Recognizing chromatographic peaks with pattern recognition methods : Part 2. Evaluation of different distance measures

The proposed method for the recognition of peaks in a chromatogram is based on the k-nearest neighbour (KNN) algorithm, in which the chromatogram is compared with a predefined peak profile. A critical part of the KNN algorithm is the selection of the distance measure used to calculate the similarity between points in the pattern space. Here, five different distance functions are evaluated. In addition to the euclidian distance, which was used in the initial tests of the algorithm, the correlation coefficient, the cross-correlation, and the angle between two vectors and its cosine are tested. All these distance measures show satisfactory behaviour. Their different characteristics are discussed.     

An automatic peak finding method for LC‐MS data using Gaussian second derivative filtering

A highly automated procedure for localising and characterising peaks in the chromatographic time domain of LC‐MS data has been developed. The work was initiated by an identified need to facilitate the detection and tracking of chromatographic peaks during method development for the analysis of impurities in pharmaceutical products. The algorithm is mainly based on a digital filter for which the settings are automatically adapted to the data set under study. The procedure was evaluated for synthetic data sets with various S/N levels, peak widths and baseline properties. It was found that even for the worst case tested with S/N=10 and a high variability in the baseline, 94% of the simulated analytical peaks could be detected without producing any false‐positive identifications. Furthermore, the number of correctly estimated peak heights and peak widths falling within a 10% error of the true values were 94 and 91%, respectively. For experimental data sets, peak height, and width estimations were more difficult, but the processed reconstructions showed an excellent agreement with the analytical signals of the raw data, and also a clearly improved visualisation in total ion‐ and base‐peak chromatograms.     

Theory of Gradient Elution Liquid Chromatography with Linear Solvent Strength: Part 2. Peak Width Formation

The process of formation of the width (σ _b) of a solute band migrating along a column and its effect on the width (σ) of a corresponding peak in a chromatogram are quantified along with the extra-column contributions (Δσ _b and Δσ) to these parameters due to insufficiently narrow injection plugs. Previously unknown expressions for σ _b and Δσ _b as functions of the band migration distance and time were found. The negative gradients in the solvent strength cause the fronts of the solute bands to travel slower than their tails. This compresses the bands (reduces their widths). Previously unknown expressions describing the band compression process as functions of the band migration distance and time are found. The band compression tends to narrow the peaks. However, as shown here, the gradients that compress the bands also reduce their elution speeds. This tends to broaden the peaks (typically ignored phenomenon) and, as shown here, can cause a slight net peak broadening under normal conditions (in spite of general expectations that the gradients should narrow the peaks). On the other hand, as shown here, the gradients can significantly suppress the harmful effect of the extra-column peak broadening.     

A computer search system for similar organic compounds in carbon-13 nuclear magnetic resonance data files

From the ¹³C-NMR spectrum of an unknown compound, the system provides a list of compounds ranked according to their similarity to the unknown. The similarity is estimated in a three-dimensional feature space, rather than by direct match of all peaks. All the spectra in the library are first converted to pattern points in the feature space by a dimensionality-reduction method. Thus, the search for similar compounds is simplified to a search for points within a given distance from the point representing the unknown. The compounds listed can be offered as the result or used for further operations (match of carbon number and peak position) in order to get a more exact result. An auto-optimization option is included to provide efficiency and user convenience.     

Characterization of warfarin unusual peak profiles on oligoproline chiral high performance liquid chromatography columns

Unusual peak profiles of warfarin were characterized on two oligoproline chiral stationary phases (CSPs). The pattern of 1st peak (S(−)) broadening and the 2nd peak (R(+)) compression was observed under mobile phase of hexane (0.1% TFA)/2-propanol (IPA) on a triproline CSP 1, and with other alcohol modifier such as ethanol, 1-propanol, 1-butanol, 2-butanol, and tert-butanol as well. Through analyzing system peak of additives, the unusual peak profile was interpreted by perturbation of TFA additive system peak. The unusual peak profile was also found in enantioseparation of coumachlor and on a covalently bonded doubly tethered diproline CSP 2. The pattern of 1st peak (S(−)) broadening and the 2nd peak (R(+)) compression can change to pattern of 1st peak compression and the 2nd peak broadening from 15 to 50 °C. Chiral separation of warfarin created nonlinear van’t Hoff plots on CSP. No peak broadening/compression were observed with methyl tertiary butyl ether or ethyl acetate as the modifier. The peak shapes of the two warfarin enantiomers can thus be tuned by varying alcohol concentration and column temperature. High separation factor and resolution may be carried out to tune the peak profiles into Langmuir/anti-Langmuir band-shape composition. Using none hydrogen donor modifier may avoid interference of the TFA system peak.     

