Combining multiple laser scans of spotted microarrays by means of a two-way ANOVA model

MOTIVATION: Assessment of gene expression on spotted microarrays is based on measurement of fluorescence intensity emitted by hybridized spots. Unfortunately, quantifying fluorescence intensity from hybridized spots does not always correctly reflect gene expression level. Low gene expression levels produce low fluorescence intensities which tend to be confounded with the local background while high gene expression levels produce high fluorescence intensities which rapidly reach the saturation level. Most algorithms that combine data acquired at different voltages of the photomultiplier tube (PMT) assume that a change in scanner setting transforms the intensity measurements by a multiplicative constant. METHODS AND RESULTS: In this paper we introduce a new model of spot foreground intensity which integrates a PMT voltage independent scanner optical bias. This new model is used to implement a "Combining Multiple Scan using a Two-way ANOVA" (CMS2A) method, which is based on a maximum likelihood estimation of the scanner optical bias. After having computed scanner bias, coefficients of the two-way ANOVA model are used for correcting the saturated spots intensities obtained at high PMT voltage by using their counterpart values at lower PMT voltages. The method was compared to state-of-the-art multiple scan algorithms, using data generated from the MAQC study. CMS2A produced fold-changes that were highly correlated with qPCR fold-changes. As the scanner optical bias is accurately estimated within CMS2A, this method allows also avoiding fold-change compression biases whatever the value of this optical bias.     

Statistical evaluation of confocal microscopy images

BACKGROUND: The coefficient of variation (CV) is defined as the standard deviation (sigma) of the fluorescent intensity of a population of beads or pixels expressed as a proportion or percentage of the mean (mu) intensity (CV = sigma/mu). The field of flow cytometry has used the CV of a population of bead intensities to determine if the flow cytometer is aligned correctly and performing properly. In a similar manner, the analysis of CV has been applied to the confocal laser scanning microscope (CLSM) to determine machine performance and sensitivity. METHODS: Instead of measuring 10,000 beads using a flow cytometer and determining the CV of this distribution of intensities, thousands of pixels are measured from within one homogeneous Spherotech 10-microm bead. Similar to a typical flow cytometry population that consists of 10,000 beads, a CLSM scanned image consists of a distribution of pixel intensities representing a population of approximately 100,000 pixels. In order to perform this test properly, it is important to have a population of homogeneous particles. A biological particle usually has heterogeneous pixel intensities that correspond to the details in the biological image and thus shows more variability as a test particle. RESULTS: The bead CV consisting of a population of pixel intensities is dependent on a number of machine variables that include frame averaging, photomultiplier tube (PMT) voltage, PMT noise, and laser power. The relationship among these variables suggests that the machine should be operated with lower PMT values in order to generate superior image quality. If this cannot be achieved, frame averaging will be necessary to reduce the CV and improve image quality. There is more image noise at higher PMT settings, making it is necessary to average more frames to reduce the CV values and improve image quality. The sensitivity of a system is related to system noise, laser light efficiency, and proper system alignment. It is possible to compare different systems for system performance and sensitivity if the laser power is maintained at a constant value. Using this bead CV test, 1 mW of 488 nm laser light measured on the scan head yielded a CV value of 4% with a Leica TCS-SP1 (75-mW argon-krypton laser) and a CV value of 1.3% with a Zeiss 510 (25-mW argon laser). A biological particle shows the same relationship between laser power, averaging, PMT voltage, and CV as do the beads. However, because the biological particle has heterogeneous pixel intensities, there is more particle variability, which does not make as useful as a test particle. CONCLUSIONS: This CV analysis of a 10-microm Spherotech fluorescent bead can help determine the sensitivity in a confocal microscope and the system performance. The relationship among the factors that influence image quality is explained from a statistical endpoint. The data obtained from this test provides a systematic method of reducing noise and increasing image clarity. Many components of a CLSM, including laser power, laser stability, PMT functionality, and alignment, influence the CV and determine if the equipment is performing properly. Preliminary results have shown that the bead CV can be used to compare different confocal microscopy systems with regard to performance and sensitivity. The test appears to be analogous to CV tests made on the flow cytometer to assess instrument performance and sensitivity. Published 2001 Wiley-Liss, Inc.     

