Kalman filter quantitative resolution of shifted ESCA spectra after optimal alignment by simulated annealing

Summary The quantitative separation of overlapped responses accomplished by the Kalman filter algorithm is deteriorated by the errors in the model due to shifts of the component peaks. This is particularly true for spectral resolution in Electron Spectroscopy for Chemical Analysis (ESCA). A computational approach for the quantitative resolution of overlapping ESCA spectra when there is loss of collinearity between the pure component peaks and the mixture peak, has been developed. The procedure makes itera tive use of the Kalman filter for resolving the mixture spectrum with the component spectra aligned according to some values of the position parameters, and of the simulated annealing algorithm to find the optimal alignment. The performance of simulated annealing in pursuing this task, has been compared with those of simplex and steepest descent, by analyzing a set of overlapped synthetic spectra and some ESCA spectra of powder mixtures of lead compounds.     

Resolution of overlapped chromatograms by means of the kalmam filter : Data Processing of Liquid Chromatographic Signals without Solvent Peaks

If several samples are injected successively at short intervals into a liquid chromatograph, overlapped chromatograms of the samples will result. This paper describes an application of this successive-injection method to determination of samples without solvent peaks. Twenty peaks in the overlapped chromatograms resulting from five successive injections of samples with four components (phenetole, biphenyl, pyrene and perylene) were resolved and quantified by a reduced four-dimensional Kalman filter. The period of the single chromatogram of the four components is ca. 14 min, and the period of the five overlapped chromatograms ca. 26 min, for injection intervals of 3 min. The calibration lines for the four components are all straight and satisfactory; the slope, A, of every line was 1.005>A>0.9996 with correlation coefficients better than 0.999992. This successive-injection method with the reduced Kalman filter is time-saving for trivial routine work.     

Resolution of overlapped chromatograms by means of the kalman filter : Dimensional reduction of error covariance matrices and state estimate vectors

If many samples are successively injected into a high-performance liquid chromatograph at short intervals, then overlapped chromatograms will be obtained. A simplified version of the Kalman-filter algorithm is described for rapid resolution of several such overlapped peaks on small laboratory computers; the dimensionalities of the error covariance matrix Pk and state estimate vector X?k are reduced to far less than the total number of the peaks. Computer simulation shows that at least twenty partially overlapped Gaussian peaks, used as a model of the successive injections can be successfully resolved, with the 4 × 4 matrix Pk and 4-vector X?k. This version is independent of the number of injections and is effective for the resolution of a finite number of peaks in that injection mode. The algorithm of small dimensions is applicable to a wide variety of peak resolution procedures.     

One-dimensional Kalman filter in a robot system for total analysis of solid dosage formulations

A one-dimensional Kalman filter for peak resolution is applied to a totally automated robot system for liquid chromatographic analysis of solid dosage formulations. Sample solutions were prepared from four tablets of clemastine fumarate (1 mg/tablet) and injected automatically at regular, short intervals onto the column by the robot system. The overlapped peaks in the resulting complicated chromatogram were resolved and evaluated quantitatively by the one-dimensional filter. The peak-resolving powers are shown to be reliable by comparison with a multidimensional Kalman filter. The applicability of the whole analytical system with the linear Kalman filter is discussed.     

Application of principal component analysis to the extraction of pure mass spectra in chemical analysis by gas chromatography/mass spectrometry

In this work, we investigated the possibility of the purification of mass spectra of coeluted substances containing at least one characteristic value of m/z using principal component analysis. Simulated and real gas chromatographic/mass spectrometric data were analyzed. For the simulated data, the resolution of the chromatographic peaks varied from 0.075 to 0.75, and the ratio of component concentrations ranged from 0.01 to 100. Noise-free simulated data and simulated data with randomly distributed noise were considered. It was shown that the method gave satisfactory results even when the chromatographic resolution (R _s ) was less than 0.05.     

