A quantitative understanding and prediction of the dynamics of entangled polymer melts is a long-standing problem. In this work we present results about the dynamical and rheological properties of atactic polystyrene melts, obtained from a hierarchical approach that combines atomistic and coarse-grained dynamic simulations of unentangled and entangled systems. By comparing short chain atomistic and coarse-grained Simulations, the time mapping constant is determined. Self-diffusion coefficients, after correcting for the chain end free volume effect, show a transition from Rouse to reptation-like behavior. In addition, the entanglement Molecular weight is calculated through a primitive path analysis. All properties are compared to experimental data.