= Ambiguous NMR distance restraint
An \b[ambiguous NMR distance restraint] represents an observation compatible with several atom-pair assignments rather than one uniquely identified pair. It combines candidate contributions according to a specified rule during an <NMR distance restraint> calculation. A single overlapping <NOESY> feature can motivate such a representation; ambiguity concerns which nuclei generated the observation.<Distance restraints in the Xplor-NIH manual>[Setup of Distance Restraints; Choice of Averaging]{ref}
For an inverse-sixth-power sum model with one molecular copy,
$$
r_{\mathrm{eff}}=\left(\sum_{(i,j)\in\mathcal A}r_{ij}^{-6}\right)^{-1/6},
$$
where $\mathcal A$ contains the candidate pairs. An upper bound applies to this effective quantity, not independently to every $r_{ij}$. Xplor-NIH's optional `OR` syntax lists alternative pairs and uses sum averaging; it avoids adding unwanted cross-combinations of broad atom selections.<Distance restraints in the Xplor-NIH manual>[Expressing ambiguous restraints using the optional OR statement, eq.20.5]{ref}
For an original example, suppose the possible assignments are pair $(a,b)$ at3angstroms and pair $(c,d)$ at8angstroms. Then
$$
r_{\mathrm{eff}}=(3^{-6}+8^{-6})^{-1/6}
\simeq2.999\,\mathrm{\mathring A}.
$$
A3.5angstrom upper bound is compatible with this sum even though one candidate pair is8angstroms apart. Enforcing a separate3.5angstrom limit on both candidates would assert stronger information than the ambiguous observation supplies.
The pair list matters too: these alternatives need not include $(a,d)$ or $(c,b)$. Selecting all atoms from $\{a,c\}$ against all atoms from $\{b,d\}$ would introduce those extra combinations and change the calculation. An explicit assignment representation preserves the intended alternatives.<Distance restraints in the Xplor-NIH manual>[Optional OR statement, relevant atom pairs for each possible assignment]{ref}
Sum normalization, molecular symmetry and the distinction between assignment ambiguity and conformational averaging must remain part of the restraint model. Reducing an effective distance during refinement does not by itself prove that a particular candidate assignment is the uniquely correct one.
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