The Often-Overlooked Power of Summary Statistics in Exploratory Data Analysis: Comparison of Pattern Recognition Entropy (PRE) to Other Summary Statistics and Introduction of Divided Spectrum-PRE (DS-PRE)

H-Bonds in Crambin: Coherence in an α-Helix

We applied coherence analysis-used by engineers to identify linear interactions in stochastic systems-to molecular dynamics simulations of crambin, a thionin storage protein found in Abyssinian cabbage. A key advantage of coherence over other analyses is that it is robust, independent of the properties, or even the existence of probability distributions often relied on in statistical mechanics. For frequencies between 0.391 and 5.08 GHz (corresponding reciprocally to times of 2.56 and 0.197 ns), the displacements of oxygen and nitrogen atoms across α-helix H-bonds are strongly correlated, with a coherence greater than 0.9; the secondary structure causes the H-bonds to effectively act as a spring. Similar coherence behavior is observed for covalent bonds and other noncovalent interactions including H-bonds in β-sheets and salt bridges. In contrast, arbitrary pairs of atoms that are physically distant have uncorrelated motions and negligible coherence. These results suggest that coherence may be used to objectively identify atomic interactions without subjective thresholds such as H-bond lengths angles and angles. Strong coherence is also observed between the average position of adjacent leaves (groups of atoms) in an α-helix, suggesting that the harmonic analysis of classical molecular dynamics can successfully describe the propagation of allosteric interactions through the structure.