SEARCH

SEARCH BY CITATION

Keywords:

  • fluorescence microscopy;
  • spectral image analysis;
  • colocalization;
  • rolling circle products

Abstract

  1. Top of page
  2. Abstract
  3. Rolling Circle Products
  4. Multiplexing and Spectral Angles
  5. Imaging Multicolored RCPs in Wide-Field Fluorescence Microscopy
  6. Materials and Methods
  7. Results
  8. Conclusions and Discussion
  9. Acknowledgements
  10. Literature Cited
  11. Supporting Information

Specific single-molecule detection opens new possibilities in genomics and proteomics, and automated image analysis is needed for accurate quantification. This work presents image analysis methods for the detection and classification of single molecules and single-molecule interactions detected using padlock probes or proximity ligation. We use simple, widespread, and cost-efficient wide-field microscopy and increase detection multiplexity by labeling detection events with combinations of fluorescence dyes. The mathematical model presented herein can classify the resulting point-like signals in dual-channel images by spectral angles without discriminating between low and high intensity. We evaluate the methods on experiments with known signal classes and compare to classical classification algorithms based on intensity thresholding. We also demonstrate how the methods can be used as tools to evaluate biochemical protocols by measuring detection probe quality and accuracy. Finally, the method is used to evaluate single-molecule detection events in situ. © 2011 International Society for Advancement of Cytometry

Quantitative image cytometry is used to measure how, where, and when biomolecules occur and interact, helping us understand their structure and function at subcellular resolution. Labeling of biomolecules with detection molecules carrying fluorophores of a variety of colors permits simultaneous investigation of multiple properties. The degree of multiplexing is generally limited by the number of available spectral channels, but combinations of fluorophores can increase the number of different biomolecules that we can observe at the same time. This work presents a wide-field fluorescence microscopy image processing method for color-based classification of point-like signals originating from single-molecule detection events. The approach combines detection of point-like signals (1) and spectral angle-based classification (2) using a novel approach for automated angle histogram thresholding.

Rolling Circle Products

  1. Top of page
  2. Abstract
  3. Rolling Circle Products
  4. Multiplexing and Spectral Angles
  5. Imaging Multicolored RCPs in Wide-Field Fluorescence Microscopy
  6. Materials and Methods
  7. Results
  8. Conclusions and Discussion
  9. Acknowledgements
  10. Literature Cited
  11. Supporting Information

Single-molecule detection using rolling circle amplification (RCA) converts a single recognition event into a point-like concentration of signals easily distinguished from low-frequency background signals such as autofluorescence. As shown in Figure 1, either a padlock probe (3, 4), a selector probe for detection of a predefined DNA or cDNA sequence (5), or proximity ligation (6, 7) mediates a recognition event for detecting protein modifications and biomolecule proximity. Each type of recognition event leads to the formation of a DNA circle that serves as a template for RCA, producing concatemeric copies consisting of hundreds of repeats complementary to the circular sequence, folding into a ball of single-stranded DNA, a so-called Rolling Circle Product (RCP). These RCPs can be visualized by hybridization with fluorescence-labeled probes. Information about the target molecule can also be encoded in the sequence of the DNA circle and decoded with the help of differentially labeled detection oligonucleotides (8, 9). Depending on the demands of the assay, the circularization is performed either in solution or on a solid substrate, that is, on fixed cells or tissues.

thumbnail image

Figure 1. Amplified single molecule detection using RCA. A: Single molecules are detected by proximity ligation, padlock probes, or selector probes. B: Upon detection of the target molecules, a circular DNA molecule is created by ligation. One or several detection sequences are incorporated in the DNA molecule. C: Subsequently, a RCA is primed, resulting in ∼1,000 concatemeric copies of the original DNA circle. This long single-stranded DNA-molecule (RCP) is visualized by hybridization of fluorescently labeled detection oligonucleotides to the detection sequences. D: Every RCP collapses into a bulk of DNA and is visible as distinct bright spot in a fluorescent microscope. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Download figure to PowerPoint

The signal intensity from fluorescent-labeled RCPs may vary due to variations in the size of the RCPs caused by suboptimal amplification conditions during RCA, and variations in the target sequence for fluorescence hybridization (10) caused by imperfect oligonucleotide synthesis. Variations in background fluorescence at different sites of the samples also influence the appearance of the signals. Regardless of these variations (that also affect ratios of intensities), we consider all RCPs equally reliable, because each one is derived from a single detection event. Therefore, to allow detection and correct classification of either single or double-colored RCPs, we devise a method for the classification of point-like signals in dual-channel wide-field fluorescence microscopy images.

