Detecting and quantifying colocalization of cell surface molecules by single particle fluorescence imaging

Single particle fluorescence imaging (SPFI) uses the high sensitivity of fluorescence to visualize individual molecules that have been selectively labeled with small fluorescent particles. The positions of particles are determined by fitting the intensity profile of their images to a 2-D Gaussian function. We have exploited the positional information obtained from SPFI to develop a method for detecting colocalization of cell surface molecules. This involves labeling two different molecules with different colored fluorophores and determining their positions separately by dual wavelength imaging. The images are analyzed to quantify the overlap of the particle images and hence determine the extent of colocalization of the labeled molecules. Simulated images and experiments with a model system are used to investigate the extent to which colocalization occurs from chance proximity of randomly distributed molecules. A method of correcting for positional shifts that result from chromatic aberration is presented. The technique provides quantification of the extent of colocalization and can detect whether colocalized molecules occur singly or in clusters. We have obtained preliminary data for colocalization of molecules on intact cells. Cells often exhibit particulate autofluorescence that can interfere with the measurements; a method for overcoming this problem by triple wavelength imaging is described.     

A guide to accurate fluorescence microscopy colocalization measurements

Biomolecular interactions are fundamental to the vast majority of cellular processes, and identification of the major interacting components is usually the first step toward an understanding of the mechanisms that govern various cell functions. Thus, statistical image analyses that can be performed on fluorescence microscopy images of fixed or live cells have been routinely applied for biophysical and cell biological studies. These approaches measure the fraction of interacting particles by analyzing dual color fluorescence images for colocalized pixels. Colocalization algorithms have proven to be effective, although the dynamic range and accuracy of these measurements has never been well established. Spatial image cross-correlation spectroscopy (ICCS), which cross-correlates spatial intensity fluctuations recorded in images from two detection channels simultaneously, has also recently been shown to be an effective measure of colocalization as well. Through simulations, imaging of fluorescent antibodies adsorbed on glass and cell measurements, we show that ICCS performs much better than standard colocalization algorithms at moderate to high densities of particles, which are often encountered in cellular systems. Furthermore, it was found that the density ratio between the two labeled species of interest plays a major role in the accuracy of the colocalization analysis. By applying a direct and systematic comparison between the standard, fluorescence microscopy colocalization algorithm and spatial ICCS, we show regimes where each approach is applicable, and more importantly, where they fail to yield accurate results.     

New algorithm to determine true colocalization in combination with image restoration and time-lapse confocal microscopy to MAP kinases in mitochondria

The subcellular localization and physiological functions of biomolecules are closely related and thus it is crucial to precisely determine the distribution of different molecules inside the intracellular structures. This is frequently accomplished by fluorescence microscopy with well-characterized markers and posterior evaluation of the signal colocalization. Rigorous study of colocalization requires statistical analysis of the data, albeit yet no single technique has been established as a standard method. Indeed, the few methods currently available are only accurate in images with particular characteristics. Here, we introduce a new algorithm to automatically obtain the true colocalization between images that is suitable for a wide variety of biological situations. To proceed, the algorithm contemplates the individual contribution of each pixel's fluorescence intensity in a pair of images to the overall Pearsońs correlation and Manders' overlap coefficients. The accuracy and reliability of the algorithm was validated on both simulated and real images that reflected the characteristics of a range of biological samples. We used this algorithm in combination with image restoration by deconvolution and time-lapse confocal microscopy to address the localization of MEK1 in the mitochondria of different cell lines. Appraising the previously described behavior of Akt1 corroborated the reliability of the combined use of these techniques. Together, the present work provides a novel statistical approach to accurately and reliably determine the colocalization in a variety of biological images.     

Empirically-determined statistical significance of the Baillie and Pilcher (1973) t statistic for British Isles oak

The “Belfast method” of statistical crossdating has been widely used in the British Isles since public domain software was released by Baillie and Pilcher (1973). Although the conceptual merits of the approach are accepted, the details of the methodology have been severely criticised, including the fact that serially correlated tree-ring time series violate a fundamental requirement for the use of Students t statistic as a measure of statistical significance. An unfortunate consequence of this has been that t values are often published without reference to the associated probability of the specific value being obtained by chance. Here we present an empirical method for determining statistical significance from analysis of many misaligned inter-site correlations amongst over 2000 dated British Isles oak chronologies. Results indicate that a t value of 3.5 has a probability of about one in 600 for series lengths of 100+ years, but this declines (becomes less rare) as series length decreases.     

