Translocation Dynamics of a Semi-flexible Chain Under a Bias: Comparison with Tension Propagation Theory

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1 Translocation Dynamics of a Semi-flexible Chain Under a Bias: Comparison with Tension Propagation Theory Aniket Bhattacharya Department of Physics, University of Central Florida, Orlando, Flor ida , USA (Dated: December 2, 2012) We study translocation dynamics of a semi-flexible polymer through a nanoscopic pore in two dimensions (2D) using Langevin dynamics simulation in presence of an external force inside the pore. We observe that for a given chain length N the mean first passage time (MFPT) τ increases for a stiffer chain. By repeating the calculation for various chain lengths N and bending rigidity parameter κ b we calculate the translocation exponent α ( τ N α ). For chain lengths N and bending rigidity κ b considered in this paper we find that the translocation exponent α satisfies the inequality α < 1 + ν, where ν is the equilibrium Flory exponent for a given chain stiffness, as previously observed in various simulation studies for fully flexible chains. We observe that the peak position of the residence time W(s) as a function of the monomer index s shifts at a lower s-value with increasing chain stiffness κ b. We also monitor segmental gyration R g(s) both at the cis and trans side during the translocation process and find that for κ b 0 the late time cis conformations are nearly identical to the early time trans conformations, and this overlap continues to increase for stiffer chains. Finally, we try to rationalize dependence of various quantities on chain stiffness κ b using Sakaue s tension propagation(tp) theory [Phys. Rev. E 76, (2007)] and Brownian Dynamics Tension Propagation (BDTP) theory due to Ikonen et al. [Phys. Rev. E (2012); J. Chem. Phys (2012)] originally developed for a fully flexible chain to a semi-flexible chain. PACS numbers: A-, H-, r I. INTRODUCTION Translocation of polymer chains threading through a narrow channel has remained an active field of research for more than a decade [1, 2]. The phenomenon is of particular interest in the context of biopolymers as translocation is an important ubiquitous process in molecular biology. Translocation of DNA and RNA across nuclear pores, protein transport through membrane channels, and virus injection are examples of such processes [3]. In a series of pioneering experiments using single stranded as well as double stranded DNA translocating through α-hemolysin protein pore and synthetic nanopores [4 7], where the histogram of the mean first passage time (MFPT) was obtained by measuring the fluctuation in the channel current, it was demonstrated that a nanopore can be used to determine sequences of a heteropolymer. Further experimental and theoretical studies revealed that the interaction of the individual nucleotides with the nanopore has remarkable manifestation not only in the characteristic MFPT but also in the residence time distribution of the individual nucleotides transported across the pore [7 9]. Therefore, it is no surprise that recently nano-pore based techniques have been commercialized and are being used to detect sequences [10]. These exciting experiments have provided enough enthusiasm to develop a proper theoretical framework for polymer translocation through a nanopore. Sung and Park [11] and Muthukumar [12] considered translocation Electronic address: aniket@physics.ucf.edu as a one dimensional barrier crossing problem and derived expression for the translocation exponent α ( τ N α ) using free energy expression for a threaded polymer through the pore (Fig. 1). These initial predictions were N s cis s trans FIG. 1: Minimalist view of a polymer chain translocating through an ideal pore in a thin wall from cis to trans side in terms of the translocation (s) coordinate. The picture shows an instant of translocation when s segments are at the trans side with remaining N s segments at the cis side of a chain of length N. followed by many others [13]- [27] using back of the envelope estimates and dynamical scaling arguments [14, 15], analyzing folds of the chains [16, 17], incorporation of memory effects [18 20], mass and energy conservations [21]-[24], and tension propagation(tp) along the chain backbone [21, 25 27]. These experimental and theoretical developments have been supplemented by a large number of simulation studies which played crucial role in the theoretical developments in the field [8, 9],[26]-[45]. Almost all of the aforementioned theoretical and simulation studies have been addressed in the context of a