Multiplexing and Spectral Angles

  1. Top of page
  2. Abstract
  3. Rolling Circle Products
  4. Multiplexing and Spectral Angles
  5. Imaging Multicolored RCPs in Wide-Field Fluorescence Microscopy
  6. Materials and Methods
  7. Results
  8. Conclusions and Discussion
  9. Acknowledgements
  10. Literature Cited
  11. Supporting Information

The degree of multiplexing is limited by how many fluorescent color dyes are distinguishable with microscope filters, just as in spectral unmixing methods (11). Multiplexing is increased by several consecutive hybridizations with fluorescent dyes, allowing the degree of multiplexing to exceed the number of fluorophores (8). Similarly, double-colored signals, showed in Figure 1D (right), have the advantage over single fluorescent colors as the incorporation of a hybridization site for an additional fluorescent color dye in the RCP can serve as a control signal to verify that the signal originates from the targeted interaction. Hence, only double-colored RCPs can be considered as true signals.

To classify multicolored RCPs, we propose classification determined by the ratio of fluorescence light intensity from different color dyes, described as vector directions in the spectral cube, that is, spectral angles. Even though using a similar approach in multicolor FISH imaging was previously criticized (12, 13) as intensity ratios of fluorphores can change at high concentrations, we are certain that RCP intensity depends on the number of concatemeric copies of the circle sequence. In addition, while popular methods for, for example, the quantification of protein–DNA interactions (14) rely on fluorophore interactions, here, fluorescent dyes label single-molecule events sparsely distributed over a larger area, hence reducing the risk that resonance energy transfer affects the spectral profile of colocalized dyes. Therefore, during RCA, the spectrum of the initial combination of fluorophores is multiplied, and intensity ratios, or spectral angles, will vary within boundaries determined by the level of noise. As shown in Figure 2, angle-based thresholding is more robust criterion for classification. Irrespectively of whether the problem is multiplexing, ratio labeling, or colocalization, signals should be classified by their spectral angles (2).

thumbnail image

Figure 2. Artificial images showing RCPs with increasing numbers of concatemeric copies of the circle sequence, affecting signal intensity from left to right. The noise follows Poisson distribution. A: If all RCPs are single-colored, signals can be detected in separate grayscale images. B: Different combinations of fluorescent dyes can be used for labeling as defined by the construction of the RCP template sequence, that is, red, red + green, and green or (C) red, red + red + green, red + green, red + green + green, and green. The solid and the dashed lines outline the signals that fall in the red-green class when applying intensity (blue solid line) and angle thresholds (yellow dashed line), respectively. D, E: Scatterplots of red and green pixel intensities from images B and C, respectively. It is not possible to classify double-colored (red + green = yellow) signals correctly using the intensity thresholds shown as solid blue lines. F, G: Scatterplots of red and green pixel intensities from images B and C, respectively, and corresponding angle-based thresholds (dashed yellow lines) extracted from (H, I) angle based histograms of images B and C. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Download figure to PowerPoint

Imaging Multicolored RCPs in Wide-Field Fluorescence Microscopy

  1. Top of page
  2. Abstract
  3. Rolling Circle Products
  4. Multiplexing and Spectral Angles
  5. Imaging Multicolored RCPs in Wide-Field Fluorescence Microscopy
  6. Materials and Methods
  7. Results
  8. Conclusions and Discussion
  9. Acknowledgements
  10. Literature Cited
  11. Supporting Information

Multicolored RCPs are imaged with a microscope CCD array whose measured intensity is linearly dependent of the number of photons emitted from imaged position, preserving predefined ratios of fluorescent colors in the resulting digital image. Exposure times should be chosen according to the dynamic range of the CCD array to suppress the effect of photon noise. Long exposure times may result in signals that look better visually, but the sensor will easily be saturated making quantitative analysis of spectral information impossible. Imaging of color or spectral information is sensitive to chromatic aberrations as the same objective lens is used for all channels. Lateral chromatic aberrations result in incorrectly overlaid channels, splitting one double-colored signal into two single-colored signals. In cases where this type of chromatic aberrations is significant, compensation as an image preprocessing step is necessary (15). On the other hand, chromatic aberrations caused by tilt, that is, when the optical axis is not perfectly orthogonal to the sample plane, they can be corrected by a rigid transformation. Uneven background, autofluorescence, and spectral bleed-through (also known as cross-talk) can also affect the quality of the results. Therefore, it is important to minimize such effects during image acquisition, for example, focusing the lamp to the plane of the aperture diaphragm before acquisition, avoiding changes in environmental illumination, and choosing appropriate filter sets. Naturally, background levels often cannot be completely suppressed, but should be kept rather constant during an experiment.

