A correlation algorithm for the automated quantitative analysis of shotgun proteomics data

Quantitative shotgun proteomic analyses are facilitated using chemical tags such as ICAT and metabolic labeling strategies with stable isotopes. The rapid high-throughput production of quantitative "shotgun" proteomic data necessitates the development of software to automatically convert mass spectrometry-derived data of peptides into relative protein abundances. We describe a computer program called RelEx, which uses a least-squares regression for the calculation of the peptide ion current ratios from the mass spectrometry-derived ion chromatograms. RelEx is tolerant of poor signal-to-noise data and can automatically discard nonusable chromatograms and outlier ratios. We apply a simple correction for systematic errors that improves the accuracy of the quantitative measurement by 32 +/- 4%. Our automated approach was validated using labeled mixtures composed of known molar ratios and demonstrated in a real sample by measuring the effect of osmotic stress on protein expression in Saccharomyces cerevisiae.     

Measurement of the isotope enrichment of stable isotope-labeled proteins using high-resolution mass spectra of peptides

Stable isotope-enriched molecules are used as internal standards and as tracers of in vivo substrate metabolism. The accurate conversion of measured ratios in the mass spectrometer to mole ratios is complicated because a polyatomic molecule containing enriched atoms will result in a combinatorial distribution of isotopomers depending on the enrichment and number of "labeled" atoms. This effect could potentially cause a large error in the mole ratio measurement depending on which isotope peak or peaks were used to determine the ratio. We report a computational method that predicts isotope distributions over a range of enrichments and compares the predicted distributions to experimental peptide isotope distributions obtained by Fourier transform ion cyclotron resonance mass spectrometry. Our approach is accurate with measured enrichments within 1.5% of expected isotope distributions. The method is also precise with 4.9, 2.0, and 0.8% relative standard deviations for peptides containing 59, 79, and 99 atom % excess (15)N, respectively. The approach is automated making isotope enrichment calculations possible for thousands of peptides in a single muLC-FTICR-MS experiment.     

散斑分数傅里叶联合变换相关测量研究

提出数字散斑联合变换分数相关测量方法,利用分数相关可以锐化相关峰的作用,在数字散斑联合变换相关运算中用分数傅里叶变换代替傅里叶变换,提高测量精度。通过对散斑图像进行相位调制,有效地解决了分数傅里叶变换的移变性带来的谱移问题。编程模拟和对拉伸试件位移场测量的结果表明,只要选择合适的分数傅里叶变换级次和相位调制函数,可以使相关峰的半宽度从4～5pixel锐化到仅1pixel,得到优于傅里叶变换相关的理想输出。     

Optimal signal processing of nonlinearity in swept-source and spectral-domain optical coherence tomography

We demonstrate the efficiency of the convolution using an optimized Kaiser-Bessel window to resample nonlinear data in wavenumber for Fourier-domain optical coherence tomography (OCT). We extend our previous experimental demonstration that was performed with a specific swept-source nonlinearity. The method is now applied to swept-source OCT data obtained for various simulated swept-source nonlinearities as well as spectral-domain OCT data obtained from both simulations and experiments. Results show that the new optimized method is the most efficient for handling all the different types of nonlinearities in the wavenumber domain that one can encounter in normal practice. The efficiency of the method is evaluated through comparison with common methods using resampling through interpolation prior to performing a fast-Fourier transform and with the accurate but time-consuming discrete Fourier transform for unequally spaced data, which involves Vandermonde matrices.     

Ultrahigh-speed calculation of isotope distributions

This paper introduces an ultrahigh-speed algorithm for calculating isotope distributions from molecular formulas, elemental isotopic masses, and elemental isotopic abundances. For a given set of input data (molecular formula, elemental isotopic masses, and elemental isotopic abundances), and assuming round-off error to be negilgible, the new algorithm rigorously produces isotope distributions whose mean and standard deviation are "correct" in the sense that an error-free algorithm would produce a distribution having the same mean and standard deviation. The peak heights are also "correct" in the sense that the height of each nominal isotope peak from the ultrahigh-speed calculation equals the integrated peak area of the corresponding nominal isotope peak from an exact calculation. As a consequence of these properties, the algorithm generally places isotope peaks within millidaltons of their true centroids. The method uses Fourier transform methods and relates closely to two other recently introduced algorithms. The suite of capabilities provided by these three algorithms is sufficient to solve an extremely wide range of problems requiring isotope distribution simulation.     

