Expert Algorithm for Substance Identification Using Mass Spectrometry: Statistical Foundations in Unimolecular Reaction Rate Theory

Abstract

This study aims to resolve one of the longest-standing problems in mass spectrometry, which is how to accurately identify an organic substance from its mass spectrum when a spectrum of the suspected substance has not been analyzed contemporaneously on the same instrument. Part one of this two-part report describes how Rice-Ramsperger-Kassel-Marcus (RRKM) theory predicts that many branching ratios in replicate electron-ionization mass spectra will provide approximately linear correlations when analysis conditions change within or between instruments. Here, proof-of-concept general linear modeling is based on the 20 most abundant fragments in a database of 128 training spectra of cocaine collected over 6 months in an operational crime laboratory. The statistical validity of the approach is confirmed through both analysis of variance (ANOVA) of the regression models and assessment of the distributions of the residuals of the models. General linear modeling models typically explain more than 90% of the variance in normalized abundances. When the linear models from the training set are applied to 175 additional known positive cocaine spectra from more than 20 different laboratories, the linear models enabled ion abundances to be predicted with an accuracy of <2% relative to the base peak, even though the measured abundances vary by more than 30%. The same models were also applied to 716 known negative spectra, including the diastereomers of cocaine: allococaine, pseudococaine, and pseudoallococaine, and the residual errors were larger for the known negatives than for known positives. The second part of the manuscript describes how general linear regression modeling can serve as the basis for binary classification and reliable identification of cocaine from its diastereomers and all other known negatives.

Keywords: binary classification; compound identification; drug identification; forensic science; search algorithm; spectral algorithm; spectral comparisons.

Figure 1

Schematic visualization of different potential energy pathways down an energy landscape. Tight transitions states can be thought of as narrow paths that take time to traverse and tend to involve rearrangements. Loose transition states can be thought of as wide-open pathways falling sharply off the mountain; they are faster and more numerous but can only be accessed from higher states.

Figure 2

Theoretical modeling to show how changes in fractional ion abundances as a function of internal energy and observation time can be linearly extrapolated between instruments: (A) modeled system and relative rates of fragmentation at the vertical dashed line in each panel; (B) modeled log(k_diss) versus internal energy at a fixed reaction time; (C) breakdown curves as a function of time at a fixed internal energy; (D) breakdown curves as a function of internal energy at fixed time; (E) ion abundances versus the abundance of C⁺ over the range of times in panel C; and (F) ion abundances versus the abundance of C⁺ over the range of internal energies in panel D. One grid width in Figures B, C, and D spans a 33% increase in internal energy and 50% increase in reaction time relative to the dashed line for the conditions in panel A.

Figure 3

Scatter plots of measured and predicted ion abundances for m/z 182 for cocaine: (A) normalized abundance of m/z 182 relative to the base peak in 128 spectra (cases) collected over 6 months; (B) scatter plot of the normalized abundance of m/z 182 versus the normalized abundance of m/z 198 in the same data; (C) scatter plot of the normalized abundance of m/z 182 versus the EASI-predicted abundances using the coefficients shown in Table 2; (D) scatter plot of the standardized residuals versus the standardized predicted abundances based on the 128 predictions in panel C; (E) frequency distribution plot of the standardized residuals of the 128 predictions in panels C and D; and (F) P–P plot of the standardized residuals in panels C and D.

Figure 4

Scatter plots of measured and modeled/predicted values for a few selected ions of cocaine: (A) m/z 182, (B) m/z 94, (C) m/z 77, and (D) m/z 272. Horizontal lines show the mean abundances for the training set from Lab 1 (light blue) and validation set from other laboratories (dark blue). The line y = x refers to the ideal case of no residual error in predictions.