Extension of the two-dimensional mass channel cluster plot method to fast separations utilizing low thermal mass gas chromatography with time-of-flight mass spectrometry

Implementation of a data reduction and visualization method for use with high-speed gas chromatography and time-of-flight mass spectrometry (GC-TOFMS) is reported. The method, called the “2D m/z cluster method” facilitates analyte detection, deconvolution, and identification, by accurately measuring peak widths and retention times using a fast TOFMS sampling frequency (500 Hz). Characteristics and requirements for high speed GC are taken into consideration: fast separations with narrow peak widths and high peak capacity, rapid data collection rate, and effective peak deconvolution. Transitioning from standard GC (10–60+ minute separations) to fast GC (1–10 min separations) required consideration of how to properly analyze the data. This report validates use of the 2D m/z cluster method with newly developed GC technology that produces ultra-fast separations (∼1 min) with narrow analyte peak widths. Low thermal mass gas chromatography (LTM-GC) operated at a heating rate of 250 °C/min coupled to a LECO Pegasus III TOFMS analyzed a 115 component test mixture in 120 s with peak widths-at-base, w_b (4σ), of 350 ms (average) to produce a separation with a high peak capacity, n_c ∼ 340 (at unit resolution R_s = 1). The 2D m/z cluster method is shown to separate overlapped analytes to a limiting R_s ∼ 0.03, so the effective peak capacity was increased nearly 30-fold to n_c ∼10,000 in the 120 s separation. The method, when coupled with LTM-GC-TOFMS, is demonstrated to provide unambiguous peak rank (i.e. the number of analytes per overlapped peak in the total ion current (TIC)), by visualizing locations of pure and chromatographically overlapped m/z. Hence, peak deconvolution and identification using MCR-ALS (multivariate curve resolution – alternating least squares) is demonstrated.     

Chemometrics-Assisted Optimization of Beta-/Gamma-Tocol Separation on a C<Subscript>30</Subscript> Stationary Phase in Reversed-Phase LC

This paper presents a chemometrics-assisted optimization study to improve the separation of tocopherol (-T) and tocotrienol (-TT) homologues on a C₃₀ stationary phase in reversed-phase HPLC. The HPLC settings were optimized using a central composite design and the response surface methodology. Flow rate, column temperature, and mobile phase composition were chosen as independent variables. Peak resolution (R_s), analysis time (t_R), and peak symmetries of the tocopherol isomers were chosen as response variables. Optimum performance in terms of R_s was obtained at a flow rate of 0.31 mL min^?1, a temperature of 8.70 °C, and % B content (methyl tert-butyl ether: methanol: water, 80:18:2, v/v/v) in the mobile phase of 38.12%. The analysis of variance and regression analysis gave adjusted R² values of 0.9841 for R_s, 0.9850 for t_R-(α-T), 0.9853 for t_R-(β-T), and 0.9204 for the peak symmetry of β-T. This confirms the good agreement of experimental data with predicted values. The close eluting peaks of β-/γ-tocol could be baseline separated at the optimized conditions at a minimized analysis time. Empirical second-order polynomial models were derived that gave statistically high significances (P?<?0.0001). Hence, the models can be successfully employed to predict the optimum separation conditions of co-eluting peaks of β-/γ-tocols. The optimized method was successfully applied to determine the individual tocol homologues in various cold pressed edible oils. Total contents ranged from 15 to almost 2600 mg tocol kg^?1 oil.     

Best practice considerations for using the selectivity factor, s, as a metric for the efficiency of kinetic resolutions

The suitability of using the selectivity factor, s, as a metric for kinetic resolution reactions and the errors associated with its measurement are considered. Investigation of the analytical error associated with HPLC analysis of a kinetic resolution reveals that one of the largest potential sources of variation arises from the ability of a practitioner to integrate the peaks from a single analysis. The consequences of this error on the reliability of reported s values are discussed, and some general rules for good practice regarding the use and reporting of s as a metric are suggested.     

