Diffusion as a probe: Anomalies in the vibrational dynamics of proteins are a consequence of fractal like structure. 

Proteins have been shown to exhibit strange/anomalous dynamics
displaying non-Debye density of vibrational states, anomalous spread
of vibrational energy, large conformational changes, non-exponential
decay of correlations and non-exponential unfolding times. The
anomalous behavior may, in principle, stem from various factors
affecting the energy landscape under which a protein
vibrates. Investigating the origins of such unconventional dynamics,
we focus on the structure-dynamics interplay and introduce a
stochastic approach to the vibrational dynamics of proteins. We use
diffusion, a method sensitive to the structural features of the
protein fold and them alone, in order to probe protein
structure. Conducting a large scale study of diffusion on over 500 PDB
structures we find it to be anomalous, an indication of a fractal-like
structure. Taking advantage of known and newly derived relations
between vibrational dynamics and diffusion, we demonstrate the
equivalence of our findings to the existence of structurally
originated anomalies in the vibrational dynamics of proteins. We
conclude that these anomalies are a direct result of the fractal-like
structure of proteins. The duality between diffusion and vibrational
dynamics allows us to make, single molecule level, experimentally
testable predictions. The time dependent vibrational mean square
displacement of an amino acid is predicted to be subdiffusive. The
thermal variance in the instantaneous distance between amino acids is
shown to grow as a power law of the equilibrium distance. Mean first
passage time analysis is offered as a practical tool that may aid in
the identification of amino acid pairs involved in large
conformational changes.