Polymer translocation through nanopore into active bathMingfeng Pu, Huijun Jiang, and Zhonghuai Hou

Citation: The Journal of Chemical Physics 145, 174902 (2016); doi: 10.1063/1.4966591View online: http://dx.doi.org/10.1063/1.4966591View Table of Contents: http://aip.scitation.org/toc/jcp/145/17Published by the American Institute of Physics

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THE JOURNAL OF CHEMICAL PHYSICS 145, 174902 (2016)

Polymer translocation through nanopore into active bathMingfeng Pu, Huijun Jiang, and Zhonghuai Houa)

Department of Chemical Physics and Hefei National Laboratory for Physical Sciences at Microscales,iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China

(Received 22 July 2016; accepted 12 October 2016; published online 1 November 2016)

Polymer translocation through nanopores into a crowded environment is of ubiquitous importancein many biological processes. Here we investigate polymer translocation through a nanopore into anactive bath of self-propelled particles in two-dimensional space using Langevin dynamics simula-tions. Interestingly, we find that the mean translocation time ⟨τ⟩ can show a bell-shape dependenceon the particle activity Fa at a fixed volume fraction φ, indicating that the translocation process maybecome slower for small activity compared to the case of the passive media, and only when theparticle activity becomes large enough can the translocation process be accelerated. In addition,we also find that ⟨τ⟩ can show a minimum as a function of φ if the particle activity is largeenough, implying that an intermediate volume fraction of active particles is most favorable forthe polymer translocation. Detailed analysis reveals that such nontrivial behaviors result from thetwo-fold effect of active bath: one that active particles tend to accumulate near the pore, providing anextra pressure hindering the translocation, and the other that they also aggregate along the polymerchain, generating an effective pulling force accelerating the translocation. Such results demonstratethat active bath plays rather subtle roles on the polymer translocation process. Published by AIPPublishing. [http://dx.doi.org/10.1063/1.4966591]

I. INTRODUCTION

The phenomenon of polymer translocation throughnanopores and channels has gained extensive researchattention in the latest decade. On the one hand, polymertranslocation is closely relevant with many crucial biologicalprocesses, such as DNA and mRNA translocation throughnuclear pores, protein transport across membrane channels,virus injection into cell,1 and so on. On the other hand,it also has far-reaching technological potentials, includinggene therapy, rapid DNA sequencing, and controlled drugdelivery.2–7 A considerable number of works in the literature,both experimentally2,8–15 and theoretically,16–28 have beendevoted to study the polymer translocation process, which maybe influenced by many factors, such as the pore structure,3,9,29

the polymer-pore interaction,9,22,24,29,30 the solvent property,31

the polymer concentrations,32,33 and so on.In real systems, polymer translocation process usually

involves crowded environments. For instance, the volumefraction of large macromolecules and other inclusions incell interior can be as large as 50%.34 Experiments haveshown that crowded environment can affect the dynamicproperties of polymer such as reaction rates, protein foldingrates, and equilibria in vivo compared with those in dilutesolutions remarkably.35–37 It was also revealed that crowdedenvironment strongly influences the polymer translocationthrough nanopore. For instance, Gopinathan et al. haveconsidered a simple model wherein crowding was modeled byrandomly distributed spherical static obstacles, and novel

a)Author to whom correspondence should be addressed. Electronic mail:hzhlj@ustc.edu.cn

scaling behaviors of the translocation time have beendiscovered by treating the entropic penalty due to crowding.38

Cao et al. have used Monte Carlo simulation to investigatethe influence of crowding on three-dimensional polymertranslocation, they have found that normal diffusion can onlybe observed in dilute solution without obstacles, or in acrowded environment with weak polymer-obstacle attraction,otherwise, a sub-diffusion behavior of polymer is observed.39

Chen and Luo have used both theoretical analysis andLangevin dynamics simulation to study the size effect ofthe mobile crowding agents. It is found that the translocationundergoes a maximum value by changing the diameters ofagents at trans side with the fixed diameters at cis side whilethe crowding agents have equal area fraction at both cis andtrans sides.40