2 2 fully flexible chain. For example, a recent important theoretical development in terms of a TP model [21, 22], its subsequent modification [25], and adoption to Brownian dynamics (BDTP) [26, 27] considers fully flexible chains. But when one considers important biopolymers, e.g., DNA, RNA, Actin filaments, all of them exhibit finite bending rigidity under various physiological conditions. Therefore, it is rather demanding to extend the TP formalism for the semi-flexible chains and wonder how the chain stiffness will affect the tension propagation and hence the dynamics of a translocating chain. Unlike fully flexible polymers, one requires another length scale to describe a semi-flexible polymer in the bulk, namely its persistence length l p [46, 47]. In coarsegrained models (section-ii) this is introduced through a bending rigidity parameter κ b (for simplicity we consider a 2D case). The details of the molecular architecture and interactions of the individual building blocks are masked in this parameter. To understand the bulk properties and for length scale larger than l p, it is often useful to think a semi-flexible polymer as a flexible polymer of basicbuildingblockoflength l p [49,50]. However, incase of polymers threading through a pore, it is not clear if such coarse-graining will be appropriate when l p greater than the pore diameter σ pore. Let us now consider some aspects of theoretical and simulation studies of driven polymer translocation through a nanopore which will serve as the motivating factors for this article. Simulation studies for a fully flexible chain have revealed that for driven polymer translocation the chain is out of equilibrium and the configurations at the cis side are different than those at the trans side [41 44]. It has also been observed in MD simulation using bead spring model of polymer that for chain length N 500 the translocation exponent α < 1+ν [38]. On the theoretical front two developments are worth mentioning. First, this out of equilibrium aspects have been nicely captured in Sakaue s TP model [21, 22]. Secondly, by including pore friction into Sakaue s TP theory Ikonen et al. have demonstrated that the physical basis of the inequality α < 1 + ν is the chain length dependent pore friction and the finite chain length effect persist up to very long chains N 10 6 [26, 27]. An important aspect of the BDTP model is that by extending Sakaue s theory [21, 22] for a finite chain length N [26, 27], it introduces a new time scale t tp when the tension front reaches the last monomer on the cis side (Fig. 2(d)). As will be discussed in more detail in section-iii, a monomer inside the pore translocating during t t tp experiences progressively increasing viscous drag due to increased number of monomers at the cis side responding to the tension front (Fig. 2(b)-(c)). For t > t tp, the viscous drag at the monomer inside the pore decreases due to the decreased number of monomers at the cis side as they translocate to the trans side [26, 27]. This results is a nonmonotonic dependence of the residence time of the individual monomers at the pore and thus explains the peak in the residence time distribution W(s) s observed in various simulations studies of polymer translocation [8, 26, 27, 30, 31]. (a) (c) M =N s" t=0 s=0 t=t" s=s" (b) M=N s (d) t=t M=N s ~ t=t tp s=s s=s ~ FIG. 2: Depiction of tension propagation(tp) along the chain backbone; (a) at t = 0 the whole chain is at the cis side and relaxed; the position of a monomer M is shown with a solid red circle; (b) at t = t tension front (dashed green arc) is at the location of the monomer M but having s monomers at the trans side, M s monomers (red dashed-dot) under tension andn M monomersarestillrelaxed. (c)sameas(b) but at a later time when the tension front has reached another monomer M > M, and (d) at t = t tp when the tension front reaches the last monomer having the s-th monomer inside the pore. Evidently, this TP idea that a segment of a chain responding to a propagating disturbance need to be restricted to a fully flexible chain. The purpose of this paper is to demonstrate that it is possible to extend the ideas of the TP theory for semi-flexible chains. By carrying out Langevin dynamics simulation for several chain lengths and of different stiffness first we demonstrate that both the MFPT τ as well as the end-to-end distance R N for a semi-flexible chain increase as a function of chain stiffness parameter κ b. We then borrow ideas from thebdtpmodelanddemonstratethatmanyofourfindings, e.g., residence time of the individual monomers, segmental gyration radii at the cis and trans sides for the semi-flexible chains can be explained in terms of the ratio t tp / τ, which we find from simulation results is a decreasing function of the chain stiffness κ b. The format of the rest of the paper is as follows. In the next section we introduce the model. Results are presented in Section- III where we calculate several physical quantities, e.g., the MFPT τ, the residence time W(s) s, segmental gyration radii R g (s), end-to-end distance R N and show this connection explicitly. We conclude in section- IV with some remarks, although somewhat speculative, how the TP idea can be used to unravel the dynamics of real biopolymers.

