Translocation of polymer chains through interacting nanopores

doi:10.1016/j.polymer.2007.10.041

Polymer

Volume 48, Issue 26, 13 December 2007, Pages 7679-7686

https://doi.org/10.1016/j.polymer.2007.10.041 Get rights and content

Abstract

The effect of the interaction between nanopore and chain segment on the translocation of polymer chains through an interacting nanopore from a confined environment (cis side, high concentration of chain) to a spacious environment (trans side, zero concentration) was studied by using dynamic Monte Carlo simulations. Results showed that a moderate attractive pore–polymer interaction accelerates the translocation of chain. The optimal interaction at which translocation is the fastest increases with the concentration of chain on the cis side. The dependence of microscopic behaviors of chain translocation on the interaction was investigated.

Introduction

The mechanism of polymers or macromolecules translocating through nanotubes or nanopores in membranes has attracted a lot of attention from experiments [1], [2], [3], [4], analytical theories [5], [6], [7], [8], [9], [10], [11], [12] and computer simulations [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23]. The translocation of chain molecule is a fundamental event in various biological processes, such as proteins transporting through channels in biological membranes [24], [25], [26], RNA molecules translocating through pores in cell nuclear membranes, DNA molecules transferring from virus to host cell and genes transferring between bacteria [27]. It also relates to the migration of DNAs through microfabricated channels and devices [28], [29], [30], [31], [32], gene therapy, drug delivery, gel electrophoresis [33], [34], and size exclusion chromatography [35]. When the size of chain molecule is larger than that of the cross section of nanopore, the chain suffers a free energy barrier because it must lose entropy in order to cross the nanopore. Polymer chains also suffer similar free energy barrier in a restrictive environment such as in a gel, in periodic gaps [36] or in random media [37]. Because of the free energy barrier, most translocation phenomena of chain require the aid of driving forces. A topic related to the translocation of chain through nanopore under driving forces is interesting and important.

Nanopore without considering its thickness is easier to be treated in theory and thus has attracted a lot of attention. The translocation of polymer chain through a non-interacting nanopore has been well studied by theory based on one-dimensional driven-diffusion system [5], [8]. The mechanism of chain translocation was discussed based on the free energy barrier F_b caused by nanopore and chemical potential difference Δμ between cis and trans sides [5], [8]. In these discussions Δμ serves as a driving force. Later, the translocation of polymer chain driven by an electric field for a three-dimensional system was simulated, and results showed that the behavior could be described by one-dimensional Smoluchowski equation with chain length independent diffusion constant [13]. The chemical potential difference Δμ can be set up by concentration difference, and it increases gradually with the increase of the concentration difference [38]. The effect of concentration difference on the translocation was also studied for chain confined in a sphere [14]. Besides the chemical potential difference and electric field, the translocation can also be driven by ratchet mechanism [6], [39]. An attractive interaction on the trans side of the membrane was recently demonstrated to be a driving force for translocation. It was found that chain worms through nanopore easily for the attractive interaction larger than an adsorption threshold, a critical point at which chain goes from a ‘mushroom’ expanded state to a ‘pancake’ adsorbed state [15], [16]. The influence of surface curvature near the nanopore on the translocation of chain was also simulated with off-lattice Monte Carlo technique [18].

However, the effect of interaction between nanopore and polymer on the translocation is not clear. A Brownian dynamic simulation study showed that the interaction affects the translocation time of chain but the details were not stated [11]. In a recent simulation study on a charged polymer translocation through a nanopore with finite length under the application of an electric field, the interaction between polymer and pore was taken into account [17]. The influence of charge and field strength on the polymer translocation was discussed but the influence of pore–polymer interaction was not mentioned. Some experiments also implied that the interaction might play an important role on the translocation of chain through small pore or narrow channel [1], [2], [40]. The present work studies the effect of the pore–polymer interaction on the translocation of chains from a high concentration region (cis side) to zero concentration region (trans side). Therefore the model system is not symmetrical for chains on the cis and trans sides. The dependence of the translocation time on the interaction is investigated. We find that the translocation time exhibits a minimum as the attractive interaction is increased. That is, a proper pore–polymer interaction can drive chains through nanopores.

Section snippets

Model and simulation method

Our simulation system is embedded in the simple cubic (SC) lattice. The simulated box is a cuboid with spacing L_x, L_y and L_z in x, y and z directions, respectively. Periodic boundary conditions (PBC) are considered in the x and y directions, while in the z direction there are two infinitely large flat walls located at z = 0 and L_z + 1, respectively. The space between these two impenetrable walls is called cis side and polymers are confined on the cis side before translocation. A nanopore is located

Simulation results and discussion

The dependence of average translocation time $〈 τ 〉$ on interaction ɛ is presented in Fig. 3 for different numbers of chain on the cis side. An interesting finding is that there exists a minimum translocation time $〈 τ 〉$ for an attractive pore. The interaction at which $〈 τ 〉$ is minimum is defined as optimal interaction ɛ_o in this work. While for the interaction above ɛ and below ɛ_o, $〈 τ 〉$ increases roughly exponentially with the interaction ɛ, indicating that the translocation of chain is very sensitive

Conclusion

We have investigated the translocation of polymer chains through an interacting nanopore from a high concentration region (cis side) to a zero concentration region (trans side) by using dynamical Monte Carlo method. The size of chain is much bigger than the size of cross section of pore thus the chain suffers a free energy barrier when it crosses the pore. The driving force for translocation is the concentration difference between the cis side and trans side. The effect of the pore–polymer

Acknowledgement

The project is sponsored by the National Natural Science Foundation of China under Grant No. 20674074.

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Translocation of polymer chains through interacting nanopores

Abstract

Introduction

Section snippets

Model and simulation method

Simulation results and discussion

Conclusion

Acknowledgement

Biophys J

Comput Phys Commun

Polymer

Physica A

Polymer

Polymer

Polymer

Cell

Biophys J

Polymer

Phys Rev Lett

Phys Rev Lett

Phys Rev Lett

Anal Chem

Phys Rev Lett

Phys Rev Lett

J Chem Phys

J Chem Phys

Macromolecules

J Chem Phys

J Chem Phys