  The generalized Gerasimov-Drell-Hearn (GDH) sum rule is known to be very
sensitive to QCD radiative and power corrections. We improve the previously
developed QCD-inspired model for the $Q^2$-dependence of the GDH sum rule. We
take into account higher order radiative and higher twist power corrections
extracted from precise Jefferson Lab data on the lowest moment of the
spin-dependent proton structure function $\Gamma_1^{p}(Q^2)$ and on the Bjorken
sum rule $\Gamma_1^{p-n}(Q^2)$. By using the singularity-free analytic
perturbation theory we demonstrate that the matching point between chiral-like
positive-$Q^2$ expansion and QCD operator product $1/Q^2$-expansion for the
nucleon spin sum rules can be shifted down to rather low $Q\simeq\Lambda_{QCD}$
leading to a good description of recent proton, neutron, deuteron and Bjorken
sum rule data at all accessible $Q^2$.
