Nonparametric Models for Peak Identification and Quantification in Mass Spectroscopy, with Application to MALDI-TOF

We present a novel nonparametric Bayesian approach based on Lévy Adaptive Regression Kernels (LARK) to model spectral data arising from MALDI-TOF (Matrix Assisted Laser Desorption Ionization Time-of-Flight) mass spectrometry. This model based approach provides identification and quantification of proteins though model parameters that are directly interpretable as the number of proteins, mass and abundance of proteins and peak resolution. Informed prior distributions, based on expert opinion and on preliminary laboratory experiments, help to distinguish true peaks from background noise and help resolve uncertainty about the peak multiplicity. Posterior distributions are obtained using a reversible jump Markov chain Monte Carlo algorithm and provide inference about the number of peaks (proteins), their masses and abundance. We show through simulation studies that the procedure has desirable trueand false-discovery rates. Finally, we illustrate the method on four example spectra: a blank spectrum, a spectrum with only the matrix of a low-molecular-weight substance used to embed target proteins, and a single spectrum and average of ten spectra from an individual lung cancer patient.