Tutorial on estimating the limit of detection using LC-MS analysis,part I: Theoretical review

A large body of literature exists on the limit of detection (LOD), but there is still a lot of confusion about this important validation parameter. This confusion mainly stems from its statistically complex background. The goal of this two-part tutorial is to discuss and clarify the topic of LOD for practitioners. The two main conclusions of this tutorial are: (1) the choice of how to estimate LOD should be based on the purpose of the analytical method that is being validated (e.g. considerable effort should not be made to estimate LOD for a method that is not used for detecting traces in the vicinity of LOD), and (2) LOD estimates are strongly dependent on different assumptions and the approach used, and therefore caution must be exercised when using the estimate or when comparing different estimates.     

Tutorial on estimating the limit of detection using LC-MS analysis,part II: Practical aspects

In part II of this tutorial, the investigated approaches of estimating the limit of detection (LOD) are applied to experimental data from LC-MS measurements. Important practical aspects specific to LC-MS and related to LOD are reviewed. The results of different tests of estimating linearity and scedasticity are compared. LOD estimates obtained with different approaches (for both simple characterization of the analysis method and accurate interpretation of the results) are applied to the data and the obtained values are compared. As a conclusion, a decision tree is proposed for estimating LOD for analytical methods using the LC-MS technique.     

Validation of a method for predicting the precision, limit of detection and range of quantitation in competitive ELISA.

The mathematical model for predicting the precision, limit of detection (LOD) and range of quantitation (ROQ) in a competitive enzyme-linked immunosorbent assay (ELISA) proposed by Hayashi et al. (Anal. Chem., 2004, 76, 1295) was validated. The model describes the relative standard deviation (RSD) of concentration estimates by the RSDs of pipetting volumes of analyte, enzyme-conjugated antigen, antibody and substrate solutions, and the standard deviation (SD) of inherent absorbances between the wells in an ELISA plate. For 6 kinds of direct competitive ELISA kits, the LOD and ROQ predicted by the model agreed well with those obtained by experiments with real samples. It was also confirmed that the model is applicable to the prediction of uncertainty that depends on the pipetting error of the viscous antiserum solution. The model was demonstrated to be useful for estimating the LOD and ROQ of competitive ELISA.     

Comparison of sample-labeling techniques in DNA microarray experiments

Usage of DNA microarrays for gene expression analysis has become a common technique in many research laboratories and industry. Several target-labeling techniques have been devised to reduce the amount of RNA required for microarray experiments. In order to facilitate comparison and sharing of microarray data across the laboratories, it is crucial to determine the relative affects of these different sample-labeling techniques on the final results obtained from these experiments. We have compared two labeling methods designed for small RNA samples, an enzyme-based tyramide method (TSA) and a nucleic acid-based dendrimer method, to a more typical direct-labeling method that requires larger amounts of RNA. We observed comparable levels of reproducibility between replicate spots, with all the techniques. The dendrimer method resulted in a minimum number of spots (0.08%) that showed differential labeling due to a bias in the dyes used but resulted in highest background with only 71.4% of the spots measurable (above background) as compared to 93.3% for the TSA technique and 79.7% for the direct-labeling method. The results from differential labeling experiments showed that the dendrimer method performed better than the TSA method in detecting the same set of differentially expressed genes as observed with the direct method. Overall, our results show that the dendrimer method performs better than the TSA method. Differential labeling experiments using the TSA method show a non-linearity in the data at high intensities, leading to skewing of a portion of the data.     

Degenerate two-photon-absorption spectral studies of highly two-photon active organic chromophores

Degenerate two-photon absorption (TPA) spectral properties of five AFX chromophore solutions have been studied using a single and spectrally dispersed sub-picosecond white-light continuum beam. In a specially designed optical configuration, optical pathways inside the sample solution for different spectral components of the focused continuum beam were spatially separated from each other. Thus, the nondegenerate TPA processes coming from different spectral components can be eliminated, and the direct nonlinear absorption spectrum attributed to degenerate TPA processes can be readily obtained. Using this new technique, the complete TPA spectra for these five highly two-photon-active compounds (AF-380, AF-350, AF-295, AF-270, and AF-50) were obtained in the spectral range from 600 to 950 nm on an absolute scale of TPA cross section. The relationship between the molecular structures and their TPA spectral behaviors are discussed. In general the measured TPA spectra are not identical with the linear absorption spectra on the scale of absorbed photon(s) energy. Moreover, for some sample (such as AF-380), the TPA spectrum is totally different from the linear spectrum, which implies the difference of molecular transition pathways and selection rules for one- and two-photon excitation processes. At high excitation intensity levels (>or=15 GW/cm(2)), the saturation behavior of TPA transition can be observed obviously in AF-350 and AF-380 solutions that exhibit much higher nonlinear absorptivity than the other chromophores investigated.     

