^{1,2}, Ying-Cai Chen

^{2}, Li-Zhen Sun

^{1}and Meng-Bo Luo

^{1,3,a)}

### Abstract

The translocation of a polymer through compound channels under external electrical field was investigated by Monte Carlo simulation on a three-dimensional simple cubic lattice. The compound channel is composed of two parts: part α with length *L* _{pα} and part β with length *L* _{pβ}. The two parts have different polymer-channel interactions: a strong attractive interaction with strength ɛ_{α} for part α and a variable interaction with strength ɛ_{β} for part β. Results show that the translocation process is remarkably affected by both ɛ_{β} and *L* _{pα}, and the fastest translocation can be achieved with a proper choice of ɛ_{β} and *L* _{pα}. When ɛ_{β} is large, the translocation is dominated by the last escaping process as it is difficult for the polymer chain to leave the channel. Whereas when *L* _{pα} is small and ɛ_{β} ≪ ɛ_{α}, the translocation is determined by the initial filling process. For this case, there is a free-energy well at the interface between the part α and the part β, which not only influences the filling dynamics but also affects the translocation probability.

This work was supported by the National Natural Science Foundation of China under Grant No. 21174132. Computer simulations were carried out at the Shanghai Supercomputer Center.

I. INTRODUCTION

II. MODEL AND SIMULATION METHOD

III. SIMULATION RESULTS AND DISCUSSION

IV. CONCLUSION

### Key Topics

- Polymers
- 70.0
- Free energy
- 47.0
- Strong interactions
- 8.0
- Entropy
- 6.0
- Cell membranes
- 3.0

##### C08F2/00

## Figures

A 2D sketch of the compound channel and the polymer model used in the simulation. The compound channel with length *L* _{p} is consisted of two parts: part α with length *L* _{pα} and part β with length *L* _{pβ} (=*L* _{p} − *L* _{pα}). Along the channel (the *x* direction), an external electrical field with strength *E* is applied inside the channel.

A 2D sketch of the compound channel and the polymer model used in the simulation. The compound channel with length *L* _{p} is consisted of two parts: part α with length *L* _{pα} and part β with length *L* _{pβ} (=*L* _{p} − *L* _{pα}). Along the channel (the *x* direction), an external electrical field with strength *E* is applied inside the channel.

The dependence of the translocation time τ on ɛ_{β} for different *L* _{pα} s (a) and that on *L* _{pα} for different ɛ_{β} s (b). Here, the chain length *n* = 80 and the electrical field *E* = 0.1.

The dependence of the translocation time τ on ɛ_{β} for different *L* _{pα} s (a) and that on *L* _{pα} for different ɛ_{β} s (b). Here, the chain length *n* = 80 and the electrical field *E* = 0.1.

The dependence of the filling time τ_{1} on *L* _{pα} for different ɛ_{β} s. Here, the chain length *n* = 80 and the electrical field *E* = 0.1.

The dependence of the filling time τ_{1} on *L* _{pα} for different ɛ_{β} s. Here, the chain length *n* = 80 and the electrical field *E* = 0.1.

Free energy *F* as a function of the head segment position *x* inside the channel for different *L* _{pα} s, where the channel length *L* _{p} = 60, the electrical field *E* = 0.1, the chain length *n* = 80, and the interaction energy between segment and β channel is ɛ_{β} = 0, respectively. and are the place of the free-energy maximum before and after *L* _{pα}, respectively. Δ*F* _{1} and Δ*F* _{2} are two free-energy barriers for the translocation of the *L* _{pα} = 25 case as an example.

Free energy *F* as a function of the head segment position *x* inside the channel for different *L* _{pα} s, where the channel length *L* _{p} = 60, the electrical field *E* = 0.1, the chain length *n* = 80, and the interaction energy between segment and β channel is ɛ_{β} = 0, respectively. and are the place of the free-energy maximum before and after *L* _{pα}, respectively. Δ*F* _{1} and Δ*F* _{2} are two free-energy barriers for the translocation of the *L* _{pα} = 25 case as an example.

The dependence of the two free-energy barriers Δ*F* _{1} and Δ*F* _{2} on *L* _{pα}, where the electrical field *E* = 0.1, the chain length *n* = 80, and the interaction energy between segment and β channel is ɛ_{β} = 0, 0.4, and 1, respectively. The intersection point at is presented for ɛ_{β} = 0. Dotted curve with a shifted value −1 in the vertical axis shows *F* _{well} for ɛ_{β} = 1.

The dependence of the two free-energy barriers Δ*F* _{1} and Δ*F* _{2} on *L* _{pα}, where the electrical field *E* = 0.1, the chain length *n* = 80, and the interaction energy between segment and β channel is ɛ_{β} = 0, 0.4, and 1, respectively. The intersection point at is presented for ɛ_{β} = 0. Dotted curve with a shifted value −1 in the vertical axis shows *F* _{well} for ɛ_{β} = 1.

The dependence of τ_{trap} on *L* _{pα} for different ɛ_{β} s and different chain lengths *n*, where the electrical field *E* = 0.1. indicates the position of the peak of τ_{trap}. The straight dash lines are fits of τ_{trap} = exp (*kL* _{pα} + *b*) for *L* _{pα} close to .

The dependence of τ_{trap} on *L* _{pα} for different ɛ_{β} s and different chain lengths *n*, where the electrical field *E* = 0.1. indicates the position of the peak of τ_{trap}. The straight dash lines are fits of τ_{trap} = exp (*kL* _{pα} + *b*) for *L* _{pα} close to .

The dependence of products on ɛ_{β} for polymer of length *n* = 80 at different driving forces. The inset gives the linear dependence of on ɛ_{β}. The straight line with the slope −0.34 is the best fit for the simulation data.

The dependence of products on ɛ_{β} for polymer of length *n* = 80 at different driving forces. The inset gives the linear dependence of on ɛ_{β}. The straight line with the slope −0.34 is the best fit for the simulation data.

The dependence of the translocation probability *P* on *L* _{pα} for different chain lengths *n* and interactions ɛ_{β} at *E* = 0.1. Here *P* _{0} represents the translocation probability for *L* _{pα} = *L* _{p}.

The dependence of the translocation probability *P* on *L* _{pα} for different chain lengths *n* and interactions ɛ_{β} at *E* = 0.1. Here *P* _{0} represents the translocation probability for *L* _{pα} = *L* _{p}.

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