The above studies for polymer translocation all take intoaccount the crowded media as passive particles, i.e., theparticles will finally relax to an equilibrium state determinedby the interaction potential and temperature. Nevertheless, thecrowded media may also be active particles that are subjectedto some external driving force which renders the system to beout of equilibrium. Actually, dynamics of active matter hasgained extensive research attention in recent years, includingthose in living systems such as bacteria,41 spermatozoa, and42

mammals.43,44 A wealth of new non-equilibrium phenomenahave been reported, such as active swarming, large scale vortexformation,45,46 and phase separation,47–51 both experimentallyand theoretically. In particular, dynamics of polymer inactive media also shows many nontrivial phenomena. Forinstance, Kaiser and Löwen have considered a fully flexiblepolymer chain in a bacterial bath(or an active solvent), findingthat active bacteria can stiffen and expand the chain in a

0021-9606/2016/145(17)/174902/8/$30.00 145, 174902-1 Published by AIP Publishing.

174902-2 Pu, Jiang, and Hou J. Chem. Phys. 145, 174902 (2016)

FIG. 1. Schematic diagram of polymer translocation through a nanopore intoan active bath of SPPs which are represented by two hemispheres. Propellingforce Fa acting on each particles is along the blue-to-red direction.

non-universal way.52 J. Harder et al. found that rigidityof polymer can lead to interesting behaviors in activebath, e.g., a rigid filament can breath between a tighthairpin and an ensemble of extended conformation forintermediate activities.53 Recent works on filaments formedby active Brownian particles showed very interestingdynamic behaviors, including periodic beating and rotationalmotions,54–56 and so on. To the best of our knowledge,however, how the active media would influence the dynamicsof polymer translocation process has not been studied yet.

Motivated by this, in the present paper, we have studiedthe translocation process of a polymer through a small poreinto an active bath. For simplicity, we have considered a two-dimensional system with only active particles at the trans side(see Figure 1). We mainly focus on how the mean translocationtime ⟨τ⟩ would depend on the particle activity Fa as well as thevolume fraction φ of the particles. Very interestingly, we findthat ⟨τ⟩ shows a bell-shape dependence on the particle activityat a fixed volume fraction, indicating that the translocationprocess becomes slower for small activity compared to thecase of passive media. Only for large activity, can the polymertranslocation be accelerated. On the other hand, we find that⟨τ⟩ also shows a non-monotonic dependence on the volumefraction φ at a fixed particle activity, but now with a minimum,implying that the translocation process is mostly acceleratedat an intermediate volume fraction. Such findings clearlydemonstrate the nontrivial role that the active media plays inthe polymer translocation process.

The remainder of this paper is organized as follows. InSec. II, we describe our model and simulation method. InSec. III, we present our results and discussion followed byconclusion in Sec. IV.

II. MODEL

The polymer is modeled by a fully flexible self-avoidingbead-spring chain consisting of N beads with diameter σ.Neighboring beads are linearly connected via a harmonicpotential Ub(ri j) = ϵb

�ri j − r0

�2, where ri j is the center-to-center distance between each pair of adjacent beads, ϵb is thespring constant, and r0 denotes the equilibrium distance. Theexcluded volume effect is realized by a short range repulsiveLennard-Jones(LJ) potential,

ULJ(ri j) =

4ϵ

(σ

ri j

)12

−(σ

ri j

)6

+14

, ri j 6 21/6σ

0, ri j > 21/6σ

, (1)

where ri j is the distance between beads i and j, and ϵ denotesthe potential strength.

We consider a two-dimensional rectangular box of size2L × L as depicted in Fig. 1, wherein the polymer passesacross the wall in the middle through a pore of width ω.The trans side is an active bath of self-propelling particles(SPPs), which repel each other via the LJ potential same asEq. (1). The purely repulsive wall consists of one monolayerof immobile repulsive LJ particles. The dynamics of the SPPsis governed by the following Langevin equations:

mri = −γri + Fani(θi) − ∂Vi

∂ri+

2γkBTξi(t), (2)

θi =

2Drξi,r(t), (3)

where m is the particle mass, γ is the friction coefficient,kB is the Boltzmann constant, T is the temperature, D andDr are, respectively, the translational and rotational diffusioncoefficients with D = 3Dr/σ

2. Vi =

i, j ULJ(ri j), where thesummation j runs over all the other particles except i atthe trans side, including the SPPs, polymer beads, and wall-particles. Fa denotes the magnitude of the self-propelling forceexerted on the particle along the direction given by ni(θi)= (cosθi,sinθi). ξi(t) and ξi,r(t) are the Gaussian white noisesfor translational and rotational motion, respectively, whichsatisfy ⟨ξi(t)⟩ = 0,

