Diagnostics of Data-Driven Models: Uncertainty Quantification of PM7 Semi-Empirical Quantum Chemical Method

A map of mass spectrometry-based in silico fragmentation prediction and compound identification in metabolomics

Metabolomics, the comprehensive study of the metabolome, and lipidomics-the large-scale study of pathways and networks of cellular lipids-are major driving forces in enabling personalized medicine. Complicated and error-prone data analysis still remains a bottleneck, however, especially for identifying novel metabolites. Comparing experimental mass spectra to curated databases containing reference spectra has been the gold standard for identification of compounds, but constructing such databases is a costly and time-demanding task. Many software applications try to circumvent this process by utilizing cutting-edge advances in computational methods-including quantum chemistry and machine learning-and simulate mass spectra by performing theoretical, so called in silico fragmentations of compounds. Other solutions concentrate directly on experimental spectra and try to identify structural properties by investigating reoccurring patterns and the relationships between them. The considerable progress made in the field allows recent approaches to provide valuable clues to expedite annotation of experimental mass spectra. This review sheds light on individual strengths and weaknesses of these tools, and attempts to evaluate them-especially in view of lipidomics, when considering complex mixtures found in biological samples as well as mass spectrometer inter-instrument variability.

Towards theoretical spectroscopy with error bars: systematic quantification of the structural sensitivity of calculated spectra

Molecular spectra calculated with quantum-chemical methods are subject to a number of uncertainties (e.g., errors introduced by the computational methodology) that hamper the direct comparison of experiment and computation. Judging these uncertainties is crucial for drawing reliable conclusions from the interplay of experimental and theoretical spectroscopy, but largely relies on subjective judgment. Here, we explore the application of methods from uncertainty quantification to theoretical spectroscopy, with the ultimate goal of providing systematic error bars for calculated spectra. As a first target, we consider distortions of the underlying molecular structure as one important source of uncertainty. We show that by performing a principal component analysis, the most influential collective distortions can be identified, which allows for the construction of surrogate models that are amenable to a statistical analysis of the propagation of uncertainties in the molecular structure to uncertainties in the calculated spectrum. This is applied to the calculation of X-ray emission spectra of iron carbonyl complexes, of the electronic excitation spectrum of a coumarin dye, and of the infrared spectrum of alanine. We show that with our approach it becomes possible to obtain error bars for calculated spectra that account for uncertainties in the molecular structure. This is an important first step towards systematically quantifying other relevant sources of uncertainty in theoretical spectroscopy.

Uncertainty quantification is applied in theoretical spectroscopy to obtain error bars accounting for the structural sensitivity of calculated spectra.