We investigated four different problems using coarse grained computational models : self-assembly of single stranded (ss) DNA virus, ejection dynamics of double stranded(ds) DNA from phages, translocation of ssDNA through MspA protein pore, and segmental dynamics of a polymer translocating through a synthetic nanopore. In the first part of the project, we investigated the self-assembly of a virus with and without its genome. A coarse-grained model was proposed for the viral subunit proteins and its genome (ssDNA). Langevin dynamics simulation, and replica exchange method were used to determine the kinetics and energetics of the self-assembly process, respectively. The self-assembly follows a nucleation-growth kind of mechanism. The ssDNA plays a crucial role in the self-assembly by acting as a template and enhancing the local concentration of the subunits. The presence of the genome does not changes the mechanism of the self-assembly but it reduces the nucleation time and enhances the growth rate by almost an order of magnitude. The second part of the project involves the investigation of the dynamics of the ejection of dsDNA from phages. A coarse-grained model was used for the phage and dsDNA. Langevin dynamics simulation was used to investigate the kinetics of the ejection. The ejection is a stochastic process and a slow intermediate rate kinetics was observed for most ejection trajectories. We discovered that the jamming of the DNA at the pore mouth at high packing fraction and for a disordered system is the reason for the intermediate slow kinetics. The third part of the project involves translocation of ssDNA through MspA protein pore. MspA protein pore has the potential for genome sequencing because of its ability to clearly distinguish the four different nucleotides based on their blockade current, but it is a challenge to use this pore for any practical application because of the very fast traslocation time. We resolved the state of DNA translocation reported in the recent experimental work . We also investigated two methods for slowing down the translocation process: pore mutation and use of alternating voltage. Langevin dynamics simulation and Poisson Nernst Planck solver were used for the investigation. We demonstrated that mutation of the protein pore or applying alternating voltage is not a perfect solution for increasing translocation time deterministically. Both strategies resulted in enhanced average translocation time as well as the width of the translocation time distribution. The increase in the width of the translocation time distribution is undesired. In the last part of the project, we investigated the applicability of the polyelectrolyte theory in the computer simulation of polyelectrolyte translocation through nanopores. We determined that the Debye Huckel approximation is acceptable for most translocation simulations as long as the coarse grained polymer bead size is comparable or larger than the Debye length. We also determined that the equilibrium translocation theory is applicable to the polyelectrolyte translocation through a nanopore under biasing condition. The unbiased translocation behavior of a polyelectrolyte chain is qualitatively different from the Rouse model predictions, except for the case where the polyelectrolyte is very small compared to the nanopore. .