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Background  Given a peptide as a string of amino acids, the masses of all its prefixes and suffixes can be found by a trivial linear scan through the amino acid masses. The inverse problem is the  ideal   de novo   peptide sequencing problem : Given all prefix and suffix masses, determine the string of amino acids. In biological reality, the given masses are measured in a lab experiment, and measurements by necessity are noisy. The (real, noisy)  de novo peptide sequencing problem  therefore has a noisy input: a few of the prefix and suffix masses of the peptide are missing and a few other masses are given in addition. For this setting, we ask for an amino acid string that explains the given masses as accurately as possible.    Results  Past approaches interpreted accuracy by searching for a string that explains as many masses as possible. We feel, however, that it is not only bad to not explain a mass that appears, but also to explain a mass that does not appear. We propose to minimize the symmetric difference between the set of given masses and the set of masses that the string explains. For this new optimization problem, we propose an efficient algorithm that computes both the best and the  k  best solutions. Proof-of-concept experiments on measurements of synthesized peptides show that our approach leads to better results compared to finding a string that explains as many given masses as possible.    Conclusions  We conclude that considering the symmetric difference as optimization goal can improve the identification rates for de novo peptide sequencing. A preliminary version of this work has been presented at WABI 2016.    Electronic supplementary material  The online version of this article (doi:10.1186/s13015-017-0104-1) contains supplementary material, which is available to authorized users.

A better scoring model for de novo peptide sequencing: the symmetric difference between explained and measured masses