Parallel factor analysis of HPLC-DAD data for binary mixtures of lidocaine and prilocaine with different levels of chromatographic separation

A set of 17 samples containing a constant amount of lidocaine (667 μM) and a decreasing amount of prilocaine (667-0.3 μM) was analysed by LC-DAD at three different levels of separation, followed by parallel factor analysis (PARAFAC) of the data obtained. In Case 1 no column was connected, the chromatographic resolution (R_s) therefore being zero, while Cases 2 and 3 had partly separated peaks (R_s=0.7 and 1.0). The results showed that in Case 1, analysed without any separation, the PARAFAC decomposition with a model consisting of two components gave a good estimate of the spectral and concentration profiles of the two compounds. In Cases 2 and 3, the use of PARAFAC models with two components resolved the underlying chromatographic, spectral and concentration profiles. The loadings related to the concentration profile of prilocaine were used for regression and prediction of the prilocaine content. The results showed that prediction of prilocaine content was possible with satisfactory prediction (RMSEP<0.01). This study shows that PARAFAC is a powerful technique for resolving partly separated peaks into their pure chromatographic, spectral and concentration profiles, even with completely overlapping spectra and the absence or very low levels of separation.     

A universal algorithm for fast and automated charge state deconvolution of electrospray mass-to-charge ratio spectra

This article describes a new algorithm for charge state determination and deconvolution of electrospray ionization (ESI) mass-to-charge ratio spectra. The algorithm (Zscore) is based on a charge scoring scheme that incorporates all above-threshold members of a family of charge states or isotopic components, and deconvolves both low- and high-resolution mass-to-charge ratio spectra, with or without a peak list (stick plot). A scoring weight factor, log (I/I ₀), in which I is the signal magnitude at a calculated mass-to-charge ratio, and I ₀ is the signal threshold near that mass-to-charge ratio, was used in most cases. For high-resolution mass-to-charge ratio spectra in which all isotopic peaks are resolved, the algorithm can deconvolve overlapped isotopic multiplets of the same or different charge state. Compared to other deconvolution techniques, the algorithm is robust, rapid, and fully automated (i. e., no user input during the deconvolution process). It eliminates artifact peaks without introducing peak distortions. Its performance is demonstrated for experimental ESI Fourier transform ion cyclotron resonance mass-to-charge ratio spectra (both low and high resolution). Charge state deconvolution to yield a “zero-charge” mass spectrum should prove particularly useful for interpreting spectra of complex mixtures, identifying contaminants, noncovalent adducts, fragments (N-terminal, C-terminal, internal), and chemical modifications of electrosprayed biomacromolecules.     

Evaluation of the number of components in multi-component liquid chromatograms of plant extracts

Optimization of the chromatographic separation of flavonoid compounds in camomile extracts by the simplex method and the Monte Carlo method is described. Evaluation fo the number of peaks at unit resolution (R_s = 1) is used as the criterion of separation quality. The Davis-Giddings theory is applied in calculating the number of components and the results are validated by numerical simulations. Peak-purity checks for three identified compounds in commercial sample extracts are reported. Capacity factor patterns for 18 flavonoid and phenolic compounds over an extended range of methanol/aqueous buffer (pH 2.8) mobile phases are described.     

Information theory of optimization in chromatography: Optimum peak separation and dependency on peak area

Summary If a peak (j=2) moves along the time axis of a chromatogram with no change in the position ₁ of the other peak (j=1) or in areas A₁ and A₂, the optimum separation, _s, is defined as the resolution R_s which provides the maximum information, called FUMI, among all possible positions ₂ of the peak (₂₁). This paper demonstrates that optimum separation, _s, of chromatographic peaks critically depends on the peak areas. As the area ratio A₂/A₁ of overlapped peaks increases, greater separation (higher resolution R_s) is needed to obtain maximum information. The quantitative relationship between _s and A₂/A₁ is derived by computer simulation.     