Recognizing chromatographic peaks with pattern recognition methods III. Application of the algorithm for peak recognition in trace analysis

Summary The application of a newly developed peak recognition algorithm is shown. This algorith is based on the KNN method, one of the pattern recognition methods. It is shown that peaks with a S/N-ratio down to one can be safely recognized. This is also possible if the baseline has not only detector noise, but has other disturbances, e.g., noise signals which are generated by a reaction detector. The recognition ability of the algorithm is demonstrated by a standard chromatogram with three different concentrations and with two different sampling rates. The improvement against the classical algorithm is demonstrated. Some properties of the algorithm are discussed.     

Synthesis and electrochemical studies of disubstituted ferrocene/dipeptide conjugates with sulfur-containing side chains

A series of 1,1′-disubstituted ferrocenoyl peptides incorporating dipeptide sidearms has been synthesized and studied electrochemically. The target peptides include ferrocene as an electrochemical reporter, sulfur-containing amino acids (l-methionine, S-methyl-l-cysteine, S-trityl-l-cysteine, S-benzhydryl-l-cysteine) as metal binding agents, and amino acids with non-polar side chains (l-alanine, l-valine, l-phenylalanine) as spacers between reporter and metal binding groups. Ferrocene/dipeptide conjugates were prepared using solution phase peptide synthesis methods employing a BOC-protecting group strategy and HBTU- (O-(benzotriazol-1-yl)-N,N,N′,N′-tetramethyluronium hexafluorophosphate) mediated peptide coupling. The electrochemical properties of these 1,1′-substituted ferrocenoyl peptides have been characterized using cyclic voltammetry. All exhibit fully reversible one electron oxidation steps; forward sweep half wave peaks (E_F), reverse sweep half wave peaks (E_R), peak separations (ΔE_P) and half wave potentials (E_1/2) are reported. Finally, towards the goal of utilizing ferrocenoyl peptides to detect heavy metals in solution, the response of these ferrocene/dipeptide conjugates to metal cations (zinc(II), mercury(II), cadmium(II), lead(II), silver(I)) has been examined. Monitoring changes in the potential of the Fe(II)/Fe(III) redox couple to follow peptide/metal interactions, we have probed the influence of the spacer unit between the redox reporter and the metal-binding amino acid, and shown that these systems respond to mercury(II) more strongly than to other heavy metal ions.     

Enantioselective fluorescent sensor for amino acid derivatives based on BINOL bearing hexahydropyrrolo[1,2-c]imidazol-1-one units

A chiral fluorescent sensor (Ra,S,l)-3 incorporating (R)-BINOL and l-prolinamide is found efficient in enantioselective recognition of N-Cbz-protected phenylglycine. It is observed that one enantiomer of N-Cbz-protected phenylglycine can obviously increase the fluorescence intensity of (Ra,S,l)-3, while the other enantiomer does not cause much fluorescence enhancement. Such highly enantioselective response makes the sensor (Ra,S,l)-3 useful for the enantioselective fluorescence recognition of other N-Cbz-protected amino acids.     

Quantitation of ion abundances in fourier transform ion cyclotron resonance mass spectrometry

