  It is well established that (1) star-forming galaxies follow a relation
between their star formation rate (SFR) and stellar mass (M$_{\star}$), the
"star-formation sequence", and (2) the SFRs of galaxies correlate with their
structure, where star-forming galaxies are less concentrated than quiescent
galaxies at fixed mass. Here, we consider whether the scatter and slope of the
star-formation sequence is correlated with systematic variations in the Sersic
indices, $n$, of galaxies across the SFR-M$_{\star}$ plane. We use a
mass-complete sample of 23,848 galaxies at $0.5<z<2.5$ selected from the 3D-HST
photometric catalogs. Galaxy light profiles parameterized by $n$ are based on
Hubble Space Telescope CANDELS near-infrared imaging. We use a single SFR
indicator empirically-calibrated from stacks of Spitzer/MIPS 24$\mu$m imaging,
adding the unobscured and obscured star formation. We find that the scatter of
the star-formation sequence is related in part to galaxy structure; the scatter
due to variations in $n$ at fixed mass for star-forming galaxies ranges from
0.14$\pm$0.02 dex at $z\sim2$ to 0.30$\pm$0.04 dex at $z<1$. While the slope of
the log(SFR)-log(M$_{\star}$) relation is of order unity for disk-like
galaxies, galaxies with $n>2$ (implying more dominant bulges) have
significantly lower SFR/M$_{\star}$ than the main ridgeline of the
star-formation sequence. These results suggest that bulges in massive $z\sim2$
galaxies are actively building up, where the stars in the central concentration
are relatively young. At $z<1$, the presence of older bulges within
star-forming galaxies lowers global SFR/M$_{\star}$, decreasing the slope and
contributing significantly to the scatter of the star-formation sequence.
