Hydrogen skeleton, mobility and protein architecture

The mobility of the proton-proton radial vectors is introduced as a quantitative measure for the structural dynamics of organic materials, especially protein molecules. As defined for the entire molecule, the hydrogen mobility (HM) is proposed as an “order parameter,” which describes the effect of motional narrowing on inter-proton dipole-dipole interactions. HM satisfies all requirements of an order parameter in the Landau molecular field theory of phase transitions. The wide-line NMR second moments needed to obtain HM are exactly defined and measurable physical quantities, which are not produced by mathematical fitting and do not carry the limitations and restrictions of any model (theoretical formalism). We first demonstrate the usefulness of HM on small organic molecules with data taken form the literature. We outline its link with structural and functional characteristics on a range of proteins: HM provides a model-free parameter based on first principles that can clearly distinguish between globular and intrinsically disordered proteins, and can also provide insight into the behavior of disease-related mutants.