  A planet's atmospheric constituents (e.g., O$_2$, O$_3$, H$_2$O$_v$, CO$_2$,
CH$_4$, N$_2$O) can provide clues to its surface habitability, and may offer
biosignature targets for remote life detection efforts. The plethora of rocky
exoplanets found by recent transit surveys (e.g., the Kepler mission) indicates
that potentially habitable systems orbiting K- and M-dwarf stars may have very
different orbital and atmospheric characteristics than Earth. To assess the
physical distribution and observational prospects of various biosignatures and
habitability indicators, it is important to understand how they may change
under different astrophysical and geophysical configurations, and to simulate
these changes with models that include feedbacks between different subsystems
of a planet's climate. Here we use a three-dimensional (3D) Chemistry-Climate
model (CCM) to study the effects of changes in stellar spectral energy
distribution (SED), stellar activity, and planetary rotation on Earth-analogs
and tidally-locked planets. Our simulations show that, apart from shifts in
stellar SEDs and UV radiation, changes in illumination geometry and
rotation-induced circulation can influence the global distribution of
atmospheric biosignatures. We find that the stratospheric day-to-night side
mixing ratio differences on tidally-locked planets remain low ($<20\%$) across
the majority of the canonical biosignatures. Interestingly however, secondary
photosynthetic biosignatures (e.g., C$_2$H$_6$S) show much greater
(${\sim}67\%$) day-to-night side differences, and point to regimes in which
tidal-locking could have observationally distinguishable effects on phase
curve, transit, and secondary eclipse measurements. Overall, this work
highlights the potential and promise for 3D CCMs to study the atmospheric
properties and habitability of terrestrial worlds.