Compact type-I coil planet centrifuge for counter-current chromatography

A compact type-I coil planet centrifuge has been developed for performing counter-current chromatography. It has a revolution radius of 10 cm and a column holder height of 5 cm compared with 37 and 50 cm in the original prototype, respectively. The reduction in the revolution radius and column length permits application of higher revolution speed and more stable balancing of the rotor which leads us to learn more about its performance and the future potential of type-I coil planet centrifuge. The chromatographic performance of this apparatus was evaluated in terms of retention of the stationary phase (S_f), peak resolution (R_s), theoretical plate (N) and peak retention time (t_R). The results of the experiment indicated that increasing the revolution speed slightly improved both the retention of the stationary phase and the peak resolution while the separation time is remarkably shortened to yield an excellent peak resolution at a revolution speed of 800 rpm. With a 12 ml capacity coiled column, DNP-DL-glu, DNP-β-ala and DNP-l-ala were resolved at R_s of 2.75 and 2.16 within 90 min at a flow rate of 0.4 ml/min. We believe that the compact type-I coil planet centrifuge has a high analytical potential.     

Kinetic resolution of P-stereogenic phosphine boranes via deprotonation using s-butyllithium/(−)-sparteine

The attempted kinetic resolution of racemic secondary phosphine boranes [t-BuPhP(BH₃)H and t-BuMeP(BH₃)H] by P–H deprotonation using 0.5 equiv of s-BuLi and (?)-sparteine was unsuccessful and generated racemic benzyl bromide-trapped adducts in 42–49% yield. In contrast, an efficient kinetic resolution was observed with racemic tertiary phosphine boranes [t-BuPhP(BH₃)Me and t-BuEtP(BH₃)Me] by C–H deprotonation on the P–Me group using 0.5 or 0.6 equiv of s-BuLi and (?)-sparteine. For example, the use of 0.6 equiv of s-BuLi/(?)-sparteine with t-BuEtP(BH₃)Me and trapping with DMF gave the (R)-aldehyde adduct in 37% yield and 83:17 er together with recovered (R)-t-BuEtP(BH₃)Me in 44% yield and 74:26 er. These are the first examples of kinetic resolution of P-stereogenic phosphine boranes via deprotonation using s-BuLi/(?)-sparteine.     

Chiral phenethylamine synergistic tricarboxylic acid modified β-cyclodextrin immobilized on porous silica for enantioseparation

In this work, a series of chiral phenethylamine synergistic tricarboxylic acid modified β-cyclodextrin bonded stationary phase for high performance liquid chromatography (HPLC) were synthesized via a simple one-pot synthesis approach. Various racemates (aryl alcohols, flavanones, triazoles, benzoin, etc.) were well separated on the tricarboxylic acid modified chiral stationary phases in both normal and reversed modes with good reproducibility and stability, and the influence of mobile phase composition on resolution (R_s) were deeply investigated. The RSD values of R_s for repeatability and column-to-column were below 1.28% and 3.05%, respectively. Hence, the fabrication of tricarboxylic acid modified chiral stationary phase (CSPs) is a new efficient strategy to improve the application of β-cyclodextrin as CSPs in the field of chromatography.     

Determination of the enantiomeric purity of albuterol on sorbents modified by macrocyclic antibiotics

The separation of albuterol enantiomers on sorbents with macrocyclic glycopeptide antibiotics immobilized on the silica surface was investigated. Commercial columns—Nautilus-E (BioKhimMak, Russia) with eremomycin as a chiral selector and ChirobioticTAG (Astec, United States) with teicoplanin aglycone as a chiral selector—were used for enantioseparation. Levalbuterol is the (R)-enantiomer of albuterol. We managed to separate albuterol enantiomers on both columns in a polar organic mode, but selectivity was higher on the ChirobioticTAG column (R _s = 1.7). The maximum resolution of enantiomer peaks (1.7) was observed in methanol–acetonitrile–triethylamine–acetic acid (90: 10: 0.05: 0.05) as the mobile phase. The detection limit of the compound calculated by a signal–background ratio of 3: 1 was 0.00002 mg/mL, which corresponds to 0.1% of (S)-enantiomer with respect to the total amount. The results made it possible to determine the enantiomeric purity of the active pharmaceutical substances of levalbuterol.     

