  Predictions for the spin dependent structure function $g_1$ of the nucleon
are presented. We use an unified approach incorporating the LO DGLAP evolution
and the resummation of double logarithmic terms $ln^2(x)$. We show, that the
singular input parametrisation as $x\to 0$ can be a substitute of the $ln^2(x)$
resummation. An impact of the `more running' coupling is discussed. We
determine the contribution to the Bjorken sum rule solving the evolution
equation for the truncated moment of $g_1^{NS}$. A comparison with the
re-analysed HERMES and COMPASS data is given.