3 3 II. THE MODEL We have used a bead spring model of a polymer chain with excluded volume, spring and bending potentials as follows [48]. The excluded volume interaction between any two monomers is given by short range Lennard-Jones (LJ) potential. U LJ (r) = 4ǫ[( σ r )12 ( σ r )6 ]+ǫ for r 2 1/6 σ = 0 for r > 2 1/6 σ. Here, σ is the effective diameter of a monomer, and ǫ is the strength of the potential. The connectivity between neighboring monomers is modeled as a Finite Extension Nonlinear Elastic (FENE) spring with U FENE (r) = 1 2 kr2 0ln(1 r 2 /R 2 0), where r is the distance between consecutive monomers, k is the spring constant and R 0 is the maximum allowed separation between connected monomers [48]. The chain stiffness is introduced by adding an angle dependent interaction between successive bonds as (Fig. 3) U bend (θ i ) = κ b (1 cosθ i ). Here θ i is the complementary angle between the bond vectors b i 1 = r i r i 1 and b i = r i+1 r i, respectively, as shown in Fig. 3. The strength of the interaction is characterized by the bending rigidity κ b. i 1 i θ i i+1 i+2 i+3 FIG. 3: Bead-spring model of a polymer chain with bending angle θ i subtended by the vectors b i = r i r i 1 and b i+1 = r i+1 r i. The purely repulsive wall consists of one monolayer(line) of immobile LJ particles of diameter σ at x = 0. The pore is created by removing two particles at the center (Fig. 4). Inside the pore, the polymer beads experience a constant force F ext and a repulsive potential from the inside wall of the pore. We use the Langevin dynamics with the following equation of motion for the i th monomer m r i = (U LJ +U FENE +U bend +U ext ) Γ v i + η i. Here Γ is the monomer friction coefficient and η i (t), is a Gaussian white noise with zero mean at a temperature T, and satisfies the fluctuation-dissipation relation: < η i (t) η j (t ) >= 6k B TΓδ ij δ(t t ). FIG. 4: Representation of the s-coordinate (s-th) monomer inside the pore in the bead-spring model of a translocating chain used in our simulation. The figure shows a N = 32 chain having the 14-th monomer (s = 14) inside the pore and the remaining N s = 18 monomers at the cis side. The springs joining the monomers are not shown. The reduced units of length, time and temperature are chosen to be σ, σ m ǫ, and ǫ/k B respectively. For the spring potential we have chosen k = 30 and R 0 = 1.5σ, the friction coefficient Γ = 0.7, the temperature is kept at 1.2/k B, and the value of the external potential is kept at F ext σ/ǫ = 5.0 throughout the simulation. The choice of the FEENE potential along with the LJ interaction parameters ensures that the average bond-length in the bulk b l = With the choice of these parameters probability of chain crossing is very low chain. These parametershavebeenchosentobethesameasinourrecent studies [8, 9, 26, 27] of polymer translocation of flexible chains for ready comparison of results. We also find that the average bond-length b l is almost independent of the range of chain stiffness parameter (κ b = 0 32) used in our simulation. The equation of motion is integrated with the reduced time step t = 0.01 following the algorithm proposed by van Gunsteren and Berendsen [51]. III. RESULTS We have studied 4 different chain lengths N =16, 32, 64, and 128 for several different values of the bending constantκ b = However, forclaritywepresentonly a limited set of data. First we equilibrated the polymer chain by placing the first monomer at the center of the pore. We then allow the polymer to translocate driven by the bias present uniformly inside the pore. For the translocation related properties we have taken statistics from at least 2000 independent runs. A. Equilibrium properties In order to understand the translocation behavior of a semi-flexible chain it is important to characterize some equilibrium bulk properties of the chain. For our purpose in this paper it is sufficient to study the average

4 4 gyration radii R g and the end-to-end distance R N = RN R N, where R N = r N r 1 is the end-to-end vector of the chain as a function of the bending parameter κ b. These properties are studied by first equilibrating the chain up to 5 times the relaxation time for each chain length, and then taking data form another 5 times relaxation time. dimensions (2D). For larger κ b the Flory exponent in- FIG. 6: Equilibrium gyration radii R g as a function of chain length on a log-log scale for κ b = 0.0 (black circles), κ b = 4.0 (red squares), κ b = 8.0 (green diamonds), κ b = 16.0 (blue uptriangles), andκ b = 32.0(magentaleft-triangles)respectively. creases and we observe a gradual crossover from the fully flexible chain limit to the rod limit when ν 1 (Table- I). B. Translocation FIG. 5: (a) Average equilibrium end-to-end distance R N as a function of κ b for chain length N = 16 (black circles), 32 (red squares), 64 (green diamonds) and 128 (blue triangles) respectively; (b) corresponding plot for R N /((N 1) b l ) to compare the relative extension of the chains. To