The isotopic distribution conundrum

Although access to high-resolution mass spectrometry (MS), especially in the field of biomolecular MS, is becoming readily available due to recent advances in MS technology, the accompanied information on isotopic distribution in high-resolution spectra is not used at its full potential, mainly because of lack of knowledge and/or awareness. In this review, we give an insight into the practical problems related to calculating the isotopic distribution for large biomolecules, and present an overview of methods for the calculation of the isotopic distribution. We discuss the key events that triggered the development of various algorithms and explain the rationale of how and why the various isotopic-distribution calculations were performed. The review is focused around the developmental stages as briefly outlined below, starting with the first observation of an isotopic distribution. The observations of Beynon in the field of organic MS that chlorine appeared in a mass spectrum as two variants with odds 3:1 lie at the basis of the first wave of algorithms for the calculation of the isotopic distribution, based on the atomic composition of a molecule. From here on, we explain why more complex biomolecules such as peptides exhibit a highly complex isotope pattern when assayed by MS, and we discuss how combinatorial difficulties complicate the calculation of the isotopic distribution on computers. For this purpose, we highlight three methods, which were introduced in the 1980s. These are the stepwise procedure introduced by Kubinyi, the polynomial expansion from Brownawell and Fillippo, and the multinomial expansion from Yergey. The next development was instigated by Rockwood, who suggested to decompose the isotopic distribution in terms of their nucleon count instead of the exact mass. In this respect, we could claim that the term "aggregated" isotopic distribution is more appropriate. Due to the simplification of the isotopic distribution to its aggregated counterpart, Rockwood was able to use the convolution for the calculation of the "aggregated" isotopic distribution. Convolution methods are computationally efficient and economic in their memory usage. We spend a section on the work introduced by Rockwood during the 1990s. Due to recent breakthroughs in mass spectrometric technology and the widespread high-resolution instruments (e.g., FTICR-MS, FTOrbitrap-MS, and TOF-MS) that provide high-resolution, isotope-resolved, accurate mass data, there is an emerging need for algorithms that can calculate isotopic distributions for large biomolecules. The number of recent publications on this topic does witness this trend. The new methods are mostly based on complex mathematical developments such as, for example, cellular automata (Meija and Caruso 2004. J Am Soc Mass Spectrom, 15(5):654-658), dynamic programming (Snider 2007. J Am Soc Mass Spectrom, 18:1511-1515), and hierarchical models (Li et al. 2008 J Am Soc Mass Spectrom, 19:1867-1874). We also comment on the ideas to use Punnet squares and Pascal's triangle to introduce the concept of the isotopic distribution for educational and didactic purposes.