The most common techniques for quantification of dual-coloring in digital images, seen as colocalization of fluorescent dyes, are based on manual (16) or automated (17) intensity thresholding, that is, providing pixel classification rules determined by intensity thresholds Tr and Tg. Another family of algorithms is object-based quantification of colocalization (18, 19). After object detection, the methods deal with binary images where spectral information and object intensities are completely neglected, and detected objects are merged into colocalized objects if they overlap as determined by a nearest-neighbor distance. In color-image analysis, such methods are often considered as “monochromatic” (20), and they do not lend themselves to quantify variations in stain intensity ratios. Another family of methods comprises correlation-based techniques. Even though several papers claim that correlation-based techniques are more accurate than other methods for some biological applications (21, 22), it is not possible to perform classification of individual signals based on one measure of overall correlation of images.

In 2009, we showed that methods based on intensity thresholding are very sensitive to signal intensity variation and noise and proposed an alternative method that provides pixel classification rules based on angle thresholds, Ar and Ag (2). In this work, we extend our previous work to include automated determination of optimal angle thresholds for signal classification, based on a multiscale pyramid search. To evaluate the applicability of the proposed automated methods for the classification of RCPs (and potentially other single molecules), we compare the results with threshold-based classification and visual inspection of a mixture of single and double-colored signals. Furthermore, we show how the methods can be used as a tool for comparison and evaluation of biochemical protocols. We evaluate a dilution series of single-colored signals in a background of double-colored signals to determine the dynamic range of the detection protocol. Here, we notice variations in staining intensity ratios and hypothesize that these variations could be due to errors during oligonucleotide synthesis (23).

We investigate this further by comparing images of RCPs generated from synthetic and clonal oligonucleotide synthesis, hypothesizing that clonally prepared oligonucleotides introduce fewer errors (10, 24). Finally, we apply our methods for classification of RCPs derived from detection of DNA–protein interactions in situ as a test for its applicability in a more complex environment like a cell where autofluorescence will also affect the analysis. In a wider context, the goal of this work is to show that data analysis is relevant for all steps of the development of biochemical methods, and imaging, image processing, and quantitative data analysis should be an integral part of protocol.

Materials and Methods

  1. Top of page
  2. Abstract
  3. Rolling Circle Products
  4. Multiplexing and Spectral Angles
  5. Imaging Multicolored RCPs in Wide-Field Fluorescence Microscopy
  6. Materials and Methods
  7. Results
  8. Conclusions and Discussion
  9. Acknowledgements
  10. Literature Cited
  11. Supporting Information

Image Acquisition

We generate RCPs using padlock probes and spread them on glass slides (8) or generate them locally from protein–DNA-interaction detection in situ, within fixed cells (Weibrecht et al., in preparation). Images of RCPs are acquired with a Zeiss Axioplan 2 epifluorescence microscope and the AxioCam MRm CCD sensor and either a 20×/0.8 Plan Achromat lens (immobilized RCPs) or a 40×/1.3 oil Plan Neofluar lens (protein–DNA interactions) together with a predefined filter set [FITC: excitation filter (ExF): HQ480/40×, dichroic beam splitter (DBS): Q505LP, Emission filter (EmF): HQ535/50m; Cy3: ExF: HQ545/30×, DBS: Q570LP, EmF: HQ610/75m; DAPI: ExF: D350/50×; DBS: 400DCLP, EmF: D460/50m] to match dyes used in sample preparation. The lateral image resolution is 320 nm and 160 nm for immobilized RCPs and protein–DNA interactions, respectively. This corresponds to the optical resolution limited by the Rayleigh criterion for wide-field microscopes and is significantly smaller than the micron-sized signal from a labeled RCP. Samples with RCPs immobilized on glass are almost flat, the third spatial dimension can be ignored, and therefore only one focal plane needs imaging. The image acquisition follows the practical guidelines described earlier.

Image Analysis

Preprocessing

The background is suppressed by subtracting the median intensity from each image, setting values less than zero equal to zero. Lateral chromatic aberrations (less than one pixel in both x and y directions) are reduced by shifting one image channel by a fraction of a pixel in both x and y directions and interpolating pixel intensities until correlation is maximized. This is successful as long as both channels contain signals. Colocalized RCPs located in two different channels should have the same intensity range. Unless the exposure times are carefully chosen to ensure similar intensity range in both channels, intensity scaling factors are determined from a training image showing colocalized signals and then applied to all images in the experiment.

Detection of point-like signals

Individual signals are detected by stable wave detection, that is, filtering the image with cosine and sine filters derived from the first harmonic of the Fourier coefficients over a range of periods P (1). If the shape of the 2D cosine filter matches the area around a local maximum, the pixel is a candidate for a true signal as it is a local extremum. Thereafter, the 2D sine filters test the slope around the pixel of interest, thus rejecting false positives and separating merged signals. Finally, signals that cannot be distinguished from photon noise are excluded by an intensity threshold.

