The protein state of matter: defining a key player in health and disease.

Protein folding-unfolding is a key issue in metabolism, also involved in several diseases, such as Alzheimer’s and Parkinson’s. Thermodynamically the folding event can be considered as a first-order phase transition. Phases can be easily defined in large thermodynamics systems, but caution is needed while speaking about single molecule. Here we tackle this problem by means of random matrix theory, using as model the molecular dynamics-derived correlation matrices of Trp-cage (a fragment of exendin-4). The eigenvalue spectra of these correlation matrices show that the low rank modes of Trp-cage dynamics are outside of the limit expected for a random system, both in folded and in unfolded conditions. This shows that the unfolded state is much less random than previously thought. We consider also the bulk eigenvalue spectra of correlation matrices, which represent localized vibrations, as probes of the protein local dynamics in different states. These last analyses show that the correlation matrices describing the folded and unfolded dynamics belong to different symmetry classes, proving that protein folding is a new type of phase transition if considered at single molecule level.