Spectral compensation for flow cytometry: visualization artifacts, limitations, and caveats.

BACKGROUND: In multicolor flow cytometric analysis, compensation for spectral overlap is nearly always necessary. For the most part, such compensation has been relatively simple, producing the desired rectilinear distributions. However, in the realm of multicolor analysis, visualization of compensated often results in unexpected distributions, principally the appearance of a large number of events on the axis, and even more disconcerting, an inability to bring the extent of compensated data down to "autofluorescence" levels. MATERIALS AND METHODS: A mathematical model of detector measurements with variable photon intensities, spillover parameters, measurement errors, and data storage characteristics was used to illustrate sources of apparent error in compensated data. Immunofluorescently stained cells were collected under conditions of limiting light collection and high spillover between detectors to confirm aspects of the model. RESULTS: Photon-counting statistics contribute a nonlinear error to compensated parameters. Measurement errors and log-scale binning error contribute linear errors to compensated parameters. These errors are most apparent with the use of red or far-red fluorochromes (where the emitted light is at low intensity) and with large spillover between detectors. Such errors can lead to data visualization artifacts that can easily lead to incorrect conclusions about data, and account for the apparent "undercompensation" previously described for multicolor staining. CONCLUSIONS: There are inescapable errors arising from imperfect measurements, photon-counting statistics, and even data storage methods that contribute both linearly and nonlinearly to a "spreading" of a properly compensated autofluorescence distribution. This phenomenon precludes the use of "quadrant" statistics or gates to analyze affected data; it also precludes visual adjustment of compensation. Most importantly, it is impossible to properly compensate data using standard visual graphical interfaces (histograms or dot plots). Computer-assisted compensation is required, as well as careful gating and experimental design to determine the distinction between positive and negative events. Finally, the use of special staining controls that employ all reagents except for the one of interest (termed fluorescence minus one, or "FMO" controls) becomes necessary to accurately identify expressing cells in the fully stained sample.     

Method to improve the sensitivity of flow cytometric membrane potential measurements in mouse spinal cord cells.

We have developed a technique to improve the sensitivity of relative membrane potential measurements in mouse spinal cord cells using the fluorescent, anionic, voltage sensitive dye, DiBa-C4(3) (Oxonol) and flow cytometry. In order to attribute cellular fluorescence primarily to membrane potential, signal variability due to cell size and shape was reduced by dividing the log fluorescence signal from each cell by either its log forward angle light scatter or log side scatter signals. The use of these ratios in place of log oxonol fluorescence reduced the coefficient of variation of the distributions while leaving the changes in mean fluorescence largely unaffected. Kolmogorov-Smirnov analysis of pre- vs. postkainate stimulation (an excitatory amino acid) showed improved sensitivity of the assay with the use of this ratio technique.     

Technique for cellular fluorescence distribution analysis

The usefulness of multidimensional slit-scan flow cytometry in whole cell measurements is dependent on extracting relevant features from the cellular fluorescence distributions (slit-scan contours). In addition, the extraction of these features must be rapid to allow for real-time data processing during acquisition. This paper describes two algorithms that have been used successfully to count the numbers of local maxima (peaks) and to find nuclear boundaries in a cellular fluorescence distribution. These routines are efficient, use only simple integer arithmetic, and have been implemented on several different microprocessors.     

The displays of the White-throated Manakin Corapipo gutturalis in Suriname

The courtship displays of the White-throated Manakin Corapipo gutturalis (Pipridae) were observed in the Brownsberg Nature Preserve, Suriname, for over 50 h on 17 days between 17 October and 17 December 1982, and the display elements and calls are described. Males perform displays from perches in trees, in flight and on mossy fallen logs. The perch displays are performed as preliminaries to the log-approach displays which are given while in flight towards the log. The log-approach displays vary in length and complexity from a short flight from a nearby perch down to the log, to a dramatic flight above the canopy and back to the log. As males land, they perform a series of aerial manoeuvres and give a complex vocal and mechanical display call. Males may also perform a slower silent moth-flight log approach. The log displays are the culminating elements of courtship and copulation is known to take place there (Davis, T.A.W. 1949. Ibis 91: 146–147). All the courtship displays can be performed either solitarily by a single male or by a group of up to seven males which compete simultaneously for access to single display sites at a series of different logs. Fourteen display logs were located dispersed in two areas 250 m wide which were separated by 350 m, but it was not determined whether these areas constituted separate leks with different pools of possible mates. The behaviour of C. gutturalis is compared with that of the White-ruffed Manakin Corapipo leucorrhoa and other manakins. Male Corapipo appear to have abandoned defence of exclusive advertisement territories in favour of simultaneous competition for a series of different display sites. This detached or mobile form of lek is unique among known manakins and a mechanism for its evolution through female choice is discussed.     