In addition to localization of signals, the method is used to correct for longitudinal chromatic aberrations, caused by the fact that signals emitting light of different wavelengths will end up in different focal planes. The shape of the point-like signal smoothed by the point spread function of the device depends on the focal depth, that is, if the specimen is focused using the “red” channel, point-like signals in the “green” channel are slightly out of focus. The range of periods for the Fourier coefficients is therefore optimized individually for each color channel using a set of training images. For instance, when we use the “red” Cy3 channel for focusing the microscope, point-like signals are detected by filter with periods PR ranging from 7 to 19, while signals in the “green” FITC channel are more smoothed by the point-spread function and therefore detected by PG defined by the range of periods 11–23.

Angle histogram

If a dual-color red-green image is thought of as a matrix of ordered couples (R,G) from a color spectrum varying from red (0°) to yellow (45°) to green (90°), the spectral angle is defined as the angular deviation of the pixel (R,G) from the red intensity axes of a scatterplot as shown in Figures 2D and 2E. Signal detection masks associated with signal detection in the two channels are overlaid using a simple Boolean union operation, and the corresponding (R,G) values are used to build an angle histogram. An angle histogram, compensated for quantification noise, is a histogram where each bin represents a given angle interval (2), and the shape of this one-dimensional representation of spectral information facilitates automated classification. For instance, the two-dimensional histogram shown in Figure 2F is decomposed into the one-dimensional angle histogram shown in Figure 2H.

In the original method for creating angle histograms, called SpecDec, nonlinear histograms are used to reduce the number of bins necessary for preserving spectral information with minimum memory requirements. In this implementation, we have chosen a linear angle histogram in order to easily apply the smoothing step of the novel angle histogram segmentation algorithm presented below. The purpose of this step is to both transform and preserve spectral information; therefore, the number of bins in the histogram should be rather high, for example, N = 800 as the theoretical minimum angle, 45°-arctan(254/255) = 0.113°, represents one bin in the 0°–90° interval.

Automated signal classification

The novel signal classification approach presented here is an automated thresholding of the angle histogram from the previous step, and different signal classes are defined by “angle thresholds.” We combine morphological processing (25) with a modification of the multiscale segmentation procedure (26, 27) and refer to this thresholding method as multiscale Spectral Decomposition or msSpecDec.

We start by splitting the initial angle histogram into two halves and search for the threshold Ar separating single-colored “red” and double-colored “yellow” signals in the left half and dually search for the threshold Ag separating single-colored “green” and double-colored “yellow” signals in the right half. For each step of the search, we apply morphological operators in the form of geodesic dilation combined with scale-space transformation to preserve relevant geometrical structures in the histogram. The original histogram f is thus smoothed until a convergence criterion is reached (i.e., two classes are detected), and the final threshold is refined by iteratively moving back to the original scale. Figure 3 shows how a scale-space pyramid is used to find Ar, the angle threshold separating “red” and “yellow” signals.

thumbnail image

Figure 3. A multiscale pyramid of an angle histogram f showing intermediate results of geodesic dilatation and scale-space transformation (marked as δg) as well as angle threshold search, from preliminary, Ar0, to final angle threshold Ar. Note that spurious minima are subsequently suppressed, while wide regional minima, that is, potential threshold candidates, remain at each of the scales until they are, one by another, merged with one of the dominant distributions in the histogram. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Download figure to PowerPoint

The following two-step procedure is initiated with f0 = f and repeated until the convergence criterion is reached:

Geodesic dilation (step 1)

Because individual “noise-like” variations actually represent colors of individual signals, local and regional maxima need to be preserved, which makes alternative techniques, like Gaussian filtering, inapplicable. Here, we define relevant morphological concepts:

  • Minimum is a connected component of bins of constant value whose external boundary bins have strictly greater values; a maximum is defined correspondingly

  • Local depth of a minimum is defined as a difference between the highest of external boundary values and the minimum itself

  • Elementary structuring element in one-dimensional histogram fi is a line segment of three bins

  • Elementary dilation δ(fi) corresponds to the maximal value of the histogram with the neighborhood defined by the elementary structuring element

  • Geodesic dilation involves a marker, histogram fi, and mask g defined over the same domain with values greater than or equal to the marker, that is, fig; geodesic dilation δg(fi) is defined as the minimum between the mask g and the elementary dilation of the marker δ(fi), that is, δg(fi) = δ(fi) ∧ g.

Here, we use geodesic dilation to remove spurious minima. First, we calculate local depths of all minima in the marker fi and then create the mask g by adding local depths to the marker. Hereafter, we analyze δg(fi) and if the number of minima is greater than one, the algorithm moves to step 2; otherwise, the convergence criterion is fulfilled. If the number of minima is equal to one, preliminary angle threshold Ainline image is placed at the bin associated with the local minimum; if there are no minima, the lowest minimum in the preceding iteration δg(fi−1) is the preliminary angle threshold.

