  Moments of the quark density, helicity, and transversity distributions are
calculated in unquenched lattice QCD. Calculations of proton matrix elements of
operators corresponding to these moments through the operator product expansion
have been performed on $16^3 \times 32$ lattices for Wilson fermions at $\beta
= 5.6$ using configurations from the SESAM collaboration and at $\beta = 5.5$
using configurations from SCRI. One-loop perturbative renormalization
corrections are included. At quark masses accessible in present calculations,
there is no statistically significant difference between quenched and full QCD
results, indicating that the contributions of quark-antiquark excitations from
the Dirac Sea are small. Close agreement between calculations with cooled
configurations containing essentially only instantons and the full gluon
configurations indicates that quark zero modes associated with instantons play
a dominant role. Naive linear extrapolation of the full QCD calculation to the
physical pion mass yields results inconsistent with experiment. Extrapolation
to the chiral limit including the physics of the pion cloud can resolve this
discrepancy and the requirements for a definitive chiral extrapolation are
described.
