QCD effects to Bjorken unpolarized sum rule for $\nu N$ deep-inelastic scattering

The possibility of the first measurement of Bjorken unpolarized sum rule for $F_1$ structure function of $\nu N$ deep-inelastic scattering at Neutrino Factories is commented. The brief summary of various theoretical contributions to this sum rule is given. Using the next-to-leading set of parton distributions functions, we simulate the expected $Q^2$-behavior and emphasize that its measurement can allow to determine the value of the QCD strong coupling constant $\alpha_s$ with reasonable theoretical uncertainty, dominated by the ambiguity in the existing estimates of the twist-4 non-perturbative $1/Q^2$-effect.