Fluorescence imaging for monitoring the colocalization of two single molecules in living cells

The interaction, binding, and colocalization of two or more molecules in living cells are essential aspects of many biological molecular processes, and single-molecule technologies for investigating these processes in live cells, if successfully developed, would become very powerful tools. Here, we developed simultaneous, dual-color, single fluorescent molecule colocalization imaging, to quantitatively detect the colocalization of two species of individual molecules. We first established a method for spatially correcting the two full images synchronously obtained in two different colors, and then for overlaying them with an accuracy of 13 nm. By further assessing the precision of the position determination, and the signal/noise and signal/background ratios, we found that two single molecules in dual color can be colocalized to within 64-100 nm (68-90% detectability) in the membrane of cells for GFP and Alexa633. The detectability of true colocalization at the molecular level and the erroneous inclusion of incidental approaches of two molecules as colocalization have to be compromised at different levels in each experiment, depending on its purpose. This technique was successfully demonstrated in living cells in culture, monitoring colocalization of single molecules of E-cadherin fused with GFP diffusing in the plasma membrane with single molecules of Alexa633 conjugated to anti-E-cadherin Fab externally added to the culture medium. This work established a benchmark for monitoring the colocalization of two single molecules, which can be applied to wide ranges of studies for molecular interactions, both at the levels of single molecules and collections of molecules.     

A consistent metric for nestedness analysis in ecological systems: reconciling concept and measurement

Nestedness has been widely reported for both metacommunities and networks of interacting species. Even though the concept of this ecological pattern has been well-defined, there are several metrics by which it can be quantified. We noted that current metrics do not correctly quantify two major properties of nestedness: (1) whether marginal totals (i.e. fills) differ among columns and/or among rows, and (2) whether the presences (1's) in less-filled columns and rows coincide, respectively, with those found in the more-filled columns and rows. We propose a new metric directly based on these properties and compare its behavior with that of the most used metrics, using a set of model matrices ranging from highly-nested to alternative structures in which no nestedness should be detected. We also used an empirical dataset to explore possible biases generated by the metrics as well as to evaluate correlations between metrics. We found that nestedness has been quantified by metrics that inappropriately detect this pattern, even for matrices in which there is no nestedness. In addition, the most used metrics are prone to type I statistical errors while our new metric has better statistical properties and consistently rejects a nested pattern for different types of random matrices. The analysis of the empirical data showed that two nestedness metrics, matrix temperature and the discrepancy measure, tend to overestimate the degrees of nestedness in metacommunities. We emphasize and discuss some implications of these biases for the theoretical understanding of the processes shaping species interaction networks and metacommunity structure.     

Deconvolving single-molecule intensity distributions for quantitative microscopy measurements

In fluorescence microscopy, images often contain puncta in which the fluorescent molecules are spatially clustered. This article describes a method that uses single-molecule intensity distributions to deconvolve the number of fluorophores present in fluorescent puncta as a way to "count" protein number. This method requires a determination of the correct statistical relationship between the single-molecule and single-puncta intensity distributions. Once the correct relationship has been determined, basis histograms can be generated from the single-molecule intensity distribution to fit the puncta distribution. Simulated data were used to demonstrate procedures to determine this relationship, and to test the methodology. This method has the advantages of single-molecule measurements, providing both the mean and variation in molecules per puncta. This methodology has been tested with the avidin-biocytin binding system for which the best-fit distribution of biocytins in the sample puncta was in good agreement with a bulk determination of the avidin-biocytin binding ratio.     

Total ancestry measure: quantifying the similarity in tree-like classification, with genomic applications

MOTIVATION: Many classifications of protein function such as Gene Ontology (GO) are organized in directed acyclic graph (DAG) structures. In these classifications, the proteins are terminal leaf nodes; the categories 'above' them are functional annotations at various levels of specialization and the computation of a numerical measure of relatedness between two arbitrary proteins is an important proteomics problem. Moreover, analogous problems are important in other contexts in large-scale information organization--e.g. the Wikipedia online encyclopedia and the Yahoo and DMOZ web page classification schemes. RESULTS: Here we develop a simple probabilistic approach for computing this relatedness quantity, which we call the total ancestry method. Our measure is based on counting the number of leaf nodes that share exactly the same set of 'higher up' category nodes in comparison to the total number of classified pairs (i.e. the chance for the same total ancestry). We show such a measure is associated with a power-law distribution, allowing for the quick assessment of the statistical significance of shared functional annotations. We formally compare it with other quantitative functional similarity measures (such as, shortest path within a DAG, lowest common ancestor shared and Azuaje's information-theoretic similarity) and provide concrete metrics to assess differences. Finally, we provide a practical implementation for our total ancestry measure for GO and the MIPS functional catalog and give two applications of it in specific functional genomics contexts. AVAILABILITY: The implementations and results are available through our supplementary website at: http://gersteinlab.org/proj/funcsim. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.     