Scale-space transformation (step 2)

Scale-space transformation is defined as linear transformation of the dilated histogram δg(fi) by a uniform kernel. We use a uniform kernel of length two, hence halving the number of bins required to describe fi+1, the resulting histogram. Changing the scale is equivalent to varying the size of the structuring element, which is not the case in fundamental morphological operations, where its shape needs to be predefined, making this procedure suitable for automation. The procedure is repeated from step 1 using the histogram fi+1.

Propagation of the preliminary angle threshold (marked with Ainline image in Fig. 3) through all scales gives the final result, Ar. In each iteration, the position of the angle threshold is shifted in the direction of steeper decline to the closest minimum. The procedure is completed when the original histogram, f, is reached. The result is the threshold marked with Ar in Figure 3.

Once the angle thresholds Ar and Ag are calculated, they are applied to classify signals1. The detected signals represented by ordered couples (R,G) are classified as single-colored “red” if G/R < tan(Ar) and “green” if G/R > tan(Ag) and double-colored “yellow” signals if tan(Ar) ≤ G/R ≤ tan(Ag).

Visual Signal Classification

Subsequent to automated signal localization with the stable wave detector, visual classification was performed on a subset of images for the purpose of evaluating performance of the classification methods. Four observers were asked to classify the detected signals as double or single-colored, independent of the perceived color, and hence there was no need to make adjustments for image display, gender, or cultural differences. We created “ground truth” by assigning each signal to the class with the most votes. Using the “ground truth,” we evaluated the automated classifiers by measuring the percentage of correctly classified signals.

Preparation of RCPs from Padlock Probes

We used two padlock probes (padlock 1 and padlock 2) designed previously for ligation with two variants of a single nucleotide polymorphism in the ATP7B gene (28). We circularized the padlocks by ligation [1× Ampligase buffer (Epicentre), 0.8 g/l BSA, 2.5 U Ampligase (Epicentre), 3 nM of synthetic target sequence (ligtemp1 or ligtemp2), and 1 nM of each of the two different padlock probes]. An initial incubation at 80°C for 2 min was followed by 65°C for 60 min. The mixture of circularized DNA was amplified by RCA for 60 min at 37°C in 125 μM dNTPs, 0.2 g/l BSA, and 50 mU/μl phi29 DNA polymerase in 1× phi29 DNA polymerase buffer (Fermentas). We terminated the reaction for 5 min at 60°C and dried a 10-μl drop of RCPs on a poly-L-lysine-coated microscope slide (Sigma-Aldrich) at 55°C for 15 min. We blocked the slide with 10 mg/l sonicated salmon sperm DNA (Invitrogen), 2× SSC buffer, and 0.05% Tween-20 (Sigma-Aldrich) for 15 min at 37°C and rinsed the slides in 1× PBS. Finally, we decoded probe identity by hybridization with 10 nM fluorescent-labeled probes (a general detection probe directed against both padlock probes and a specific detection probe directed against padlock 2 only) in 0.05% Tween-20, 2× SSC buffer, and 5% dextran sulfate. We incubated hybridization reactions at 55°C for 60 min and rinsed in 1× PBS and 1 min in 70% ethanol. Thereafter, slides were spun dry, mounted with 10 μl VectaShield (Immunkemi) and a cover slip, and imaged as described.

Preparation of clonally pure oligonucleotides.

To prepare clonally pure oligonucleotides, we amplified one clone with correct sequence for each probe by polymerase chain reaction (PCR) with a biotinylated primer in the antisense strand (0.02 U/μl Pfu polymerase, 1× Pfu polymerase buffer, 2 mM MgCl2, 200 nM dNTPs, 500 nM primers A bio and B, 40 cycles; 15 s, 95°C; 30 s, 55°C; and 120 s, 72°C). We removed nonincorporated primers by GFX column purification (GE healthcare) and nicked 8 pmol of the purified PCR product with 1 U/μl Nb.BtsI and 0.5 U/μl Nt.BspQI in buffer 3 (NEB) for 1 h at 37°C. The nicked PCR product was bound to 100 μg streptavidin-coated magnetic beads (M280, Dynal) and washed. The nonbiotinylated, nicked strand was eluted with 10 μl 100 mM NaOH and the supernatant neutralized immediately with 1 μmol HCl and 500 nmol Tris pH 7.5 (final volume 25 μl).