To improve the analytical usefulness of Fourier transform ion cyclotron resonance mass spectrometry (FTICR-MS), an extensive survey of various methods for quantitation of peak magnitudes has been undertaken using a series of simulated transient response signals with varying signal-to-noise ratio. Both peak height (five methods) and peak area (four methods) were explored for a range of conditions to determine the optimum methodology for quantitation. Variables included dataset size, apodization function, damping constant, and zero filling. Based on the results obtained, recommended procedures for optimal quantitation include: apodization using a function appropriate for the peak height ratios observed in the spectrum (i.e., Hanning for ratios of about 1:10, three-term Blackman-Harris for ratios of ～1:100, or Kaiser-Bessel for ratios of ～1:1000); zero filling until the peaks of interest are represented by 10–15 points (generally obtained with one order of zero filling); and use of the polynomial y=(ax ²+bx+c) ⁿ and the three data points of highest intensity of the peak to locate the peak maximum, Y _max=(?b ²/4a+c) ⁿ . In this peak fitting procedure, which we have termed the “Comisarow method,” n is 5.5, 9.5, and 12.5 for the Hanning, three-term Blackman-Harris, and Kaiser-Bessel apodization functions, respectively. Accuracy of quantitation using an optimal peak height determination is about equal to that for peak area measurements. These recommendations were found to be valid when tested with real FTICR-MS spectra of xenon isotopes.     

Novel fragmentation of N-diisopropyloxyphosphoryl dipeptides and tripeptides by fast atom bombardment mass spectrometry

Positive ion fast atom bombardment mass spectrometry of N-diisopropyloxyphosphoryl dipeptides and tripeptides showed a novel cleavage pattern in that only the N-phosphoryl fragment ions gave intense peaks while the C-terminal series of ions was suppressed. The base peak was the N-phosphoryl imino ion responding to the N-terminal residue. These advantages are superior to those of other types of N-protecting groups.     

Possibilities and Limitations of Computer-Assisted Method Development in HILIC: A Case Study

In the present study, we investigated the possibilities and limitations of computer-assisted method development (CAMD) for the HILIC separation optimization of a mixture of 13 isomeric hydroxy- and aminobenzoic acids on a ZIC-HILIC column. The isocratically obtained Neue and Kuss retention parameters enabled the accurate gradient retention modeling for peaks eluting well within the gradient (mean error of 2.7 %). The prediction errors for peaks eluting at the end of the gradient could be reduced from 8.8 to 6.1 % by implementing the isocratic regime after the gradient into the expression for the gradient retention factor. The prediction of the corresponding peak widths improved significantly for certain compounds and gradient profiles using individual gradient N values for each compound compared to employing a single N value for all compounds and gradient profiles. Two gradient optimization strategies (constructing the R _s map based on individual retention modeling and predictive elution stretching and shifting, PEWS²) resulted in a reasonable separation of the challenging mixture of 13 isomeric hydroxy- and aminobenzoic acids on the ZIC-HILIC column. Overall, the optimization was limited by the steep decrease in N (dropping to the isocratic N value) and corresponding increase in peak width when increasing the gradient time. The discrimination factors d ₀ were used to assess the resolution between peaks varying widely in height. The best separation was found to be obtained via the PEWS² approach. Both the individual retention modeling and PEWS² strategies corresponded to a total instrument time less than 12 h (including equilibration). Finally, it was found that the salt concentration had a significant effect on both the retention and the peak shape of the compounds, resulting in a small “solution domain” at 10 mM. Coupled columns with higher efficiencies are suggested to improve the resolution and robustness of the separation.     

Gallery structure and exfoliation of organophilized montmorillonite: effect on composite properties

Wyoming montmorillonite was organophilized to different extents with N-cetylpyridinium chloride and its gallery structure was studied by WAXS. PP nanocomposites were prepared using this silicate and their structure, as well as tensile properties were determined as a function of composition. Two peaks were observed in the WAXS patterns of some of the treated silicates, one of which disappeared during processing. The orientation of the organic compound in the galleries depends on its size and amount, as well as on the ion density of the filler. Multiple peaks appearing in the WAXS pattern of organophilized silicate may arise from interference, but they may also indicate the presence of several populations of layer distances. Water is absorbed between the galleries of partially organophilized silicates leading to the separation of the layers resulting in the appearance of new scattering peaks. Exfoliation occurs only above a critical gallery distance, which corresponds to the thickness of two aliphatic chains. Although exfoliation of the silicate is determined by its organophilization and gallery structure, composite properties are dominated by interfacial interaction.     

