On the Fine Isotopic Distribution and Limits to Resolution in Mass Spectrometry

Mass spectrometry enables the study of increasingly larger biomolecules with increasingly higher resolution, which is able to distinguish between fine isotopic variants having the same additional nucleon count, but slightly different masses. Therefore, the analysis of the fine isotopic distribution becomes an interesting research topic with important practical applications. In this paper, we propose the comprehensive methodology for studying the basic characteristics of the fine isotopic distribution. Our approach uses a broad spectrum of methods ranging from generating functions--that allow us to estimate the variance and the information theory entropy of the distribution--to the theory of thermal energy fluctuations. Having characterized the variance, spread, shape, and size of the fine isotopic distribution, we are able to indicate limitations to high resolution mass spectrometry. Moreover, the analysis of "thermorelativistic" effects (i.e., mass uncertainty attributable to relativistic effects coupled with the statistical mechanical uncertainty of the energy of an isolated ion), in turn, gives us an estimate of impassable limits of isotopic resolution (understood as the ability to distinguish fine structure peaks), which can be moved further only by cooling the ions. The presented approach highlights the potential of theoretical analysis of the fine isotopic distribution, which allows modeling the data more accurately, aiming to support the successful experimental measurements.