Estimation of Rates of Reactions Triggered by Electron Transfer in Top-Down Mass Spectrometry

Electron transfer dissociation (ETD) is a versatile technique used in mass spectrometry for the high-throughput characterization of proteins. It consists of several concurrent reactions triggered by the transfer of an electron from its anion source to sample cations. Transferring an electron causes peptide backbone cleavage while leaving labile post-translational modifications intact. The obtained fragmentation spectra provide valuable information for sequence and structure analyses. In this study, we propose a formal mathematical model of the ETD fragmentation process in the form of a system of stochastic differential equations describing its joint dynamics. Parameters of the model correspond to the rates of occurring reactions. Their estimates for various experimental settings give insight into the dynamics of the ETD process. We estimate the model parameters from the relative quantities of fragmentation products in a given mass spectrum by solving a nonlinear optimization problem. The cost function penalizes for the differences between the analytically derived average number of reaction products and their experimental counterparts. The presented method proves highly robust to noise in silico. Moreover, the model can explain a considerable amount of experimental results for a wide range of instrumentation settings. The implementation of the presented workflow, code-named ETDetective, is freely available under the two-clause BSD license.