Synthesis of (3S,3S′,4S,4S′)-1,1′-ethylenedipyrrolidine-3,3′,4,4′-tetraol and related diamino diols: donor–acceptor hydrogen-bonding motifs of the C2 symmetric 3,4-dihydroxypyrrolidine unit

Enantiopure 1,1′-ethylenedipyrrolidines possessing 3,4-disubstitution have been prepared from esters of l-(+)-tartaric acid. Although diacylation routes via the diacetoxypyrrolidin-2,5-diones were problematic, N,N-dialkylation protocols proved to be reliable and led to the synthesis of (3S,3S′,4S,4S′)-1,1′-ethylenedipyrrolidine-3,3′,4,4′-tetraol, (3R,3′S,4R,4′S)-3,4-diamino-1,1′-ethylenedipyrrolidine-3′,4′-diol and (3R,3′R,4S,4′S)-3,3′-diamino-1,1′-ethylenedipyrrolidine-4,4′-diol. The tetraol possesses a crystal structure that exhibits an unusual zig-zag intermolecular pattern comprising a network of hydrogen bonds involving the terminal hydroxyl groups and a nitrogen atom of one of the pyrrolidine rings.     

Information-theoretical complexity for the hydrogenic identity S N 2 exchange reaction

We investigate the complexity of the hydrogenic identity S _N 2 exchange reaction by means of information-theoretic functionals such as disequilibrium (D), exponential entropy (L), Fisher information (I), power entropy (J) and joint information-theoretic measures, i.e., the I–D, D–L and I–J planes and the Fisher–Shannon (FS) and López-Mancini-Calbet (LMC) shape complexities. The several information-theoretic measures of the one-particle density were computed in position (r) and momentum (p) spaces. The analysis revealed that the chemically significant regions of this reaction can be identified through most of the information-theoretic functionals or planes, not only the ones which are commonly revealed by the energy, such as the reactant/product (R/P) and the transition state (TS), but also those that are not present in the energy profile such as the bond cleavage energy region (BCER), the bond breaking/forming regions (B–B/F) and the charge transfer process (CT). The analysis of the complexities shows that the energy profile of the identity S _N 2 exchange reaction bears no simple behavior with respect to the LMC and FS measures. Most of the chemical features of interest (BCER, B–B/F and CT) are only revealed when particular information-theoretic aspects of localizability (L or J), uniformity (D) and disorder (I) are considered.     

Three-dimensional derivative spectrochimatograms in high-performance liquid chromatography and their implications for peak homogeneity validation

The full ultraviolet spectra generated by a photodiode-array detector are transformed to the nth derivative (dⁿA/dλⁿ). The bipolar, three-dimensional data matrix (dⁿA/dλⁿ, λ, t) is presented with computer-aided graphics as an extension of the spectrochromatogram concept to aid peak validation. Existing display algorithms are modified to yield several presentations which reveal the full topography of the elution profile. These include rotation in three-dimensional space and inspection of the positive and negative data planes. A novel contour-plot representation is proposed to enable the derivative spectrochromatographic data to be presented in a two-dimensional format. Two planes of data (i.e., positive and negative amplitudes of (dⁿA/dλⁿ) in the (λ, t) plane) can be displayed as required for derivative data presentation. The technique is used to assess the homogeneity of overlapping peaks of ethynyloestradiol and norethisterone.     

Peak width and reagent dispersion in flow injection analysis

Accurate equations are derived for relating peak width to injected concentration for single-line and merging-stream manifolds in which a well stirred mixing chamber is used to generate concentration gradients. The consequences of making an approximation to produce a linear relationship between peak width and the natural logarithm of the injected concentration are evaluated and shown to have little practical effect. The concept of reagent dispersion coefficient, D^R, is used in certain derivations and a relationship between this and the conventional dispersion coefficient is derived and investigated experimentally. The use of D^R to evaluate the likely performance of other flow-injection models is illustrated for the calculation of reagent-to-sample concentration ratios and the case of reversed f.i.a. (reagent injected into sample carrier stream). An extension of the usual peak-width method is in f.i.a. described; a low-dispersion coefficient manifold is used and the product concentration profile is monitored. The analytical information in the double peaks obtained is discussed and illustrated for the peak-width mode by the injection of copper(II) ions (1.6 × 10^?6?0.16 M) into a carrier stream of 10^?4 M EDTA. The single well stirred mixing chamber model is used as a basis for the evaluation of the results and is applied to discussion of other manifolds not containing a real mixing chamber, in particular for the calculation of peak base-widths.     

