 NMR distance restraint

An NMR distance restraint is a restriction on distances between selected atoms used in a structural calculation from nuclear magnetic resonance data. It often specifies an allowed interval or upper bound, with a penalty for a candidate structure violating it. Distances inferred from the nuclear Overhauser effect, including NOESY cross-peak information, are important examples. The restraint combines experimental interpretation with atom assignments and a model; it is not simply an exact ruler reading.^[ref]

For an original interval example, suppose a proton pair has allowed separation $l=2.0$ to $u=3.5$ angstroms. A flat-bottom quadratic penalty isA candidate distance of4.0angstroms contributes $0.25k{\mathring{\mathrm{A}}}^2$, whereas3.0angstroms contributes zero. Here $k$ has units of energy per squared length; the penalty is a fitting objective, not a measured pair interaction energy. Many restraints and stereochemical terms together constrain a protein structure.^[ref]

An ambiguous NMR distance restraint may describe several possible atom pairs contributing to one observation. In one inverse-sixth-power sum convention,For original candidate distances2 and4angstroms, this gives about1.995angstroms. Dividing the sum by2 before taking the inverse sixth root instead gives about2.239angstroms: an average and a sum are different models. An ambiguous assignment also does not assert that every candidate pair separately satisfies the nominal bound.^[ref]

Cross-peak overlap, nuclear spin diffusion and conformational averaging affect interpretation. A structural calculation therefore retains assignment and averaging information alongside its distance bounds; an absent or weak peak alone need not establish a large separation.