Monte Carlo Simulations On The Translocation Of Polymer Through Pores

The dynamics of polymer chain translocating through small pores or channels is an active topic of current research. It has wide application in chemical and biological systems, such as DNA and RNA worming through nuclear pores, protein transporting through membrane channels, and RNA molecules transferring from virus to host cell. The translocation is also of technological application, such as rapid DNA sequencing, controlled drug delivery, and so on.It is also an interesting topic in condensed matter physics as the translocation process is mainly controlled by two key ingredients:free energy landscape and external driving force. The free energy landscape is dependent on the confinement of polymer chain, polymer-pore interaction, and interaction between polymer and crowding environment, while the driving force can be simply a chemical potential difference or an electric field for charged polymer.In this dissertation, we focus on the dynamic process of polymer translocating through pores under driving. By using dynamic Monte Carlo method, we have simulated the translocation of a three-dimentional self-avoiding polymer from cis side through a pore into trans side. The interaction between the polymer and pore, driving, the crowded environment, and attractive wall at the trans side, have been considered in our simulation. The translocation time has been simulated at different conditions. The scaling relations of translocation time on chain length and driving force have been checked and discussed, the diffusion properties of polymer chain in crowded environment is also investigated. The main conclusions are listed in the following:(1)We have simulated the translocation of polymer through an interacting pore under chemical potential difference. Three translocation modes, dependent on the polymer-pore interaction ε and chemical potential difference Δμ, are discovered. The translocation is found to be an off-equilibrium process as there is not enough time to adjust polymer configuration during the translocation, which influences the relation of translocation time τ on ε and Δμ. The translocation time decreases in a power-law relation with the increase of Δμ, with an interaction dependent exponent β. For weak attractions, we get the exponent β<1, which can be explained by off-equilibrium process of the translocation.(2) The lattice one-site bond fluctuation polymer chain is found of Rouse dynamic in dilute solution. The scaling relation τ～NαFδ is studied for both biased and unbiased driving. For a non-interacting pore, we find α=2.48for unbiased driving, which is consistent with theoretical predicted value α=2+2v-γ1, and α=1.35for strong biased driving. The exponent a is dependent on the polymer-pore interaction. At strong attraction, α=2.35for unbiased driving and α=1.22for strong biased case. Thus the experiment value α=1.27for fast DNA translocation is included in our simulation. The exponent δ=0.86for intermediate driving and which is only weakly dependent on polymer-pore interaction for long chain.(3) We have studied the translocation of eight-site bond fluctuation model (BFM) polymer through a small pore with an attractive wall at the trans side under driving. The wall at the trans side show two contrary effects:its excluded volume effect hinders the translocation of polymer, while its attraction decreases the free energy thus accelerates the translocation. At critical polymer-wall interaction ε*,we find that the translocation time is roughly independent of the separation distance between wall and pore at distance R>RG/2.Moreover, the value of the critical attraction is roughly independent of chain length and chemical potential difference.The value of ε*is consistent with the value of critical adsorption interaction for polymer adsorbing on surface. The scaling relation of translocation time and chain length is investigated, with exponent1.30±0.05at strong driving. The scaling exponent is independent of chemical potential difference and attractive polymer-wall interaction as long as NΔμ is large enough.(4) The effect of crowded environment with static obstacles on polymer translocation is studied. Obstacles can speed up or slow down the translocation process, depending on the concentration of obstacle and polymer-obstacle interaction. There exists a special polymer-obstacle interaction at which the translocation time is the same as that of the obstacle-free case, and the strength of the special interaction is roughly independent of chain length N, but depending on the chemical potential difference. Scaling relation between translocation time and chain length is observed for strong driving with exponent1.25. The diffusion property of polymer chain is also influenced by obstacles. Normal diffusion is only observed in dilute solution without obstacles or in a crowded environment with weak polymer-obstacle attraction. Otherwise, subdiffusion behavior of polymer is observed.