The influence of uncompensated solution resistance on the determination of standard electrochemical rate constants by cyclic voltammetry,and some comparisons with a.c. voltammetry

a digital simulation analysis is presented of the deleterious effects of uncompensated solution resistance, R_us, on the evaluation of standard rate constant, k^s_ob, by cyclic voltammetry. The results are expressed in terms of systematic deviations of “apparent measured” rate constants, k^s_ob(app), evaluated in the conventional manner without regard for R_us, from the corresponding actual values, k^s_ob(true), as a function of R_us and other experimental parameters. Attention is focused on the effects of altering the electrode area and the double-layer capacitance on the extent of the deviations between k^s_ob(app) and k^s_ob(true), and on comparisons with corresponding simulated results obtained from phase-selective a.c. impedance data. The extent to which k^s_ob(app) <k^s_ob(true) for small R_us values was found to be similar for the cyclic and a.c. voltammetric techniques. The latter method is, however, regarded as being preferable under most circumstances in view of the greater ease of minimising, as well as evaluating, R_us for a.c. impedance measurements. The influence of solution resistance on k^s_ob measurements with microelectrodes and without iR compensation is also considered.     

Science based calibration for the extraction of 'analyte-specific' HPLC-DAD chromatograms in environmental analysis

Multivariate science based calibration (SBC) has been applied to the resolution of overlapped peaks in liquid chromatography with diode array detection (LC-DAD). Complex river water samples spiked with 11 pharmaceutical substances resulted in poorly resolved chromatograms containing additional peaks from interfering matrix compounds and a change in the background absorbance due to the mobile phase gradient. Applying the present multivariate approach it was possible to resolve all 11 analytes from overlapping peaks, obtaining linear calibration lines (R² > 0.96). Recovery percentages on spiked samples ranged between 74.6 and 113.5%, which are quite satisfactory taking into account the low concentration ranges considered to 1-7 μg L⁻¹.     

Semiclassical variational study of size effects in neutral and charged jellium droplets

An analytic expression for the total energy of metallic clusters composed ofN identical atoms of valencev and with net chargeQ is obtained by means of a variational solution of the Thomas-Fermi-Weizsäcker energy density functional within the spherical jellium model. The minimum energy is given as an expansion in decreasing powers of the cluster radiusR=r _s Z ^1/3, withZ=vN andr _s the radius per electron of the bulk metal. The coefficients are obtained as functions ofr _s . Terms of volume (R ³), surface (R ²), curvature (R), constant (R ⁰), (1/R) and (1/R ²) are clearly separated in the formula, as well as the different contributions (kinetic, coulombic and exchange-correlation) to each of them. The asymptotic values (R→∞) for the work functions,W(r _s ), and surface energies σ(r _s ), are compared to analogous semiclassical and Kohn-Sham calculations of jellium-like surfaces and to the experimental values. The size dependent behaviour of chemical potentials, μ(R), electron affinities,AF(R), and ionization potentials,IP(R), are easily obtained for any kind of metallic clusters. In particular we discuss the Coulomb and quantum corrections to the coefficients β, δ in the asymptotic formulae:IP?W+β/R andAF?W+δ/R.     

Resolution of Overlapping Chromatographic Peaks Using a Genetic Algorithm

ABSTRACT

A genetic algorithm for resolution of overlapping chromatographic peaks (GAROCP) using real-number coding, non-uniform mutation and arithmetical crossover methods is described in this paper. It was applied to resolution of highly overlapped multicomponent high-performance liquid chromatographic peaks by fitting experimental chromatogram to the exponentially modified Gaussian (EMG) model. The genetic algorithm was used to find the minimum of fitting error to optimize the parameters in the EMG functions which determine the shape and area of each peak. The applicability of the method was investigated with both simulated signals calculated by EMG functions and experimental multicomponent overlapping chromatograms.