Statistical adjustment of signal censoring in gene expression experiments

MOTIVATION: Numerical output of spotted microarrays displays censoring of pixel intensities at some software dependent threshold. This reduces the quality of gene expression data, because it seriously violates the linearity of expression with respect to signal intensity. Statistical methods based on typically available spot summaries together with some parametric assumptions can suggest ways to correct for this defect. RESULTS: A maximum likelihood approach is suggested together with a sensible approximation to the joint density of the mean, median and variance-which are typically available to the biological end-user. The method 'corrects' the gene expression values for pixel censoring. A by-product of our approach is a comparison between several two-parameter models for pixel intensity values. It suggests that pixels separated by one or two other pixels can be considered independent draws from a Lognormal or a Gamma distribution. AVAILABILITY: The R/S-Plus code is available at http://www.stats.gla.ac.uk/~microarray/software.     

Profound influence of microarray scanner characteristics on gene expression ratios: analysis and procedure for correction

Background  

High throughput gene expression data from spotted cDNA microarrays are collected by scanning the signal intensities of the corresponding spots by dedicated fluorescence scanners. The major scanner settings for increasing the spot intensities are the laser power and the voltage of the photomultiplier tube (PMT). It is required that the expression ratios are independent of these settings. We have investigated the relationships between PMT voltage, spot intensities, and expression ratios for different scanners, in order to define an optimal scanning procedure.     

Weighted analysis of microarray gene expression using maximum-likelihood

MOTIVATION: The numerical values of gene expression measured using microarrays are usually presented to the biological end-user as summary statistics of spot pixel data, such as the spot mean, median and mode. Much of the subsequent data analysis reported in the literature, however, uses only one of these spot statistics. This results in sub-optimal estimates of gene expression levels and a need for improvement in quantitative spot variation surveillance. RESULTS: This paper develops a maximum-likelihood method for estimating gene expression using spot mean, variance and pixel number values available from typical microarray scanners. It employs a hierarchical model of variation between and within microarray spots. The hierarchical maximum-likelihood estimate (MLE) is shown to be a more efficient estimator of the mean than the 'conventional' estimate using solely the spot mean values (i.e. without spot variance data). Furthermore, under the assumptions of our model, the spot mean and spot variance are shown to be sufficient statistics that do not require the use of all pixel data.The hierarchical MLE method is applied to data from both Monte Carlo (MC) simulations and a two-channel dye-swapped spotted microarray experiment. The MC simulations show that the hierarchical MLE method leads to improved detection of differential gene expression particularly when 'outlier' spots are present on the arrays. Compared with the conventional method, the MLE method applied to data from the microarray experiment leads to an increase in the number of differentially expressed genes detected for low cut-off P-values of interest.     

Spot shape modelling and data transformations for microarrays

MOTIVATION: To study lowly expressed genes in microarray experiments, it is useful to increase the photometric gain in the scanning. However, a large gain may cause some pixels for highly expressed genes to become saturated. Spatial statistical models that model spot shapes on the pixel level may be used to infer information about the saturated pixel intensities. Other possible applications for spot shape models include data quality control and accurate determination of spot centres and spot diameters. RESULTS: Spatial statistical models for spotted microarrays are studied including pixel level transformations and spot shape models. The models are applied to a dataset from 50mer oligonucleotide microarrays with 452 selected Arabidopsis genes. Logarithmic, Box-Cox and inverse hyperbolic sine transformations are compared in combination with four spot shape models: a cylindric plateau shape, an isotropic Gaussian distribution and a difference of two-scaled Gaussian distribution suggested in the literature, as well as a proposed new polynomial-hyperbolic spot shape model. A substantial improvement is obtained for the dataset studied by the polynomial-hyperbolic spot shape model in combination with the Box-Cox transformation. The spatial statistical models are used to correct spot measurements with saturation by extrapolating the censored data. AVAILABILITY: Source code for R is available at http://www.matfys.kvl.dk/~ekstrom/spotshapes/     

CMEIAS Color Segmentation: An Improved Computing Technology to Process Color Images for Quantitative Microbial Ecology Studies at Single-Cell Resolution