Wavelet transform as a potential tool for ECG analysis and compression

The recently introduced wavelet transform is a member of the class of time-frequency representations which include the Gabor short-time Fourier transform and Wigner-Ville distribution. Such techniques are of significance because of their ability to display the spectral content of a signal as time elapses. The value of the wavelet transform as a signal analysis tool has been demonstrated by its successful application to the study of turbulence and processing of speech and music. Since, in common with these subjects, both the time and frequency content of physiological signals are often of interest (the ECG being an obvious example), the wavelet transform represents a particularly relevant means of analysis. Following a brief introduction to the wavelet transform and its implementation, this paper describes a preliminary investigation into its application to the study of both ECG and heart rate variability data. In addition, the wavelet transform can be used to perform multiresolution signal decomposition. Since this process can be considered as a sub-band coding technique, it offers the opportunity for data compression, which can be implemented using efficient pyramidal algorithms. Results of the compression and reconstruction of ECG data are given which suggest that the wavelet transform is well suited to this task.     

Marginalized Zero-Altered Models for Longitudinal Count Data

Count data often exhibit more zeros than predicted by common count distributions like the Poisson or negative binomial. In recent years, there has been considerable interest in methods for analyzing zero-inflated count data in longitudinal or other correlated data settings. A common approach has been to extend zero-inflated Poisson models to include random effects that account for correlation among observations. However, these models have been shown to have a few drawbacks, including interpretability of regression coefficients and numerical instability of fitting algorithms even when the data arise from the assumed model. To address these issues, we propose a model that parameterizes the marginal associations between the count outcome and the covariates as easily interpretable log relative rates, while including random effects to account for correlation among observations. One of the main advantages of this marginal model is that it allows a basis upon which we can directly compare the performance of standard methods that ignore zero inflation with that of a method that explicitly takes zero inflation into account. We present simulations of these various model formulations in terms of bias and variance estimation. Finally, we apply the proposed approach to analyze toxicological data of the effect of emissions on cardiac arrhythmias.     

Two-parameter data acquisition system for rapid slit-scan analysis of mammalian chromosomes

A data acquisition system is described for recording two independent signals simultaneously from a laser-based flow cytometer for rapid slit-scan chromosome analysis. High-aperture microscope optics allow recording of fluorescence distributions along the longest axis of metaphase chromosomes with a spatial resolution better than 1 micron. Fluorescence and small angle forward light scatter as well as dual-wavelength fluorescence signals from Indian muntjac chromosomes stained with propidium iodide (PI) or acridine orange (AO) have been recorded simultaneously. While maintaining the multi-user operation of the computer, photomultiplier signals are digitized at a rate of 400 signals per second, stored temporarily in high-speed cache memories, and transferred subsequently to a minicomputer for further storage. Extensive software packages for data acquisition, analysis, and display of the results are described. Data acquisition is generally done in list mode, allowing complete reconstruction of individual signals (profiles) at any time. The distribution of stained constituents along the chromosomes can be displayed. Furthermore, histograms of various parameters of the input signals may be generated.     

Optimizing transformations for automated,high throughput analysis of flow cytometry data

Background  

In a high throughput setting, effective flow cytometry data analysis depends heavily on proper data preprocessing. While usual preprocessing steps of quality assessment, outlier removal, normalization, and gating have received considerable scrutiny from the community, the influence of data transformation on the output of high throughput analysis has been largely overlooked. Flow cytometry measurements can vary over several orders of magnitude, cell populations can have variances that depend on their mean fluorescence intensities, and may exhibit heavily-skewed distributions. Consequently, the choice of data transformation can influence the output of automated gating. An appropriate data transformation aids in data visualization and gating of cell populations across the range of data. Experience shows that the choice of transformation is data specific. Our goal here is to compare the performance of different transformations applied to flow cytometry data in the context of automated gating in a high throughput, fully automated setting. We examine the most common transformations used in flow cytometry, including the generalized hyperbolic arcsine, biexponential, linlog, and generalized Box-Cox, all within the BioConductor flowCore framework that is widely used in high throughput, automated flow cytometry data analysis. All of these transformations have adjustable parameters whose effects upon the data are non-intuitive for most users. By making some modelling assumptions about the transformed data, we develop maximum likelihood criteria to optimize parameter choice for these different transformations.     

