scholarly journals Stable Topological Summaries for Analyzing the Organization of Cells in a Packed Tissue

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1723
Author(s):  
Nieves Atienza ◽  
Maria-Jose Jimenez ◽  
Manuel Soriano-Trigueros
Keyword(s):  
Classification Accuracy ◽  
Persistent Homology ◽  
Wing Disc ◽  
Topological Data Analysis ◽  
Random Forest Algorithm ◽  
Drosophila Wing ◽  
Segmented Image ◽  
Normalization Methods ◽  
Segmented Images ◽  
Stability Results

We use topological data analysis tools for studying the inner organization of cells in segmented images of epithelial tissues. More specifically, for each segmented image, we compute different persistence barcodes, which codify the lifetime of homology classes (persistent homology) along different filtrations (increasing nested sequences of simplicial complexes) that are built from the regions representing the cells in the tissue. We use a complete and well-grounded set of numerical variables over those persistence barcodes, also known as topological summaries. A novel combination of normalization methods for both the set of input segmented images and the produced barcodes allows for the proven stability results for those variables with respect to small changes in the input, as well as invariance to image scale. Our study provides new insights to this problem, such as a possible novel indicator for the development of the drosophila wing disc tissue or the importance of centroids’ distribution to differentiate some tissues from their CVT-path counterpart (a mathematical model of epithelia based on Voronoi diagrams). We also show how the use of topological summaries may improve the classification accuracy of epithelial images using a Random Forest algorithm.

Quantitative EM of gap junction distribution in mutant drosophila wing discs

1983 ◽  
Vol 41 ◽  
pp. 720-721
Author(s):  
J.S. Ryerse
Keyword(s):  
Gap Junctions ◽  
Growth Control ◽  
Intercellular Junctions ◽  
Wing Disc ◽  
En Bloc ◽  
Metabolic Cooperation ◽  
Drosophila Wing ◽  
Adult Wing ◽  
Wing Discs ◽  
Wing Pouch

Gap junctions are intercellular junctions found in both vertebrates and invertebrates through which ions and small molecules can pass. Their distribution in tissues could be of critical importance for ionic coupling or metabolic cooperation between cells or for regulating the intracellular movement of growth control and pattern formation factors. Studies of the distribution of gap junctions in mutants which develop abnormally may shed light upon their role in normal development. I report here the distribution of gap junctions in the wing pouch of 3 Drosophila wing disc mutants, vg (vestigial) a cell death mutant, 1(2)gd (lethal giant disc) a pattern abnormality mutant and 1(2)gl (lethal giant larva) a neoplastic mutant and compare these with wildtype wing discs.The wing pouch (the anlagen of the adult wing blade) of a wild-type wing disc is shown in Fig. 1 and consists of columnar cells (Fig. 5) joined by gap junctions (Fig. 6). 14000x EMs of conventionally processed, UA en bloc stained, longitudinally sectioned wing pouches were enlarged to 45000x with a projector and tracings were made on which the lateral plasma membrane (LPM) and gap junctions were marked.

scholarly journals Classification of apatite structures via topological data analysis: a framework for a ‘Materials Barcode’ representation of structure maps

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Scott Broderick ◽  
Ruhil Dongol ◽  
Tianmu Zhang ◽  
Krishna Rajan
Keyword(s):  
Machine Learning ◽  
Data Analysis ◽  
Crystal Chemistry ◽  
Persistent Homology ◽  
Hierarchical Classification ◽  
Topological Data Analysis ◽  
Learning Tool ◽  
Coordination Polyhedra ◽  
Machine Learning Tool ◽  
Topological Data

AbstractThis paper introduces the use of topological data analysis (TDA) as an unsupervised machine learning tool to uncover classification criteria in complex inorganic crystal chemistries. Using the apatite chemistry as a template, we track through the use of persistent homology the topological connectivity of input crystal chemistry descriptors on defining similarity between different stoichiometries of apatites. It is shown that TDA automatically identifies a hierarchical classification scheme within apatites based on the commonality of the number of discrete coordination polyhedra that constitute the structural building units common among the compounds. This information is presented in the form of a visualization scheme of a barcode of homology classifications, where the persistence of similarity between compounds is tracked. Unlike traditional perspectives of structure maps, this new “Materials Barcode” schema serves as an automated exploratory machine learning tool that can uncover structural associations from crystal chemistry databases, as well as to achieve a more nuanced insight into what defines similarity among homologous compounds.