Bootstrap method for the estimation of measurement uncertainty in spotted dual-color DNA microarrays

DNA microarrays permit the measurement of gene expression across the entire genome of an organism, but the quality of the thousands of measurements is highly variable. For spotted dual-color microarrays the situation is complicated by the use of ratio measurements. Studies have shown that measurement errors can be described by multiplicative and additive terms, with the latter dominating for low-intensity measurements. In this work, a measurement-error model is presented that partitions the variance into general experimental sources and sources associated with the calculation of the ratio from noisy pixel data. The former is described by a proportional (multiplicative) structure, while the latter is estimated using a statistical bootstrap method. The model is validated using simulations and three experimental data sets. Monte-Carlo fits of the model to data from duplicate experiments are excellent, but suggest that the bootstrap estimates, while proportionately correct, may be underestimated. The bootstrap standard error estimates are particularly useful in determining the reliability of individual microarray spots without the need for replicate spotting. This information can be used in screening or weighting the measurements.     

Stabilization of sulfide and sulfite and ion-pair chromatography of mixtures of sulfide, sulfite, sulfate and thiosulfate

Ion chromatography of sulfide, sulfite, sulfate and thiosulfate in a mixture is often difficult because of instability of sulfide and sulfite, poor separation of sulfide from common anions such as bromide or nitrate and similar elution-times for sulfite and sulfate. An ion-pair chromatographic method for the determination of these sulfur anions has been established by stoichiometric conversion of sulfide and sulfite into stable thiocyanate and sulfate, respectively, prior to the chromatographic run. Sulfate, thiosulfate and thiocyanate were resolved on an octadecylsilica column with an acetonitrile-water mobile phase containing tetrapropylammonium salt (TPA) as an ion-paring reagent, and thiosulfate and thiocyanate in the effluent could be measured with a photometric detector (220 nm) and sulfate with a suppressed conductivity detector. When an acetonitrile-water (6:94, v/v) mobile phase (pH 5.0) containing 15 mM TPA and small amounts of acetic acid was used at a flow-rate of 0.6 ml min(-1), the three anions could be eluted within 32 min. Calibration plots of peak height versus concentration for sulfide (detected as thiocyanate) and thiosulfate gave straight lines up to 35 and 60 microM, respectively. The calibration plot for sulfide coincided with that obtained by using thiocyanate. A calibration plot for sulfite, measured as sulfate, was also linear up to 135 microM and was in accord with that of sulfate. Each calibration plot gave a correlation coefficient greater than 0.999. For six replicates obtained for a mixture of 30.0 microM sulfide, 50.0 microM sulfite, 50.0 microM sulfate and 20.0 microM thiosulfate, the proposed method gave a mean value of 30.1 microM with a standard deviation (SD) of 0.77 microM and a relative standard deviation (RSD) of 2.6% for sulfide, 101 microM (SD = 3.5 microM, RSD = 3.5%) for the total of sulfite and sulfate and 20.1 microM (SD = 0.44 microM, RSD = 2.2%) for thiosulfate. Recoveries for sulfide, sulfite plus sulfate, and thiosulfate in hot-spring water samples using the proposed method were found to be quantitative.     

