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<p>Electron paramagnetic
resonance (EPR) distance measurements are making increasingly important
contributions to studies of biomolecules underpinning health and disease by
providing highly accurate and precise geometric constraints. Combining
double-histidine (dH) motifs with Cu<sup>II</sup> spin labels shows promise for
further increasing the precision of distance measurements, and for
investigating subtle conformational changes. However, non-covalent coordination-based
spin labelling is vulnerable to low binding affinity. Dissociation constants of
dH motifs for Cu<sup>II</sup>-nitrilotriacetic acid were previously
investigated <i>via </i>relaxation induced dipolar modulation enhancement
(RIDME), and demonstrated the feasibility of exploiting the double histidine
motif for EPR applications at sub-μM protein concentrations. Herein, the
feasibility of using modulation depth quantitation in Cu<sup>II</sup>-Cu<sup>II
</sup>RIDME to simultaneously estimate a pair of non-identical independent <i>K<sub>D</sub></i>
values in such a tetra-histidine model protein is addressed. Furthermore, we
develop a general speciation model to optimise Cu<sup>II </sup>labelling
efficiency, in dependence of pairs of identical or disparate <i>K<sub>D</sub></i>
values and total Cu<sup>II</sup> label concentration. We find the dissociation
constant estimates are in excellent agreement with previously determined values,
and empirical modulation depths support
the proposed model. </p>
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