Control-Normalized Fisher Ratio Analysis of Comprehensive Two-Dimensional Gas Chromatography Time-of-Flight Mass Spectrometry Data for Enhanced Biomarker Discovery in a Metabolomic Study of Orthopedic Knee-Ligament Injury.

An innovative form of Fisher ratio (F-ratio) analysis (FRA) is developed for use with comprehensive two-dimensional gas chromatography/time-of-flight mass spectrometry (GC × GC-TOFMS) data and applied to the investigation of the changes in the metabolome in human plasma for patients with injury to their anterior cruciate ligament (ACL). Specifically, FRA provides a supervised discovery of metabolites that express a statistically significant variance in a two-sample class comparison: patients and healthy controls. The standard F-ratio utilizes the between-class variance relative to the pooled within-class variance. Because standard FRA is adversely impacted by metabolites expressed with a large within-class variance in the patient class, "control-normalized FRA" has been developed to provide complementary information, by normalizing the between-class variance to the variance of the control class only. Thirty plasma samples from patients who recently suffered from an ACL injury, along with matched controls, were subjected to GC × GC-TOFMS analysis. Following both standard and control-normalized FRA, the concentration ratio for the top 30 "hits" in each comparison was obtained and then t-tested for statistical significance. Twenty four out of 30 metabolites plus the therapeutic agent, naproxen (24/30), passed the t-test for the control-normalized FRA, which included 8/24 unique to control-normalized FRA and 16/24 in common with the standard FRA. Likewise, standard FRA provided 21/30 metabolites passing the t-test, with 5/21 undiscovered by control-normalized FRA. The complementary information obtained by both F-ratio analyses demonstrates the general utility of the new approach for a variety of applications.

Development of gas chromatographic pattern recognition and classification tools for compliance and forensic analyses of fuels: A review.

Gas chromatography (GC) is undoubtedly the analytical technique of choice for compositional analysis of petroleum-based fuels. Over the past twenty years, as comprehensive two-dimensional gas chromatography (GC × GC) has evolved, fuel analysis has often been highlighted in scientific reports, since the complexity of fuel analysis allows for illustration of the impressive peak capacity gains afforded by GC × GC. Indeed, several research groups in recent years have applied GC × GC and chemometric data analysis to demonstrate the potential of these analytical tools to address important compliance (tax evasion, tax credits, physical quality standards) and forensic (arson investigations, oil spills) applications involving fuels. None the less, routine use of GC × GC in forensic laboratories has been limited largely by (1) legal and regulatory guidelines, (2) lack of chemometrics training, and (3) concerns about the reproducibility of GC × GC. The goal of this review is to highlight recent advances in one-dimensional GC (1D-GC) and GC × GC analyses of fuels for compliance and forensic applications, to assist scientists in overcoming the aforementioned hindrances. An introduction to 1D-GC principles, GC × GC technology (column stationary phases and modulators) and several chemometric methods is provided. More specifically, chemometric methods will be broken down into (1) signal preprocessing, (2) peak decomposition, identification and quantification, and (3) classification and pattern recognition. Examples of compliance and forensic applications will be discussed with particular emphasis on the demonstrated success of the employed chemometric methods. This review will hopefully make 1D-GC and GC × GC coupled with chemometric data analysis tools more accessible to the larger scientific community, and aid in eventual widespread standardization.

Statistical inference of mass channel purity from Fisher ratio analysis using comprehensive two-dimensional gas chromatography with time of flight mass spectrometry data.

Tile-based Fisher ratio (F-ratio) analysis has recently been developed and validated for discovery-based studies of highly complex data collected using comprehensive two-dimensional gas chromatography coupled with time-of-flight mass spectrometry (GC×GC-TOFMS). In previous studies, interpretation and utilization of F-ratio hit lists has relied upon manual decomposition and quantification performed by chemometric methods such as parallel factor analysis (PARAFAC), or via manual translation of the F-ratio hit list information to peak table quantitative information provided by the instrument software (ChromaTOF). Both of these quantification approaches are bottlenecks in the overall workflow. In order to address this issue, a more automatable approach to provide accurate relative quantification for F-ratio analyses was investigated, based upon the mass spectral selectivity provided via the F-ratio spectral output. Diesel fuel spiked with 15 analytes at four concentration levels (80, 40, 20, and 10 ppm) produced three sets of two class comparisons that were submitted to tile-based F-ratio analysis to obtain three hit lists, with an F-ratio spectrum for each hit. A novel algorithm which calculates the signal ratio (S-ratio) between two classes (eg., 80 ppm versus 40 ppm) was applied to all mass channels (m/z) in the F-ratio spectrum for each hit. A lack of fit (LOF) metric was utilized as a measure of peak purity and combined with F-ratio and p-values to study the relationship of each of these metrics with m/z purity. Application of a LOF threshold coupled with a p-value threshold yielded a subset of the most pure m/z for each of the 15 spiked analytes, evident by the low deviations (< 5%) in S-ratio relative to the true concentration ratio. A key outcome of this study was to demonstrate the isolation of pure m/z without the need for higher level signal decomposition algorithms.