Method validation for the analysis of 169 pesticides in soya grain, without clean up, by liquid chromatography-tandem mass spectrometry using positive and negative electrospray ionization

Part of a comprehensive study on the comparison of different extraction methods, GC-MS(/MS) and LC-MS/MS detection methods and modes, for the analysis of soya samples is described in this paper. The validation of an acetone-based extraction method for analysis of 169 pesticides in soya, using LC-MS/MS positive and negative electrospray ionisation (ESI) mode, is reported. Samples (5 g) were soaked with 10 g water and subsequently extracted with 100 mL of a mixture of acetone, dichloromethane and light petroleum (1:1:1), in the presence of 15 g anhydrous sodium sulphate. After centrifugation, aliquots of the extract were evaporated and reconstituted in 1.0 mL of methanol, before direct injection of the final extract (corresponding with 0.05 g soya mL(-1)) into the LC-MS/MS system. Linearity, r(2) of calibration curves, instrument limit of detection/quantitation (LOD/LOQ) and matrix effect were evaluated, based on seven concentrations measured in 6-fold. Good linearity (at least r(2)> or =0.99) of the calibration curves was obtained over the range from 0.1 or 0.25 to 10.0 ng mL(-1), corresponding with pesticide concentrations in soya bean extract of 2 or 5-200 microg kg(-1). Instrument LOD values generally were 0.1 or 0.25 ng mL(-1). Matrix effects were negligible for approximately 90% of the pesticides. The accuracy, precision and method LOQ were determined via recovery experiments, spiking soya at 10, 50, 100 microg kg(-1), six replicates per level. In both ESI modes, method LOQ values were mostly 10 or 50 microg kg(-1) and more than 70% of pesticides analysed by each mode met the acceptability criteria of recovery (70-120%) and RSD (< or =20%), at one or more of the three levels studied. A fast, easy and efficient method with acceptable performance was achieved for a difficult matrix as soya, without cleanup.     

Prediction of precision from signal and noise measurement in liquid chromatography: Limit of detection

Summary A method to determine the limit of detection (LOD) in high performance liquid chromatography (HPLC) is described. The power spectral density of instrumental baseline variation is fitted by the simplex least squares methods with a mixed random process of white noise and Markov process as a model. The white noise is characterized by standard deviation (SD),; the Markov process by the SD, , and auto-correlation degree, ρ. All required parameters for calculating the LOD signal are obtained by experiment without repeat measurements. No arbitrary constants are needed. The LOD signal is uniquely determined and is characterized by 33.3 % relative standard deviation (RSD) of analyte measurements and 0.13 % of the error of the first type. This signal also specifies that the signal-to-noise ratio =3, using the definition of noise originating from the white noise and Markov process. The theoretical conclusion is verified by the Monte Carlo simulation using real baseline and peaks. The LOD concentrations for naphthalene, acenaphthene, pyrene and perylene are given. First part of series cited as Ref. [1].     

Theoretical Studies on the One‐ and Two‐Photon Absorption Properties of Double‐bis(styryl)benzene Derivatives

Two series of bis(styryl)benzene derivatives (BSBD), namely the single‐BSBD and the double‐BSBD, were investigated. The equilibrium geometries and electronic structures were obtained by using the density functional theory B3LYP and 6‐31G basis set. In succession, the one‐ and two‐photon absorption properties of all the molecules were studied theoretically with a ZINDO‐SOS (sum‐over‐states) method in detail. It can be seen that the double‐BSBDs have larger two‐photon absorption (TPA) cross sections in the visible‐IR range than the corresponding single‐BSBDs, demonstrating that increasing the molecular dimension is a very effective method to enhance the values of the TPA cross sections. On the other hand, it can be also noticed that the values of the TPA cross sections are correlative with the ability of donating (accepting) electrons of the terminal substituent groups R [N(CH₃)₂, CH₃, H and CF₃] in these molecules. That is, the intramolecular charge transfer is also a factor for the enhancement of the TPA efficiency. To sum up, the idea of increasing the molecular dimension to enhance the TPA cross section value is a helpful direction to explore better TPA materials for practical applications. And the double‐BSBD molecules are promising TPA materials for the further investigation from the standpoint of the high transparency and the larger TPA cross sections.     

