We present a Langevin dynamics simulation study of enzyme-modulated translocation of a single-stranded DNA molecule through a cylindrical nanopore. The toroidal-shaped enzyme placed along the axis of the pore, threads a DNA molecule at a constant rate. As a result of this controlled release process, the length of DNA available for translocation varies with time. We examine the effect of time-dependent conformational entropy of the DNA on the translocation process. In addition, we also examine the effects of both the separation between the exonuclease and the pore, and the rate at which DNA is released by the enzyme. Our results indicate that the separation distance primarily influences the entry of the DNA into the pore. The length of the DNA released by the exonuclease that is most likely to enter the pore is nearly equal to separation distance between the pore and the exonuclease despite the flexibility of the polymer. However, the speed at which the DNA, translocates through the nanopore is solely determined by the rate at which the exonuclease releases the DNA. We find that the translocation velocity is directly proportional to the rate of release.