EDENetworks: A user‐friendly software to build and analyse networks in biogeography,ecology and population genetics

The recent application of graph‐based network theory analysis to biogeography, community ecology and population genetics has created a need for user‐friendly software, which would allow a wider accessibility to and adaptation of these methods. EDENetworks aims to fill this void by providing an easy‐to‐use interface for the whole analysis pipeline of ecological and evolutionary networks starting from matrices of species distributions, genotypes, bacterial OTUs or populations characterized genetically. The user can choose between several different ecological distance metrics, such as Bray‐Curtis or Sorensen distance, or population genetic metrics such as F_ST or Goldstein distances, to turn the raw data into a distance/dissimilarity matrix. This matrix is then transformed into a network by manual or automatic thresholding based on percolation theory or by building the minimum spanning tree. The networks can be visualized along with auxiliary data and analysed with various metrics such as degree, clustering coefficient, assortativity and betweenness centrality. The statistical significance of the results can be estimated either by resampling the original biological data or by null models based on permutations of the data.     

Detection of blob objects in microscopic zebrafish images based on gradient vector diffusion.

The zebrafish has become an important vertebrate animal model for the study of developmental biology, functional genomics, and disease mechanisms. It is also being used for drug discovery. Computerized detection of blob objects has been one of the important tasks in quantitative phenotyping of zebrafish. We present a new automated method that is able to detect blob objects, such as nuclei or cells in microscopic zebrafish images. This method is composed of three key steps. The first step is to produce a diffused gradient vector field by a physical elastic deformable model. In the second step, the flux image is computed on the diffused gradient vector field. The third step performs thresholding and nonmaximum suppression based on the flux image. We report the validation and experimental results of this method using zebrafish image datasets from three independent research labs. Both sensitivity and specificity of this method are over 90%. This method is able to differentiate closely juxtaposed or connected blob objects, with high sensitivity and specificity in different situations. It is characterized by a good, consistent performance in blob object detection.     

A statistical procedure to assess the significance level of barriers to gene flow

Although several methods are available to study the extent of isolation by distance （IBD） among natural populations, comparatively few exist to detect the presence of sharp genetic breaks in genetic distance datasets. In recent years, Monmonier＇s maximum-difference algorithm has been increasingly used by population geneticists. However, this method does not provide means to measure the statistical significance of such barriers, nor to determine their relative contribution to population differentiation with respect to IBD. Here, we propose an approach to assess the significance of genetic boundaries. The method is based on the calculation of a multiple regression from distance matrices, where binary matrices represent putative genetic barriers to test, in addition to geographic and genetic distances. Simulation results suggest that this method reliably detects the presence of genetic barriers, even in situations where IBD is also significant. We also illustrate the methodology by analyzing previously published datasets. Conclusions about the importance of genetic barriers can be misleading if one does not take into consideration their relative contribution to the overall genetic structure of species.     

Accounting for the causal basis of collinearity when measuring the effects of habitat loss versus habitat fragmentation

Collinearity among metrics of habitat loss and habitat fragmentation is typically treated as a nuisance in landscape ecology, and it is the norm to use statistical approaches that remove collinear information prior to estimating model parameters. However, collinearity may arise from causal relationships among landscape metrics and may therefore signal the occurrence of indirect effects (where one model predictor influences the response variable by driving changes in another influential predictor). Here we suggest that, far from being merely a statistical nuisance, collinearity may be crucial for accurately quantifying the effects of habitat loss versus habitat fragmentation. We use simulation modelling to create datasets of collinear landscape metrics in which collinearity arose from causal relationships, then test the ability of two statistical approaches to estimate the effects of these metrics on a simulated response variable: 1) multiple regression, which statistically removes collinearity, and was identified in a recent study as the best approach for estimating the effects of collinear landscape metrics (although this study did not account for any indirect effects implied by collinearity among metrics); and 2) path analysis, which accounts for the causal basis of collinearity. In agreement with this previous study, we found that multiple regression gave unbiased estimates of direct effects (effects not mediated by other model predictors). However, it gave biased estimates of total (direct + indirect) effects when indirect effects occurred. In contrast, path analysis reliably identified the causal basis of collinearity and gave unbiased estimates of direct, indirect, and total effects. We suggest that effective research on the impacts of habitat loss versus fragmentation will often require tools that can empirically test whether collinear landscape metrics are causally related, and if so, account for the indirect effects that these causal relationships imply. Path analysis, but not multiple regression, provides such a tool.     

