WPAlign pseudocode.

<p>Note that all substeps shown here are available in a variety of standard toolboxes, open-source and otherwise. For our particular implementation, all code was written in Matlab with dependencies in the Image Processing Toolbox and the Bioinformatics Toolbox (which implements the graph data structure and shortest path finding functionality).</p

Comparison of time scaling for WPAlign and the Reisner approach.

<p>Empirical time scaling results for both techniques on identical kymographs ranging between ∼ 10² and ∼ 10⁵ pixels in width, where ∼ 10⁵ pixels is roughly the length of an intact human genome at current resolutions. Power law curves of the form <i>ax</i>^<i>b</i> were fit to these data (solid lines), yielding <i>b</i> = 1.1 for WPAlign, and <i>b</i> = 2.2 for the Reisner method. Thus WPAlign exhibits approximately <i>O</i>(<i>n</i>) time scaling with barcode width, while the Reisner method scales approximately with <i>O</i>(<i>n</i>²). Scaling data beyond ∼ 10³ pixels was projected for the Reisner approach (dashed line), as alignment times became prohibitive. Simulated kymographs were generated by concatenating experimental T4GT7 kymographs from above.</p

A Fast and Scalable Kymograph Alignment Algorithm for Nanochannel-Based Optical DNA Mappings

<div><p>Optical mapping by direct visualization of individual DNA molecules, stretched in nanochannels with sequence-specific fluorescent labeling, represents a promising tool for disease diagnostics and genomics. An important challenge for this technique is thermal motion of the DNA as it undergoes imaging; this blurs fluorescent patterns along the DNA and results in information loss. Correcting for this effect (a process referred to as kymograph alignment) is a common preprocessing step in nanochannel-based optical mapping workflows, and we present here a highly efficient algorithm to accomplish this via pattern recognition. We compare our method with the one previous approach, and we find that our method is orders of magnitude faster while producing data of similar quality. We demonstrate proof of principle of our approach on experimental data consisting of melt mapped bacteriophage DNA.</p></div

Quality comparison of barcodes aligned via the Reisner approach and WPAlign.

<p>(Top) Representative kymographs aligned via the Reisner approach (above) and WPAlign (below). (Bottom) Average intensity traces from kymographs in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0121905#pone.0121905.g007" target="_blank">Fig 7</a> aligned via WPAlign (red) and the Reisner approach (black). The information score is displayed below each trace for both methods, quantifying the contrast between neighboring features. Notably, ⟨(IS_<i>W</i> − IS_<i>R</i>)/IS_<i>R</i>⟩ = 0.78, indicating that WPAlign on average produced time-traces with slightly more information than the Reisner method over our sample set. Note that the plots are in the same order as the corresponding kymographs in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0121905#pone.0121905.g007" target="_blank">Fig 7</a> and are ordered by decreasing IS_<i>W</i>.</p

Connectivity between nodes.

<p>Connectivity between nodes.</p

Typical T4GT7 denaturation mapping kymographs, raw and aligned via WPAlign.

<p>The numbered kymographs represent the raw data, and the aligned versions are displayed directly below each.</p

Network assembly.

<p>The Laplacian response image, <i>K</i>, (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0121905#pone.0121905.g002" target="_blank">Fig 2c</a>) has been rescaled into (A) <i>K</i>_<i>D</i> and (B) <i>K</i>_<i>B</i>, images that emphasize dark and bright regions in <i>K</i>, respectively. White pixels represent barriers that potential features cannot cross, while continuous dark regions indicate likely features. (C) Here we show one example network, although separate networks are indeed assembled for <i>K</i>_<i>B</i> and <i>K</i>_<i>D</i>. Each node (square) within the rectangular region represents a pixel in K_<i>B</i> or <i>K</i>_<i>D</i>. The top and bottom nodes (which we term “peripheral nodes”) are added to provide starting/ending points for the shortest path finding algorithm. The width of the edges corresponds to the inverse of the edge weight, and the darkness of the nodes represents the average weight of incoming edges. The red line illustrates the shortest path through the network. For the sake of visual clarity, this network was created using a small subsection of an actual Laplacian response with <i>k</i> = 1.</p

Effect of time axis length on aligned kymograph noise.

<p>Kymographs with time axes varying from 20 to 200 time frames in length were aligned by both methods. The resulting column-wise variances </p><p></p><p></p><p><mi>σ</mi><mi>R</mi><mn>2</mn></p><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><p></p><p></p> and <p></p><p></p><p><mi>σ</mi><mi>W</mi><mn>2</mn></p><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><p></p><p></p> were calculated as in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0121905#pone.0121905.g008" target="_blank">Fig 8</a>. Here we plot, for each kymograph, the mean of these column variances, i.e., <p></p><p><mo stretchy="false">⟨</mo></p><p><mi>σ</mi><mi>R</mi><mn>2</mn></p><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">⟩</mo><p></p><p></p> and <p></p><p><mo stretchy="false">⟨</mo></p><p><mi>σ</mi><mi>W</mi><mn>2</mn></p><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo stretchy="false">⟩</mo><p></p><p></p>, showing that kymograph noise increases with time axis length for the Reisner method but remains constant for WPAlign.<p></p

Feature detection and recursion in WPAlign.

<p>(A) A raw, unaligned kymograph is given as input (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0121905#pone.0121905.g001" target="_blank">Fig 1</a>). (B) The “best” feature is identified from the input kymograph. (C) The feature identified in (B) is aligned via linear interpolation. (D, E) The feature identification process is called recursively on the regions to the right (D) and to the left (E) of the newly-aligned feature. (F) This process is continued until all features have been aligned.</p