  The variation of total nuclear level densities (NLDs) and level density
parameters with proton number $(Z)$ are studied around the $\beta$-stable
isotope, $Z_{0}$, for a given mass number. We perform our analysis for a mass
range $A=40$ to 180 using the NLDs from popularly used databases obtained with
the single-particle energies from two different microsopic mass-models. These
NLDs which include microscopic structural effects such as collective
enhancement, pairing and shell corrections, do not exhibit inverted parabolic
trend with a strong peak at $Z_{0}$ as predicted earlier. We also compute the
NLDs using the single-particle energies from macroscopic-microscopic
mass-model. Once the collective and pairing effects are ignored, the inverted
parabolic trends of NLDs and the corresponding level density parameters become
somewhat visible. Nevertheless, the factor that governs the $(Z-Z_{0})$
dependence of the level density parameter, leading to the inverted parabolic
trend, is found to be smaller by an order of magnitude. We further find that
the $(Z-Z_{0})$ dependence of NLDs is quite sensitive to the shell effects.