FITC-lectin avidity of Cryptococcus neoformans cell wall and capsular components

Flow cytometry and confocal microscopy were used to quantify and visualize FITC-lectin binding to cell-surface carbohydrate ligands of log and stationary phase acapsular and capsular Cryptococcus neoformans strains. Cell populations demonstrated marked avidity for terminal α-linked mannose and glucose specific FITC-Con A, mannose specific FITC-GNL, as well as N-acetylglucosamine specific FITC-WGA. Exposure to other FITC-lectins specific for mannose, fucose and N-acetylgalactosamine resulted in little cell-surface fluorescence. The nature of cell-surface carbohydrates was investigated further by measurement of the fluorescence from surfaces of log and stationary phase cell populations after exposing them to increasing concentrations of FITC-Con A and FITC-WGA. Cell fluorescence increased significantly with small increases in FITC-Con A and FITC-WGA concentrations attaining reproducible maxima. Measurements of this nature supported calculation of the lectin binding determinants EC 50, Hn, Fmax and relative Bmax values. EC50 values indicated that the yeast-cell surfaces had greatest affinity for FITC-WGA, however, relative Bmax values indicated that greater numbers of Con A binding sites were present on these same cell surfaces. Hn values suggested a co-operative lectin-carbohydrate ligand interaction. Imaging of FITC-Con A and FITC-WGA cell-surface fluorescence by confocal microscopy demonstrated marked localization of both lectins to cell surfaces associated with cell division and maturation, indicative of dynamic carbohydrate ligand exposure and masking. Some fluorescence was associated with entrapment of FITC-Con A by capsular components, but FITC-Con A and FITC-WGA readily penetrated the capsule matrix to bind to the same cell surfaces labelled in acapsular cells.     

Vector electron paramagnetic resonance spectroscopy with first and second harmonic displays of ferrihemoglobin

Superimposed plots of electron paramagnetic resonance spectra with the first and second harmonic displays of ferrihemoglobin at pH 9.1 and 90 K were measured at 20 degree intervals of phase angle using a phase-sensitive detector. The high spin signal in the g = 6 region was observed in both displays, and a small splitting of the signal was found in the calculated amplitude spectrum of the second harmonic display, with g values of 5.95 and 6.05. Low spin signals were observed at g = 2.55, 2.25 and 1.82 in both harmonic displays. A signal in the g = 2.05 region was observed only in the second harmonic display. The signal is probably associated with the low spin spectrum; however, its origin is obscure.     

Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution

We prove that the generalized Poisson distribution GP(theta, eta) (eta > or = 0) is a mixture of Poisson distributions; this is a new property for a distribution which is the topic of the book by Consul (1989). Because we find that the fits to count data of the generalized Poisson and negative binomial distributions are often similar, to understand their differences, we compare the probability mass functions and skewnesses of the generalized Poisson and negative binomial distributions with the first two moments fixed. They have slight differences in many situations, but their zero-inflated distributions, with masses at zero, means and variances fixed, can differ more. These probabilistic comparisons are helpful in selecting a better fitting distribution for modelling count data with long right tails. Through a real example of count data with large zero fraction, we illustrate how the generalized Poisson and negative binomial distributions as well as their zero-inflated distributions can be discriminated.     

Correction of cellular autofluorescence in flow cytometry by mathematical modeling of cellular fluorescence

A method for the correction of background fluorescence in flow cytometry with special relevance to the quantitation of low levels of cellular surface membrane antigens is presented. The method is based on the mathematical modeling of cellular fluorescence distributions of background fluorescence (autofluorescence control or irrelevant antibody control) and total fluorescence (positively stained cells). Algorithms based on two models and utilizing only the routinely available background and total fluorescence histograms are developed and implemented in computer programs. These allow estimation of the fluorescence histogram corresponding exclusively to immunofluorescence staining of the cell surface antigen of interest. Thus, the correction of background fluorescence is effected solely with software processing of routinely available data; no additional hardware or parameter determinations are necessary. Two models were chosen to be physically plausible and to represent extremes in correlation between background and probe fluorescence. Extremes were chosen to assess the solution dependence on model and to provide bounds to the actual solution when no information on correlation is available. Results are presented for both computer simulations and for an actual assay of the CR1 complement receptor on human erythrocytes to test and illustrate the technique. Alternatively, data can be tested assuming a particular model to explore the relationship, if any, between specific and nonspecific fluorescence.     

Measurements of wrist and forearm positions and movements: effect of, and compensation for, goniometer crosstalk.

