Effect of response factor variations on the response distribution of complex mixtures

The goal of "comprehensive" or "untargeted" analysis is to generate a list of all the compounds of a particular type in a complex mixture. To this end, modern analytical techniques, including high-resolution mass spectrometry, enable the individual detection of hundreds to tens of thousands of compounds, which can have response magnitudes that span several orders of magnitude. Moreover, we and others have found that many comprehensive analyses of complex mixtures result in a log-normal distribution of measured responses. The response distribution is not the concentration distribution but is related to it through the distribution of component response factors (RFs). Here, we present a theoretical investigation of how the shape of the RF distribution can impact the distribution of measured responses. We show that several distributions of RFs combined with a log-normal distribution of concentrations result in log-normal distributions of responses. Additionally, we find that deviations from log-normal responses depend on the shape of the RF distribution, and that, when they occur, these deviations occur in the low-response regions of the response distribution, which would often be below the detection limits for real measurements. In all cases, applying a distribution of RFs to a concentration distribution results in a response distribution that is both broader than the original concentration distribution and has a lower mean value than it would if the RFs for all the components were unity. Further, the distorting effect of the RF distribution can impair the determination of the original concentration distribution and the prediction of the number and concentrations of the undetected components.