Appendix 1. Revised FTIR Algorithm for Functional Group Identification
FTIR spectra were analyzed using a revised algorithm for baselining and spectral smoothing, fitting overlapping peaks, and integrating absorbance before converting to mass with standard calibrations. Table S-1 summarizes the regions and parameters used in the algorithm.
Baselining and spectral smoothing. A third-order polynomial is used to baseline each spectra, in order to reduce both bias (with respect to zero) and variance in baselines of blank filter spectra over a linear baseline. CO interference is removed with an interpolated spline, and interference from H O is minimized with wavelet de-noising methods.
Spectral resolution of carboxylic acid absorption. The O-H stretching band in carboxyl groups is very broad and span between 3100-2400 cm-1 [Lambert et al., 1998]; overlapping with a significant number of peaks that we quantify. To resolve the shape of peaks within this type of spectra, we retrieved a series of carboxylic acids with varying quantities of aliphatic C-H and COOH groups (adipic, glutaric, malonic, azelaic, decanoic, stearic, and succinic acids) from the NIST Chemistry Webbook ( and searched for a two-factor solutions using Positive Matrix Factorization as our factor analysis technique. A sum of Gaussian peaks were selected to represent the COOH component such that when fitted to adipic acid reference spectra produced in our laboratory, quantitatively reproduced the saturated aliphatic C- H absorptivity observed in non-carboxylic acid species (docosanol and docosene).
Band-fitting. Fixed carboxylic C-OH and ammonium spectra are subtracted from each spectrum based on a simple scaling algorithm. Absorption peaks for the remaining groups are fitted using box constraints primarily determined from reference spectra analyzed in the laboratory [Gilardoni et al. 2007]; multiple sets of initial values are provided to the least-squares fitting routine and the final set of parameters is selected based upon the analysis of residuals.
Oxygenated groups. The quantity of carboxylic COOH (“acid groups”) is determined from examining mole ratios of carboxylic C=O and carboxylic C-OH. The acid group is quantified by averaging moles of carbonyl and carboxylic C-OH when they are approximately equal, or the minimum of either group when their molar quantities significantly differ. Non-carboxylic carbonyl is determined as the carbonyl in significant excess of carboxylic C-OH, and this is interpreted to be carbonyls associated with aldehyde and ketonic species. “Excess Acid” is defined as carboxylic C-OH in excess of reported carbonyl, as can occur when we miss quantification of amino acid and conjugated carbonyls because of significant shifts in peak absorption, and is included in the reported carboxylic acid group fraction.
“Excess Alcohol” is determined by area of unidentified residuals in the region approximately between 3400 and 2900 cm-1. While alcohol and phenolic absorbance generally occurs in the region 3600-3200 cm-1 [Lambert et al., 1998], we report the total absorbance in this region in mass units of alcohol C-OH to provide an upper bound to the concentration.
Detection Limits. Detection limits are determined as the minimum area statistically distinguishable (2σ) above errors estimated from baselining and ammonium subtraction for each Appendix 2. Positive Matrix Factorization for FTIR Spectra and Correlation to Elemental
Positive Matrix Factorization [Paatero and Tapper, 1994] was implemented as our multivariate curve resolution technique to statistically reduce our 128 ambient spectra into a few “components” that share significant co-variation in absorbance across wavenumbers. Baselined and smoothed sample spectra were provided to PMF as the data matrix. The scaling coefficient is the reciprocal of variance in analytical error (1/σ2), as determined by variability in baselining of blank sample spectra determined at each wavenumber. The scaling factor is estimated from possible baselining error at each wavenumber. A set of field blanks was collected with each sample, and spectra from these were baselined similarly to the sample spectra. On average, the baselining errors are zero at each wavenumber, but the variability about the mean is used to estimate the baselining error for each sample.
We systematically explored the solution space of two parameters: number of factors (p) and rotation parameter (FPEAK). We applied singular value decomposition to the entire data set and also sectionally, by fixed-size moving window analysis (Keller and Massart, 1991). The trace of eigenvalues in each case was used to constrain the value of p to those values which provided sufficient data reconstruction (approximately 90% data recovery). FPEAK was restricted to the domain in which the Q value (value of the least squares) objective function was comparable to or below the theoretical expected value defined by E(Qm) = (n×m)-p(n+m). E(Qm) is the expected value of the portion of Q (the objective function) that arises from the data-fitting (excluding penalty terms) and nxm are the dimensions of the data matrix.
Table S-1. Absorbance frequencies, quantified peak ranges, absorptivity coefficients anddetection limits used in quantifying organic functional groups from FTIR spectra.
Functional Group



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Volume 10 • Supplement 1 • 2005 H E L I C O B A C T E R Helicobacter pylori and Non-malignant Diseases Limas Kupcinskas* and Peter Malfertheiner†*Department of Gastroenterology, Kaunas University of Medicine, Kaunas, Lithuania; †Otto-von-Guericke-Universität, Magdeburg, Zentrum für Innere Medizin, Klinik für Gastroenterologie, Hepatologie und Infectiologie, Magdeburg, Germany

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