Probability of failure of the watershed algorithm for peak detection in comprehensive two-dimensional chromatography

The watershed algorithm is the most common method used for peak detection and integration in two-dimensional chromatography. However, the retention time variability in the second dimension may render the algorithm to fail. A study calculating the probabilities of failure of the watershed algorithm was performed. The main objective was to calculate the maximum second-dimension retention time variability, Δ²t_R,crit, above which the algorithm fails. Several models to calculate Δ²t_R,crit were developed and evaluated: (a) exact model; (b) simplified model and (c) simple-modified model. Model (c) gave the best performance and allowed to deduce an analytical expression for the probability of failure of the watershed algorithm as a function of experimental Δ²t_R, modulation time and peak width in the first and second dimensions. It could be demonstrated that the probability of failure of the watershed algorithm under normal conditions in GC × GC is around 15–20%. Small changes of Δ²t_R, modulation time and/or peak width in the first and second dimension could induce subtle changes in the probability of failure of the watershed algorithm. Theoretical equations were verified with experimental results from a diesel sample injected in GC × GC and were found to be in good agreement with the experiments.     

Two-dimensional liquid chromatography/mass spectrometry/mass spectrometry separation of water-soluble metabolites

Off-line two-dimensional liquid chromatography with tandem mass spectrometry detection (2D-LC/MS-MS) was used to separate a set of metabolomic species. Water-soluble metabolites were extracted from Escherichia coli and Saccharomyces cerevisae cultures and were immediately analyzed using strong cation exchange (SCX)-hydrophilic interaction chromatography (HILIC). Metabolite mixtures are well-suited for multidimensional chromatography as the range of components varies widely with respect to polarity and chemical makeup. Some currently used methods employ two different separations for the detection of positively and negatively ionized metabolites by mass spectrometry. Here we developed a single set of chromatographic conditions for both ionization modes and were able to detect a total of 141 extracted metabolite species, with an overall peak capacity of ca. 2500. We show that a single two-dimensional separation method is sufficient and practical when a pair or more of unidimensional separations are used in metabolomics.     

Application of displacement chromatography for the proteome analysis of a human plasma protein fraction

It was the aim of this study to compare the performance of displacement chromatography with gradient elution chromatography both applied as the cation-exchange separation step for a proteome analysis in a bottom-up approach using multidimensional chromatography for the separation of tryptic peptides prior to their mass spectrometric analysis. The tryptic digest of the human Cohn fraction IV-4 served as a sample. For both chromatography modes commonly used operating parameters were chosen thus ensuring optimal separation results of equal sample amounts for each mode. All resulting fractions were analyzed with an HPLC-chip–LC–MS system. The eluate of the HPLC-chip column was ionized by electrospray ionization (ESI) and analyzed with an ion-trap mass spectrometer. For guaranteeing high confidence concerning the identity of the peptides, the mass spectrometric data were processed by different bioinformatic tools applying stringent criteria. By the displacement approach the total amount of identified proteins (78) was significantly higher than in the gradient mode (58). The results showed that displacement chromatography is a well suited alternative in comparison to gradient elution separation for analysis of proteomes via the bottom-up approach applying multidimensional chromatography, especially in those cases when larger quantities of proteins are available.     

Chemical markers’ fishing and knockout for holistic activity and interaction evaluation of the components in herbal medicines

A strategy based on chemical markers’ fishing and knockout has been proposed for holistic activity and interaction evaluation of the bioactive components in herbal medicines (HMs). It was devised to screen bioactive-compound group that represents the efficacy of HM, estimate the bioactivity contribution of each component and elucidate the interactions of multi-components. This strategy was accomplished through the following steps: (1) screen out the chemical markers (target peaks) in a HM fingerprint using online two-dimensional turbulent flow chromatography/liquid chromatography–mass spectrometry technique, (2) fish target peaks and knockout any interested peak, and (3) evaluate the bioactivities of fishing and knockout portions. After comparison of the bioactivities of samples containing different target peaks, the efficacy of target-peak group, bioactivity contribution of each compound, and the interactions of multi-components are elucidated. Using Acetylcholinesterase (AChE) and Bulbs of Lycoris radiata (L. Herit.) Herb. (BLR) as the experimental materials, four target peaks were screened out as the AChE binders. By target peaks’ fishing and knockout, combined with activity evaluation, we observed that the bioactivity of the four-peak mixture is similar with the global bioactivity of BLR extract, and there are significant suppressive actions among these four target peaks. These results indicate that this proposed strategy is a useful approach for holistic screening of bioactive-compound group and elucidation of the multi-component interactions in HM.     

