Simulation Study On The Translocation And Separation Of Copolymer

The translocation of biomolecules or polymers through a nanopore or channel, which is related to physics, chemistry, and biology, has been extensively studied by many researchers. It plays important roles in many biological systems, such as DNA and RNA worming across nuclear pores, protein transporting through membrane channels, and DNA transferring from virus to host cell. Moreover, with the development of science and technology, the process provides a promising potentiality on the application, such as gene therapy, controlled drug delivery, and rapid DNA sequence. In order to study the translocation, most theories and simulations regard the biomolecule as homogenuous polymer model, consisted of identical monomers. However, a biomolecule may have different types of bases in real systems, such as amino acids in protein, nuclean acids in DNA. Different bases have different structures, charges, and so on. Therefore, comparing with the homogenuous polymer model, the copolymer model is better to describe real biomolecules.We use Monte Carlo (MC) simulation method to investigate the translocation of copolymers, and try to separate different copolymers by using the translocation. The movement of the copolymer chain is achieved through bond-fluctuation on a three-dimensional cubic lattice. The self-avoiding walking copolymer chain (AnCm)t, is formed by two types of monomers A and C. In our model, different interactions εA and εC are considered for the monomers A and C with the nanopore or channel. If εA<0, it means that the interaction is attraction, or the interaction is repulsion. The chain length of (AnCm)/is N=(n+m)xl, and the length of repeat unit AnCm is M=(n+m). The fraction of monomer A in the whole copolymer is fA=n/M. The main conclusions of this paper are summarized in the following:(1) At first, we investigate the influence of the polymer-pore interaction on the translocation of a homogenuous polymer. We calculate the free-energy landscapes of the polymer translocation at different polymer-pore interactions by using exact enumeration method. When the interaction is repulsion or weak attraction, there is a free-energy barrier at the pore for the polymer. Whereas, when the interaction is strong attraction, the barrier will change to a free-energy well. Based on the free-energy landscapes, the total time for the polymer migrating from cis side to trans side and the translocation time for the polymer worming through the pore are calculated with the Fokker-Planck equation. It shows that there is a minimal total time at a moderate attraction. Meanwhile, the translation time decreases with weakening the attraction at strong attractions, and it is nearly a constant at weak attraction and repulsion.(2) Secondly, the translocation of copolymer AnCn through an interacting nanopore is studied by MC simulation, and the free-energy landscape is calculated by using Rosenbluth-Rosenbluth method. There are two translocation orientations for the copolymer entering the pore, orientation A for monomer A entering pore first and orientation C for monomer C entering pore first. The probabilities of the two orientations are mainly dependent on εA and εC, and a larger attraction for one type of monomer will lead to a larger probability. With a fixed εA, we find that the translocation time first decreases and then increases with the increase in εC, which is different from the behavior of a homogenuous polymer. The relation between the translocation time and the interaction is explained qualitatively based on the free-energy landscapes.(3) Thirdly, the translocation of copolymer (AnCm), with chain length N=64through a nanopore is studied by Monte Carlo simulation. With a fixed monomer fraction, the height and the number of free-energy barrier (or free-energy well) is dependent on the length of repeat unit (AnCm). These two competitive variables can influence the probabilities of translocation orientations and the translocation time. Then with a fixed length of repeat unit, we also investigate the influence of the monomer fraction on the dynamic behaviors of copolymers, and the result is explained by the free-energy landscapes. Besides, it is found that different copolymers with different monomers or different monomer fractions can be successfully separated. However, for the copolymers with the same monomers and fraction but with different repeat unit length, like (A2C2)16and A32C32, we find that they can’t be separated by using the nanopore although they have different translocation times.(4) At last, we design a setup with alternating large reservoirs and small channels to separate copolymers with different repeat unit length, like (A2C2)16,(A8C8)4, and A32C32. For this end, we first study the process of a single copolymer worming through a channel from a reservoir to another one by Monte Carlo simulation. Under weak driving force and weak attraction between monomer A and the channel, the copolymer will be trapped at the exit of the channel at εC<<0, and the leaving time is highly dependent on the copolymer’s structure and the interaction. Then, by choosing appropriate simulation parameters, we separate successfully the three copolymers (A2C2)16,(A8C8)4,and A32C32by our setup.