A Bayesian approach for constituent estimation in nucleic acid mixture models

Mass spectrometry (MS) is a powerful analytical method used for various purposes such as drug development, quality assurance, food inspection, and monitoring of pollutants in the environment. In recent years, with the active development of antibodies and nucleic acid-based drugs, impurities with various modifications are produced. These can lead to a decrease in drug stability, pharmacokinetics, and efficacy, making it crucial to differentiate these impurities. Previously, attempts have been made to estimate the monoisotopic mass and ion amounts in the spectrum generated by electrospray ionization (ESI). However, conventional methods could not explicitly estimate the number of constituents, and discrete state evaluations, such as the probability that the number of constituents is k or k+1, were not possible. We propose a method where, for each possible number of constituents in the sample, mass spectrometry is modeled using parameters like monoisotopic mass and ion counts. Using Simulated Annealing, NUTS, and stochastic variational inference, we determine the parameters for each constituent number model and the maximum posterior probability. Finally, by comparing the maximum posterior probabilities between models, we select the optimal number of constituents and estimate the monoisotopic mass and ion counts under that scenario.