A nonhuman primate's perception of object relations: experiments on cottontop tamarins, Saguinus oedipus

Objects in nature often have spatial and functional relationships with other objects. For example, fruit may be connected to tree branches, bushes sometimes function as landmarks for home, and stones are functionally associated with nuts when they are used to crack the nuts open. Although animals may use the spatial and functional relationships between specific objects, it is important for ethologists interested in cognitive mechanisms to ask whether animals understand the spatial relationship between objects in a more general and abstract way. In this experiment, we ask whether a small New World monkey, the cottontop tamarin, is capable of perceiving the abstract relational concept of ‘connectedness’. Using a traditional operant paradigm, subjects were required to press one button to images with connected objects, and another button to images with separated objects. In Phase 1 of the experiment, subjects received training with only one connected and one separated image. Following training, probe images were presented in which features such as colour, texture and shape were systematically manipulated to determine which features were more important in stimulus classification. Accuracies and reaction times of responses were recorded. On the basis of their performance, the tamarins appeared to recognize that changes in the colour or texture of two objects plays no functional role in determining whether such objects are connected or separated. In contrast, changes in the shape and distance between two objects does play an important functional role, and the tamarins appeared to be sensitive to such changes. In Phase 2, subjects received training with a larger set of images. After this training, classification accuracy remained significantly above chance with most probes, suggesting that the tamarins had acquired a more general connectedness concept. In Phase 3, novel images were presented. Classification accuracy was significantly above chance for many of the novel images. Overall, results suggest that tamarins perceive spatial relationships between stimuli to some extent and can classify images based in part on their spatial relationship. Other recent experiments have shown that cottontop tamarins respond to spatial relationships even better than in the current experiment when they have to act directly on the objects. The difference between these results suggests that tamarins perceive the spatial relationships between objects more readily in the context of an ecologically valid problem.     

Optimization of Regularization Parameters in Compressed Sensing of Magnetic Resonance Angiography: Can Statistical Image Metrics Mimic Radiologists' Perception?

In Compressed Sensing (CS) of MRI, optimization of the regularization parameters is not a trivial task. We aimed to establish a method that could determine the optimal weights for regularization parameters in CS of time-of-flight MR angiography (TOF-MRA) by comparing various image metrics with radiologists’ visual evaluation. TOF-MRA of a healthy volunteer was scanned using a 3T-MR system. Images were reconstructed by CS from retrospectively under-sampled data by varying the weights for the L1 norm of wavelet coefficients and that of total variation. The reconstructed images were evaluated both quantitatively by statistical image metrics including structural similarity (SSIM), scale invariant feature transform (SIFT) and contrast-to-noise ratio (CNR), and qualitatively by radiologists’ scoring. The results of quantitative metrics and qualitative scorings were compared. SSIM and SIFT in conjunction with brain masks and CNR of artery-to-parenchyma correlated very well with radiologists’ visual evaluation. By carefully selecting a region to measure, we have shown that statistical image metrics can reflect radiologists’ visual evaluation, thus enabling an appropriate optimization of regularization parameters for CS.     

Automated measurements on cell nuclei in tissue sections. Validation procedures

A methodology was developed for fully automated measurements of nuclear features in Feulgen-stained tissue sections by means of videomicroscopy and image analysis. Segmentation is performed within one minute on 512 X 512 optical density (OD) images covering about 75 nuclei, resulting in a graphic contour overlay. The corresponding image subset is scanned by an object data extraction program, producing the raw figures for statistical interpretation. The segmentation software was evaluated by three tests, involving comparison with manual delineation and assessment of the influence of OD. Two case studies (ACTH-stimulated adrenal cortex and pancreatic carcinoma) illustrate the biologic accuracy and medical significance of the described methodology.     