get an idea to what extent chains are stretched with increasing bending stiffness κ b in Fig. 5 we have shown the average end-to-end distance R N as a function of κ b for several chain length. As expected, with increased stiffness parameter the chain becomes more extended and the relative extension compared to R N (κ b = 0) becomes more effective for shorter chain lengths as shown in the inset of Fig. 5. For the highest stiffness parameter κ b = 32 we observe that the shortest chain (N = 16) and longest chain (N = 128) become almost 90% and 70% elongated, compared to their respective contour lengths. We will find in section-iii-b that for a stiffer chain this will be a major contributing factor for the increase in translocation time. Likewise, we have also monitored the gyration radii for the stiff chains as shown in Fig. 6. For κ b = 0 the calculated Flory exponent ν = 0.76 from the log-log plot for the chain lengths N = is consistent with the theoretical value for the Flory exponent ν = 0.75 in two Now we discuss translocation of these semi-flexible chains under a bias inside the pore. One immediate question that comes to mind is that what happens to the MFPT for a stiffer chain compared to a flexible chain of same contour length? Our simulation results show that for a given chain length the average translocation time increases monotonically as a function of κ b (Fig. 7). Initially for small values of κ b the translocation time increases rapidly, but then slowly towards its saturation value for larger value of κ b when R N (N 1) l b so that d R N /dκ b becomes progressively small. For a fully flexible chain with n segments at the trans side the entropic barrier is given by S/k B = nlnn+(n n)ln(n n). This entropy barrier is maximum when n = N/2 and is given by S max = 2k B ln(n/2). Therefore, when the chain becomes stiffer the effective chain length is reduced to N/l p which implies that the barrier height is reduced. But a stiffer chain is more elongated. When such a stiff chain is protruded through the pore, it also loses its translational and orientational entropy which will increase the entropic barrier. Therefore, it is not obvious how the chain stiffness affects the actual translocation time. We observe that the entropy associated with the chain elongation and stiffness wins over the reduction of the entropy due to chain flexibility and for a given chain length the MFPT increases for a stiffer chain as evident from Fig 7. By comparing Fig. 5 and Fig 7 one can say that chain

5 5 elongation is the primary factor that contributes for the increased translocation time. This trend is self-evident from the fact that the translocation exponent α 2 for a rigid rod (although this argument is strictly true in one dimension). For a fully flexible chains of finite length N < it is now well established from the work of Ikonen et al. [26, 27] that for forced translocation the translocation exponent satisfies the inequality α < 1 + ν. The upper bound of the exponent 1 + ν was suggested by Kantor and Kardar based on the assumption τ R g / v CM, where v CM is the velocity of the center of mass of the chain [15]. If one assumes R g N ν and v CM 1/N and neglects pore friction then one gets τ N 1+ν. From simulation results for chain length up to N = 500 the observed translocation exponent satisfies α < 1 + ν. Ikonen et al. [26, 27] showed that the chain length dependent pore friction is significant even for chain of length N 10 5 (much larger than typically considered in regular MD simulation) and the exponent α 1+ν very slowly. In Table-I we show the translocation exponents obtained from Fig. 8 and the Flory exponents (Fig. 6) for the chains for several values of κ b. For the chain length and chain flexibility considered here we observe that the inequality α < 1+ν is satisfied for all values of κ b. This can be rationalized considering that both the finite chain length effect and the pore friction which lowers the value of α need not be special for a fully flexible chain and that the physical picture can be extended for semi-flexible chains is evident from the results shown in Table-I. FIG. 7: MFPT τ as a function of the bending rigidity κ b for four different chain lengths (a) N = 16, (b) N = 32, (c) N = 64, and (d) N = 128 respectively. We have determined the translocation exponent α ( τ N α )fordifferentchainstiffnessκ b showninfig.8. We observe that the translocation exponent increases from roughly 1.5 to 1.7 from a fully flexible chain to a chain characterized by the bending stiffness κ b = TABLE I: Comparison of translocation exponent α with 1+ν for different values of κ b showing the inequality α < 1+ν is satisfied for all values of κ b. κ b ν 1+ν α How translocation of the individual monomers are affected by the chain rigidity? A plot of the residence time W(s) as a function of the translocation index s reveals further details of the translocation process. Please note that W(s) is defined as the time that a monomer with index s (Fig. 4) spends inside the pore so that it satisfies the sum rule N W(s) = τ. m=1 FIG. 8: MFPT τ as a function of chain length on log-log scale κ b. Symbols have the same meaning as in Fig. 6. Previously residence time for a translocating chain has been studied in great detail for a fully flexible chain [8, 26, 27, 30]. Fig. 9(a) shows what has been previously observed for a fully flexible chain, although our parameters are slightly different. For a fully flexible chain with increasing chain length the peak position of the residence time shifts at a higher-s value. With increasing chain stiffness our simulation results show (Fig. 9(b)-(c)) that this trend is no longer true for κ b 0. However, for a

