  When a self-localized quasiparticle excitation propagates along a discrete
one dimensional lattice, it becomes subject to a dissipation that converts the
kinetic energy into lattice vibrations. Eventually the kinetic energy does no
longer enable the excitation to cross over the minimum energy barrier between
neighboring sites, and the excitation becomes localized within a lattice cell.
In the case of a protein, the lattice structure consists of the C-alpha
backbone. The self-localized quasiparticle excitation is the elemental building
block of loops. It can be modeled by a kink which solves a variant of the
discrete non-linear Schroedinger equation (DNLS). We study the propagation of
such a kink in the case of protein G related albumin-binding domain, using the
UNRES coarse-grained molecular dynamics force field. We estimate the height of
the energy barriers the kink needs to cross over, in order to propagate along
the backbone lattice. We analyse how these barriers gives rise to both stresses
and reliefs which control the kink movement. For this, we deform a natively
folded protein structure by parallel translating the kink along the backbone
away from its native position. We release the transposed kink, and we follow
how it propagates along the backbone towards the native location. We observe
that the dissipative forces which are exerted on the kink by the various energy
barriers, have a pivotal role in determining how a protein folds towards its
native state.
