  We introduce a probabilistic model for protein sliding motion along DNA
during the search of a target sequence. The model accounts for possible effects
due to sequence-dependent interaction between the nonspecific DNA and the
protein. As an example, we focus on T7 RNA-polymerase and exploit the available
information about its interaction at the promoter site in order to investigate
the influence of bacteriophage T7 DNA sequence on the dynamics of the sliding
process. Hydrogen bonds in the major groove are used as the main
sequence-dependent interaction between RNA-polymerase and DNA. The resulting
dynamical properties and the possibility of an experimental verification are
discussed in details. We show that, while at large times the process reaches a
pure diffusive regime, it initially displays a sub-diffusive behavior. The
subdiffusive regime can lasts sufficiently long to be of biological interest.
