  We explore the possibility to construct higher-twist parton distributions in
a nucleon at some low reference scale from convolution integrals of the
light-cone wave functions (WFs). To this end we introduce simple models for the
four-particle nucleon WFs involving three valence quarks and a gluon with total
orbital momentum zero, and estimate their normalization (WF at the origin)
using QCD sum rules. We demonstrate that these WFs provide one with a
reasonable description of both polarized and unpolarized gluon parton densities
at large values of Bjorken variable x > 0.5. Twist-three parton distributions
are then constructed as convolution integrals of qqqg and usual three-quark
WFs. The cases of the polarized structure function g_2(x,Q^2) and single
transverse spin asymmetries are considered in detail. We find that the
so-called gluon-pole contribution to twist-three distributions relevant for
single spin asymmetry vanishes in this model, but is generated perturbatively
at higher scales by the evolution, in the spirit of GRV parton distributions.
