Computational Methods and Stochastic Models in Proteomics

The thesis addresses three problems arising from mass spectrometry (MS) data processing. It describes computational methods for solving them and stochastic models that formalize some of them. The first problem is redundancy elimination in liquid chromatography MS (LC-MS) images of peptides. An algorithm for isotopic envelopes detection based on the sweeping method is presented. It consists of grouping peaks corresponding to different isotopic versions of the same particle kind and automatic determination of the charge of the group. A dynamic programming algorithm is given that proposes amino acid composition for a given weight of a peptide which helps to asses the quality of isotopic envelopes. Two solutions are presented to the second problem — the problem of LC-MS spectra alignment. The first one estimates retention time shifting and scaling with a Metropolis-Hastings algorithm. The second one uses a two stage clustering approach consisting of a DBSCAN algorithm pass and gaussian mixture model based clustering (estimation is based on the Expectation-Maximization algorithm). The last problem is inferring peptidase activity from LC-MS data. Firstly, a bayesian model based on the chemical master equation for exopeptidases is presented together with a Metropolis-Hastings algorithm for parameter estimation. The model is tested on synthetic and real datasets. Then an extended version is developed that handles also endopeptidases and integrates knowledge from the MEROPS peptidase database. Parameter estimation involves solving non-linear least squares problem.