Masserstein: robust linear deconvolution by optimal transport

Abstract

A common theme in many applications of computational mass spectrometry is fitting a linear combination of reference spectra to an experimental one in order to estimate the quantities of different ions, potentially with overlapping isotopic envelopes. In this work, we study this procedure in an abstract setting, in order to develop new approaches applicable to a diverse range of experiments. We introduce an application of a new spectral dissimilarity measure, known in other fields as the Wasserstein or the Earth Movers distance, in order to overcome the sensitivity of ordinary linear regression to measurement inaccuracies. Usinga a data set of 200 mass spectra, we demonstrate that our approach is capable of accurate estimation of ion proportions without extensive pre-processing required for state-of-the-art methods. The conclusions are further substantiated using data sets simulated in a way that mimics most of the measurement inaccuracies occurring in real experiments. We have implemented our methods in a Python 3 package, freely available at https://github.com/mciach/masserstein.