Quantitative microscopy and digital image analysis are underutilized in microbial ecology largely because of the laborious task to segment foreground object pixels from background, especially in complex color micrographs of environmental samples. In this paper, we describe an improved computing technology developed to alleviate this limitation. The system’s uniqueness is its ability to edit digital images accurately when presented with the difficult yet commonplace challenge of removing background pixels whose three-dimensional color space overlaps the range that defines foreground objects. Image segmentation is accomplished by utilizing algorithms that address color and spatial relationships of user-selected foreground object pixels. Performance of the color segmentation algorithm evaluated on 26 complex micrographs at single pixel resolution had an overall pixel classification accuracy of 99+%. Several applications illustrate how this improved computing technology can successfully resolve numerous challenges of complex color segmentation in order to produce images from which quantitative information can be accurately extracted, thereby gain new perspectives on the in situ ecology of microorganisms. Examples include improvements in the quantitative analysis of (1) microbial abundance and phylotype diversity of single cells classified by their discriminating color within heterogeneous communities, (2) cell viability, (3) spatial relationships and intensity of bacterial gene expression involved in cellular communication between individual cells within rhizoplane biofilms, and (4) biofilm ecophysiology based on ribotype-differentiated radioactive substrate utilization. The stand-alone executable file plus user manual and tutorial images for this color segmentation computing application are freely available at . This improved computing technology opens new opportunities of imaging applications where discriminating colors really matter most, thereby strengthening quantitative microscopy-based approaches to advance microbial ecology in situ at individual single-cell resolution.     

Quality determination and the repair of poor quality spots in array experiments

Background  

A common feature of microarray experiments is the occurence of missing gene expression data. These missing values occur for a variety of reasons, in particular, because of the filtering of poor quality spots and the removal of undefined values when a logarithmic transformation is applied to negative background-corrected intensities. The efficiency and power of an analysis performed can be substantially reduced by having an incomplete matrix of gene intensities. Additionally, most statistical methods require a complete intensity matrix. Furthermore, biases may be introduced into analyses through missing information on some genes. Thus methods for appropriately replacing (imputing) missing data and/or weighting poor quality spots are required.     

Statistical estimation of gene expression using multiple laser scans of microarrays

We propose a statistical model for estimating gene expression using data from multiple laser scans at different settings of hybridized microarrays. A functional regression model is used, based on a non-linear relationship with both additive and multiplicative error terms. The function is derived as the expected value of a pixel, given that values are censored at 65 535, the maximum detectable intensity for double precision scanning software. Maximum likelihood estimation based on a Cauchy distribution is used to fit the model, which is able to estimate gene expressions taking account of outliers and the systematic bias caused by signal censoring of highly expressed genes. We have applied the method to experimental data. Simulation studies suggest that the model can estimate the true gene expression with negligible bias. AVAILABILITY: FORTRAN 90 code for implementing the method can be obtained from the authors.     

Unsupervised technique for robust target separation and analysis of DNA microarray spots through adaptive pixel clustering

MOTIVATION: Microarray images challenge existing analytical methods in many ways given that gene spots are often comprised of characteristic imperfections. Irregular contours, donut shapes, artifacts, and low or heterogeneous expression impair corresponding values for red and green intensities as well as their ratio R/G. New approaches are needed to ensure accurate data extraction from these images. RESULTS: Herein we introduce a novel method for intensity assessment of gene spots. The technique is based on clustering pixels of a target area into foreground and background. For this purpose we implemented two clustering algorithms derived from k-means and Partitioning Around Medoids (PAM), respectively. Results from the analysis of real gene spots indicate that our approach performs superior to other existing analytical methods. This is particularly true for spots generally considered as problematic due to imperfections or almost absent expression. Both PX(PAM) and PX(KMEANS) prove to be highly robust against various types of artifacts through adaptive partitioning, which more correctly assesses expression intensity values. AVAILABILITY: The implementation of this method is a combination of two complementary tools Extractiff (Java) and Pixclust (free statistical language R), which are available upon request from the authors.     

Combining signals from spotted cDNA microarrays obtained at different scanning intensities

MOTIVATION: The analysis of spotted cDNA microarrays involves scanning of color signals from fluorescent dyes. A common problem is that a given scanning intensity is not usually optimal for all spotted cDNAs. Specifically, some spots may be at the saturation limit, resulting in poor separation of signals from different tissues or conditions. The problem may be addressed by multiple scans with varying scanning intensities. Multiple scanning intensities raise the question of how to combine different signals from the same spot, particularly when measurement error is not negligible. RESULTS: This paper suggests a non-linear latent regression model for this purpose. It corrects for biases caused by the saturation limit and efficiently combines data from multiple scans. Combining multiple scans also allows reduction of technical error particularly for cDNA spots with low signal. The procedure is exemplified using cDNA expression data from maize. AVAILABILITY: All methods were implemented using standard procedures available in the SAS/STAT module of the SAS System. Programming statements are available from the first author upon request. CONTACT: piepho@uni-hohenheim.de SUPPLEMENTARY INFORMATION: The supplementary data are available at Bioinformatics online.     