ξi(t)ξ j(t ′)� = δi jδ(t − t ′), and

ξi,r(t)�

= 0,ξi,r(t)ξi,r(t ′)� = δ(t − t ′). Similarly, the dynamics of

a polymer bead i is described by

mri = −γri + Fext −∂V ′i∂ri+

2γkBTξi(t), (4)

where V ′i =

i, j ULJ(ri j) +Ub(ri, i+1) +Ub(ri, i−1) includesthe interactions of bead i with its two nearest neighbor beads(note that each of the two end-beads has only one nearestneighbor) and all other particles. For simplicity, the bead massm, friction coefficient γ, the temperature T , and the diffusionconstant D are chosen to be the same as those of the SPPs inEq. (2). In particular, Fext = Fextx denotes a constant externalforce inside the pore toward the trans side.

We use m, σ, and kBT as the fundamental units for mass,length, and energy, respectively. The dimensionless time unitis then τ0 =

mσkBT

. The parameters for our simulation are fixed

to be ϵb = 800kBT/σ2, r0 = 21/6σ, ϵ = 10kBT , γ = 10.0τ−10 ,

L = 50, and ω = 1.3σ. The external force in the pore isFext = 100.0, the length of polymer is N = 100, and the volumefraction of active particles is φ = 0.1, if not otherwise stated.In case of varying φ at the trans side, the value is in the rangefrom 0.01 to 0.3, which is below the threshold value for thespontaneous phase separation induced by activity.48,57 At thebeginning of translocation, the first monomer is fixed at thecenter of the pore and released after necessary relaxations. Allof the obtained results presented in this paper are averagedover at least 1000 independent runs.

174902-3 Pu, Jiang, and Hou J. Chem. Phys. 145, 174902 (2016)

III. RESULTS AND DISCUSSION

In the present work, we are mainly interested in how theactivity bath at the trans side would influence the polymertranslocation. To this end, we have investigated how theaverage translocation time ⟨τ⟩ would depend on the particleactivity Fa. To highlight the effect of activity, we havecalculated the relative translocation time ⟨τ⟩net = ⟨τ⟩ − ⟨τ⟩0,where ⟨τ⟩0 is the translocation time without particles at thetrans side. In Fig. 2, ⟨τ⟩net as a function of Fa at a fixedvolume fraction φ = 0.1 is presented. Very interestingly, ⟨τ⟩netshows a non-monotonic dependence on the active force Fa,i.e., ⟨τ⟩net first increases gradually for small values of Fa,reaches a maximum at a certain intermediate value of Fa,and then decreases for large Fa. Moreover, ⟨τ⟩net is largerthan 0 for small Fa, indicating that the particle activity atthe trans side hinders the polymer translocation in this case.When the particle activity becomes large enough, however, theactive bath can obviously accelerate the translocation process.Note that the occurrence of this nontrivial phenomenoncan be observed for varying Fext as also shown in Fig. 2.With decreasing external force, the non-monotonic behaviorbecomes more pronounced with the peak position shiftedtowards small values of Fa.

One should note that the nontrivial dependence of ⟨τ⟩on Fa as demonstrated above is quite counter-intuitive atthe first glance. Since an active particle tends to keep itsdirection during the persistence time period until it takesrandom rotation, the effect of active bath should be differentfrom that of a passive bath. Generally, one expects that theactive particles should considerably influence the polymertranslocation, since they may exert some kind of force on thepolymer segments that have already passed across the pore.This force could accelerate or suppress the translocation,depending on how active particles interact with the polymerbeads, as one may think. Nevertheless, that the effect canchange from a negative one, i.e., ⟨τ⟩net > 0, to a positive onewith ⟨τ⟩net < 0 as shown in Fig. 2, is quite not easy to beunderstood straightforwardly.

FIG. 2. Relative translocation time ⟨τ⟩net as a function of active force Fa fordifferent external force Fext with volume fraction φ = 0.10. The green dottedline indicates ⟨τ⟩net= 0.

