Markov Additive Chains and Applications to Fragment Statistics for Peptide Mass Fingerprinting

Peptide mass fingerprinting is a technique to identify a protein from its fragment masses obtained by mass spectrometry after enzymatic digestion. Recently, much attention has been given to the question of how to evaluate the significance of identifications; results have been developed mostly from a combinatorial perspective. In particular, existing methods generally do not capture the fact that the same amino acid can have different masses because of, e.g., isotopic distributions or variable chemical modifications. We offer several new contributions to the field: We introduce probabilistically weighted alphabets, where each character can have different masses according to a probability distribution, and random weighted strings as a fundamental model for random proteins. We develop a general computational framework, Markov Additive Chains, for various statistics of cleavage fragments of random proteins, and obtain general formulas for these statistics. Special results are given for so-called standard cleavage schemes (e.g., Trypsin). Computational results are provided, as well as a comparison to proteins from the SwissProt database.