  We study a model for polaron-like charge transport mechanism along DNA
molecules with emphasis on the impact of parametrical and structural disorder.
Our model Hamiltonian takes into account the coupling of the charge carrier to
two different kind of modes representing fluctuating twist motions of the base
pairs and H-bond distortions within the double helix structure of
$\lambda-$DNA. Localized stationary states are constructed with the help of a
nonlinear map approach for a periodic double helix and in the presence of
intrinsic static parametrical and/or structural disorder reflecting the impact
of ambient solvent coordinates. It is demonstrated that charge transport is
mediated by moving polarons respectively breather compounds carrying not only
the charge but causing also local temporal deformations of the helix structure
through the traveling torsion and bond breather components illustrating the
interplay of structure and function in biomolecules.
