Melting curves for two small nucleolar RNAs (snoRNA) from family RF00158 from Rfam version 9.0 [56].

<p>For each RNA sequence, over a range of temperatures, temperature-dependent base pair probabilities were computed using four different software packages: RNAenn, RNAnn, version 1.8.5 of RNAfold <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0085412#pone.0085412-Hofacker2" target="_blank">[40]</a> and RNAstructure <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0085412#pone.0085412-Reuter1" target="_blank">[38]</a>. The software RNAenn (RNA extended nearest-neighbor) is our implementation of the algorithms described in this paper, while the software RNAnn (RNA nearest-neighbor) is our implementation of the following algorithms: Zuker's minimum free energy structure algorithm <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0085412#pone.0085412-Zuker3" target="_blank">[51]</a>, McCaskill's partition function algorithm <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0085412#pone.0085412-McCaskill1" target="_blank">[19]</a>, and the Ding-Lawrence sampling algorithm <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0085412#pone.0085412-Ding1" target="_blank">[22]</a>. Each algorithm was run without dangle or coaxial free energies. At each temperature , for each algorithm, the expected number of base pairs was computed as ; for each algorithm, the collection of such points generates a melting profile obtained by that algorithm. <i>(Left)</i> Melting curves for the 72 nt small nucleolar RNA (snoRNA) from <i>Ornithorhynchus anatinus</i> (platypus) with GenBank accession code AAPN01359272.1/4977–5048 and sequence given by AGCACAAAUG AUGAGCCUAA AGGGACUUAA UACUGAAACC UGAUGUAACU AAAUAAUAUA UGCUGAUCGU GC<i>(Right)</i> Melting curves for the 69 nt small nucleolar RNA (snoRNA) from <i>Otolemur garnetti</i> (small-eared galago) with GenBank accession code AQR01179445.1/1047–1115 and sequence given by GGCACAAAUG AUGAAUGACA AGGGACUUAA UACUGAAACC UGAUGUUACA UUACAAUGUG CUGAUGUGC.</p

Feynman diagram to pictorially describe recursions described in this proposal for partition function with respect to extended nearest neighbor model.

<p>For simplicity, this diagram depicts , but not , which correspond to a special treatment for particular left/right bulges of size , that are treated as stacked base pairs.</p

Depiction of elements of RNA secondary structure for which experimentally determined free energy parameters are available.

<p>In this 61 nt RNA, the hairpin loop closed by base pair between nucleotides at position 43 and 48 is known as a <i>tetraloop</i>, or hairpin loop of size 4. Similarly, the hairpin loop of size 7 is closed by a base pair between nucleotides at positions 17 and 25. Free energy parameters for bulges and internal loops (two-sided bulges, not shown in the figure) are available, while an affine approximation is used for the free energy of a multiloop or junction.</p

Pseudocode for Brown's algorithm.

<p>Pseudocode for Brown's algorithm.</p

Values of sensitivity and positive predictive value (ppv) for RNAfold and RNAenn with respect to various RNA families.

<p>Sensitivity is the ratio of number of correctly predicted base pairs divided by the number of base pairs in the native structure; positive predictive value is the ratio of the number of correctly predicted base pairs divided by the number of base pairs in the predicted structure. Since RNAenn currently does not include energy contributions for dangles (single stranded, stacked nucleotides), RNAfold was used without dangles (version 1.8.5 with -d flag). To our knowledge, there has not been a careful benchmarking of structure prediction accuracy between the Turner 1999 energy model and the newer Turner 2004 energy model, though it is interesting to note that RNAenn has better structure prediction when using Turner 1999 for base stacking. Overall, it is clear that RNAfold outperforms RNAenn (Turner99), although a few cases, such as <b>ec</b> and <b>rnap2</b> RNAenn have better sensitivity. Nevertheless, we expect much better performance in the future when our triplet and base stacking energy terms have been refined by using knowledge-base potentials. The database of RNA structures in this benchmarking set comes from a data collection of D.H. Mathews (personal communication), which derives from published databases <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0085412#pone.0085412-Sprinzl1" target="_blank">[26]</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0085412#pone.0085412-Gutell1" target="_blank">[54]</a>, etc. See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0085412#pone.0085412-Mathews4" target="_blank">[55]</a> for a citation of original data sources.</p

Establishing connectivity among AJ vertices to segment epithelial tissues.

