  We investigate the possibility to draw conclusions on the sign of the
spin-dependent gluon distribution, $\Delta G(x, Q^2)$, from existing polarized
DIS data. The spin-dependent parton distributions $\Delta u_v, \Delta d_v,
\Delta {\bar u}, \Delta {\bar d}, \Delta {s}$, and $\Delta G$ are constructed
in the framework of a phenomenological procedure taking into account some
assumptions on signs of valence and sea parton distributions motivated by 't
Hooft's mechanism of quark-quark interaction induced by instantons. The axial
gluon anomaly and data on integral quark contributions to the proton spin,
$\Delta \tilde u, \Delta \tilde d$, and $\Delta \tilde s$, are also taken into
account. Predictions for the $x$- and $Q^2$-dependencies of the polarized
proton and neutron structure functions, $g_1^p$ and $g_1^n$, are compared to
experimental data. It is shown that the neutron structure function, $g_1^n$, is
especially sensitive to the sign of $\Delta G(x, Q^2)$. The results of our
analysis supports the conclusion that this sign should be positive.