Proteolytic 18O labeling for comparative proteomics: model studies with two serotypes of adenovirus

A new method for proteolytic stable isotope labeling is introduced to provide quantitative and concurrent comparisons between individual proteins from two entire proteome pools or their subfractions. Two 18O atoms are incorporated universally into the carboxyl termini of all tryptic peptides during the proteolytic cleavage of all proteins in the first pool. Proteins in the second pool are cleaved analogously with the carboxyl termini of the resulting peptides containing two 16O atoms (i.e., no labeling). The two peptide mixtures are pooled for fractionation and separation, and the masses and isotope ratios of each peptide pair (differing by 4 Da) are measured by high-resolution mass spectrometry. Short sequences and/or accurate mass measurements combined with proteomics software tools allow the peptides to be related to the precursor proteins from which they are derived. Relative signal intensities of paired peptides quantify the expression levels of their precursor proteins from proteome pools to be compared, using an equation described in the paper. Observation of individual (unpaired) peptides is mainly interpreted as differential modification or sequence variation for the protein from the respective proteome pool. The method is evaluated here in a comparison of virion proteins for two serotypes (Ad5 and Ad2) of adenovirus, taking advantage of information already available about protein sequences and concentrations. In general, proteolytic 18O labeling enables a shotgun approach for proteomic studies with quantitation capability and is proposed as a useful tool for comparative proteomic studies of very complex protein mixtures.     

Chemometrics approach to the determination of polymorphism of a drug compound by infrared spectroscopy

A chemometrics approach, multivariate calibration in particular, was used to determine the polymorphism of a drug compound based on Fourier transform infrared (FTIR) spectroscopy. The partial least-squares projection to latent structure makes use of all of the data, and the latent variables created by the method make use of hidden or partially separated peaks for quantitation. This paper illustrates the usefulness of the partial least-squares multivariate calibration method as an efficient tool to determine the polymorphism of a drug. Also, the analysis suggests the use of information from the modeling as diagnostic tools to gain more insight from the data. In particular, the diagnostic tools allow an analyst to assess design characteristics and any shortcomings of a calibration experiment for the polymorphism of a drug compound.     

Chemometrics Approach to the Determination of Polymorphism of a Drug Compound by Infrared Spectroscopy

A chemometrics approach, multivariate calibration in particular, was used to determine the polymorphism of a drug compound based on Fourier transform infrared (FTIR) spectroscopy. The partial least-squares projection to latent structure makes use of all of the data, and the latent variables created by the method make use of hidden or partially separated peaks for quantitation. This paper illustrates the usefulness of the partial least-squares multivariate calibration method as an efficient tool to determine the polymorphism of a drug. Also, the analysis suggests the use of information from the modeling as diagnostic tools to gain more insight from the data. In particular, the diagnostic tools allow an analyst to assess design characteristics and any shortcomings of a calibration experiment for the polymorphism of a drug compound.     

Recursive algorithm for phase retrieval in the fractional fourier transform domain

We first discuss the discrete fractional Fourier transform and present some essential properties. We then propose a recursive algorithm to implement phase retrieval from two intensities in the fractional Fourier transform domain. This approach can significantly simplify computational manipulations and does not need an initial phase estimate compared with conventional iterative algorithms. Simulation results show that this approach can successfully recover the phase from two intensities.     

Fractional Fourier transformer of variable order based on a modular lens system

The fractional Fourier transform is a new topic in optics. To make use of the fractional Fourier transform as an experimental tool, I design a fractional Fourier transformer of variable order: I introduce a lens system that is able to perform equidistant fractional Fourier transforms that cover the whole range of orders and that consist of a minimum number of modules. By module, I mean an elementary fractional Fourier transform of certain order that consists of a lens between two free-space lengths. Because of the commutative additivity of the transform, various fractional orders can be achieved by means of different constellations of the modules. It is possible to perform a large variety of fractional Fourier transforms with a small number of modules.     

基于分数阶傅里叶变换的NURBS曲面拟合

为了实现对自由曲面模型的高精度非均匀有理B样条(NURBS)曲面拟合,提出了一种基于分数阶傅里叶变换的NURBS曲面拟合方法.首先,借助分数阶傅里叶变换对自由曲面模型点云数据的高程图像展开分析,从中提取出表征自由曲面表面三维结构的特征点;然后,利用外切圆取点法结合提取的特征点选取用于NURBS曲面拟合的数据点;最后,利...     

