We apply our self-consistent PDE model for the electrical response of field-effect sensors to the 3D simulation of nanowire PSA (prostate-specific antigen) sensors. The charge concentration in the biofunctionalized boundary layer at the semiconductor-electrolyte interface is calculated using the propka algorithm, and the screening of the biomolecules by the free ions in the liquid is modeled by a sensitivity factor. This comprehensive approach yields excellent agreement with experimental current-voltage characteristics without any fitting parameters. Having verified the numerical model in this manner, we study the sensitivity of nanowire PSA sensors by changing device parameters, making it possible to optimize the devices and revealing the attributes of the optimal field-effect sensor.