^{1}, Shiben Li

^{2}, Linxi Zhang

^{2,a)}, Ateeq ur Rehman

^{1}and Haojun Liang

^{3}

### Abstract

The translocation of -helix chains through a nanopore is studied through Langevin dynamics simulations. The -helix chains exhibit several different characteristics about their average translocation times and the -helix structures when they transport through the nanopores under the driving forces. First, the relationship between average translocation times and the chain length satisfies the scaling law, , and the scaling exponent depends on the driving force for the small forces while it is close to the Flory exponent in the other force regions. For the chains with given chain lengths, it is observed that the dependence of the average translocation times can be expressed as for the small forces while can be described as in the large force regions. Second, for the large driving force, the average number of -helix structures decreases first and then increases in the translocation process. The average waiting time of each bead, especially of the first bead, is also dependent on the driving forces. Furthermore, an elasticity spring model is presented to reasonably explain the change of the -helix number during the translocation and its elasticity can be locally damaged by the large driving forces. Our results demonstrate the unique behaviors of -helix chains transporting through the pores, which can enrich our insights into and knowledge on biopolymers transporting through membranes.

This research was financially supported by the National Natural Science Foundation of China (Grant Nos. 20774066, 20974081, and 20934004), the Program for New Century Excellent Talents in University (Grant No. NCET-05-0538), the National Basic Research Program of China (Grant No. 2005CB623800), and the Natural Science Foundation of Zhejiang Province (Grant No. Y4080098). We also thank the referees for their critical reading of the manuscript and their good ideas.

I. INTRODUCTION

II. MODEL AND METHOD

A. The -helix chain and pore model

B. The Langevin dynamics simulation method

III. RESULTS AND DISCUSSION

A. The average translocation time

B. The -helix structures

IV. CONCLUSIONS

### Key Topics

- Nanoporous materials
- 49.0
- Proteins
- 24.0
- Friction
- 10.0
- Free energy
- 9.0
- Polymers
- 9.0

## Figures

A sketch map of -helix chains translocation through a nanopore. Here the nanopore length is , the average helical pitch is , and the diameter is . The red arrow represents the direction of external driving force.

A sketch map of -helix chains translocation through a nanopore. Here the nanopore length is , the average helical pitch is , and the diameter is . The red arrow represents the direction of external driving force.

(a) The dihedral angle of each bond for the 150-bond -helix chain at four different moments during the translocation process for one random run. Here and the translocation time of this run is . (b) The bond length distributions of the 150-bond -helix chain at three different driving forces with the middle bead of the chain just translocating through the nanopore.

(a) The dihedral angle of each bond for the 150-bond -helix chain at four different moments during the translocation process for one random run. Here and the translocation time of this run is . (b) The bond length distributions of the 150-bond -helix chain at three different driving forces with the middle bead of the chain just translocating through the nanopore.

The average translocation times as a function of chain lengths for three different chain models. (a) The -helix chains with , 20, and 200, and the SAW chains with in the inset. (b) Semirigid chains without any hydrogen bond interactions for , 20, and 200.

The average translocation times as a function of chain lengths for three different chain models. (a) The -helix chains with , 20, and 200, and the SAW chains with in the inset. (b) Semirigid chains without any hydrogen bond interactions for , 20, and 200.

The scaling exponents as a function of driving forces for two different types of chains. The insert shows the mean-square end-to-end distance and the shape factor as a function of chain lengths . (a) The -helix chains. (b) Semirigid chain.

The scaling exponents as a function of driving forces for two different types of chains. The insert shows the mean-square end-to-end distance and the shape factor as a function of chain lengths . (a) The -helix chains. (b) Semirigid chain.

The average translocation times as a function of driving forces for three different chain lengths , 100, and 150. The solid curves represent the relation of .

The average translocation times as a function of driving forces for three different chain lengths , 100, and 150. The solid curves represent the relation of .

The average waiting time of the bead for the 150-bond -helix chains with three different driving forces of , 26, and 100.

The average waiting time of the bead for the 150-bond -helix chains with three different driving forces of , 26, and 100.

The resultant force acting on the 80th bead along the -axis direction during the waiting time of 80th bead for the 150-bond -helix chains at one run.

The resultant force acting on the 80th bead along the -axis direction during the waiting time of 80th bead for the 150-bond -helix chains at one run.

The distribution of translocation time for the 100-bond -helix chains with four different driving forces , 13.5, 26, and 100.

The distribution of translocation time for the 100-bond -helix chains with four different driving forces , 13.5, 26, and 100.

The average total number of -helix structures as a function of with three different driving forces for (a) and (b) . Here, represents the certain time of translocation process and is the translocation time of this run.

The average total number of -helix structures as a function of with three different driving forces for (a) and (b) . Here, represents the certain time of translocation process and is the translocation time of this run.

The average probability of forming the -helix structures for the bead of the 150-bond -helix chains at four different moments .

The average probability of forming the -helix structures for the bead of the 150-bond -helix chains at four different moments .

The average number of -helix structures as a function of driving force for the -helix chains with the middle bead of -helix chains just translocating through the nanopore. (a) , (b). , and (c) a possible elasticity spring model.

The average number of -helix structures as a function of driving force for the -helix chains with the middle bead of -helix chains just translocating through the nanopore. (a) , (b). , and (c) a possible elasticity spring model.

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