  We present the results of a search for unidentified emission lines in deep
Suzaku X-ray spectra for the central regions of the four X-ray brightest galaxy
clusters: Perseus, Coma, Virgo and Ophiuchus. We employ an optimized energy
range for our analysis (3.2-5.3 keV) that is relatively free of instrumental
features, and a baseline plasma emission model that incorporates the abundances
of elements with the strongest expected emission lines at these energies (S,
Ar, Ca) as free parameters. For the Perseus Cluster core, employing this
baseline model, we find evidence for an additional emission feature at an
energy $3.51^{+0.02}_{-0.01}$ keV with a flux of ~$2.87\times10^{-7}$
ph/s/cm^2/arcmin^2. At slightly larger radii, we detect an emission line at
3.59+/-0.02 keV with a flux of ~$4.8\times10^{-8}$ ph/s/cm^2/arcmin^2. The
energies and fluxes of these features are broadly consistent with previous
claims, although the radial variation of the line strength appears in tension
with standard dark matter (DM) model predictions. Assuming a decaying DM origin
for the Perseus emission features allows us to predict the energies and line
fluxes for the other clusters in our sample. Critically, we do not detect an
emission feature at the predicted energy and line flux in the Coma, Virgo and
Ophiuchus clusters. The formal 99.5 per cent upper limits on the strengths of
an emission line in each cluster are below the decaying DM model predictions,
scaling from the Perseus Cluster center, apparently ruling the model out. In
the light of these results, we search for other explanations for the ~3.55 keV
emission feature in Perseus. Our results suggest that systematic effects
associated with modeling the complex spectra for the Perseus Cluster core,
details of the assumed ionization balance, and errors in the predicted
emissivities of the spectral lines may in part be responsible for the ~3.5 keV
feature.