Fractional free space, fractional lenses, and fractional imaging systems

Continuum extensions of common dual pairs of operators are presented and consolidated, based on the fractional Fourier transform. In particular, the fractional chirp multiplication, fractional chirp convolution, and fractional scaling operators are defined and expressed in terms of their common nonfractional special cases, revealing precisely how they are interpolations of their conventional counterparts. Optical realizations of these operators are possible with use of common physical components. These three operators can be interpreted as fractional lenses, fractional free space, and fractional imaging systems, respectively. Any optical system consisting of an arbitrary concatenation of sections of free space and thin lenses can be interpreted as a fractional imaging system with spherical reference surfaces. As a special case, a system departing from the classical single-lens imaging condition can be interpreted as a fractional imaging system.     

Spherical particle size determination by analytical inversion of the UV-visible-NIR extinction spectrum

An analytic inversion method, based on the anomalous diffraction approximation for nonabsorbing spherical particles, was developed to retrieve the size distribution from the optical turbidity or extinction spectrum. This method makes use of a differential Fourier cosine transform approach and provides a simple and fast inversion by means of fast Fourier transform and the Savitzky-Golay filter. The applicability of this algorithm was tested on the extinction data generated by the Mie solution. The effects of noise, modality, band limits, and data set size were analyzed by comparison with simulated data. This method can be used to reconstruct the original monomodal and bimodal distributions from 10% noise-corrupted data. The peak position and ratio of peak heights can be recovered with 10% or less deviation. The experiments with latex spheres showed that the inversion result from this method compares favorably with that from the dynamic light scattering measurement.     

Software for quantitative proteomic analysis using stable isotope labeling and data independent acquisition

Many software tools have been developed for analyzing stable isotope labeling (SIL)-based quantitative proteomic data using data dependent acquisition (DDA). However, programs for analyzing SIL-based quantitative proteomics data obtained with data independent acquisition (DIA) have yet to be reported. Here, we demonstrated the development of a new software for analyzing SIL data using the DIA method. Performance of the DIA on SYNAPT G2MS was evaluated using SIL-labeled complex proteome mixtures with known heavy/light ratios (H/L = 1:1, 1:5, and 1:10) and compared with the DDA on linear ion trap (LTQ)-Orbitrap MS. The DIA displays relatively high quantitation accuracy for peptides cross all intensity regions, while the DDA shows an intensity dependent distribution of H/L ratios. For the three proteome mixtures, the number of detected SIL-peptide pairs and dynamic range of protein intensities using DIA drop stepwise, whereas no significant changes in these aspects using DDA were observed. The new software was applied to investigate the proteome difference between mouse embryonic fibroblasts (MEFs) and MEF-derived induced pluripotent stem cells (iPSCs) using (16)O/(18)O labeling. Our study expanded the capacities of our UNiquant software pipeline and provided valuable insight into the performance of the two cutting-edge MS platforms for SIL-based quantitative proteomic analysis today.     

Fractional fourier domain encrypted holographic memory by use of an anamorphic optical system

We propose and demonstrate a fractional Fourier domain encrypted holographic memory using an anamorphic optical system. The encryption is done by use of two statistically independent random-phase codes in the fractional Fourier domain. If the two random-phase codes are statistically independent white sequences, the encrypted data are stationary white noise. We exploit the capability of an optical system to process information in two dimensions by using two different sets of parameters along the two orthogonal axes to encode the data. The fractional Fourier transform parameters along with the random-phase codes constitute the key to the encrypted data. The knowledge of the key is essential to the successful decryption of data. The decoding of the encoded data is done by use of phase conjugation. We present a few experimental results.     

Determination of Block Length Distributions of Poly(oxypropylene) and Poly(oxyethylene) Block Copolymers by MALDI-FTICR Mass Spectrometry

Matrix-assisted laser desorption/ionization (MALDI) was performed on an external ion source Fourier transform ion cyclotron resonance mass spectrometer (FTICR-MS) to analyze the block length distributions of triblock polymers of poly(oxypropylene) and poly(oxyethylene). The first series of results presented demonstrate that the apparent molecular weight distributions are distorted. This distortion is induced by the flight-time-induced mass discrimination inherent in the experimental technique, the variation of isotopic patterns over the measured mass range, and the overlap of peaks in the spectrum. Subsequently, a method for the treatment of molecular weight distributions measured by MALDI on an external ion source FTICR-MS is developed to yield the actual molecular weight distribution and, from that, the individual block length distributions. For the first time, detailed and accurate molecular weight data were obtained on a complex sample using this methodology, which independently validates the data provided by the manufacturer. The experimentally verified random coupling hypothesis proves the validity of the methodology.     