Results

  1. Top of page
  2. Abstract
  3. Rolling Circle Products
  4. Multiplexing and Spectral Angles
  5. Imaging Multicolored RCPs in Wide-Field Fluorescence Microscopy
  6. Materials and Methods
  7. Results
  8. Conclusions and Discussion
  9. Acknowledgements
  10. Literature Cited
  11. Supporting Information

First, we evaluate our image analysis algorithms for the classification of multicolored RCPs on a mixture of single and double-colored RCPs immobilized on glass slides and compare the performance to other classification methods as well as visual scoring. Next, we evaluate the methods on a set of images of a mixture of single and double-colored RCPs at different dilution. Thereafter, we investigate sequence variations in clonally and synthetically prepared oligonucleotides and, finally, apply the methods to distinguish RCPs representing true detected DNA–protein interactions from background signals in situ.

Evaluation of Signal Classification When Compared with Visual Inspection

RCPs from two different images, each containing 100 RCPs immobilized on a glass surface, were visually scored. To make a fair comparison between classification by angle-based thresholding (msSpecDec) and classification by intensity thresholding, we chose dyes and filter sets resulting in cross-talk-free images as specified in (16, 17). However, it is worth noting that angle-based thresholding is insensitive to cross-talk.

First, the number of correctly classified signals is calculated for each possible combination of angle thresholds (Ar, Ag) and intensity thresholds (Tr, Tg), respectively, as presented in Figure 4. White regions represent pairs of angle thresholds (left) and intensity thresholds (right) where more than 95% of the signals are correctly classified. Angle-based thresholds provide a wider range of thresholds that result in correct classification when compared with intensity-based thresholding and is therefore more robust. Note that signals that fall below both intensity thresholds are lost and thus considered incorrectly classified.

thumbnail image

Figure 4. Plots show percentages of correctly classified signals when compared with visual inspection of two different data sets. Abscissae and ordinate axes of each plot represent threshold settings for angle-based thresholding (left) and intensity-based thresholding (right). The threshold range is selected to cover all possible choices of angle thresholds, that is, 0°–40° and 50°–90° for Ar and Ag, respectively, and all intensity thresholds for which Tr and Tg result in correct classification as well as to include the result of automated Costes' thresholding. White regions represent threshold pairs that result in more than 95% correct signal classification, while black regions are associated with less than 90% correct classification. The larger white area for the angle-based thresholding indicates that the approach is more robust than intensity-based thresholding. Thresholds selected by automated msSpecDec and Costes' methods, respectively, are shown by black squares.

Download figure to PowerPoint

Next, we compare two automated thresholding methods, the novel angle-based msSpecDec and Costes' automated intensity thresholding; msSpecDec results in thresholds that fall in the area associated with high percentage of correctly classified signals (100% correct classification for dataset 1 and 97% correct classification for data set 2), while Costes' automated intensity thresholding does not result in values close to the optimal intensity thresholds, as shown by the labeled squares in Figure 4 (56% correct classification for dataset 1 and 36% correct classification for data set 2). Classification by manual thresholding (16) can give reasonable results in cross-talk-free images, but the process of selecting thresholds is sensitive to user bias and image-to-image variations.

Supporting Information Table S1 shows confusion matrices of classification results from visual inspection by four persons, from using optimal angle-based and intensity-based thresholding (which is generated by brute force search for the best possible solution), as well as from automated methods. To summarize, we note that Manders' manual intensity thresholding can produce reasonable results, while Costes'automated method is prone to premature stopping. On the other hand, the automated method proposed in this work, msSpecDec, performs almost as an optimal classifier.

Evaluation of Signal Detection and Classification Using Dilution Series

We evaluate the dynamic range and multiplexing precision as quantified by automated signal detection and classification on a set of images with decreasing concentrations of single-colored (“red”) RCPs mixed with a constant concentration of double-colored (“red” + “green” = “yellow”) RCPs. The RCPs are made from two padlock probes (padlock 1 and 2) designed to ligate with two variants of a single nucleotide polymorphism in the ATP7B gene. The two probes differ by one base at the target-complementary site and by the detection sequence element in the probe backbone. We hybridized decreasing concentrations of padlock 1 and a constant concentration of padlock 2 to their respective synthetic target sequences and ligated to form DNA circles subject to RCA. We immobilized RCPs on microscope slides and stained with single (“red”) or double (“red” + “green”) fluorescently labeled detection probes for padlock 1 and 2, respectively.