In order to understand in more detail about such nontrivialdependence of ⟨τ⟩ on Fa, we have analyzed the translocationprocess by studying the waiting time W (s) which is theaverage time between monomer s and monomer s + 1 tofirst pass through the pore. W (s) then measures how longit takes averagely for the monomer s to pass through thepore. We can also investigate the accumulative waiting timeτ(s) defined as τ(s) = s

i=1 W (s), which describes how longit takes from the beginning to the moment as the monomers + 1 passes through the pore. In Fig. 3, the dependences ofW (s) and τ(s) as functions of s for Fext = 100.0 are depictedfor a relatively small active force Fa = 15.0 and a largerone Fa = 50.0, respectively, compared to the case Fa = 0 fora passive system. For small activity Fa = 15.0 as shown inFig. 3(a), the curve for W (s) is slightly above that for passivesystem with Fa = 0, for all the monomers. Accordingly,τ(s) (Fa = 15.0) is always larger than τ(s) (Fa = 0.0) for anys as shown in Fig. 3(b) and its inset. Therefore, for Fa = 15.0,the polymer translocation is always suppressed during thewhole translocation process, as compared to the passive casewith Fa = 0. For relatively large activity Fa = 50.0 as shown inFigs. 3(c) and 3(d), the situation is quite different. Overall, wesee that the curve for W (s) (Fa = 50) is apparently below thatfor Fa = 0, indicating that particle activity at the trans side nowapparently accelerates the translocation process in accordancewith Fig. 2. Interestingly, for small s (.12), one can see thatW (s) (Fa = 50) is still larger than W (s) (Fa = 0), indicatingthat the translocation is hindered by the active particles in theearly stage. After that, W (s) (Fa = 50) becomes considerablysmaller than W (s) (Fa = 0) indicating apparent acceleration byparticle activity. This is also demonstrated in Fig. 3(b), wherethe difference τ(s) (Fa = 50) − τ(s) (Fa = 0) first increases alittle and then decreases substantially with the increment ofmonomer index s.

The above analysis suggests that the active particlestend to suppress the translocation process at the early stage,whether the active force is large or not. While at the latterstage, large active force may help the translocation process.To get more insight into these effects, we have depicted sometypical snapshots of the polymer and active particles at thetrans side in Fig. 4 at early and late translocation stagesfor Fa = 15 and Fa = 50, respectively. In the early stages,for both small and large particle activities, one can see thatthe particles aggregate near the pore and thus produce anextra effective pressure to the cis side which is unfavorableto the translocation. Actually, this is in accordance with thephenomenon reported in the literature that active particlestend to accumulate near walls or angles when they move ina confined space.58,59 Such an activity-induced aggregationis more pronounced for larger driving forces; hence, thedeceleration effect is larger for Fa = 50 than that for Fa = 15at the early stage as discussed in the last paragraph. However,at the late stage when many monomers have passed across thepore, the active particles can also aggregate along the longexposed part of the polymer chain at the trans side as shownin Figs. 4(b) and 4(d). Active particles aggregating around thepolymer tend to maintain their movement directions and thusalso exert a force on the chain to bring the polymer movingtogether. For large active force Fa = 50 as demonstrated

174902-4 Pu, Jiang, and Hou J. Chem. Phys. 145, 174902 (2016)

FIG. 3. Waiting timeW (s) ((a) and (b)) and cumulative waiting time τ(s) ((c) and (d)) for the translocation of flexible polymer into different active environmentswith Fa = 15.0 ((a) and (c)) and Fa = 50.0 ((b) and (d)). Ones for Fa = 0.0 are also plotted for comparison. The values of τ(s) for Fa = 15.0 and Fa = 50.0relative to the one for Fa = 0.0 are presented in insets of (c) and (d), respectively.

FIG. 4. Typical snapshots of polymer configuration at the very beginningof translocation process for (a) Fa = 15.0 and (c) Fa = 50.0, and at thelatter stage for (b) Fa = 15.0 and (d) Fa = 50.0. Here, active particles awayfrom the polymer are rendered with a semitransparent filter to give a clearpicture.

in Fig. 4(d), this extra force leads to an extension of thepolymer chain and thus accelerates the polymer translocationprocess. Therefore, we think that it is the two-fold effect ofthe active particles: one that they tend to accumulate nearthe pore and the other that they also aggregate along thepolymer chain, the relative strength of which depends on theactive force, that results in the non-monotonic dependenceof the translocation time τ on the active force as shown inFig. 2.

