Kymographs from plasmids

<div>DNA barcodes used in 'Noise Reduction in Single Time Frame Optical DNA Maps' (2017), PLOS One. </div><div><br></div><div>DNA kymographs from plasmids obtained from nano-channel based competitive binding assays. The set consists of 32 kymograph from three types of plasmids: pUUH239.2 (8 kymographs), pEC005A (11 kymographs) and pEC005B (13 kymographs). Each kymograph corresponds to one molecule and contains 200 single time frames of 0.1s each (6400 single time frames in total).</div><div><br></div><div>The 32 raw kymographs are in named 'plasmidName_moleculeNumber'. </div><div><br></div

Increase in the Pearson correlation coefficient between filtered a single time frame and the aligned kymograph time average.

<p>The table shows the improvement, , in the Pearson correlation coefficient, (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0179041#pone.0179041.e011" target="_blank">Eq (2)</a>), between each single time frame barcode and its aligned kymograph time average after filtering the single frame. Correlation coefficients were averaged over all 6400 time-frame barcodes (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0179041#pone.0179041.g003" target="_blank">Fig 3</a>) for each type of filter used (Gaussian, Moving Average and Windowed-Sinc filter). The improvement is defined as , where is the correlation coefficient between the filtered single time-frame (<i>fst</i>) barcode and the time averaged (<i>ta</i>) barcode, and is the correlation coefficient between the unfiltered (noisy) single time frame barcode and the kymograph time average. We see that all filters lead to a similar average improvement in the correlation, roughly 0.2 points. Results for by type of plasmid (<i>pUUH</i>, <i>pEC005A</i>, <i>pEC005B</i>) are found in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0179041#pone.0179041.s001" target="_blank">S1 Table</a> in Supplementary Information.</p

Plasmid ID by comparing individual experimental barcodes to a theory database.

<p>(Left) Pearson correlation coefficients between the experimental barcodes (<i>pUUH</i>, <i>pEC005A</i> and <i>pEC005B</i>) and the plasmid theory database (as in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0179041#pone.0179041.ref024" target="_blank">24</a>]) were calculated and turned into histograms. As input experimental barcode we used: unfiltered single-time frame (<i>ust</i>) barcodes, filtered (with Gaussian filter) single-time frame (<i>fst</i>) barcodes, and time-averaged (<i>ta</i>) barcodes. The vertical line gives the correlation coefficient for the correct plasmid. Notice that <i>ust</i> barcodes are not very good at plasmid ID (s-scores between 0.4-10%), but, <i>fsb</i> and <i>ta</i> barcodes are better (with s-scores less than 3%). Experiments were only matched to theory barcodes which had a length within ±3<i>σ</i>_length of the experimental barcode, with <i>σ</i>_length = {23, 7, 15} pixels for <i>pUUH, pEC005A and pEC005B</i>, respectively. The Gumbel fits to the histograms were done using the same method as in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0179041#pone.0179041.ref024" target="_blank">24</a>]. (Right) The panels on the right show the change in between the experiment and the theoretical barcode (i.e., theory barcodes from <i>pUUH</i>, <i>pEC005A</i> or <i>pEC005B</i>, respectively) after filtering single time frame barcodes. On the top-right plot, in grey is shown the correlation coefficients for the case without filtering, and in blue/green the correlation after filtering. The four lines in the top plot are smoothed for visualization purposes and are moving averages of the result over the 300 nearest neighbor barcodes (each of the three plasmid types treated separately). The right-bottom panel shows the change for all 6400 single time-frames for the case of Gaussian filter. On average, the single frames match to theory improves by 0.11 ± 0.04 points after filtering (average over all three filters).</p

Examples of optical mapping kymographs (raw, aligned and time averaged) from a linearized plasmid DNA stretched in a nanochannel.