We used the presented methods to count “red,” “yellow,” and “green” signals. In theory, no “green” signals should be present as all RCPs are either single-colored “red” (padlock 1) or double-colored “yellow” (padlock 2). We normalized counts of “red” and “green” signals by the total number of “yellow” signals to approximate local concentrations. Figure 5 shows that the relative number of single-colored “green” signals representing noise is constant around 1% of the total number “yellow” signals while the concentration of single-colored “red” RCPs decreases exponentially according to the dilutions. However, low concentrations of RCPs cannot be distinguished from noise.

thumbnail image

Figure 5. This dilution series shows normalized concentrations of single-colored and double-colored RCPs immobilized on glass. We use the automated method msSpecDec to confirm that the number of single-colored “red” signals normalized by the number of “yellow” signals decreases exponentially at dilution. The number of single-colored “green” signals normalized by the number of “yellow” signals represents the level of “biochemical noise”, which would in theory be equal to zero. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Download figure to PowerPoint

Estimation of Sequence Variation in Clonally and Synthetically Prepared Oligonucleotides

Padlock probes as well as other types of single-molecule detection probes leading to RCPs are synthetic oligonucleotides, and errors in the oligonucleotide synthesis (10) will be present in each repeat of concatenated sequences of the RCP. If an error is located at the target sequence for the detection oligonucleotides, the error will affect the hybridization efficiency of one or both detection probes in a dual-colored RCP resulting in shifted intensity ratios when compared with target sequences without errors.

Thus, errors during synthesis should be minimized to ensure reliable classification of single, dual, or multicolored RCPs and increase the degree of multiplexing. To study the effect of errors, we produced clonally pure oligonucleotides used as padlock probes with single (padlock 1) and dual (padlock 2) detection sequences and compared them to their chemically synthesized counterparts.

We immobilized RCPs from clonally and synthetically prepared padlock probes with single and double-colored detection sequences in equal ratios on microscope slides, stained with fluorescence labeled detection probes, and imaged. Figure 6 shows the variation in red-green intensity ratios from one image of clonally and synthetically prepared padlock probes, respectively, presented as angle histograms. In the ideal case, the angle histogram should show a narrow peak at 0° (single-colored “red” signals) and a narrow peak at 45° (dual-colored “yellow” signals). A wider distribution means a higher error rate. Based on the results shown in histogram 6A, clonally prepared oligonucleotides seem to contain slightly fewer errors than synthetic oligonucleotides.

thumbnail image

Figure 6. Signals from clonally (A) and synthetically (B) prepared padlock probes mixed in approximately equal ratios of single-colored “red” and double-colored “yellow” RCPs, seen as peaks in the left (red) and central (yellow) part of the angle histograms. The dashed lines represent angle thresholds Ar and Ag, computed by msSpecDec, the method used to classify signals into three classes: single-colored “red” [0°,Ar], Ar] double-colored [Ar, Ag] and single-colored “green” [Ag, 90°]. The distribution in the angle histogram of the clonally prepared padlock probes (A) is more narrow and thus indicates better quality than the synthetically prepared padlock probes where many mutated probes appear as “orange” signals. [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Download figure to PowerPoint

Next, we tested the consistency of the difference between clonally and synthetically prepared oligonucleotides. We acquired two sets of eight images containing ∼5,000 signals per square millimeter from clonally (C1) and synthetically (S1) prepared oligonuclotides, respectively. Moreover, two additional sets of eight images were created by diluting the original mixtures to ∼2,000 signals per square millimeter (C2 and S2). As the experiments and imaging were conducted under the same conditions, parameters were optimized for a separate set of training images, and the same parameters were used to evaluate all 32 images in the test set. To quantify the error rate of the oligonucleotides, we calculated the count of “orange” signals, that is, “yellow” signals characterized by angles close to the angle threshold Ar, normalized by the total number of “yellow” signals. As the automated method computed slightly different Ar values for the two training images, they were averaged and set to Ar = 13.5°.

The error rate is similar for sets S1 and S2, but the same cannot be claimed for sets C1 and C2 (see Supporting Information Table S2). Sample-to-sample variations measured using the Student's test (29, Supporting Information Table S3) shows that intraclass differences are greater than interclass differences, that is, between synthetically and clonally prepare oligonucleotides.

Proximity Probes for Interaction Studies

Finally, we apply our method to in situ images to quantify RCPs representing protein–DNA interactions (Weibrecht et al., in preparation). Two data sets were available with three images each; one set with positive controls where most of the RCPs signals should be double-colored and one set with negative controls that should only contain single-colored RCPs (see Fig. 7). One image from each set was used for training the method, and optimized parameters were subsequently applied to the remaining images from each set. All parameters in sample preparation, image acquisitions, and data analysis are identical. DAPI-stained cell nuclei were automatically segmented (30). The resulting box plots show percentages of “red”, “green”, and “yellow” signals representing correctly and incorrectly ligated probes in the two control experiments.

thumbnail image

Figure 7. A: An example of positive control cell with DAPI-stained nucleus and mostly double-colored RCPs, that is, point-like signals visible in both FITC and Cy3 channels. B: An example of negative control cell with point-like signals visible in Cy3. C: Angle histograms normalized to the unit area show signal-color distribution in two training images. D, E: Classification rules computed based on angle histograms in (C) were applied to the cell nuclei shown in (A) and (B), respectively. F: We used the proposed automated quantification methods to evaluate the entire protocol, from specimen preparation to cell image analysis in presence of background fluorescence. Whisker's box plots of signal classification in the two test sets (each containing 20 cells). In the negative control (left), all signals should be “red,” while in the positive control, all signals should be double-colored (“yellow”). [Color figure can be viewed in the online issue, which is available at wileyonlinelibrary.com.]

