Dynamics Of A Polymer Chain Closure And Chaperone-assisted Polymer Translocation Through A Nanopore

In this dissertation, we have investigated the dynamics of chaperone-assisted poly-mer translocation through a nanopore, as well as that of a polymer chain closure by using the Langevin dynamics simulations.First, we confirmed that the chaperone-assisted polymer translocation is indeed a force-driven process by using the stiff chain model. Further from the simulation re-sults, we found that the mean translocation time shows a minimum as a function of the binding energy (between the chaperone and the chain segment), and the chaperone con-centration. A reasonable explanation was given from the perspective of the driving and frictional forces acting on the chain during the translocation process.Considered that the real polymers have certain flexibility, we have performed sim-ulations for fully flexible chains and semiflexible ones to investigate the effects of chain flexibility on the translocation dynamics. For fully flexible chains, we found that in-creasing the binding energy and the chaperone concentration can greatly improve the translocation probability. The exception was that with increasing the chaperone con-centration, a maximum translocation probability is observed for weak binding. Inter-estingly, the mean translocation time rapidly decreases and then almost saturates with increasing the binding energy for a short chain; however, it has a minimum for longer chains at a low chaperone concentration. Furthermore, we also showed that the mean translocation time has a minimum as a function of the chaperone concentration.For semiflexible chains, we showed that the mean translocation time increases monotonically with increasing the binding energy due to an increase in the radius of gyration and a decrease in the center of mass velocity of the chain. The correspond-ing translocation coordinate of the maximum waiting time gets smaller with increasing chain rigidity. This phenomenon could be understood from the decrease of the ten-sion propagation time, i.e., the characteristic time representing the disturbance due to the bias arriving at the last monomer. At an extremely low chaperone concentration, how the mean translocation time varies with increasing the binding energy depends on the magnitude of chain rigidity. When the chain rigidity is small, a minimum in the mean translocation time occurs; while for large chain rigidity, the mean translocation time decreases monotonically with increasing the binding energy. By calculating the waiting times and the cumulative waiting times and by capturing the snapshots of the chain just after the translocation, we considered that the conformational transition from a folded one to a globular one might be as the possible physical origin of the different behaviors of the mean translocation time with increasing the binding energy for chains with different rigidity.Next, we investigated the dynamics of loop formation of chains with excluded volume interactions, and the stability of the formed loop. The mean looping time scales with chain length and corresponding scaling exponent increases linearly with the capture radius due to the effect of finite chain length. We also showed that the probability density function of the looping time can be well fitted by a single exponential, indicating that the excluded volume effect do not alter the nearly Poisson statistical characteristics of the looping process. Finally, we found that stability of the formed loop hardly depends on chain length and grows linearly with the capture radius.In the last chapter, we reported the investigation about the effects of the internal friction and the solvent quality on the dynamics of a polymer chain closure. We showed that the chain closure in good solvents is a purely diffusive process. By extrapolation to zero solvent viscosity, we found that the internal friction of a chain plays a non-ignorable role in the dynamics of the chain closure. When the solvent quality changes from good to poor, the mean closure time decreases by about an order of magnitude. Furthermore, the mean closure time has a minimum as a function of the solvent quality, which is an overall result of the competition between the decreasing energy barrier for the chain closure and the poorer mobility of the relative motion of two end segments. Finally, the distributions of the closure time in poor solvents can also be well fitted by a single exponential, suggesting that the negative excluded volume of segments has no effect upon the nearly Poisson statistical characteristics of the process of the chain closure. We believed that our results have clarified the role of the internal friction on the dynamics of the chain closure. In addition, these findings shed light on the effect of the solvent quality on the dynamics of the chain closure.