Discovery-based analysis and quantification for comprehensive three-dimensional gas chromatography flame ionization detection data.

Basic principles are introduced for implementing discovery-based analysis with automated quantification of data obtained using comprehensive three-dimensional gas chromatography with flame ionization detection (GC3-FID). The GC3-FID instrument employs dynamic pressure gradient modulation, providing full modulation (100% duty cycle) with a fast modulation period (PM) of 100 ms. Specifically, tile-based Fisher-ratio analysis, previously developed for comprehensive two-dimensional gas chromatography with time-of-flight mass spectrometry (GC×GC-TOFMS), is adapted and applied for GC3-FID where the third chromatographic dimension (3D) is treated as the "spectral" dimension. To evaluate the instrumental platform and software implementation, ten "non-native" compounds were spiked into a ninety-component base mixture to create two classes with a concentration ratio of two for the spiked analyte compounds. The Fisher ratio software identified 95 locations of potential interest (i.e., hits), with all ten spiked analytes discovered within the top fourteen hits. All 95 hits were quantified by a novel signal ratio (S-ratio) algorithm portion of the F-ratio software, which determines the time-dependent S-ratio of the 3D chromatograms from one class to another, thus providing relative quantification. The average S-ratio for spiked analytes was 1.94 ± 0.14 mean absolute error (close to the nominal concentration ratio of two), and 1.06 ± 0.16 mean absolute error for unspiked (i.e., matrix) components. The appearance of the S-ratio as a function of 3D retention time in the GC3 dataset, referred to as an S-ratiogram, provides indication of peak purity for each hit. The unique shape of the S-ratiogram for hit 1, α-pinene, suggested likely 3D overlap. Parallel factor analysis (PARAFAC) decomposition of the hit location confirmed that overlap was occurring and successfully decomposed α-pinene from a highly overlapped (3Rs = 0.1) matrix interferent.

Impact of data bin size on the classification of diesel fuels using comprehensive two-dimensional gas chromatography with principal component analysis.

Principal component analysis (PCA) is a widely applied chemometric tool for classifying samples using comprehensive two-dimensional (2D) gas chromatography (GC × GC) separation data. Classification via PCA can be improved by 2D binning of the data. A "standard operating procedure (SOP) bin size" is often applied to improve the S/N and to mitigate potential retention time misalignment issues. The SOP bin size is generally selected to be slightly larger than the typical 2D peak dimensions. In this study we examine to what extent a single SOP bin size is optimal for all of the class comparisons that can be made in a single PCA scores plot. For this purpose, a GC × GC-FID dataset comprised of 5 different diesel fuels (i.e., 5 sample classes), each run with 4 replicates using a reverse column configuration (polar 1D column and non-polar 2D column) was utilized. The dataset was collected within about one day, which minimized retention time misalignment in order to allow the study to focus on S/N enhancement concurrent with maintaining the chemical selectivity provided by the GC × GC separations. A total of 110 bin sizes were evaluated. Degree-of-class separation (DCS) was utilized as a quantitative metric to assess the impact of binning in improving separation in the scores plot. The DCS was calculated pair-wise between nearest neighbor sample classes for each of the 5 sample classes in the scores plot (5 sample class pairs). Results indicated the SOP bin size did not provide the highest DCS for any of the 5 fuel pairs. Each fuel pair is found to have its own optimal bin size, suggesting the binning finds the balance between S/N optimization concurrent with leveraging the chemical selectivity information differences in the samples as manifested in their GC × GC separation "patterns". Robustness of the findings in this study were supported by leaving out one fuel at a time and re-running the PCA models.

Impact of comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry experimental design on data trilinearity and parallel factor analysis deconvolution.

