BRAIN 2.0: Time and Memory Complexity Improvements in the Algorithm for Calculating the Isotope Distribution
 Piotr Dittwald,
 Dirk Valkenborg
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Abstract
Recently, an elegant iterative algorithm called BRAIN (Baffling Recursive Algorithm for Isotopic distributioN calculations) was presented. The algorithm is based on the classic polynomial method for calculating aggregated isotope distributions, and it introduces algebraic identities using NewtonGirard and Viète’s formulae to solve the problem of polynomial expansion. Due to the iterative nature of the BRAIN method, it is a requirement that the calculations start from the lightest isotope variant. As such, the complexity of BRAIN scales quadratically with the mass of the putative molecule, since it depends on the number of aggregated peaks that need to be calculated. In this manuscript, we suggest two improvements of the algorithm to decrease both time and memory complexity in obtaining the aggregated isotope distribution. We also illustrate a concept to represent the element isotope distribution in a generic manner. This representation allows for omitting the root calculation of the element polynomial required in the original BRAIN method. A generic formulation for the roots is of special interest for higher order element polynomials such that root finding algorithms and its inaccuracies can be avoided.
Graphical abstract
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 Title
 BRAIN 2.0: Time and Memory Complexity Improvements in the Algorithm for Calculating the Isotope Distribution
 Open Access
 Available under Open Access This content is freely available online to anyone, anywhere at any time.
 Journal

Journal of The American Society for Mass Spectrometry
Volume 25, Issue 4 , pp 588594
 Cover Date
 20140401
 DOI
 10.1007/s1336101307965
 Print ISSN
 10440305
 Online ISSN
 18791123
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Isotopic distribution
 Isotopic abundance’s ratios
 Mass spectrometry
 Proteomics
 BRAIN algorithm
 Industry Sectors
 Authors

 Piotr Dittwald ^{(1)} ^{(2)}
 Dirk Valkenborg ^{(3)} ^{(4)} ^{(5)}
 Author Affiliations

 1. College of Interfaculty Individual Studies in Mathematics and Natural Sciences, University of Warsaw, Warsaw, Poland
 2. Institute of Informatics, University of Warsaw, Warsaw, Poland
 3. Applied Bio and Molecular Systems, VITO, Mol, Belgium
 4. Interuniversity Institute for Biostatistics and Statistical Bioinformatics, Hasselt University, Diepenbeek, Belgium
 5. Center for Proteomics, Antwerp, Belgium