Mathematical Model of Mass Spectrometry Data Based on Gaussian Mixture Models

The article presents construction, adjustment and implementation of mathematical model of mass spectra. The model is based on Gaussian Mixture Models (GMM) applied to the mean spectrum. The complete analysis process composed of several steps is also presented. All results were obtained using an authorial tool dedicated to Maldi-Tof (Matrix-Assisted Laser Desorption Ionization-Time of Flight) mass spectra analysis. The method used for the analysis is based on the Gaussian mixture decomposition, whereas the fitting is done with Expectation-Maximization algorithm (EM) based on maximizing of the likelihood function. The analysis may be performed for several spectra simultaneously. User may decide wherever to analyze spectra individually or use the mean spectrum to make calculations faster and more efficient. The tool is also able to provide information about proteins involved in the spectrum. Information about proteins is obtained on the basis of m/z value of peaks detected in the process of the analysis. This further analysis is aimed into biological context achieving.