Considering Dependencies Amongst Genes Helps to Adjust the Significance Rank of DEGs

Lists of differentially expressed genes (DEGs) detected often show low reproducibility even in technique replicate experiments. The reproducibility is even lower for those real cancer data with large biological variations and limited number of samples. Since existing methods for identifying differentially expressed genes treat each gene separately, they cannot circumvent the problem of low reproducibility. Considering correlation structures of genes may help to mitigate the effect of errors on individual gene estimates and thus get more reliable lists of DEGs. We borrowed information from large amount of existing microarray data to define the expression dependencies amongst genes. We use this prior knowledge of dependencies amongst genes to adjust the significance rank of DEGs. We applied our method and four popular ranking algorithms including mean fold change (FC), SAM, t‐statistic and Wilcoxon rank sum‐test on two cancer microarray datasets. Our method achieved higher reproducibility than other methods across a range of sample sizes. Furthermore, our method obtained higher accuracy than other methods, especially when the sample size is small. The results demonstrate that considering the dependencies amongst genes helps to adjust the significance rank of genes and find those truly differentially expressed genes.     

Least squares with non-normal data: estimating experimental variance functions

Contrary to popular belief, the method of least squares (LS) does not require that the data have normally distributed (Gaussian) error for its validity. One practically important application of LS fitting that does not involve normal data is the estimation of data variance functions (VFE) from replicate statistics. If the raw data are normal, sampling estimates s(2) of the variance sigma(2) are chi(2) distributed. For small degrees of freedom, the chi(2) distribution is strongly asymmetrical -- exponential in the case of three replicates, for example. Monte Carlo computations for linear variance functions demonstrate that with proper weighting, the LS variance-function parameters remain unbiased, minimum-variance estimates of the true quantities. However, the parameters are strongly non-normal -- almost exponential for some parameters estimated from s(2) values derived from three replicates, for example. Similar LS estimates of standard deviation functions from estimated s values have a predictable and correctable bias stemming from the bias inherent in s as an estimator of sigma. Because s(2) and s have uncertainties proportional to their magnitudes, the VFE and SDFE fits require weighting as s(-4) and s(-2), respectively. However, these weights must be evaluated on the calculated functions rather than directly from the sampling estimates. The computation is thus iterative but usually converges in a few cycles, with remaining 'weighting' bias sufficiently small as to be of no practical consequence.     

Determination of trace levels of dinitrophenolic compounds by microporous membrane liquid-liquid extraction in environmental water samples

A fast and simple hollow fibre-based microporous membrane liquid-liquid extraction (MMLLE) method is proposed for the determination of trace levels of dinitrophenolic compounds in water samples. The optimization step was performed using a three-variables Doehlert matrix design, involving the fibre length, the quantity of trioctylphosphine oxide (TOPO) in the acceptor phase and the extraction time. Using the established experimental conditions, some other parameters such as stirring speed, salt content, humic acids and different organic solvents as the acceptor phase were studied. Validation of the method included calibration experiments, linearity studies and determination of method LOD (MLD). The RSD was around 11% in all the experiments on different days at different concentrations. Separation and detection of four dinitrophenols were performed in 10 min with an RP-LC and a C(8 )column ACN-citric buffer gradient elution and diode array detection.     

Sensitive protein microarray synergistically amplified by polymer brush-enhanced immobilizations of both probe and reporter

Great challenge remains to continuously improve sensitivity of protein microarrays for broad applications. A copolymer brush is in situ synthesized on both substrate and silica nanoparticle (SNP) surface to efficiently immobilize probe and reporter protein respectively for synergistic amplification of protein microarray signals. As a demonstration, sandwich immunoassay for a cancer biomarker carcinoembryonic antigen (CEA) detection is performed on microarray platform, showing a limit of detection (LOD) of 10 pg/ml and dynamic range of 10 pg/ml to 100 ng/ml. Two orders improvement of LOD is achieved in comparison to the small crosslinker-activated substrate. The improved sensitivity is attributed to not only the high immobilization amount of both probe and reporter but also the favorite protein binding orientations offered by the flexible brushes. This work provides a universal approach to inexpensively and significantly improve protein microarray sensitivity.     

