The (generalized) hydrogen rule for organic molecules

Abstract

Dear editor, We would like to bring to your attention the existence of the hydrogen rule. 1,2 This rule states that for a neutral organic molecule of the form C nC H nH N nN O nO S nS , the sum of its nominal mass and the number of hydrogen atoms is divisible by four. Or, more formally, n H + m nom ð Þ mod 4 = 0, ð1Þ where m nom denotes the nominal mass of the neutral molecule. The hydrogen rule can be generalized to all neutral organic molecules, except of hypervalent molecules and free radicals, as follows: X n Y × m Y + m nom h i mod 4 = 0, ð2Þ where the sum is over all elements Y with an odd nominal mass m Y and n Y denotes the number of Y-atoms. The (generalized) hydrogen rule can be derived as a consequence of the definition of the nominal mass of a molecule 2 and the molecular formula for organic molecules. For a detailed derivation, we refer the reader to Claesen et al. 3 We illustrate the (generalized) hydrogen rule with two examples: angiotensin II and the halogenated fatty acid 2-Bromo-2-chloroacetic acid. For angiotensin II, with molecular formula C 50 H 71 N 13 O 12 , the sum of the number of hydrogens, 71, and the nominal mass, 1045, equals 1116, which is a multiple of four: 71 + 1045 = 1116 = 4 × 279: Hence, the elemental composition of angiotensin II is compliant with the hydrogen rule (1). For the halogenated fatty acid 2-Bromo-2-chloroacetic acid, the nominal mass is 172 dalton. The elemental composition of this molecule is C 2 H 2 Br 1 Cl 1 O 2 , which is compliant with the generalized hydrogen rule (2): 2 × 1 + 1 × 79 + 1 × 35 + 172 = 288 = 4 × 72: The hydrogen rule can be used to filter a set of predicted molecular formulae. Let us consider arginine, C 6 H 14 N 4 O 2 , which has a mon-oisotopic mass of 174.1117 Da. There are three theoretically possible elemental compositions of the form C nC H nH N nN O nO S nS within a 20-ppm wide mass-tolerance-window, ie, C 4 H 12 N 7 O 1 , C 6 H 14 N 4 O 2 , and C 8 H 16 N 1 O 3. All three elemental compositions have a nominal mass of 174 Da. The molecular formula C 6 H 14 N 4 O 2 is the only one that is compliant with the hydrogen rule (1), because 14 + 174 = 188 = 4 × 47. The elemental composition of organic compounds can also be predicted with the help of the hydrogen rule. For the monoisotopic mass of 174.1117 Da, pacMASS 3 predicts only one molecular formula, C 6 H 14 N 4 O 2 , which is the elemental composition of arginine. While the nitrogen rule 2,4 is an accepted definition in mass spec-trometry, the related hydrogen rule is less known. Given its validity for organic molecules commonly studied in mass spectrometry, such as proteins, peptides, and lipids, and given its practical use in molecular formulae filtering or in molecular formulae prediction, we propose to consider the term "hydrogen rule" as a new definition in the field of mass spectrometry. ORCID Jürgen Claesen https://orcid.org/0000-0001-7615-5322 Dirk Valkenborg https://orcid.org/0000-0002-1877-3496 REFERENCES 1. Claesen J, Valkenborg D, Burzykowski T. De novo prediction of the elemental composition of peptides and proteins based on a single mass. J Mass Spectrom. 2019. https://doi.