Observations and calculations of two-dimensional angular optical scattering (TAOS) patterns of a single levitated cluster of two and four microspheres

We use single bi-sphere particles levitated in an electrodynamic balance to record two-dimensional angular scattering patterns at different angles of the coordinate system of the aggregate relative to the incident laser beam. Due to Brownian motion the particle covers the whole set of possible angles with time and allows to select patterns with high symmetry for analysis. These are qualitatively compared to numerical calculations. A small cluster of four spheres shows complex scattering patterns, comparison with computations suggest a low compactness for these clusters. An experimental procedure is proposed for studying restructuring effects occurring in mixed particles upon evaporation.     

Light propagation and oscillations in two-dimensional graded square photonic lattices

We have studied the optical oscillations and transitions in two-dimensional graded square photonic lattices (GSPL) formed by evanescently coupled optical waveguide arrays with parabolic confinements in all transverse directions. When we retain only the orthogonal couplings, decoupled one-dimensional models can be used to obtain the various normal modes, which correspond to a variety of optical oscillations. Six different combinations of Bloch oscillation (BO), dipole oscillation (DO), and reflections from the boundaries of finite lattice are classified on the phase diagram. If we include the diagonal couplings, transitions among various oscillations are obtained with the Hamiltonian optics approach and confirmed by the field-evolution analysis. We studied in detail a typical example in which a switching occurs from the constituent BO and DO to both DOs in the two orthogonal directions. The method to analyze the complex field evolution in GSPL can be extended to similar systems with different types of lattices and/or confinements.     

A general solution to the Schrödinger–Poisson equation for a charged hard wall: Application to potential profile of an AlN/GaN barrier structure

A general, system-independent, formulation of the parabolic Schrödinger–Poisson equation is presented for a charged hard wall in the limit of complete screening by the ground state. It is solved numerically using iteration and asymptotic boundary conditions. The solution gives a simple relation between the band bending and sheet charge density at an interface. Approximative analytical expressions for the potential profile and wave function are developed based on properties of the exact solution. Specific tests of the validity of the assumptions leading to the general solution are made. The assumption of complete screening by the ground state is found be a limitation; however, the general solution provides a fair approximate account of the potential profile when the bulk is doped. The general solution is further used in a simple model for the potential profile of an AlN/GaN barrier structure. The result compares well with the solution of the full Schrödinger–Poisson equation.     

Two-dimensional electron transport in AlGaN/GaN heterostructures

We present a theoretical study of electron transport properties of two-dimensional electron gas in AlGaN/GaN heterostructures. By assuming a drifted Fermi–Dirac distribution and taking into account all major scattering mechanisms, including polar optical and acoustic phonons, background impurities, dislocation and interface roughness, the momentum- and energy-balance equations derived from Boltzmann equation are solved self-consistently. The dependence of the electron drift velocity and electron temperature as a function of the applied electric field are obtained and discussed.     

The off-line group seat reservation problem

In this paper we address the problem of assigning seats in a train for a group of people traveling together. We consider two variants of the problem. One is a special case of two-dimensional knapsack where we consider the train as having fixed size and the objective is to maximize the utilization of the seats in the train. The second is a special case of two-dimensional bin packing where all requests must be accommodated while trying to minimize the number of passenger cars needed. For both variants of the problem we present a number of bounds and develop exact algorithms. Computational results are presented for various instances based on realistic data, and from the packing literature adapted to the problems addressed.     

Design and implementation of an array of micro-electrochemical detectors for two-dimensional liquid chromatography—Proof of principle

Simultaneous two-dimensional liquid chromatography (2D-LC) is an implementation of two-dimensional liquid chromatography which has the potential to provide very fast, yet highly efficient separations. It is based on the use of time × space and space × space separation systems. The basic principle of this instrument has been validated long ago by the success of two-dimensional thin layer chromatography. The construction of a pressurized wide and flat column (100 mm × 100 mm × 1 mm) operated under an inlet pressure of up to 50 bar was described previously. However, to become a modern analytical method, simultaneous 2D-LC requires the development of detectors suitable for the monitoring of the composition of the eluent of this pressurized planar, wide column. An array of five equidistant micro-electrochemical sensors was built for this purpose and tested. Each sensor is a three-electrode system, with the working electrode being a 25 μm polished platinum micro-electrode. The auxiliary electrode is a thin platinum wire and the reference electrode an Ag/AgCl (3 M sat. KCl) electrode. In this first implementation, proof of principle is demonstrated, but the final instrument will require a much larger array.