A mathematical programming for predicting molecular formulas in accurate mass spectrometry

The prediction of correct molecular formulas in mass spectra is a challenge since a large number of chemically possible candidate formulas are obtained in higher mass regions. This study presents a neural network based mathematical programming approach to reduce the search of candidate formulas to a smaller volume in the chemical space of given constituent elements. The approach consists of following steps: 1) The problem of assigning a molecular formula to the observed peak data (i.e. experimentally observed mass and relative abundance value of the isotopes) is converted to a mathematical programming problem. 2) The formulated mathematical programming is solved using a recurrent neural network of a low computational complexity. 3) The errors in the experimentally observed mass and relative isotopic abundances will be affecting the solution. Thus, a number of mathematical programming solutions, corresponding to the different values of the mass and relative abundances lying within the error limits, are obtained. 4) The obtained set of solutions is evaluated to assess the upper and lower limits on the number of constituent elements (C, H, N, O, etc) present in the candidate formulas. These limits define a volume (being referred to as solution volume) in the chemical space where the correct formulas lie. Finally, the molecular formulas in the solution volume which are likely to be wrong can be excluded with the use of existing filtering algorithm e.g. of.