  Using first-principles quantum transport simulations, based on the
nonequilibrium Green function formalism combined with density functional theory
(NEGF+DFT), we examine changes in the total and local electronic currents
within the plane of graphene nanoribbon with zigzag edges (ZGNR) hosting a
nanopore which are induced by inserting a DNA nucleobase into the pore. We find
a sizable change of the zero-bias conductance of two-terminal ZGNR + nanopore
device after the nucleobase is placed into the most probable position
(according to molecular dynamics trajectories) inside the nanopore of a small
diameter \mbox{$D=1.2$ nm}. Although such effect decreases as the nanopore size
is increased to \mbox{$D=1.7$ nm}, the contrast between currents in ZGNR +
nanopore and ZGNR + nanopore + nucleobase systems can be enhanced by applying a
small bias voltage $V_b \lesssim 0.1$ V. This is explained microscopically as
being due to DNA nucleobase-induced modification of spatial profile of local
current density around the edges of ZGNR. We repeat the same analysis using
NEGF combined with self-consistent charge density functional tight-binding
(NEGF+SCC-DFTB) or self-consistent extended H\"{u}ckel (NEGF+SC-EH)
semi-empirical methodologies. The large discrepancy we find between the results
obtained from NEGF+DFT vs. those obtained from NEGF+SCC-DFTB or NEGF+SC-EH
approaches could be of great importance when selecting proper computational
algorithms for {\em in silico} design of optimal nanoelectronic sensors for
rapid DNA sequencing.
