Data normalization strategies in metabolomics: Current challenges, approaches, and tools

Data normalization is a big challenge in quantitative metabolomics approaches, whether targeted or untargeted. Without proper normalization, the mass-spectrometry and spectroscopy data can provide erroneous, sub-optimal data, which can lead to misleading and confusing biological results and thereby result in failed application to human healthcare, clinical, and other research avenues. To address this issue, a number of statistical approaches and software tools have been proposed in the literature and implemented over the years, thereby providing a multitude of approaches to choose from – either sample-based or data-based normalization strategies. In recent years, new dedicated software tools for metabolomics data normalization have surfaced as well. In this account article, I summarize the existing approaches and the new discoveries and research findings in this area of metabolomics data normalization, and I introduce some recent tools that aid in data normalization.

Choosing proper normalization is essential for discovery of sparse glycan biomarkers

In this work we assess the effect of different normalization methods on variable selection in an emerging field of glycomics.

Circadian variation in the release of small extracellular vesicles can be normalized by vesicle number or TSG101

Numerous candidate biomarkers in urine extracellular vesicles (EVs) have been described for kidney diseases, but none are yet in clinical use, possibly due to a lack of proper normalization. Proper normalization corrects for normal biological variation in urine flow rate or concentration, which can vary by over one order of magnitude. Here, we observed inter- and intra-animal variation in urine excretion rates of small EVs (<200 nm in diameter) in healthy rats as a series of six 4-h fractions. To visualize intra-animal variation, we normalized a small EV excretion rate to a peak excretion rate, revealing a circadian pattern for each rat. This circadian pattern was distinct from urine volume, urine albumin, urine creatinine, and urine albumin-to-creatinine ratio. Furthermore, urine small EV excretion was not significantly altered by sex, food/water deprivation, or ischemic acute kidney injury. Urine excretion of the exosomal/small EV marker protein tumor susceptibility gene 101 (TSG101) displayed a similar circadian pattern to urine small EV excretion; both measurements were highly correlated ( R2 = 0.85), with an average stoichiometry of 10.0 molecules of TSG101/vesicle in healthy rats. The observed stoichiometry of TSG101/vesicle in rat urine translated to human spot urine samples (10.2 molecules/vesicle) and cultured kidney-derived cell lines (human embryonic kidney-293 and normal rat kidney 52E cells). Small EV number and its surrogate, TSG101 protein, can normalize for circadian variation when testing candidate biomarkers in small EVs. Just as creatinine has emerged as the customary normalization factor for liquid-phase urine biomarkers, vesicle number and its surrogate, molecules of exosome/small EV-associated TSG101, should be considered as viable, normalizing factors for small EV biomarkers.

Normalization of Distance and Similarity in Sequence Analysis

We explore the relations between the notion of distance and a feature set–based concept of similarity and show that this concept of similarity has a spatial interpretation that is complementary to distance: it is interpreted as “direction.” Furthermore, we show how proper normalization leads to distances that can be directly interpreted as dissimilarity: Closeness in normalized space implies and is implied by similarity of the same objects, while remoteness implies and is implied by dissimilarity. Finally, we show how, in research into destandardization of the life course, properly normalizing may drastically and unequivocally change our interpretation of intercohortal distances.

Proton mass decomposition

We report the results on the proton mass decomposition and also on the related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of Nf = 2 + 1 DWF configurations with three lattice spacings and volumes, and several pion masses including the physical pion mass. With 1-loop pertur-bative calculation and proper normalization of the glue operator, we find that the u, d, and s quark masses contribute 9(2)% to the proton mass. The quark energy and glue field energy contribute 31(5)% and 37(5)% respectively in the MS scheme at µ = 2 GeV. The trace anomaly gives the remaining 23(1)% contribution. The u, d, s and glue momentum fractions in the MS scheme are consistent with the global analysis at µ = 2 GeV.

Non-Hermitian model for asymmetric tunneling

We present a simple non-Hermitian model to describe the phenomenon of asymmetric tunneling between two energy-degenerate sites coupled by a non-reciprocal interaction without dissipation. The system was described using a biorthogonal family of energy eigenvectors, the dynamics of the system was determined by the Schrödinger equation, and unitarity was effectively restored by proper normalization of the state vectors. The results show that the tunneling rates are indeed asymmetrical in this model, leading to an equilibrium that displays unequal occupation of the degenerate systems even in the absence of external interactions.

TWO-LOGARITHM MATRIX MODEL WITH AN EXTERNAL FIELD

We investigate the two-logarithm matrix model with the potential XΛ+α log (1+X)+β log (1-X) related to an exactly solvable Kazakov–Migdal model. In the proper normalization, using Virasoro constraints, we prove the equivalence of this model and the Kontsevich–Penner matrix model and construct the 1/N-expansion solution of this model.