  We investigate the influences of the nuclear composition on the weak
interaction rates of heavy nuclei during the core collapse of massive stars.
The nuclear abundances in nuclear statistical equilibrium (NSE) are calculated
by some equation of state (EOS) models including in-medium effects on nuclear
masses. We systematically examine the sensitivities of electron capture and
neutrino-nucleus scattering on heavy nuclei to the nuclear shell effects and
the single nucleus approximation. We find that the washout of shell effects at
high temperatures brings significant change to weak rates by smoothing the
nuclear abundance distribution: the electron capture rate decreases by
$\sim$20$\%$ in the early phase and increases by $\sim$40$\%$ in the late phase
at most, while the cross section for neutrino-nucleus scattering is reduced by
$\sim$15$\%$. This is because the open-shell nuclei become abundant instead of
those with closed neutron shells as the shell effects disappear. We also find
that the single-nucleus description based on the average values leads to
underestimations of weak rates. Electron captures and neutrino coherent
scattering on heavy nuclei are reduced by $\sim$80$\%$ in the early phase and
by $\sim$5$\%$ in the late phase, respectively. These results indicate that NSE
like EOS accounting for shell washout is indispensable for the reliable
estimation of weak interaction rates in simulations of core-collapse
supernovae.
