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Nowadays, monoisotopic mass is used as an important feature in top-down proteomics. Knowing the exact monoisotopic mass is helpful for precise and quick protein identification in large protein databases. However, only in spectra of small molecules the monoisotopic peak is visible. For bigger molecules like proteins, it is hidden in noise or undetected at all, and therefore its position has to be predicted. By improving the prediction of the peak, we contribute to a more accurate identification of molecules, which is crucial in fields such as chemistry and medicine. In this work, we present the envemind algorithm, which is a two-step procedure to predict monoisotopic masses of proteins. The prediction is based on an isotopic envelope. Therefore, envemind is dedicated to spectra where we are able to resolve the one dalton separated isotopic variants. Furthermore, only single-molecule spectra are allowed, that is, spectra that do not require prior deconvolution. The algorithm deals with the problem of off-by-one dalton errors, which are common in monoisotopic mass prediction. A novel aspect of this work is a mathematical exploration of the space of molecules, where we equate chemical formulas and their theoretical spectrum. Since the space of molecules consists of all possible chemical formulas, this approach is not limited to known substances only. This makes optimization processes faster and enables to approximate theoretical spectrum for a given experimental one. The algorithm is available as a Python package envemind on our GitHub page https://github.com/PiotrRadzinski/envemind. [ABSTRACT FROM AUTHOR]

As high-resolution mass spectrometry (HRMS) becomes increasingly available, the need of software tools capable of handling more complex data is surging. The complexity of the HRMS data stems partly from the presence of isotopes that give rise to more peaks to interpret compared to lower resolution instruments. However, a new generation of fine isotope calculators is on the rise. They calculate the smallest possible sets of isotopologues. However, none of these calculators lets the user specify the joint probability of the revealed envelope in advance. Instead, the user must provide a lower limit on the probability of isotopologues of interest, that is, provide minimal peak height. The choice of such threshold is far from obvious. In particular, it is impossible to a priori balance the trade-off between the algorithm speed and the portion of the revealed theoretical spectrum. We show that this leads to considerable inefficiencies. Here, we present IsoSpec: an algorithm for fast computation of isotopologues of chemical substances that can alternate between joint probability and peak height threshold. We prove that IsoSpec is optimal in terms of time complexity. Its implementation is freely available under a 2-clause BSD license, with bindings for C++, C, R, and Python.