Comprehensive two-dimensional gas chromatography coupled with time-of-flight mass spectrometry (GC × GC-TOFMS) is a powerful instrument for the analysis of complex samples. Deconvolution of overlapped analytes using a suitable chemometric data analysis method such as Parallel Factor Analysis (PARAFAC) is often required. However, PARAFAC is designed to require a strict data trilinearity requirement. In this study we examine how strict this requirement is in the context of GC × GC experimental conditions, and demonstrate that under suitable conditions the data is sufficiently trilinear to achieve accurate deconvolution. The term trilinear deviation ratio (TDR) was previously introduced as a quantitative metric to predict the accuracy of PARAFAC deconvolution. Trilinear deviation ratio is defined as the run-to-run retention time shift, Δ2tR, for a given analyte on the second dimension (2D) separation, divided by the 2D analyte peak width-at-base, 2Wb. We demonstrate that experimental conditions impact the TDR range produced and PARAFAC performance. Column selection and modulation period, PM, are shown to significantly influence the TDR range. Two column sets were evaluated, giving rise to different k' ranges for the 2D separations. Each column set was used with an optimum PM as well as a longer PM to demonstrate the effect of PM selection on the TDR range and PARAFAC quantification. A PM of 6 s produced a Δ2tR range from -19.5 ms to -98 ms and TDRs from 0.157 to 0.439, translating into a PARAFAC bias from +1.6% to -13.5%. However, a PM of 1.5 s produced a Δ2tR range of -1.1 ms to -8.8 ms, and significantly lower TDRs from 0.013 to 0.057, translating into PARAFAC errors from +2.1% to -3.9%, with an average of -1.1% ± 1.4. These results validate the idea that a suitable GC × GC experimental design will provide accurate quantification with PARAFAC.

Development of Ultrafast Separations Using Negative Pulse Partial Modulation To Enable New Directions in Gas Chromatography.

Partial modulation via a pulse flow valve operated in the negative pulse mode is developed for high-speed one-dimensional gas chromatography (1D-GC), comprehensive two-dimensional (2D) gas chromatography (GC × GC), and comprehensive three-dimensional gas chromatography (GC3). The pulse flow valve readily provides very short modulation periods, PM, demonstrated herein at 100, 200, and 300 ms, and holds significant promise to increase the scope and applicability of GC instrumentation. The negative pulse mode creates an extremely narrow, local analyte concentration pulse. The reproducibility of the negative pulse mode is validated in a 1D-GC mode, where a pseudosteady-state analyte stream is modulated, and 8 analytes are baseline resolved (resolution, Rs ≥ 1.5) in a 200 ms window, providing a peak capacity, nc, of 14 at unit resolution ( Rs = 1.0). Additionally, the pulse width, pw, of the pulse flow valve "injection" relationship to peak width-at-base, wb, resolution between peaks and detection sensitivity are studied. To demonstrate the applicability to GC × GC, a high-speed separation of a 20-component test mixture of similar, volatile analytes is shown. Analytes were separated on the second-dimension column, 2D, with 2 wb ranging from 7 to 12 ms, providing an exceptional 2D peak capacity, 2 nc, of ∼12 using a modulation period ( PM) of 100 ms. Next, a 12 min separation of a diesel sample using a PM of 300 ms is presented. The 1 wb is ∼4 s, resulting in a 1 nc of ∼180, and 2 wb is ∼18 ms, resulting in a 2 nc of ∼17, thus achieving a nc,2D of ∼3000 in this rapid GC × GC diesel separation. Finally, GC3 with time-of-flight mass spectrometry (TOFMS) detection using a PM of 100 ms applied between the 2D and 3D columns is reported. Narrow third dimension, 3D, peaks with 3 wb of ∼15 ms were obtained, resulting in a GC3 peak capacity, nc,3D, of ∼35 000 in a 45 min separation.

Targeted analyte deconvolution and identification by four-way parallel factor analysis using three-dimensional gas chromatography with mass spectrometry data.

Comprehensive three-dimensional gas chromatography with time-of-flight mass spectrometry (GC3-TOFMS) creates an opportunity to explore a new paradigm in chemometric analysis. Using this newly described instrument and the well understood Parallel Factor Analysis (PARAFAC) model we present one option for utilization of the novel GC3-TOFMS data structure. We present a method which builds upon previous work in both GC3 and targeted analysis using PARAFAC to simplify some of the implementation challenges previously discovered. Conceptualizing the GC3-TOFMS instead as a one-dimensional gas chromatograph with GC × GC-TOFMS detection we allow the instrument to create the PARAFAC target window natively. Each first dimension modulation thus creates a full GC × GC-TOFMS chromatogram fully amenable to PARAFAC. A simple mixture of 115 compounds and a diesel sample are interrogated through this methodology. All test analyte targets are successfully identified in both mixtures. In addition, mass spectral matching of the PARAFAC loadings to library spectra yielded results greater than 900 in 40 of 42 test analyte cases. Twenty-nine of these cases produced match values greater than 950.