A liquid crystal pixel array for signal discrimination in array biosensors

A new optical design uses a liquid crystal pixel array (LCPA) to discriminate multiple fluorescence signals on a two-dimensional biosensor array. The LCPA can selectively control the transmission of fluorescence generated from multiple biosensing elements on a planar waveguide. This device sequentially acquires the fluorescence data from the substrate by making multiple individual measurements of the sensing elements on the waveguide. The biosensing elements are patterned according to the pixel layout of the LCPA and optically aligned so that each electronically driven pixel can either transmit or filter out the fluorescence signal as specified by the user. The primary advantage of this system is that a single detection channel (i.e. photomultiplier tube (PMT)) can be used to measure multiple fluorescence signals from a two-dimensional substrate while the LCPA provides for spatial resolution. We evaluate the performance of the LCPA by testing the optical homogeneity of the liquid crystal pixels and linear dynamic range for transmitting light. The LCPA is also used with well-developed biosensing chemistry modified for this optical format.     

Correlation statistics for cDNA microarray image analysis

In this paper, correlation of the pixels comprising a microarray spot is investigated. Subsequently, correlation statistics, namely, Pearson correlation and Spearman rank correlation, are used to segment the foreground and background intensity of microarray spots. The performance of correlation-based segmentation is compared to clustering-based (PAM, k-means) and seeded-region growing techniques (SPOT). It is shown that correlation-based segmentation is useful in flagging poorly hybridized spots, thus minimizing false-positives. The present study also raises the intriguing question of whether a change in correlation can be an indicator of differential gene expression.     

Pre-cut Filter Paper for Detecting Anti-Japanese Encephalitis Virus IgM from Dried Cerebrospinal Fluid Spots

BackgroundThe use of filter paper as a simple, inexpensive tool for storage and transportation of blood, ‘Dried Blood Spots’ or Guthrie cards, for diagnostic assays is well-established. In contrast, there are a paucity of diagnostic evaluations of dried cerebrospinal fluid (CSF) spots. These have potential applications in low-resource settings, such as Laos, where laboratory facilities for central nervous system (CNS) diagnostics are only available in Vientiane. In Laos, a major cause of CNS infection is Japanese encephalitis virus (JEV). We aimed to develop a dried CSF spot protocol and to evaluate its diagnostic performance using the World Health Organisation recommended anti-JEV IgM antibody capture enzyme-linked immunosorbent assay (JEV MAC-ELISA).Conclusions/SignificanceThe novel design of pre-cut filter paper saturated with CSF could provide a useful tool for JEV diagnostics in settings with limited laboratory access. It has the potential to improve national JEV surveillance and inform vaccination policies. The saturation of filter paper has potential use in the wider context of pathogen detection, including dried spots for detecting other analytes in CSF, and other body fluids.     

Donuts, scratches and blanks: robust model-based segmentation of microarray images

MOTIVATION: Inner holes, artifacts and blank spots are common in microarray images, but current image analysis methods do not pay them enough attention. We propose a new robust model-based method for processing microarray images so as to estimate foreground and background intensities. The method starts with a very simple but effective automatic gridding method, and then proceeds in two steps. The first step applies model-based clustering to the distribution of pixel intensities, using the Bayesian Information Criterion (BIC) to choose the number of groups up to a maximum of three. The second step is spatial, finding the large spatially connected components in each cluster of pixels. The method thus combines the strengths of the histogram-based and spatial approaches. It deals effectively with inner holes in spots and with artifacts. It also provides a formal inferential basis for deciding when the spot is blank, namely when the BIC favors one group over two or three. RESULTS: We apply our methods for gridding and segmentation to cDNA microarray images from an HIV infection experiment. In these experiments, our method had better stability across replicates than a fixed-circle segmentation method or the seeded region growing method in the SPOT software, without introducing noticeable bias when estimating the intensities of differentially expressed genes. AVAILABILITY: spotSegmentation, an R language package implementing both the gridding and segmentation methods is available through the Bioconductor project (http://www.bioconductor.org). The segmentation method requires the contributed R package MCLUST for model-based clustering (http://cran.us.r-project.org). CONTACT: fraley@stat.washington.edu.     

