Scale dependence of the chiral-odd twist-3 distributions $h_L(x)$ and $e(x)$

We evaluate the complete leading order evolution kernels for the chiral-odd twist-3 distributions $e(x)$ and $\widetilde h_L(x)$ of the nucleon. We establish the connection between the evolution equations in light-cone position and the light-cone fraction representations which makes correspondence between the nonlocal string operator product expansion and QCD inspired parton model. The compact expression obtained for the local anomalous dimension matrix coincides with previous calculations. In the multicolour QCD as well as in the large-$x$ limit the twist-3 distributions obey simple DGLAP equations. Combining these two limits we propose improved DGLAP equations and compare them numerically with the solutions of the exact evolution equations.