  The interplay between higher orders of the perturbative QCD (pQCD) expansion
and higher-twist contributions in the analysis of recent Jefferson Lab data on
the lowest moment of the spin-dependent proton $\Gamma_1^{p} (Q^2)$ at
$0.05<Q^2< 3 {\rm GeV}^2$ is studied. We demonstrate that the values of the
higher-twist coefficients $\mu^{p,n}_{2k} $ extracted from the data by using
the singularity-free analytic perturbation theory provide a better convergence
of the higher-twist series than with the standard perturbative QCD. From the
high-precision proton data, we extract the value of the singlet axial charge
$a_0(1 {\rm GeV}^2)=0.33\pm0.05$. We observe a slow $Q^2$ dependence of fitted
values of the twist coefficient $\mu_4$ and $a_0$ when going to lower energy
scales, which can be explained by the renormalization group evolution of
$\mu_4(Q^2)$ and $a_0(Q^2)$. As the main result, a good quantitative
description of all the Jefferson Lab data sets down to $Q \simeq 350 MeV is
achieved.