<p>A) Voronoi regions are expanded from vertex locations to generate the Voronoi Diagram associating each voxel to the nearest AJ vertex. B) Supervertices are expanded inside Voronoi regions to link adjacent vertices. C) The AJs graph is built adding an edge between contiguous vertices through pairs of adjacent supervertices. D) Vertices, Voronoi regions and supervertices are superimposed.</p

Segmentation and Tracking of Adherens Junctions in 3D for the Analysis of Epithelial Tissue Morphogenesis

<div><p>Epithelial morphogenesis generates the shape of tissues, organs and embryos and is fundamental for their proper function. It is a dynamic process that occurs at multiple spatial scales from macromolecular dynamics, to cell deformations, mitosis and apoptosis, to coordinated cell rearrangements that lead to global changes of tissue shape. Using time lapse imaging, it is possible to observe these events at a system level. However, to investigate morphogenetic events it is necessary to develop computational tools to extract quantitative information from the time lapse data. Toward this goal, we developed an image-based computational pipeline to preprocess, segment and track epithelial cells in 4D confocal microscopy data. The computational pipeline we developed, for the first time, detects the adherens junctions of epithelial cells in 3D, without the need to first detect cell nuclei. We accentuate and detect cell outlines in a series of steps, symbolically describe the cells and their connectivity, and employ this information to track the cells. We validated the performance of the pipeline for its ability to detect vertices and cell-cell contacts, track cells, and identify mitosis and apoptosis in surface epithelia of <i>Drosophila</i> imaginal discs. We demonstrate the utility of the pipeline to extract key quantitative features of cell behavior with which to elucidate the dynamics and biomechanical control of epithelial tissue morphogenesis. We have made our methods and data available as an open-source multiplatform software tool called TTT (<a href="http://github.com/morganrcu/TTT" target="_blank">http://github.com/morganrcu/TTT</a>)</p></div

The developed system for the preprocessing, segmentation and tracking of epithelial cells.

<p>A) Schematic of the computational pipeline from the acquisition of 3D time lapse data to image preprocessing, cell segmentation and tracking. After segmenting the cells, we define symbolically their structure using a planar graph connecting detected AJ vertices with edges (green). Then we identify the cells in the tissue as the faces of the AJ graph and build the Cell graph to describe cell connectivity (blue). Finally, we establish correspondence between cells among frames (colored lines connecting cell centroids) obtaining cell trajectories. (B-G) Part of an epithelium of a <i>Drosophila</i> leg at early pupal stages. This tissue dramatically narrows and elongates at this stage to generate a narrow and hollow cylinder while the epithelium at presumptive joints invaginates. B) Maximum intensity projection of an image stack through the leg epithelium marked with E-cad∷GFP to highlight cell outlines. Distal up, narrow region—presumptive joint; wider regions part of the presumptive segment. C) Projection of the denoised and deconvoluted volume. D) The output of the filters employed to detect AJs (green) and AJ vertices (red). E) AJ graph representing the AJs structure. F) Cell graph representing neighborhood relationships among cells in the tissue. G) Polygonal representation of the cells, colored according to assigned temporal identifiers.</p

Performance assessment of the automated detection of vertices, cell-cell contacts and cell tracks.

<p>A-D) Evaluation of the vertex detector, E-H) edge detector, and I-J) cell tracker. C-D), G-H) Green—true detections, blue—missed detections, red—false detections. A) Precision-Recall curve for AJ vertex detection. B) Variation of the <i>F</i>1 score of the vertex detector relative to changes in detection threshold <i>T</i>_<i>V</i>. Vertex detection of C) Notum and D) Leg datasets. Vertex location accuracy highly depends on properly tuning up <i>T</i>_<i>v</i>. E) Precision-Recall curve for AJ edge detection. F) Variation of the <i>F</i>1 score relative to changes in propagation threshold <i>T</i>_<i>E</i>. Edge detection in G) Notum and H) Leg datasets. Edge detection is more robust than vertex detection. I), J), K) and L) 2D projection of the trajectories respectively found for the cells in E) Notum, F) Leg, G) Mitosis in notum and H) Apoptosis in notum datasets. The system recovers accurate cell trajectories in different scenarios.</p

Detection of mitosis and apoptosis events.

<p>In addition to cell movements, notum morphogenesis involves extensive cell delamination at the dorsal midline [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004124#pcbi.1004124.ref030" target="_blank">30</a>] and extensive cell proliferation required for notum expansion [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004124#pcbi.1004124.ref007" target="_blank">7</a>]. We therefore incorporated into the tracker algorithms to detect mitotic and apoptotic events. A) The large light green cell in the upper left region splits to produce two daughter cells marked by the same color. B) The dark brown cell in the center reduces its area until it disappears.</p