Regeneration from duplicating fragments of the Drosophila wing disc

Development ◽  
1981 ◽  
Vol 66 (1) ◽  
pp. 117-126
Author(s):  
Jane Karlsson ◽  
R. J. Smith
Keyword(s):  
Imaginal Disc ◽  
General Rule ◽  
Wing Disc ◽  
The Other ◽  
Posterior Compartment ◽  
Drosophila Wing ◽  
Polar Coordinate ◽  
New Type ◽  
Coordinate Model

It is a general rule that of two complementary Drosophila imaginal disc fragments, one regenerates and the other duplicates. This paper reports an investigation of an exception to this rule. Duplicating fragments from the periphery of the wing disc which lacked presumptive notum were found to regenerate notum structures during and after duplication. The propensity for this was greatest in fragments lying close to the presumptive notum, with the exception of a fragment confined to the posterior compartment, which did not regenerate notum. Structures were added sequentially, and regeneration stopped once most of the notum was present. These results are not easily explained by the polar coordinate model, which states that regeneration cannot occur from duplicating fragments. Since compartments appear to be involved in this type of regeneration as in others, it is suggested that a new type of model is required, one which permits simultaneous regeneration and duplication, and assigns a major role to compartments.

scholarly journals Topological Segmentation of Time-Varying Functional Connectivity Highlights the Role of Preferred Cortical Circuits

2020 ◽  
Author(s):  
Jacob Billings ◽  
Manish Saggar ◽  
Shella Keilholz ◽  
Giovanni Petri
Keyword(s):  
Functional Connectivity ◽  
Brain Function ◽  
Persistent Homology ◽  
Brain Regions ◽  
Topological Data Analysis ◽  
Time Varying ◽  
Imaging Data ◽  
Experimental Conditions ◽  
Common Time ◽  
Brain Imaging Data

Functional connectivity (FC) and its time-varying analogue (TVFC) leverage brain imaging data to interpret brain function as patterns of coordinating activity among brain regions. While many questions remain regarding the organizing principles through which brain function emerges from multi-regional interactions, advances in the mathematics of Topological Data Analysis (TDA) may provide new insights into the brain’s spontaneous self-organization. One tool from TDA, “persistent homology”, observes the occurrence and the persistence of n-dimensional holes presented in the metric space over a dataset. The occurrence of n-dimensional holes within the TVFC point cloud may denote conserved and preferred routes of information flow among brain regions. In the present study, we compare the use of persistence homology versus more traditional TVFC metrics at the task of segmenting brain states that differ across a common time-series of experimental conditions. We find that the structures identified by persistence homology more accurately segment the stimuli, more accurately segment volunteer performance during experimentally defined tasks, and generalize better across volunteers. Finally, we present empirical and theoretical observations that interpret brain function as a topological space defined by cyclic and interlinked motifs among distributed brain regions, especially, the attention networks.

scholarly journals Endocytosis of Wingless via a dynamin-independent pathway is necessary for signaling in Drosophila wing discs

2016 ◽  
Vol 113 (45) ◽  
pp. E6993-E7002 ◽  
Author(s):  
Anupama Hemalatha ◽  
Chaitra Prabhakara ◽  
Satyajit Mayor
Keyword(s):  
Signal Transduction ◽  
Wing Disc ◽  
Low Ph ◽  
Endocytic Pathway ◽  
Apical Surface ◽  
Receptor Complexes ◽  
Drosophila Wing ◽  
Wing Discs ◽  
Ph Dependent ◽  
Endocytic Pathways

