The translocation of a single DNA molecule through a nanometer-sized pore presents the exciting possibility of ultra-fast genome sequencing in a cost-effective manner. However, translocation through nanopores takes place at the rate of about a million nucleotides a second, which is too fast from a technological perspective. In order to achieve single-base resolution using a nanopore, the translocation process needs to be slowed down to about a hundred to a thousand bases a second. We use Langevin dynamics simulations to study the enzyme-modulated motion of a single-stranded DNA molecule as it translocates through a nanopore. The enzyme, an exonuclease, binds to the DNA and releases it at a rate determined by solution conditions, thus acting as a molecular brake and slowing down translocation. The translocation of the DNA is driven by an externally applied electric field, and is opposed by the favorable configurational entropy outside the nanoscopic confinement of the pore. However, the controlled release of the DNA in the region outside the nanopore leads to an entropy which varies in a time-dependent fashion. We apply principles of polymer physics to analyze these two competing effects and thereby suggest strategies which may aid ultra-fast genomic analysis.