We describe a methodology to steeply enhance streptavidin protein preconcentration within physiological media over that achieved by negative dielectrophoresis (NDEP) through utilizing a DC offset to the AC field at nanoscale constriction gap devices. Within devices containing approximately 50-nm constriction gaps, we find that the addition of a critical DC field offset (1.5 V/cm) to the NDEP condition ( 200 Vpp/cm at 1 MHz) results in an exponentially enhanced extent of protein depletion across the device to cause a rapid and steeply rising degree of protein preconcentration. Under these conditions, an elliptical-shaped protein depletion zone that is extended along the device centerline axis forms instantaneously around the constrictions to result in protein preconcentration along the constriction sidewall direction. Through a potential energy diagram to describe the electrokinetic force balance across the device, we find that the potential energy barrier due to NDEP is gradually tilted upon addition of DC fields, to cause successively steeper potential wells along the sidewall direction for devices containing smaller constriction gaps. Hence, for approximately 50-nm constriction gaps at a critical DC field, the ensuing narrow and deep potential energy wells enable steep protein preconcentration, due to depletion over an exponentially enhanced extent across the device.