To obtain data similar to that from PLIMSTEX, the concentration of insulin in solution is varied and amide exchange is initiated, followed by quenching the exchange, and injecting the ice-cold solution into the ESI source of a mass spectrometer. After the quench, the oligomers dissociate into monomers, but the increase in mass of the monomer (compared to the control) gives a weighted average of the increase in mass of the various oligomers. These data can be used to obtain a species-specific deuterium number for each oligomer and to calculate the association constants for the oligomerization. For fitting the insulin self-association data, the modeling is modified to acknowledge that both ligand and protein are the same .
The insulin amide exchange during the self-association shows that the number of exchangeable hydrogens decreases with increasing concentration of insulin, demonstrating that, as the self-association occurs, fewer amide hydrogens undergo exchange. The AD values in the case of insulin represent changes in the solvent accessibility of the oligomer compared to that of the monomer. Assuming a monomer ^ dimer ^ hexamer model gives a good fit for the data. At convergence, the dimerization constant, K12, is 7 x 105 M_1 and the hexamerization constant, K26 (from dimer to hexamer), is 2 x 109 M_1, and these agree with the literature values (1.4 x 105 M_1 and 4 x 108 M_1)  within a factor of 5. The corresponding DD12 and AD26 are 14 and 23, respectively (Table 11.1), quantifying the number of amide hydrogens in the dimer and hexamer (with respect to monomer) that lose solvent accessibility in the self-associations.
A similar approach is fruitful for investigating insulin mutants that may be under consideration as replacements for wild-type insulin in human therapy. For lispro insulin (in which positions P28 and K29 in human insulin are reversed), and for several other insulin mutants, PLIMSTEX clearly can distinguish the self-association properties and binding constants of lispro and r-human insulins .
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