Localization improvement of deuterium uptake in hydrogen/deuterium exchange in proteins

We present a procedure for localization of deuterium uptake from overlapping proteolytic peptides to contiguous protein parts called segments. A system of linear equations expressing experimental peptide uptakes in segments cannot be solved by ordinary methods because of insufficient rank and/or linearly dependent peptides. Solvable segments are identified, and their uptakes and associated variances are evaluated by using the Moore-Penrose pseudoinverse. The method also allows consistency check of experimental data and detection of outliers. The conditions for segment solvability are formulated in a peptide graph. From the peptide graph, it is easy to find more useful information hidden in the experimental data, like sums or differences of unsolvable segment uptakes. Expected localization gain was estimated from simulations with random peptide arrangements. The recently proposed averaging method (Keppel TR, Weis DD. J. Am. Soc. Mass Spectrom. 2015; 26: 547) for resolution of exchange halftimes was extended to resolution of uptakes and combined with the present approach to achieve maximum uptake localization, which is also consistent with experimental data.