分子印迹固相萃取-电化学发光检测牛奶中氯霉素

基于氯霉素(CAP)能强烈抑制Ru(bpy)32+/TPA体系的电化学发光(ECL)信号,结合分子印迹固相萃取(MISPE)样品前处理技术,建立了一种高灵敏度检测牛奶中CAP残留量的方法。在最优实验条件下,体系的ECL猝灭值ΔI与CAP浓度呈良好线性关系,线性范围为1.0×10-13～1.0×10-11g/mL,检测限为3×10-12g/mL,精密度和准确度好,可用于牛奶中CAP残留量的测定。     

Determination of quinolone residues in chicken and fish by capillary electrophoresis-mass spectrometry

A specific pressure-assisted CE-MS method is described for the analysis of five quinolone residues. MS using a single quadrupole is compared with multiple-stage MS using a quadrupole IT (QIT-MS(n)). The procedure involves a common sample preparation by SPE on disposable cartridges. The most suitable electrolyte is 60 mM (NH(4))(2)CO(3) at pH 9.2. Single quadrupole does not provide enough fragmentation to confirm identities according to the current legislation. However, QIT-MS(n) achieves selective fragmentation. Using this method, danofloxacin, enrofloxacin, flumequine, ofloxacin, and pipemidic acid are analyzed in fortified samples of chicken and fish. Recoveries at levels of 50 ng/g were 62-99%, except for flumequine, which gives recoveries > or =45%. RSDs are from 9 to 16% and the LOD is equal (20 ng/g) for the five analytes. Confirmation of the quinolones' identity is achieved using QIT-MS(3). Forty samples of chicken and fish taken from different local markets are analyzed. Enrofloxacin is also determined in incurred chicken muscle using this method.     

Validation of a gas chromatography/triple quadrupole mass spectrometry based method for the quantification of pesticides in food commodities

A new multiresidue method has been validated in cucumber matrix for the routine analysis of 130 multiclass pesticide residues by gas chromatography/triple quadrupole mass spectrometry. The pesticides were extracted with ethyl acetate. A first identification of the pesticides was based on a tandem mass spectrometric (MS/MS) screening method, which monitors a single transition for each target compound, in less than 12 min. After that, potentially non-negative samples were analyzed again by the MS/MS confirmation/quantification method, which monitors two or three MS/MS transitions for each compound, also in less than 12 min. Performance characteristics, such as trueness, precision, linear range, detection limit (LOD) and quantification limit (LOQ), for each pesticide were calculated. The average recoveries obtained ranged between 70 and 120% at three different fortification levels (25, 200 and 500 microg/kg) with precision, expressed as relative standard deviation (RSD), values lower than 15%. The calculated LOD and LOQ were typically <3.2 and 9.6 microg/kg, respectively. Such limits were much lower than the maximum residue levels (MRLs) established by European legislation. The proposed methodology was applied to the determination of pesticides in real vegetable samples from Almería (Spain).     

Improving the power to detect differentially expressed genes in comparative microarray experiments by including information from self-self hybridizations

Our ability to detect differentially expressed genes in a microarray experiment can be hampered when the number of biological samples of interest is limited. In this situation, we propose the use of information from self-self hybridizations to acuminate our inference of differential expression. A unified modelling strategy is developed to allow better estimation of the error variance. This principle is similar to the use of a pooled variance estimate in the two-sample t-test. The results from real dataset examples suggest that we can detect more genes that are differentially expressed in the combined models. Our simulation study provides evidence that this method increases sensitivity compared to using the information from comparative hybridizations alone, given the same control for false discovery rate. The largest increase in sensitivity occurs when the amount of information in the comparative hybridization is limited.     

Methylation pattern analysis using high-throughput microarray of solid-phase hyperbranched rolling circle amplification products

Monitoring the methylation pattern of a single tumor cell might be important in understanding the mechanism of tumor initiation and progression. In this study, we developed a method based on molecular cloning microarray strategy for analyzing methylation patterns of a single DNA fragment from a group of tumor cells. In the method, a microarray of single monoclones of bisulfate-treated PCR products was fabricated by two-primer hyperbranched rolling circle amplification (HRCA) in polyacrylamide gel, in which a library of the bisulfate-treated PCR products with different methylated status from tumor cells were ligated to circle molecules to form HRCA templates, and one of the HRCA primers was modified with acrylamide on its 5'-end. Due to the diffusion retardation of HRCA products in a polyacrylamide matrix, the HRCA products are localized near their respective templates, and formed to a microarray of monoclones. After the nonimmobilized strands were removed, three pairs of probes were used to detect different CpG sites of each clone simultaneously by hybridization. We successfully analyzed the methylation patterns of P16 gene for three cases of stomach tumor tissues. This method could provide a significant tool in detecting the distribution of cells with different methylation patterns in one tumor tissue.