6 6 given chain length N in this case the peak position of W(s) m shifts at a lower-s value for a stiffer chain as shown in Fig. 10. We argue below that these results (Fig. 9 and Fig. 10) can be understood extending the physical picture of the BDTP theory for a semi-flexible chain as follows. becomes maximum for the monomer s = s inside the pore, causing W max (s) = W( s) (please see Fig. 2). For t > t tp the number of monomers responding to the drag force begins to decrease as the monomers exit through the pore to the trans side causing the W(s) to decrease for s > s. BDTP theory thus explains the peak at the W(s) s and relates it to the tension propagation time t tp. While this argument was given for a fully flexible chain the idea of tension propagation should not be limited to a fully flexible chain only. Our simulation results show that for a semi-flexible chain the position of this peak is an decreasing function of the chain stiffness as shown in Fig. 10. We have used the W(s) s plot to extract tension propagation time by equating the mean first passage time of s to t tp τ( s) = t tp. (1) This is shown in Table-II for a chain of length N = 128. Wenoticethatforafixedchainlengthwhileboth τ and TABLE II: τ, t tp, and the ratio t tp τ for different values of κ b for chain length N = 128. t κ b τ t tp tp τ FIG. 9: Residence time of the individual monomers as a function of the reduced coordinate s/n for three chain lengths N = 32, 64, and 128. (a) κ b = 0.0 (b) κ b = 8.0, and (c) κ b = 32.0 respectively. An important ingredient in the TP theory is the introduction of the tension propagation time t tp. This time corresponds the time when the tension propagation reaches the last monomer (N) at the cis side (Fig. 2(d)). If we denote the monomer inside the pore s(s-coordinate) at t = t tp then according to TP theory W max (s) = W( s). Thistensionpropagationtimet tp makesaqualitativedifference in the residence time of the individual monomers which is a consequence of the BDTP theory and can be understood qualitatively as follows. The propagating tension front sets the monomers to respond to the driving force applied at the pore. As time proceeds an increasing number of monomers at the cis side responds to this drag force causing the viscous force on the s monomer inside the pore to increase. This process continues until the tension front hits the last monomer when this drag force t tp increases for a stiffer chain the ratio ttp τ decreases indicating the tension propagates relatively faster for stiffer chain and will become negligible compared to the MFPT τ in the limit of a very stiff chain. Likewise, we also observe from Fig. 9(a) that for a fully flexible chain this ratio ttp τ increases with chain length.. One can then rationalize the peak positions for κ b 0 as in 9(b)-(c) by noting that for a given κ b (which is essentially a measure of the chain persistence length) the relative flexibility of a chain will depend on its chain length N also (Fig. 5) and therefore, the value of s, or the ratio ttp τ will depend on both κ b and N. We have also looked at the segmental gyration radii both at the trans and cis side during the translocation process [42]. Previously we studied this quantity for a fully flexible chain which relates the relative relaxation and conformations of the subchains with respect to the time each subchain arrives at the trans side [42]. Let us denote Rg cis (s) and Rg trans (s) as the segmental gyration radii when there are s monomers either at the cis or trans side respectively. Therefore, at the beginning of translocation Rg cis (t = 0) = Rg cis (N) and Rg trans (t = 0) = Rg trans (0). For simplicity we have omitted the superscripts trans and cis in Fig. 11 where we have shown the segmental gyration radii for a N = 64 chain for various stiffness. Please note that for the trans segments the index s increases as translocation proceeds

