  Fractal structure of shortest paths depends strongly on interresidue
interaction cutoff distance. The dimensionality of shortest paths is calculated
as a function of interaction cutoff distance. Shortest paths are self similar
with a fractal dimension of 1.12 when calculated with step lengths larger than
6.8 {\AA}. Paths are multifractal below 6.8 {\AA}. The number of steps to
traverse a shortest path is a discontinuous function of cutoff size at short
cutoff values, showing abrupt decreases to smaller values as cutoff distance
increases. As information progresses along the direction of a shortest path a
large set of residues are affected because they are interacting neighbors to
the residues of the shortest path. Thus, several residues are involved
diffusively in information transport which may be identified with the present
model. An algorithm is introduced to determine the residues of a given shortest
path. The shortest path residues are the highly visited residues during
information transport. These paths are shown to lie on the high entropy
landscape of the protein where entropy is taken to increase with abundance of
visits to nodes during signal transport.
