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Resolution of protein H/D exchange by fitting amide exchange probabilities to the peptide isotopic envelopes.

RATIONALE
Mass spectra processing in protein H/D exchange has been remarkably improved by introducing fitting of the amide exchange probabilities to peptide isotopic envelope intensities (Kan et al., 2013), in contrast to methods in which only the peptide deuterium uptakes (centroid shifts of isotopic envelopes) are used. However, the known implementations are based on the general fitting routines that use only the objective function values. Besides, applicability of more than one fitting method makes necessary their comparative evaluation.


METHODS
Two fitting methods were considered: the common least squares and the fitting of the multinomial distribution representing the number of deuteriums exchanged in the individual peptides. Both methods were applied either directly to the isotopic envelope data or to the deuterium distributions obtained by envelope deconvolution (i.e. de-isotoping).


RESULTS
An autonomous Matlab script was prepared, based on the exact expressions for the gradient and Hessian of the objective function, with the trust-region algorithm implemented in the compact analytical form recently made available. The least squares fitting to the envelope data produced the best results, with the greatest precision and good coverage of exact values by the confidence intervals. The deuterium distributions were sensitive to the (simulated) experimental error whose progression by envelope deconvolution caused degradation in accuracy. The multinomial distribution fitting exhibited poor performance due to inadequate representation of the experimental error and missing of the appropriate weight parameters. Some specific peptide arrangement details were discussed as potential sources of ambiguity in the fitting results.


CONCLUSIONS
The method of fitting to peptide isotopic envelopes has been improved by using the exact gradient and Hessian of the objective function. The fitting should be repeated with different initial guesses in order to find not only the global minimum but also the local minima with similar depths which may exist due to eventual ambiguity of the fitting results.