The above results are obtained at a fixed volume fractionof the active particle φ = 0.1. One may then wonder how thetranslocation process depends on the volume fraction φ. InFig. 5, the dependences of the mean translocation time ⟨τ⟩ onφ for three different values of active force Fa are presented.Interestingly, we find that ⟨τ⟩ undergoes a clear-cut minimumwith the increment of φ, indicating that there exists an optimalvolume fraction of active particles in the trans bath that is mostfavorable to the polymer translocation. This optimal behavioris more pronounced for a larger active force, and for Fa = 30as shown in the figure, the curve already becomes nearlymonotonic-increasing with φ. Therefore, this non-monotonicdependence on φ would not be observed for a passive bathwhere Fa = 0. We have also analyzed the behaviors of W (s)and τ(s) at different volume fractions with given Fa = 50,as demonstrated in Fig. 6. Compared to the case φ = 0.1,where the translocation time ⟨τ⟩ is the smallest, W (s) forφ = 0.3 is larger for all s, indicating that the translocation is

174902-5 Pu, Jiang, and Hou J. Chem. Phys. 145, 174902 (2016)

FIG. 5. Average translocation time ⟨τ⟩ as a function of volume fraction φ fordifferent active forces Fa = 0.0,30.0, 50.0, and 70.0.

slower during the whole process. For φ = 0.01, overall thetranslocation is also slower than that for φ = 0.1, while itis a little bit faster in the early stage (s . 18) as shown inFigs. 6(a) and 6(c).

The reason why there exists an optimal value of φwhich is the most helpful for translocation is not easy

to be understood. Here we just try to give a qualitativeillustration. For Fa = 50, the activity is already large enoughsuch that the positive “pulling” effect of the active particlesdominates the negative “pressure” effect, as discussed in thelast paragraph. Nevertheless, to make this positive “pulling”effect work, enough number of active particles should benecessary to aggregate along the polymer chain. In Figs. 3and 4, the volume fraction is φ = 0.1 which is demonstratedto be enough. If we reduce the volume fraction of activeparticles (equally decrease the number of active particles), say0.01, the number of particles aggregating along the polymerchain decreases, such that the translocation becomes slower inFig. 7(a). However, if the volume fraction is too large, say 0.3here, the trans side gets crowded and the particles may formclusters as shown in Fig. 7(c), thus also leading to a slowingdown of the translocation.

The above findings strongly suggest us to performextensive simulations to study the dependence of thetranslocation time ⟨τ⟩ in the Fa − φ parameter plane. Fig. 8presents the contour plot of ⟨τ⟩net. Clearly, two types ofnon-monotonic behaviors can be observed. On the one hand,at a fixed volume fraction φ, ⟨τ⟩net undergoes a maximumwith increasing Fa, indicating that an intermediate level ofparticle activity suppresses the translocation process moststrongly. Moreover, the position of maximum shifts to largerFa with increasing volume fraction φ. On the other hand,

FIG. 6. Waiting timeW (s) ((a) and (b)) and cumulative waiting time τ(s) ((c) and (d)) for the translocation of flexible polymer into different active environmentswith φ = 0.10 ((a) and (c)) and φ = 0.30 ((b) and (d)). Ones for φ = 0.03 are also plotted for comparison. The values of τ(s) for φ = 0.10 and φ = 0.20 relativeto the one for φ = 0.01 are presented in the insets of (c) and (d), respectively.

174902-6 Pu, Jiang, and Hou J. Chem. Phys. 145, 174902 (2016)

FIG. 7. Typical snapshots of polymer configuration atthe later stage of translocation process for (a) φ = 0.01,(b) φ = 0.10, and (c) φ = 0.30. The active force is Fa

= 50.0. For the sake of clarity, the active particles awayfrom the polymer are rendered with a semitransparentfilter.

⟨τ⟩net shows a clear-cut minimum with the variation of φ if theactive force Fa is fixed and large enough. This means that thetranslocation process is mostly accelerated in an active bathwith an intermediate volume fraction. The optimal value of φbecomes larger with increasing active force Fa. Therefore, theactive bath facilitates us to control the polymer translocationvia tuning the particle activity or volume fraction. To suppressthe translocation most efficiently, an intermediate value of Fa

and a high volume fraction are preferred. On the other hand,to accelerate the translocation, the volume fraction shouldbe at an optimal value and the particle activity should belarge.

