Statistical Methods for Mass Spectrometry Proteomics Data with Multiple Membership Structure

Abstract

Proteins carry out most functions of cells. Proteomics, the study of all proteins in a biological system such as a cell or a tissue, is thus essential to all biomedical research. A core technology capable of determining both identities and quantities of proteins in a sample is mass spectrometry (MS). It has found use in many areas of academic and applied research involving proteins, including drug discovery, clinical proteomics, structural studies, the study of protein-protein interactions, and post-translational modifications.

Mass spectrometry studies generate large and complex data sets that require advanced computational methods at various stages of processing, from extracting signal from raw data through normalization and filtering, to inferring protein sequences based on the masses of observed molecules, and downstream statistical analysis. This dissertation addresses practical problems in the analysis of mass spectrometry-based data, which require the development and benchmarking of statistical models, as well as software developments. Statistical problems considered in this thesis both involve data that fall into the multiple membership category. In this class of problems, some observations can be assigned to multiple groups and therefore participate in the estimation of multiple effects simultaneously, unlike in standard analysis of variance models, where each observation belongs to exactly one group.

First, we describe a statistical model for quantifying abundances of proteins based on peptide-level mass spectrometry with peptides that can match to multiple proteins. We propose to jointly estimate average abundances of proteins and weights that describes the similarity between quantitative patterns of peptides and overall protein-level trends. This leads to a complex statistical model with a biconvex loss function.

Then, we introduce a statistical model for inferring exchange probabilities based on hydrogen-deuterium exchange mass spectrometry data for smaller units than observable peptides. We model the probability distributions of exchanged hydrogens in overlapping parts of peptide sequences and use convolutions of these distributions to generate expected isotopic distributions that can be compared to observed spectra.

We propose and implement method of fitting both models to data and evaluate their performance on biological and simulated data sets. Moreover, we describe the redesign and refactoring of an existing suite of statistical programs for analyzing the differential abundance of proteins based on mass spectrometry data, MSstats, developed by Prof. Olga Vitek's group at Northeastern University (US). One of the models developed in this dissertation was integrated into the MSstats framework.