Endocytosis of ligand-receptor complexes regulates signal transduction during development. In particular, clathrin and dynamin-dependent endocytosis has been well studied in the context of patterning of the Drosophila wing disc, wherein apically secreted Wingless (Wg) encounters its receptor, DFrizzled2 (DFz2), resulting in a distinctive dorso-ventral pattern of signaling outputs. Here, we directly track the endocytosis of Wg and DFz2 in the wing disc and demonstrate that Wg is endocytosed from the apical surface devoid of DFz2 via a dynamin-independent CLIC/GEEC pathway, regulated by Arf1, Garz, and class I PI3K. Subsequently, Wg containing CLIC/GEEC endosomes fuse with DFz2-containing vesicles derived from the clathrin and dynamin-dependent endocytic pathway, which results in a low pH-dependent transfer of Wg to DFz2 within the merged and acidified endosome to initiate Wg signaling. The employment of two distinct endocytic pathways exemplifies a mechanism wherein cells in tissues leverage multiple endocytic pathways to spatially regulate signaling.

scholarly journals Topological data analysis for true step detection in periodic piecewise constant signals

2018 ◽  
Vol 474 (2218) ◽  
pp. 20180027 ◽  
Author(s):  
Firas A. Khasawneh ◽  
Elizabeth Munch
Keyword(s):  
Data Analysis ◽  
Persistent Homology ◽  
Topological Data Analysis ◽  
Future Research ◽  
Accurate Identification ◽  
Piecewise Constant ◽  
Higher Dimensional ◽  
Powerful Approach ◽  
Hadamard Transforms ◽  
Topological Data

This paper introduces a simple yet powerful approach based on topological data analysis for detecting true steps in a periodic, piecewise constant (PWC) signal. The signal is a two-state square wave with randomly varying in-between-pulse spacing, subject to spurious steps at the rising or falling edges which we call digital ringing. We use persistent homology to derive mathematical guarantees for the resulting change detection which enables accurate identification and counting of the true pulses. The approach is tested using both synthetic and experimental data obtained using an engine lathe instrumented with a laser tachometer. The described algorithm enables accurate and automatic calculations of the spindle speed without any choice of parameters. The results are compared with the frequency and sequency methods of the Fourier and Walsh–Hadamard transforms, respectively. Both our approach and the Fourier analysis yield comparable results for pulses with regular spacing and digital ringing while the latter causes large errors using the Walsh–Hadamard method. Further, the described approach significantly outperforms the frequency/sequency analyses when the spacing between the peaks is varied. We discuss generalizing the approach to higher dimensional PWC signals, although using this extension remains an interesting question for future research.

Role of the EGF receptor pathway in growth and patterning of the Drosophila wing through the regulation of vestigial

Development ◽  
1999 ◽  
Vol 126 (5) ◽  
pp. 975-985 ◽  
Author(s):  
R. Nagaraj ◽  
A.T. Pickup ◽  
R. Howes ◽  
K. Moses ◽  
M. Freeman ◽  
...  
Keyword(s):  
Egf Receptor ◽  
Regulatory Gene ◽  
Ectopic Expression ◽  
Wing Disc ◽  
Loss Of Function ◽  
Drosophila Wing ◽  
Expression Studies ◽  
Coordinated Expression ◽  
Wing Pouch

Growth and patterning of the Drosophila wing disc depends on the coordinated expression of the key regulatory gene vestigial both in the Dorsal-Ventral (D/V) boundary cells and in the wing pouch. We propose that a short-range signal originating from the core of the D/V boundary cells is responsible for activating EGFR in a zone of organizing cells on the edges of the D/V boundary. Using loss-of-function mutations and ectopic expression studies, we show that EGFR signaling is essential for vestigial transcription in these cells and for making them competent to undergo subsequent vestigial-mediated proliferation within the wing pouch.

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