Isotopic peak intensity ratio based algorithm for determination of isotopic clusters and monoisotopic masses of polypeptides from high-resolution mass spectrometric data

Determining isotopic clusters and their monoisotopic masses is a first step in interpreting complex mass spectra generated by high-resolution mass spectrometers. We propose a mathematical model for isotopic distributions of polypeptides and an effective interpretation algorithm. Our model uses two types of ratios: intensity ratio of two adjacent peaks and intensity ratio product of three adjacent peaks in an isotopic distribution. These ratios can be approximated as simple functions of a polypeptide mass, the values of which fall within certain ranges, depending on the polypeptide mass. Given a spectrum as a peak list, our algorithm first finds all isotopic clusters consisting of two or more peaks. Then, it scores clusters using the ranges of ratio functions and computes the monoisotopic masses of the identified clusters. Our method was applied to high-resolution mass spectra obtained from a Fourier transform ion cyclotron resonance (FTICR) mass spectrometer coupled to reverse-phase liquid chromatography (RPLC). For polypeptides whose amino acid sequences were identified by tandem mass spectrometry (MS/MS), we applied both THRASH-based software implementations and our method. Our method was observed to find more masses of known peptides when the numbers of the total clusters identified by both methods were fixed. Experimental results show that our method performed better for isotopic mass clusters of weak intensity where the isotopic distributions deviate significantly from their theoretical distributions. Also, it correctly identified some isotopic clusters that were not found by THRASH-based implementations, especially those for which THRASH gave 1 Da mismatches. Another advantage of our method is that it is very fast, much faster than THRASH that calculates the least-squares fit.     

Generalized joint fractional fourier transform correlators: a compact approach

Fractional correlation was introduced recently. We generalize the architecture of a joint (Fourier) transform correlator (JTC) to achieve the joint fractional (Fourier) transform correlator (JFrTC) such that fractional correlation can be obtained. Here the Fourier transform in the JTC is replaced by the fractional Fourier transform, and four different JFrTC architectures can be implemented. The mathematical derivations for these JFrTC architectures are given, together with the simulation verifications. The JFrTC can provide a correlation signal similar to a delta function but with a small discrimination ratio, such that it is insensitive to additive noise. In a conventional JTC the distance between the two desired correlation signals at the output plane is fixed and depends on the distance between the input and the reference signals. However, with a given fractional order and an additional phase mask the separation distance between the two correlation signals at the output plane of a JFrTC can be larger or smaller than that of a JTC. This property is useful for the applications of real-time target tracking. Unlike in a previous approach [Appl. Opt. 36, 7402 (1997)], we need only two fractional Fourier transformations instead of three to achieve fractional correlation.     

Radon-Wigner display: a compact optical implementation with a single varifocal lens

A new optical implementation of the Radon-Wigner display for one-dimensional objects is presented, making use of the fractional Fourier transform approach. The proposed setup makes use of only two conventional refractive elements: a cylindrical lens and a varifocal lens. Although the exact magnifications cannot be achieved simultaneously for all the fractional transforms, an optimum design can be obtained through balancing the conflicting magnification requirements. Experimental results are obtained with a commercially available progressive addition lens. For comparison, computer simulations are also provided.     

Top-down identification and quantification of stable isotope labeled proteins from Aspergillus flavus using online nano-flow reversed-phase liquid chromatography coupled to a LTQ-FTICR mass spectrometer

Online liquid chromatography-mass spectrometric (LC-MS) analysis of intact proteins (i.e., top-down proteomics) is a growing area of research in the mass spectrometry community. A major advantage of top-down MS characterization of proteins is that the information of the intact protein is retained over the vastly more common bottom-up approach that uses protease-generated peptides to search genomic databases for protein identification. Concurrent to the emergence of top-down MS characterization of proteins has been the development and implementation of the stable isotope labeling of amino acids in cell culture (SILAC) method for relative quantification of proteins by LC-MS. Herein we describe the qualitative and quantitative top-down characterization of proteins derived from SILAC-labeled Aspergillus flavus using nanoflow reversed-phase liquid chromatography directly coupled to a linear ion trap Fourier transform ion cyclotron resonance mass spectrometer (nLC-LTQ-FTICR-MS). A. flavus is a toxic filamentous fungus that significantly impacts the agricultural economy and human health. SILAC labeling improved the confidence of protein identification, and we observed 1318 unique protein masses corresponding to 659 SILAC pairs, of which 22 were confidently identified. However, we have observed some limiting issues with regard to protein quantification using top-down MS/MS analyses of SILAC-labeled proteins. The role of SILAC labeling in the presence of competing endogenously produced amino acid residues and its impact on quantification of intact species are discussed in detail.