The intracellular pupil mechanism and photoreceptor signal: noise ratios in the fly Lucilia cuprina

The function of the intracellular pupil mechanism is examined by comparing the responses of photoreceptors in normal flies with those from white-eyed flies that lack the pupil. In white-eyed flies the response to an intensity increment of fixed contrast decreases at high background intensities. There is a smaller decrease in noise amplitude so that the signal:noise ratio falls. The intensity dependence of the photoreceptor signal:noise ratio fits a simple model in which activated photopigment molecules compete for 3 X 10(4) transduction units. The signal:noise ratio decreases at high intensities because the transduction units are saturated. This model is supported by a noise analysis, which provides three estimates of the number of events generating photoreceptor responses. In white-eyed flies the event number saturates at high background intensities, suggesting that a maximum of 2 X 10(4) events can be simultaneously active. Wild-type flies do not exhibit saturation effects over the range of intensities studied. The signal:noise ratio rises with intensity to reach a stable asymptote, close to the maximum observed for white-eyed flies. Pupil attenuation is calculated from measurements of signal:noise ratio in white-eyed and wild-type flies. The pupil is progressively activated over a two log unit intensity range and when fully closed attenuates the effective intensity by 99%. The threshold of this pupil effect coincides with the threshold of pupil activation measured optically. We conclude that the intracellular pupil attenuates the light flux to prevent receptor saturation and to extend the range of intensities at which fly photoreceptors operate close to their maximum signal:noise ratio. This upper limit is determined by the number of transduction units generating a cell's response.     

Statistical Inference for Hardy-Weinberg Proportions in the Presence of Missing Genotype Information

In genetic association studies, tests for Hardy-Weinberg proportions are often employed as a quality control checking procedure. Missing genotypes are typically discarded prior to testing. In this paper we show that inference for Hardy-Weinberg proportions can be biased when missing values are discarded. We propose to use multiple imputation of missing values in order to improve inference for Hardy-Weinberg proportions. For imputation we employ a multinomial logit model that uses information from allele intensities and/or neighbouring markers. Analysis of an empirical data set of single nucleotide polymorphisms possibly related to colon cancer reveals that missing genotypes are not missing completely at random. Deviation from Hardy-Weinberg proportions is mostly due to a lack of heterozygotes. Inbreeding coefficients estimated by multiple imputation of the missings are typically lowered with respect to inbreeding coefficients estimated by discarding the missings. Accounting for missings by multiple imputation qualitatively changed the results of 10 to 17% of the statistical tests performed. Estimates of inbreeding coefficients obtained by multiple imputation showed high correlation with estimates obtained by single imputation using an external reference panel. Our conclusion is that imputation of missing data leads to improved statistical inference for Hardy-Weinberg proportions.     

A Novel Gaussian Extrapolation Approach for 2D Gel Electrophoresis Saturated Protein Spots

Analysis of images obtained from two-dimensional gel electrophoresis (2D-GE) is a topic of utmost importance in bioinformatics research, since commercial and academic software available currently has proven to be neither completely effective nor fully automatic, often requiring manual revision and refinement of computer generated matches. In this work, we present an effective technique for the detection and the reconstruction of over-saturated protein spots. Firstly, the algorithm reveals overexposed areas, where spots may be truncated, and plateau regions caused by smeared and overlapping spots. Next, it reconstructs the correct distribution of pixel values in these overexposed areas and plateau regions, using a two-dimensional least-squares fitting based on a generalized Gaussian distribution. Pixel correction in saturated and smeared spots allows more accurate quantification, providing more reliable image analysis results. The method is validated for processing highly exposed 2D-GE images, comparing reconstructed spots with the corresponding non-saturated image, demonstrating that the algorithm enables correct spot quantification.     

Pixel-based analysis of multiple images for the identification of changes: a novel approach applied to unravel proteome patterns [corrected] of 2-D electrophoresis gel images

A novel approach for revealing patterns of proteome variation among series of 2-DE gel images is presented. The approach utilises image alignment to ensure that each pixel represents the same information across all gels. Gel images are normalised, and background corrected, followed by unfolding of the images to 1-D pixel vectors and analysing pixel vectors by multivariate data modelling. Information resulting from the data analysis is refolded back to the image domain for visualisation and interpretation. The method is rapid and suitable for automatic routines applied after the gel alignment. The approach is compared with spot volume analysis to illustrate how this approach can solve persistent problems like mismatch of protein spots, erroneous missing values and failure to detect variation in overlapping proteins. The method may also detect variation in the border area of saturated proteins. The approach is given the name pixel-based analysis of multiple images for the identification of changes (PMC). The method can be used for multiple images in general. Effects of pretreatment of the images are discussed.