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[en] We discuss the interplay between higher orders of the perturbative QCD expansion and higher-twist contributions in the analysis of recent Jefferson Lab data on the lowest moments of spin-dependent proton and neutron structure functions Γ1p,n(Q2) and Bjorken sum rule function Γ1p-n(Q2) at 0.05< Q2<3 GeV2. We demonstrate that the values of the higher-twist coefficients μ2kp,n extracted from the mentioned 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 a0(1 GeV2)=0.33±0.05. We observe a slow Q2 dependence of fitted values of the twist coefficient μ4 and a0 when going to lower energy scales, which can be explained by the well-known renormalization group evolution of μ4(Q2) and a0(Q2). As the main result, a good quantitative description of all the Jefferson Lab data sets down to Q≅350 MeV is achieved.