A quantitative determination of multi-protein interactions by the analysis of confocal images using a pixel-by-pixel assessment algorithm

MOTIVATION: Recent advances in confocal microscopy have allowed scientists to assess the expression, and to some extent, the interaction/colocalization of multiple molecules within cells and tissues. In some instances, accurately quantifying the colocalization of two or more proteins may be critical. This can require the acquisition of multiple Z plane images (Z stacks) throughout a specimen and, as such, we report here the successful development of a freeware, open-source image analysis tool, IMAJIN_COLOC, developed in PERL (v. 5.8, build 806), using the PERLMagick libraries (ImageMagick). Using a pixel-by-pixel analysis algorithm, IMAJIN_COLOC can analyze images for antigen expression (any number of colors) and can measure all possible combinations of colocalization for up to three colors by analyzing a Z stack gallery acquired for each sample. The simultaneous (i.e. in a single pass) analysis of three-color colocalization, and batch analysis capabilities are distinctive features of this program. RESULTS: A control image, containing known individual and colocalized pixel counts, was used to validate the accuracy of IMAJIN_COLOC. As further validation, pixel counts and colocalization values from the control image were compared to those obtained with the software packaged with the Zeiss laser-scanning microscope (LSM AIM, version 3.2). The values from both programs were found to be identical. To demonstrate the applicability of this program in addressing novel biological questions, we examined the role of neurons in eliciting an immune reaction in response to viral infection. Specifically, we successfully examined expression of the chemokine RANTES in measles virus (MV) infected hippocampal neurons and quantified changes in RANTES production throughout the disease period. The resultant quantitative data were also evaluated visually, using a gif image created during the analysis. AVAILABILITY: PERL (ActivePerl, version 5.8) is available at activestate.com; the PERLMagick libraries are available at imagemagick.org, and IMAJIN_COLOC, the source code and user documentation can be downloaded from http://www.fda.gov/cber/research/imaging/imageanalysis.htm.     

Using Hamming Distance as Information for SNP-Sets Clustering and Testing in Disease Association Studies

The availability of high-throughput genomic data has led to several challenges in recent genetic association studies, including the large number of genetic variants that must be considered and the computational complexity in statistical analyses. Tackling these problems with a marker-set study such as SNP-set analysis can be an efficient solution. To construct SNP-sets, we first propose a clustering algorithm, which employs Hamming distance to measure the similarity between strings of SNP genotypes and evaluates whether the given SNPs or SNP-sets should be clustered. A dendrogram can then be constructed based on such distance measure, and the number of clusters can be determined. With the resulting SNP-sets, we next develop an association test HDAT to examine susceptibility to the disease of interest. This proposed test assesses, based on Hamming distance, whether the similarity between a diseased and a normal individual differs from the similarity between two individuals of the same disease status. In our proposed methodology, only genotype information is needed. No inference of haplotypes is required, and SNPs under consideration do not need to locate in nearby regions. The proposed clustering algorithm and association test are illustrated with applications and simulation studies. As compared with other existing methods, the clustering algorithm is faster and better at identifying sets containing SNPs exerting a similar effect. In addition, the simulation studies demonstrated that the proposed test works well for SNP-sets containing a large proportion of neutral SNPs. Furthermore, employing the clustering algorithm before testing a large set of data improves the knowledge in confining the genetic regions for susceptible genetic markers.     

Colocalization of fluorescent markers in confocal microscope images of plant cells

This protocol describes the steps needed to perform quantitative statistical colocalization on two-color confocal images, specifically of plant cells. The procedure includes a calibration test to check the chromatic alignment of the confocal microscope. A software tool is provided to calculate the Pearson and Spearman correlation coefficients ('Pearson-Spearman correlation colocalization' ImageJ plug-in) across regions of interest within the image. Steps are included to help the user practice using the software. The result is a quantitative estimate of the amount of colocalization in the images. Manual masking takes about 1-15 min per image, depending on the detail required, and calculating the correlation coefficients is almost instantaneous. Examples of suitable dyes for such two-color colocalization include Oregon Green or Alexa Fluor 488 dyes in the green range (excited with 488-nm laser line) and Alexa Fluor 555 dye in the red range (excited with 543-nm laser line).     

Recent advances in quantitative colocalization analysis: Focus on neuroscience

Quantitative colocalization analysis is an advanced digital imaging tool to characterize the spatial expression of molecules of interest in immunofluorescence images obtained using confocal microscopes. It began from simple pixel counting and, with introduction of specialized algorithms, transformed into a powerful image analyzing technique capable of identifying the exact locations of various molecules in tissues and cells and describing their subtle changes in dynamics. Applications of quantitative colocalization in the field of neuroscience proved to be particularly informative by helping to obtain observations not otherwise achievable using other techniques. In this article, we review the background and applicability of quantitative colocalization with special focus on neuroscience research.