Alignment of Protein Mass Spectrometry Data by Integrated Markov Chain Shifting Method

Abstract

Motivation: Mass spectrometer such as SELDI-TOF (surface enhanced laser desorption/ionization time-of-flight) and MALDITOF (matrix assisted laser desorption and ionization time-of-flight) measure the relative abundance of different protein ions or protein fragments (peptides) indexed by the mass-to- charge ratio (m/z). A special characteristic of the MS spectra is its variabilities in both m/z values (x-axis) and intensity magnitudes (y-axis). Alignment of massto- charge ratio (m/z) so that the spectra or curves are at the same time or phase scale is an inevitable step towards characterizing and analyzing mass spectrometry (MS) data. Methods: Based on the observation that the second-order differences of m/ z demonstrate a certain Markovian property, we propose modelling the log- intensities by a semiparametric model and the m/z by the integrated Markov chain shifting (IMS) model, for which the second-order differences of the random effects are assumed to be a second-order Markov chain. Alignment of spectra is done through averaging over the random shifts given the observed intensity information. The unknown parameters are solved by an iterative nonparametric maximum profile likelihood method and a kernel approximation. Our approach is a self-modelling method which does not use internal/external calibration and can be easily implemented by Monte Carlo using the importance sampling method. Results: We run extensive simulations to evaluate the performance of the proposed method and algorithms. It is shown that the proposed approach can achieve satisfactory alignment. We also applied this method to a real MS data set from a liver cancer study.