  We discuss the implications of a "constituent quark" structure of the nucleon
for the leading (1/Q^2-) power corrections to the spin structure functions. Our
basic assumption is the presence of quark-gluon correlations in the nucleon
wave function, whose size, rho ~ 0.3 fm, is small compared to the nucleon
radius, R (two-scale picture). We argue that in this picture the isovector
twist-4 matrix element in the proton has a sizable negative value, M_N^2
|f_2^{u - d}| ~ rho^{-2}, while the twist-3 matrix elements are small, M_N^2
d_2 ~ R^{-2}. These findings are in agreement with the result of a QCD fit to
the g_1 world data, including recent neutron data from HERMES and Jefferson Lab
Hall A, which gives M_N^2 f_2^{u - d} = -0.28 +/- 0.08 GeV^2.