<p>(a) A raw kymograph (i.e. a stack of images of stretched and fluorescently labeled DNA) from a linearized plasmid obtained using the competitive binding assay described in [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0179041#pone.0179041.ref038" target="_blank">38</a>]. The horizontal direction corresponds to the nano-channel extension (i.e., the direction of the stretched DNA) and vertical axes are different time points (0.1 s between time frames). The kymograph consists of 200 single time frame images (d, e). (b) The raw kymograph is aligned (using <i>WPAlign</i> from [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0179041#pone.0179041.ref041" target="_blank">41</a>]) and subsequently averaged over all 200 time frames in order to produce (c, f) noise-reduced, time averaged DNA barcodes. The noisy curves in (d, e) represent the intensities along two single time-frame (snap-shot) barcodes, see (a). For visualization purposes, the snap-shot barcodes were shifted globally to the position where they have the maximum correlation coefficient with the time-averaged barcode. The challenge addressed in this study is how to make the noisy single-time frame barcodes of the form illustrated above resemble the (more reproducible) time-averaged barcode to a higher degree by using low-pass filtering. The barcodes shown are from plasmid <i>pEC005A</i>, see [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0179041#pone.0179041.ref024" target="_blank">24</a>] for further information about the experiments.</p

Summary of three low-pass filters used in this study: Gaussian, Moving average and Window-Sinc filter.

<p>Summary of three low-pass filters used in this study: Gaussian, Moving average and Window-Sinc filter.</p

Example barcode filtered using our noise-reducing filtering method.

<p>(grey) A noisy single time-frame (snap-shot) barcode taken with 0.1s exposure time. (orange) The time average of the aligned kymograph. Such time-averages are used as reference (“true” barcode) throughout this study and used to judge the quality of the filtering process. (blue barcodes) From top to bottom Gaussian, Moving average and Sinc filter, respectively, is applied recursively to the single-time frame barcode (grey) until all peaks in the filtered barcode have a FWHM of at least that of the FWHM of the PSF of the system. Notice the visual similarity of the filtered barcodes to the time-averaged barcode. The Pearson correlation coefficient between the time average of the aligned kymograph and the barcode before and after the the filtering changes from 0.6 without the filtering, to 0.8 after filtering. The original raw kymograph consists of 200 single time-frame shots (exposure time 0.1s) from plasmid <i>pEC005B</i>.</p

Estimates of the chip parameters for an EMCCD camera at different gain settings.

The calibration data shown in S1 Fig in S1 Text was used, and the chip parameters were calculated using Eqs (4)–(7) in Materials and Methods.</p

Photophysical image binarization.

Synthetic images of fluorescent beads were generated as described in Sec. S4 in S1 Text at different signal-to-noise ratios (with known values of λbg and λsig). For these images we know the ground truth pixel identity, i.e., which pixels are background and which are signal. (a) Estimated λbg compared to the ground truth value. (b-f) Our image binarization method was applied to the synthetic images (with binarization threshold pbinarize). The result was then compared to ground truth pixel identity, with success rates quantified through five statistical observables (blue). The orange marks correspond to our a priori prediction of the same observables (obtained without the knowledge of the ground truth). We also show Otsu’s method compared to ground truth pixel identities (red). In our method we have excellent control over the FPR, i.e., the fraction of white pixels in background regions. We also have good control over the FNR. Particularly important to notice is that our a priori prediction (orange) for all statistical observables agree very well with ground truths (blue). This agreement is the strength of our novel thresholding method, which hence opens up for unsupervised image thresholding where the error for the classification for each pixel is obtained a priori. The image count threshold for the binarization was determined through a p-value threshold pbinarize = 0.01.</p

Detailed description of our methods and supporting figures.

We here provide all necessary details of our PIA methods and supporting figures. (PDF)</p

Estimating λ_<i>bg</i> for an image which contains both background and signal.

(a) Experimental fluorescence microscopy image of fluorescent beads. Here, the image is split into tiles of size 64x64 pixels, where each tile is given a label {row, column}, where in this example row, column = 1, …, 8. The contrast is set to better display the background noise and glass slide artifacts. (b) Estimating λbg: A histogram of the image counts for a single tile, here tile {4, 1}. The blue bars represent pixels regarded as true background, while the orange bars represent the outliers (not true background or signal pixels). The image counts threshold, , separating the blue and orange bars was determined using a p-value threshold, pGoF = 0.01, for the goodness-of-fit tests. The dashed black curve shows the fitted PMF for the estimated λbg, extended to the full range of image counts (in our method, we fit a truncated PMF to the blue bars). In S5 Fig in S1 Text, we provide the estimates of λbg and for all tiles in panel a). In S8 Fig in S1 Text, we also provide two more examples of image count histograms with overlaid fits. Examples of fits to histograms for synthetic images at varying SNR is found in Sec. S7 in S1 Text. A major novelty of our method is that we are able to estimate λbg for a arbitrary fluorescence image even though the image contains signal pixels.</p