Download figure to PowerPoint

Conclusions and Discussion

  1. Top of page
  2. Abstract
  3. Rolling Circle Products
  4. Multiplexing and Spectral Angles
  5. Imaging Multicolored RCPs in Wide-Field Fluorescence Microscopy
  6. Materials and Methods
  7. Results
  8. Conclusions and Discussion
  9. Acknowledgements
  10. Literature Cited
  11. Supporting Information

In this work, we present a method for quantification of colocalization of RCPs, msSpecDec. The three main steps of the pipeline are imaging by wide-field fluorescence microscopy, detection of point-like signals, and signal classification by spectral angles. The automated classification method is used to detect and classify RCPs spread on glass and to show that the preference of clonally instead of synthetically prepared oligonucleotides is not statistically significant. Finally, the methods are applied in quantitative cytometry for biochemical method evaluation of single-molecule interaction detection methods in situ.

Quantification of colocalization by spectral angles is accurate as long as color or spectral information is captured properly, that is, chromatic aberrations are avoided or corrected. Longitudinal chromatic aberrations are avoided in signal detection step. In addition, lateral chromatic aberrations are compensated using a rigid transformation. On the other hand, by neglecting cells localized close to the image border, we apply the method only to the central region where the quality is suitable for quantitative analysis. Therefore, correction for different magnifications at different wavelengths, a common source of lateral chromatic aberrations close to the image border, does not need to be corrected.

The SpecDec has previously shown immunity to cross-talk (2), and, here, the novel msSpecDec helps constituting appropriate classification rules for single-molecule detection in the presence of background fluorescence. Although single-colored RCPs immobilized on glass are “pure red” (Fig. 6), “red” signals in the negative control experiment (Fig. 7C) are affected by nonzero background imaged in the “green” channel. Therefore, in this situation, intensity-based thresholds fail. The number of potentially misclassified RCPs immobilized on the glass does not exceed 1% when the presented method is used (as seen in Supporting Information Table S2), making it possible to use other fluorescent dye combinations to increase multiplexing as shown in Figure 2C.

The principles shown in this work are applicable to other similar imaging systems, for example, confocal microscopy. Also, we believe that extension to analysis of three-dimensional image data is straightforward as the proposed classification algorithm is independent of the number of spatial dimensions, and the algorithm for the detection of point-like signals can be used for three-dimensional signal localization (1, 31).

Acknowledgements

  1. Top of page
  2. Abstract
  3. Rolling Circle Products
  4. Multiplexing and Spectral Angles
  5. Imaging Multicolored RCPs in Wide-Field Fluorescence Microscopy
  6. Materials and Methods
  7. Results
  8. Conclusions and Discussion
  9. Acknowledgements
  10. Literature Cited
  11. Supporting Information

The authors thank Cris Luengo at the Centre for Image Analysis, Swedish University of Agricultural Sciences, Ewert Bengtsson and Ingrid Carlbom at the Centre for Image Analysis, Department for Information Technology, Uppsala University and Jenny Göransson at the Department of Immunology, Genetics and Pathology, Uppsala University, for fruitful discussions regarding the methods and manuscript.

  1. 1

    In Figure 3, the star at 35° in histogram f shows where the simple, but less robust, algorithm for determining classification rules presented in (2) would place Ar.

Literature Cited

  1. Top of page
  2. Abstract
  3. Rolling Circle Products
  4. Multiplexing and Spectral Angles
  5. Imaging Multicolored RCPs in Wide-Field Fluorescence Microscopy
  6. Materials and Methods
  7. Results
  8. Conclusions and Discussion
  9. Acknowledgements
  10. Literature Cited
  11. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. Rolling Circle Products
  4. Multiplexing and Spectral Angles
  5. Imaging Multicolored RCPs in Wide-Field Fluorescence Microscopy
  6. Materials and Methods
  7. Results
  8. Conclusions and Discussion
  9. Acknowledgements
  10. Literature Cited
  11. Supporting Information

Additional supporting information may be found in the online version of this article.

FilenameFormatSizeDescription
CYTO_21087_sm_suppinfo1.doc93KSupporting Information 1.
CYTO_21087_sm_suppinfo2.doc25KSupporting Information 2.
CYTO_21087_sm_suppinfo3.doc29KSupporting Information 3.

Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.