Undetected Components in Natural Mixtures: How Many? What Concentrations? Do They Account for Chemical Noise? What Is Needed to Detect Them?

Abstract

By definition, information about the set of components in a complex mixture below the detection limit is not directly available. However, if the composition of natural mixtures follows a natural law, the application of this law would enable the prediction of analytically important characteristics of that "hidden" fraction of the mixture. We have found that the analytical responses of compounds in three disparate natural mixtures (extracellular metabolites, light crude oil, and plant extracts) follow a log-normal (LN) distribution to a very high degree of correlation. Through the application of the LN model, the total number of components potentially detectable and the LN parameters of their analytical response distribution have been determined. From this distribution, one can predict the degree of analytical selectivity and dynamic range that would be required to detect any additional fraction of the components present. The data analyses of the studied mixtures reveal that the LN distribution parameters differ from one mixture type to another and that important information regarding the sample and the method employed is obtained. Further, the background level or "chemical noise" in the determinations studied agrees with the predicted cumulative responses of the undetected components. If generally applicable, the LN model will provide characterization parameters for mixture types, a means to assess completeness of analytical methods, and a model for theorists in mixture composition.