#### Abstract

In this article, we present a computation- and memory-efficient method to calculate the probabilities of occurrence and exact center-masses of the aggregated isotopic distribution of a molecule. The method uses fundamental mathematical properties of polynomials given by the Newton-Girard theorem and Viete's formulae. The calculation is based on the atomic composition of the molecule and the natural abundances of the elemental isotopes in normal terrestrial matter. To evaluate the performance of the proposed method, which we named BRAIN, we compare it with the results obtained from five existing software packages (IsoPro, Mercury, Emass, NeutronCluster, and IsoDalton) for 10 biomolecules. Additionally, we compare the computed mass centers with the results obtained by calculating, and subsequently aggregating, the fine isotopic distribution for two of the exemplary biomolecules. The algorithm will be made available as a Bioconductor package in R, and is also available upon request.