Random protein association analyses of MALDI-TOF mass spectra of two- and three-component protein systems using binomial and multinomial distribution

Abstract The phenomenon of protein randomly associating among themselves during MALDI-TOF mass spectrometric measurements is manifest on all the proteins tested here. The magnitude of this random association seems to be protein-dependent. However, a detailed mathematical analysis of this process has not been reported so far. Here, binomial and multinomial equations are used to analyze the relative populations of multimer ions formed by random protein association during MALDI-TOF mass spectrometric measurements. Hemoglobin A (which consists of two α-globins and two β-globins) and biotinylated insulin (which contains intact, singly biotinylated, and doubly biotinylated insulin) are used as the test cases for two- and three-component protein systems, respectively. MALDI-TOF spectra are acquired using standard MALDI-TOF techniques and equipment. The binomial distribution matches the relative populations of multimer ions of Hb A perfectly. For biotinylated insulin sample, taking lesser relative populations for doubly biotinylated insulin and intact insulin compared with singly biotinylated insulin into account, the relative populations of multimer ions of the biotinylated insulin confirms the prediction of multinomial equation. The pairs of unrelated proteins such as myoglobin, avidin, and lysozyme show lesser intensities for heteromultimers than for homomultimers, indicating weaker propensities to associate between different proteins during MALDI-TOF mass spectrometric measurements. Contrary to the suggestion that the multimer ions are formed in the solution phase prior to MALDI-TOF mass spectrometric measurement through multistage sequential reactions of the aggregation of protein molecules, we postulate that multimer ions of proteins are formed after the protein molecules have been vaporized into the gas phase through the assistance of the laser and matrix.