7 7 FIG. 10: Actual residence time of the individual monomers as a function of κ b for chain length N = 128. Please note that the peak position shifts at a lower s-value for a higher value of κ b. and is exactly the opposite for the cis segments. We immediately notice that the conformations at the cis and trans side continue to overlap up to a certain s value which increases with chain stiffness. This implies that the chain conformations up to the first s monomers translocated are very similar to the chain conformations for the last s monomers at the cis side (i.e. monomers with index N,N 1, N s+1). This conformational overlap can also be qualitatively understood from the TP theory. We just found that for a stiffer chain τ is longer resulting in a lower value of s. Therefore, a larger portion of the polymer remains on the cis side yet to be translocated when the tension front reaches the last bead. All these monomers under tension make the chain conformation straight which are similar to the conformations of the chain segments translocated initially. We verify this qualitative picture by calculating the slopes of the overlapping regions of the insets in each case of Fig. 11 where we find that R g (s) s. IV. SUMMARY & DISCUSSION In summary, we have studied translocation of semiflexible homopolymers through a nanopore in 2D using Langevin dynamics simulation. First we find that for a fixed chain length the MFPT increases with increasing chain stiffness. We also observe that the translocation exponent increases as well, as one expects that with increased chain stiffness there will be a gradual crossover to the rod limit and in the limit of very long chain α should scale as N 2. The calculated translocation exponent for chains of various stiffens still satisfies the inequality α < 1+ν as observed previously for fully flexible chains. For fully flexible chains this inequality was explained by BDTP theory invoking finite chain length effect and the pore friction. Our simulation studies indicate that these effects are present for semi-flexible chains, FIG. 11: Gyration radii as a function of the chain segment s both at the cis (black circles) and trans (red squares) for (a) κ b = 0.0, (b) κ b = 8.0 (c) κ b = 16.0, and (d) κ b = 32.0 for a chain of length N = 64. The insets show the corresponding log-log plot for trans (black lines) and cis (red dashed lines) segments. as expected. We have also calculated the tension propagation time t tp as a function of chain stiffness and chain length using Eqn. 1 which follows from BDTP theory. We find that the ratio t tp / τ (i) increases with chain length N for a fully flexible chain and (ii) decreases for a stiffer chain for a fixed chain length N. We have also rationalized the overlap of the late time conformations of the cis segments with the early time conformations of the trans segments by invoking tension propagation picture. From these studies we conclude that the TP picture to study polymer translocation through narrow pore can be extended to semi-flexible chains. The advantage of BDTP theory is that it is extremely fast so that, unlike regular Brownian dynamics or molecular dynamics simulations very large chain length can be simulated using this scheme. Therefore, it will be worthwhile to extend the BDTP theory for semi-flexible chains. Probably a good starting point will be to renormalize the Pincus blobs [52] by the chain persistent length. Then a combination of BD simulations and BDTP simulations will be very effective to study translocation of long biopolymers through nanopore for a variety of applications. We have calculated the tension propagation time t tp indirectly using Eqn. 1 which is a consequence of the

8 8 BDTP theory. We find that t tp is not decoupled from the MFPT τ. For a stiffer chain τ increases, and so does t tp which is somewhat counterintuitive, although we find the ratio t tp / τ 0 in the limit κ b. In order to address this issue one needs to calculate t tp directly from the simulation and study the effect of chain stiffness κ b on t tp. The most direct way to obtain t tp is to monitor the time dependence of the last monomer at the cis side. It turns out that this requires much more statistics to extract t tp directly. However, our preliminary data for κ b = 0.0 and 4.0 are in good agreement with t tp reported in the present manuscript which provides further support for the tension propagation picture of translocation through nanopore based on BDTP theory [53]. Finally, for prospective nano pore based applications it is also important to wonder to what extent the TP ideas can have practical usefulness for translocation of stiff biopolymers through nano pores and nano channels? Evidently, if t tp << τ for a given biopolymer then tension will propagate too fast and we will have a much simpler system. On the contrary if t tp < τ then it will be useful to calculate t tp from less coarse-grained models. This information will be useful to understand translocation of of various denatured proteins and double-stranded DNA, m-rna through nanopore. We hope that the results reported in this paper will promote further work along this direction. V. ACKNOWLEDGEMENT The research has been supported in part by the NSF- CHEM Grant No and a seed grant from UCF College of Sciences and Office of Research and Commercialization. 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