Finally, we have also investigated the dependence ofthe translocation time ⟨τ⟩ on the chain length N . Bothexperiments and numerical simulations have suggested apower law dependence between ⟨τ⟩ and N , i.e., τ ∼ Nα.The exponent α may depend on the friction force thepolymer is experienced, or the range of the polymer length.It was found that for transmembrane process at moderatevalues of the friction, the scaling exponents are close to2v and 1 + v for relatively short and long polymers,28,60,61

respectively, where v is the Flory exponent. At high friction,only α = 1 + v is observed even for short chains.60 For oursystem considered here, due to that trans side contains agreat amount of active particles, the space confinement onlyallows us to consider relatively short polymers. Fig. 9(a)shows the log-log plots of ⟨τ⟩ as a function of N fordifferent Fa under a fixed volume fraction φ = 0.10. Thescaling exponent presented here should be considered as aneffective value due to the fact that the simulated polymer

FIG. 8. Contour plot of the relative translocation time ⟨τ⟩net= ⟨τ⟩− ⟨τ⟩0 inthe Fa–φ plane.

is relatively short. It is shown that the effective scalingexponent α is not a constant but varies with Fa in therange of chain length under consideration. For comparison,the scaling law for φ = 0.0 is also shown (dashed line)where the exponent is α = 1.66 which is slightly largerthan 2v and close to 1 + v , where v = 0.75 is the Floryexponent in two dimension. As demonstrated in Fig. 9(a), theexponent α decreases with the increment of Fa, which is inaccordance with the fact that a higher friction usually leads toa larger effective value of α.60 We have also studied how theexponent α depends on the volume fraction φ, as shown inFig. 9(b). Generally, α decreases monotonically with φ, andthe decreasing tendency becomes stronger with increasingparticle activity. Overall, larger Fa and φ result in smaller αsince active force balances the friction force or increases thedriving force.

FIG. 9. (a) Translocation time ⟨τ⟩ as a function of the chain length N and(b) the scaling exponent α as a function of the volume fraction φ for adifferent active force Fa. The black dashed line in (a) indicates the onewithout particles at the trans side.

174902-7 Pu, Jiang, and Hou J. Chem. Phys. 145, 174902 (2016)

IV. CONCLUSIONS

In conclusion, the dynamics of polymer translocationinto an active environment has been investigated in a two-dimensional space. It has been found that active bath can resultin two-fold effects on polymer translocation: one of which isthat accumulation of active particles near the pore providesan extra “pushing” force and the other is that aggregationof active particles near the polymer generates an effective“pulling” force. Such effects lead to a non-monotonic meantranslocation time ⟨τ⟩ varying with active force Fa at a fixedvolume fraction φ, or with varying φ at a fixed particleactivity. Consequently, the polymer translocation process maybecome slower in an active bath than that in a passive one,if the particle activity is small. The translocation processcan be accelerated by the active bath only when the particleis large enough. Interestingly, an intermediate number ofparticles in the active bath may be the most favorable for thetranslocation due to the competition between activity-inducedpulling and the crowding effect. Such a global picture isclearly demonstrated in the contour plot of ⟨τ⟩ in the Fa–φplane, which guides how one can control the translocationprocess via tuning the particle activity or volume fraction. Wehave also investigated how ⟨τ⟩ depends on the chain length N ,finding that good power-law scaling relations hold while theexponent decreases monotonically with Fa and φ. It should bepointed out that the non-trivial behavior as illustrated above isobtained under the two-dimensional confinement. For systemsin three dimensions (not simulated in the presented paper),the situation may differ. Since the wall is 2-dimensionalwhile the polymer remains 1-dimensional, the probability ofcollision between active particles and the polymer will reducein relative to the one of collision between active particles andwalls. We expect that, compared to a 2d system, increasing thedimension of the system will result in a weaker acceleratingeffect but a stronger decelerating effect. Besides the influenceof polymer stiffness on translocation time is also worthy tobe simulated, which should be discussed in the further work.Our results highlight the nontrivial role of active bath onpolymer translocation which may shed some new lights onunderstanding such an important process in real biologicalsystems.

ACKNOWLEDGMENTS

This work is supported by the National Basic ResearchProgram of China (Grant No. 2013CB834606), by theNational Science Foundation of China (Grant Nos. 21521001,21473165, and 21403204), by the Ministry of Science andTechnology of China (Grant No. 2016YFA0400904), and bythe Fundamental Research Funds for the Central Universities(Grant Nos. WK2060030018, 2030020028, and 2340000074).

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