A Mixed Integer Linear Optimization Framework for the Identification and Quantification of Targeted Post-translational Modifications of Highly Modified Proteins Using Multiplexed Electron Transfer Dissociation Tandem Mass Spectrometry*

Here we present a novel methodology for the identification of the targeted post-translational modifications present in highly modified proteins using mixed integer linear optimization and electron transfer dissociation (ETD) tandem mass spectrometry. For a given ETD tandem mass spectrum, the rigorous set of modified forms that satisfy the mass of the precursor ion, within some tolerance error, are enumerated by solving a feasibility problem via mixed integer linear optimization. The enumeration of the entire superset of modified forms enables the method to normalize the relative contributions of the individual modification sites. Given the entire set of modified forms, a superposition problem is then formulated using mixed integer linear optimization to determine the relative fractions of the modified forms that are present in the multiplexed ETD tandem mass spectrum. Chromatographic information in the mass and time dimension is utilized to assess the likelihood of the assigned modification states, to average several tandem mass spectra for confident identification of lower level forms, and to infer modification states of partially assigned spectra. The utility of the proposed computational framework is demonstrated on an entire LC-MS/MS ETD experiment corresponding to a mixture of highly modified histone peptides. This new computational method will facilitate the unprecedented LC-MS/MS ETD analysis of many hypermodified proteins and offer novel biological insight into these previously understudied systems.