobility of tracers is independent of the degree of crowding. Meanwhile, it is sensitive to the degree of crowding for δ〉l. Our results are helpful in deepening the understanding of the diffusive properties of biomacromolecules that lie within crowded intracellular environments, such as proteins, DNA and ribosomes.

Effective transport of passive particles induced by chiral-active particles in microchannel

Transport of passive particles induced by chiral-active particles in microchannel is investigated by using the overdamped Langevin dynamics simulation in a two-dimensional model system. Due to the chirality of active particles and special structure of microchannel, effective ratchet transport of passive particles is achieved. Effective transport of passive particles depends on the width of microchannel（d）, the density（ρ）, and the angular velocity（ω） of chiral-active particles.There exist optimal parameters for d and ω at which the transport efficiency for passive particles takes its maximal value.This investigation can help us understand the necessity of active motion for living systems to maintain a number of vital processes such as materials transport inside cells and the foraging dynamics of mobile organisms.

Pseudopotential Density-Functional Calculations for Structures of Small CarbonClusters CN （N=2-8）

We introduce a first-principles density-functional theory,i.e.the finite-difference pseudopotential density- functional theory in real space and the Langevin molecular dynamics annealing technique,to the descriptions of structures and some properties of small carbon clusters(C_N,N=2～8).It is shown that the odd-numbered clusters have linear structures and most of the even-numbered clusters prefer cyclic structures.

Two-dimensional Langevin modeling of fission dynamics of the excited compound nuclei ^(188)Pt,^(227)Pa and ^(251)Es

A stochastic approach based on one-and two-dimensional Langevin equations is applied to calculate the pre-scission neutron multiplicity,fission probability,anisotropy of fission fragment angular distribution,fission cross section and the evaporation cross section for the compound nuclei ^188Pt,^227Pa and ^251Es in an intermediate range of excitation energies.The chaos weighted wall and window friction formula are used in the Langevin equations.The elongation parameter,c,is used as the first dimension and projection of the total spin of the compound nucleus onto the symmetry axis,K,considered as the second dimension in Langevin dynamical calculations.A constant dissipation coefficient of K,γk=0.077（MeV zs）^-1/2）,is used in two-dimensional calculations to reproduce the above mentioned experimental data.Comparison of the theoretical results of the pre-scission neutron multiplicity,fission probability,fission cross section and the evaporation cross section with the experimental data shows that the results of two-dimensional calculations are in better agreement with the experimental data.Furthermore,it is shown that the two-dimensional Langevin equations together with a dissipation coefficient of K,γk=0.077（MeV zs）^-1/2,can satisfactorily reproduce the anisotropy of fission fragment angular distribution for the heavy compound nucleus^251Es.However,a larger value of γk=0.250（MeV zs）^-1/2is needed to reproduce the anisotropy of fission fragment angular distribution for the lighter compound nucleus^227Pa.

Diffusion of nanochannel-confined knot along a tensioned polymer

The knots frequently occur in biopolymer and their diffusion plays an active role in the gene regulation.In this work,Langevin dynamics simulations were carried out to detect the diffusion behaviours of a knot along a tensioned polymer in different spatial constraints.The polymer accommodating a knot was tethered to two macrospheres to block the unravelling of the knot.As a result,the curves for the diffusion coefficients of the knot with different bending stiffness as a function of the tension in different spatial constraints were obtained.In the space without constraints or with weak constraints,the corresponding curves for the knot with relatively large bending stiffness exhibited two turnover behaviours.On the contrary,for the knot with relatively small bending stiffness,the diffusion coefficients were monotonically reduced with increasing tension.However,in a space with strong constraints,all the curves showed one turnover behaviour regardless of the bending stiffness.The turnover behaviours divided the curves into different regimes,and the dominant diffusion mechanisms in the regimes,namely,knot-region breathing,self-reptation,and internal friction,were clearly identified.The effective friction coefficientsξof the knots with 3_(1),4_(1),5_(1) and 5_(2) types as a function of the knot size N at a fixed tension were well fitted by the relationξ∝N.The effective friction coefficients of the knots at relatively large tension f>3 sharply increased with the knot complexity,which is not dependent on the spatial constraints.By contrast,the values of these coefficients at relatively small tension f≤3 were remarkably dependent on the spatial constraints.Our work not only provides valuable simulation results to assist the understanding of the diffusion of DNA knot,but also highlights the single-molecule design for the manipulation of DNA knots in future.

