  We applied coherence analysis to molecular dynamics simulations of the plant
protein crambin, a thionin storage protein found in Abyssinian cabbage.
Coherence analysis was developed by engineers to identify linear interactions,
without statistical assumptions. Coherence is greater than 0.9 between the
displacement of oxygen and nitrogen atoms of H bonds in alpha helices for
frequencies between 0.391 GHz and 5.08 GHz (corresponding reciprocally to times
of 2.56 ns and 0.197 ns). These H bonds act much like a linear system.
Unrelated atoms have uncorrelated motions and much smaller coherence, say 0.02.
Groups of atoms (that form a layer of an alpha helix) were averaged and the
coherence function of two groups was evaluated. Layers of the alpha helix form
a linear system, suggesting that the harmonic analysis of classical molecular
dynamics can successfully describe the allosteric interactions of the layers of
an alpha helix.
