Random Matrix Theory in molecular dynamics analysis

- PCA performed on short-time MD experiments leads to cosine-shaped projections.
- Also PCA performed on multidimensional Brownian dynamics leads to the same result.
- We use Random Matrix Theory tools in order to compare MD data with Brownian systems.
- We show that protein dynamics is not really Brownian also at very short time-scale.
- We suggest that Random Matrix Theory can be very useful in MD data analysis.

It is well known that, in some situations, principal component analysis (PCA) carried out on molecular dynamics data results in the appearance of cosine-shaped low index projections. Because this is reminiscent of the results obtained by performing PCA on a multidimensional Brownian dynamics, it has been suggested that short-time protein dynamics is essentially nothing more than a noisy signal. Here we use Random Matrix Theory to analyze a series of short-time molecular dynamics experiments which are specifically designed to be simulations with high cosine content. We use as a model system the protein apoCox17, a mitochondrial copper chaperone. Spectral analysis on correlation matrices allows to easily differentiate random correlations, simply deriving from the finite length of the process, from non-random signals reflecting the intrinsic system properties. Our results clearly show that protein dynamics is not really Brownian also in presence of the cosine-shaped low index projections on principal axes.