Low-Resistant Band-Passing Noise and Its Dynamical Effects

We propose an n-order noise,which is realized by driving an n-order linear differential equation with aGaussian white noise.The time-derivative noise is a low-resistant band-passing noise.If the derivative noise is regardedas a thermal one,the system has a vanishing effective friction and it should induce ballistic diffusion of a free particleat long times.The simulation method for the generalized Langevin equation driven by the n-order noise is discussedsystematically.The features of three-order derivative noises are presented when they are applied to a ratchet system.

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.

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.

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.

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.

Modified fusion probability by reflection boundary

We investigate the time-dependent probability for a Brownian particle passing over the barrier to stay at a metastable potential pocket against escaping over the barrier. This is related to the whole fusion-fission dynamical process and can be called the reverse Kramers problem. By the passing probability over the saddle point of an inverse harmonic potential multiplying the exponential decay factor of a particle in the metastable potential, we present an approximate expression for the modified passing probability over the barrier, in which the effect of the reflection boundary of the potential is taken into account. Our analytical result and Langevin Monte-Carlo simulation show that the probability of passing and against escaping over the barrier is a non-monotonous function of time and its maximal value is less than the stationary result of the passing probability over the saddle point of an inverse harmonic potential.