Automated peak width measurements for targeted analysis of ion mobility unresolved species

Peak broadening in ion mobility (IM) is a relatively predictable process and abnormally broad peaks can be indicative of the presence of unresolved species. Here, we introduce a new ion mobility peak fitting (IM_FIT) software package for automated and systematic determination of traveling wave ion mobility (TWIM) unresolved species. To identify IM unresolved species, the IM_FIT software generates a trend line by plotting ions' mobility peak widths as a function of their arrival times. Utilizing user-defined thresholds, IM_FIT allows for automated and rapid detection of ions that deviate from the peak width trend line. To demonstrate the advantages of IM_FIT for automated detection of IM unresolved species, IM-mass spectrometry (IM-MS) data from a sample mixture containing polypropylene glycol and multiple peptides were analyzed. A total of 14 out of the 34 observed singly-charged IM peaks above 5% relative abundance (i.e., signal-to-noise ratios above ∼200) were tagged as potentially co-eluting ions by IM_FIT. Subsequently, the 14 IM peaks tagged as potentially unresolved (presumably, peaks corresponding to co-eluting compounds), were further analyzed by automated IM deconvolution (AIMD), liquid chromatography-IM-MS (LC-IM-MS), and/or ultra-high resolution mass spectrometry. Using the aforementioned techniques, more than 85% of the tagged IM peaks (12 out of 14) were confirmed to contain co-eluting ions. As an additional new finding, IM_FIT facilitated the discovery of an unexpected sequence-scrambled y-type fragment ion.     

Chemistry of thienopyridines. XXIII. Mass spectra of some N-oxides,sulfoxides, and sulfones

The mass spectral fragmentation patterns of a series of thienopyridine N-oxides, S-oxides, and S,S-dioxides were elaborated as a means of structural determination. Observation of a significant (M-16) peak is diagnostic for the presence of either an N-oxide or an S-oxide function (indistinguishable from one another by this method) but does not occur for an S,S-dioxide function. For a substituted thieno[2,3-b]pyridine 7-oxide, structural rearrangement to a pyridone (followed by emission of carbon monoxide or formyl radical) or side-chain fission may be competitive with de-N-oxygenation. For two tricyclic parent S-oxides, rearrangement and de-S-oxygenation are competing initial processes. For parent S,S-dioxides structural rearrangement precedes fragmentation, wherein the oxygen is ejected in such forms as sulfur monoxide, carbon monoxide, formyl or cyanate radicals, and ketene.     

Long-range magnetic ordering of quasi-one-dimensional S=1/2 Heisenberg antiferromagnet Sr2Cu(PO4)2

Magnetic properties of quasi-one-dimensional S=1/2 Heisenberg antiferromagnet Sr₂Cu(PO₄)₂ were investigated by temperature and field dependence of AC susceptibility down to 0.03 K. A sharp peak was observed at on the temperature dependence of AC susceptibility indicating long-range magnetic ordering. Taking into account the exchange constant, (Hamiltonian =J∑S_iS_i+1), the ratio k_BT_N/J is 0.06%. Sr₂Cu(PO₄)₂ is, therefore, one of the best one-dimensional Heisenberg antiferromagnet known so far.     

Acylative kinetic resolution of racemic amines using N-phthaloyl-(S)-amino acyl chlorides

A comparative study of the kinetic resolution of racemic 2-methyl-1,2,3,4-tetrahydroquinoline and 2,3-dihydro-3-methyl-4H-1,4-benzoxazine using N-phthaloyl-(S)-amino acyl chlorides as chiral acylating agents is described. Temperature and solvent effects on the stereochemical features have been examined. It has been found that N-phthaloyl-(S)-phenylalanyl and N-phthaloyl-(S)-2-phenylglycyl chlorides bearing aromatic substituents close to the stereogenic centre are more stereoselective acylating agents than N-phthaloyl-(S)-alanyl chloride. For the preparative kinetic resolution of racemic amines N-phthaloyl-(S)-phenylalanyl chloride proved to be the most appropriate chiral acylating agent.