Flexible biaxial goniometers are extensively used for measuring wrist positions and movements. However, they display an inherent crosstalk error. The aim was to evaluate the effect, of this error, on summary measures used for characterizing manual work. A goniometer and a torsiometer were combined into one device. An algorithm that effectively compensated for crosstalk was developed. Recordings from 25 women, performing five worktasks, were analyzed, both with and without compensation for crosstalk. The errors in the 10th, 50th and 90th percentiles of the flexion/extension distributions were small, on average <1 degrees. The ulnar/radial deviation distributions were weakly dependent on forearm position. The flexion/extension velocity measures were, for the 50th and 90th percentiles, as well as the mean velocity, consistently underestimated by, on average, 3.9%. For ulnar/radial deviation, the velocity errors were less consistent. Mean power frequency, which is a measure of repetitiveness, was insensitive (error <1%) to crosstalk. The forearm supination/pronation angular distributions were wider, and the velocities higher, than for the wrists. Considering wrist/hand exposure in epidemiologic studies, as well as for establishing and surveillance of exposure limits for prevention of work-related upper extremity musculoskeletal disorders, the crosstalk error can, when considering other errors and sources to variation, be disregarded.     

Variance stabilization and normalization for one-color microarray data using a data-driven multiscale approach

MOTIVATION: Many standard statistical techniques are effective on data that are normally distributed with constant variance. Microarray data typically violate these assumptions since they come from non-Gaussian distributions with a non-trivial mean-variance relationship. Several methods have been proposed that transform microarray data to stabilize variance and draw its distribution towards the Gaussian. Some methods, such as log or generalized log, rely on an underlying model for the data. Others, such as the spread-versus-level plot, do not. We propose an alternative data-driven multiscale approach, called the Data-Driven Haar-Fisz for microarrays (DDHFm) with replicates. DDHFm has the advantage of being 'distribution-free' in the sense that no parametric model for the underlying microarray data is required to be specified or estimated; hence, DDHFm can be applied very generally, not just to microarray data. RESULTS: DDHFm achieves very good variance stabilization of microarray data with replicates and produces transformed intensities that are approximately normally distributed. Simulation studies show that it performs better than other existing methods. Application of DDHFm to real one-color cDNA data validates these results. AVAILABILITY: The R package of the Data-Driven Haar-Fisz transform (DDHFm) for microarrays is available in Bioconductor and CRAN.     

Experimental trait mismatches uncover specificity of evolutionary links between multiple signaling traits and their interactions in hummingbirds*

Many animal signals co‐occur, and these signals may coevolve due to their interactive properties. Previous work has demonstrated ecological drivers of evolutionary relationships between signals and the environment, which leads to questions about why specific signal pairs evolved among species that possess multiple signals. We asked whether the coloration of different species was optimized for presentation with its natural behavioral display. We investigated this in “bee” hummingbirds, where males exhibit angle‐dependent structurally‐colored plumage and a stereotyped courtship (shuttle) display, by experimentally creating mismatches between the behavior and plumage of five species and quantifying how these mismatches influenced male color appearance during a display. Specifically, we photographed the plumage from a given species as we moved its feathers through the position‐and‐orientation‐specific courtship display path of other species and quantified the resulting color appearance during the display in order to compare the mismatched color appearance to each species’ natural color appearance. We found that mismatches significantly altered display flashiness (% change in coloration during displays) compared to the natural plumage‐behavior pairings, and that such departures in flashiness were predicted by differences in shuttle behaviors alone. These results illustrate a tight evolutionary relationship between shuttle displays and color flashiness in these hummingbirds. Further, we found that interspecific variation in male plumage, behavior, and natural color appearance predicted deviations between natural and mismatched flashy color appearance. Altogether, our work provides a new method for testing signal coevolution and highlights the complex evolutionary relationships between multiple signals and their interactions.     

Visualization of near-optimal sequence alignments

MOTIVATION: Mathematically optimal alignments do not always properly align active site residues or well-recognized structural elements. Most near-optimal sequence alignment algorithms display alternative alignment paths, rather than the conventional residue-by-residue pairwise alignment. Typically, these methods do not provide mechanisms for finding effectively the most biologically meaningful alignment in the potentially large set of options. RESULTS: We have developed Web-based software that displays near optimal or alternative alignments of two protein or DNA sequences as a continuous moving picture. A WWW interface to a C++ program generates near optimal alignments, which are sent to a Java Applet, which displays them in a series of alignment frames. The Applet aligns residues so that consistently aligned regions remain at a fixed position on the display, while variable regions move. The display can be stopped to examine alignment details.