Ejection Dynamics of Semiflexible Polymers out of a Nanochannel

Using theoretical analysis and three-dimensional Langevin dynamics simulations, we investigate the influence of chain rigidity on the ejection dynamics of polymers from a nanochannel. We find that there exist two distinct dynamical regimes divided by a critical chain length for both flexible and semiflexible chains. At the short chain regime, semiflexible chains eject faster than flexible chains of the same chain length due to the longer occupying length. In contrast, at the long chain regime, semiflexible chains eject slower than flexible ones as the effective entropic driving force decreases. Based on these results, we propose that the nanochannels could be used to separate flexible and semiflexible chains effectively.

Conformational Behavior of Single Circular Semiflexible Polyelectrolyte in the Presence of Multivalent Counterions

Langevin dynamics simulations are employed to explore the effects of chain stiffness and electrostatic interaction(EI) on the conformational behavior of a circular semiflexible polyelectrolyte(CSPE) in presence of trivalent counterions.We investigate the effect of bending energy b and the dimensionless Bjerrum length A on the conformational behavior of the CSPE with a fixed chain length.The competition among the EIs,chain stiffness and entropy of the system leads to rich conformations for the CSPE.As the b is less than or equal to 50,The shape of the CSPE changes from a oblate ring to a rod at small A,then to a toroid at intermediate A,and finally to a globule at very large A.However,the globular conformation is not observed for large b.In addition,we find that the number of torus ring increases with A increase,while decreases with b increase.This study should be helpful in gaining insight into the conformational behaviour of charged biopolymer.

Translocation of Heterogeneous Flexible Polymers Assisted by Binding Particles

A polymer chain usually contains two or more types of monomeric species from the perspective of polymer chemistry,which poses achallenge to the understanding of structure-property relationships.It is of course true in the field of polymer translocation.In the present work,Iinvestigate the translocation dynamics of heterogeneous flexible polymers composed of two types of monomers labeled A and B through ananopore assisted by binding particles(BPs)by using the coarse-grained Langevin dynamics simulations in two-dimensional domains.Specifically,multiblock copolymers with different block lengths and monomeric components are considered.I critically examine how thetranslocation dynamics responds to the variations in the block length and the monomeric content.Interestingly,it is found that the periodicstructure of a multiblock copolymer causes an obvious fingerprint feature in the residence time of individual monomers in which the number ofpeaks is exactly equal to the number of blocks.These findings provide a basic understanding about the sequence-dynamics relationship for theBPs-assisted translocation of heterogeneous flexible polymers.

Effect of Solvent Viscosity on the Driven Translocation of Charged Polymers through Nanopores

The effect of viscosity of non-translocated(cis)side,ηcis,on the driven translocation of charged polymers through nanopores is investigated using Langevin dynamics simulation.Results show that the translocation of polymer chains can be regulated by changingηcis.Asηcis decreases,the translocation timeτdecreases,and the exponentδin the scaling relation with driving force f,τ~f-δ,increases whereasαin the scaling relation with chain length N,τ~Nα,decreases.Simultaneously,the conformation of the polymer chain at the cis side gravitates towards an equilibrium state.The results imply a relationship between the translocation and the conformation of polymer chains.To verify this hypothesis,we change the conformation of polymer by artificially relaxing the translocating polymer via adding an additional relaxation time in the simulation.A sufficient large additional relaxation time for the translocating polymer chain at the cis side only or at both cis and trans sides results in exponentsαandδboth close to 1,in contrast toα=1.36 andδ=0.8 for the translocation without the additional relaxation.The additional relaxation for the polymer chain at the cis side accelerates the translocation and plays a more important role than that for polymer chain at the trans side.