The Computer Simulation On The Dynamics Of A Single Polymer Chain In Confined Environments

Studying the dynamics of a polymer chain in the confined medium has attracted considerable attention in recent years. Understanding this process is very helpful for us to comprehend many phenomena in cell biology. On the other hand, it has widespread and important prospect on technological applications. The dynamics of a polymer chain in the confined medium is complicated, thus resulting in much difficulty of di-rect experimental detection in detail. However, theoretical calculation faces some dif-ficulties in dealing with the excluded-volume effect. As an alternate, computer simu-lation has been an important and useful method in this field. With the development of computer hardware and the putting forward of new simulation technology and model, computer simulation will play a more important role.Compared with all-atom model in continuous space, the coarse-grained lattice model is, at the cost of spatial resolution, beneficial for CPU time. Lattice model is specifically suitable for Monte Carlo simulation. Monte Carlo simulation can be applied to study the dynamics process, if a proper algorithm is adopted.This Ph.D thesis focuses on the dynamics process of a single polymer chain in confined mediums with dynamical Monte Carlo simulation. To compare with the sim-ulation results of a SAW chain, we study the translocation process of an ideal chain confined in a square through a nano-scale channel theoretically.The main achievements are summarized as follows:1. Theoretically study the translocation dynamical process of a single Gaussian chain from a square to another larger square through a nano-scale channel. The free energy barrier and mean translocation timeτare calculated. The potential interaction between the polymer and channel significantly modifies the entropic barrier landscape of translocation. As the channel length increases, the translocation process undergoes a transition from entropic barrier mechanism to a mechanism dominated by the pore-polymer interaction. This shift in mechanism leads to nonmonotonic dependence ofτon the pore length. Explicit formulas are derived for the dependence ofτon chain length, pore length, sizes of the donor and recipient squares. The calculated results provide guidance for tuning the rate of polymer translocation through narrow pores.2. Study the dynamical process of the translocation for a single SAW chain con- fined in a square through a narrow channel with Monte Carlo simulation. The de-pendence of the height of the entropic barrier that the polymer need overcome when entering the channel and translocation time on chain length N and pore length M are achieved. The height of the entropic barrier depends linearly on N and M. The translo-cation times for the first and second steps increase linearly with N and the third step time dos not vary when M keeps constant. On the other hand, the simulation results reveal thatτ1-M2.62,τ2 increases linearly with M andτ3-M1.90. Furthermore, We get the dependence of the translocation times for each step by solving the Fokker-Planck equation numerically and, the results are quite consistent with our simulation results.3. The effct of the pore-polymer interaction on the translocation of a single poly-mer chain confined in a finite size square through an interacting nanopore to a large space has been studied using Monte Carlo methods. The whole process consists of two stages. In the first stage, the chain experiences a period of trapping time, Ttrap, to overcome the free energy barrier. In the second stage, the chain successfully es-capes through the nanopore without totally pulled back to the donor square, and the consumed time is defined as Tesc. log(τtrap) decreases linearly with the chain length N and, the slopes of the lines for different pore-polymer interaction (?) are same all. How-ever, log(τtrap) increases linearly with the length of the nanopore M and the slope of line increases with (?). It is found that strong attractive as well as repulsive pore-polymer interaction adds the difficulty of the chain translocation through the nanopore, leading to the nonmonotonical dependence of the translocation time on the pore-polymer in-teraction.4. The translocation of a polymer chain through a narrow pore in a membrane induced by the temperature difference on two sides of the membrane is studied by using theoretical approach and Monte Carlo simulations. We investigate the dependence of the translocation timeτon the chemical potential per monomerμ, the polymer length N, and the temperature difference of two sides. Our results reveal that positive chemical potential per monomerμis favorable for the translocation of the polymer from cis (of T1) to trans (of T2) side for the case of Ti< T2. The translocation timeτis inversely proportional toμ, and increases linearly with N. IncreasingΔT will accelerate the translocation of the chain from cis to trans side.5. Using bond-fluctuation model (BFM), study the the motion of a long charged polymer chain inside an array of microscopic entropic traps. In the three-dimensional space, with the electric field increasing, the mobility of the chain inside the arrays in-creases gradually to a constant value. For same fields, long polymers are faster than shorter ones. The mean trapping time for the molecules inside the entropic trap ar-ray, Ttrap, exponentially increases with the reciprocal of the electric field,1/∈. The simulation results are in good agreement with the experimental observations. The size-separation mechanism relies mainly on the overall deformation of the molecules as the chain approaches the narrow constrictions. The simulation study of the motion for a polymer chain inside the two-dimensional arrays validates our analysis for the separa-tion mechanism mentioned above.6. Stretching and relaxation of a single DNA molecule tethered in a specially designed thin slit were studied using Monte Carlo simulation combined with 3D bond fluctuation model (BFM). It was found that the extension and relaxation of the single DNA molecule are greatly affected by the confined environment. If the extent of the confined environment is increased by decreasing the distance between the two planar surfaces of the slit, the extension of the single DNA molecule increases, due to the screening of the hydrodynamic interaction of DNA segments by the planar surfaces of the slit. The relaxation of the single DNA molecule in different confined environments verifies this assumption completely. The correlation between the end-to-end separation and flow velocity obtained by Monte Carlo simulation is in good agreement with either the experimental results or theoretical consideration reported previously.7. A part of a long DNA chain was driven into the confined environment by an electric field, with the other remains in the higher-entropy region. Upon removal of the field, the chain recoils to the higher-entropy rcgion spontaneously. This dynamical process has been investigated by Monte Carlo simulations. The simulation reproduces the experimental observed phenomenon that the recoil of the DNA chain is initially slow and gradually increases in speed. It is due to a confinement-entropic force, distinct from entropic elasticity. How the dimension and spacing of the nanopillars influence the recoil velocity was investigated and further analysis suggests that the characteristic entropy per monomer in the confinement is proportional to the area fraction of free part in the confinement.