nearest neighbor delaunay triangulation Search Results


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Dsearchn Function, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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MathWorks Inc delaunay triangulation matlab script
Representative images of focal adhesions immunostained with paxillin (top) and paxillin/F- actin (bottom) for siCT(A), siCRB3 (B), siARP2/3 (C), at 0hr and siCT (A’), siCRB3 (B’), Arp2/3 (C’) at 10r.. Scale bars 10µm. Representative maps of the <t>Delaunay</t> <t>Triangulation</t> of paxillin for siCT (D), siCRB3 (E), siARP2/3 (F) at 0hr and siCT (D’), siCRB3 (E’), siARP2/3 (F’) at 10hr. Scale Bar 10µm. G) Quantification of the major length of the focal contacts is represented as dashed box plots (0hr) and empty box plot (10hr). Data are represented as mean ± Min Max. H) Quantification of the orientation of the focal contacts is represented as dashed box plots (0hr) and empty box plot (10hr). Data are represented as mean ± Min Max. The total number of focal contacts quantified for siCT, blue, n = 2530, 6 fields of view, 0hr, n= 6652, 15 fields of view, 10hr; siCRB3, red, n=2230, 4 fields of view, 0hr,n=7410, 17 fields, 10hr; siARP2/3, grey, n=1476, 4 fields of view, 0hr, n =5806, 13 fields of view, 10hr. Data are presented as mean ± Min Max. I) Quantification of the area of the triangle obtained by a Delaunay triangulation over all the focal contacts for each siRNA condition at 0hr (dashed boxplot) and at 10hr (empty boxplot). The box plots represent the mean ± Min Max of all the triangles measured for each siRNAs. siCT, blue, n=23232, 7 fields of view, 0hr, n= 25140, 16 fields of view, 10hr; siCRB3, red, n= 12917, 4 fields of view, 0hr, n=37164, 18 fields of view, 10hr, siARP2/3, grey, n= 11737, n=4, 0hr, n= 13816, 6 fields of view, 10hr.
Delaunay Triangulation Matlab Script, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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MathWorks Inc nearest neighbor delaunay triangulation
Representative images of focal adhesions immunostained with paxillin (top) and paxillin/F- actin (bottom) for siCT(A), siCRB3 (B), siARP2/3 (C), at 0hr and siCT (A’), siCRB3 (B’), Arp2/3 (C’) at 10r.. Scale bars 10µm. Representative maps of the <t>Delaunay</t> <t>Triangulation</t> of paxillin for siCT (D), siCRB3 (E), siARP2/3 (F) at 0hr and siCT (D’), siCRB3 (E’), siARP2/3 (F’) at 10hr. Scale Bar 10µm. G) Quantification of the major length of the focal contacts is represented as dashed box plots (0hr) and empty box plot (10hr). Data are represented as mean ± Min Max. H) Quantification of the orientation of the focal contacts is represented as dashed box plots (0hr) and empty box plot (10hr). Data are represented as mean ± Min Max. The total number of focal contacts quantified for siCT, blue, n = 2530, 6 fields of view, 0hr, n= 6652, 15 fields of view, 10hr; siCRB3, red, n=2230, 4 fields of view, 0hr,n=7410, 17 fields, 10hr; siARP2/3, grey, n=1476, 4 fields of view, 0hr, n =5806, 13 fields of view, 10hr. Data are presented as mean ± Min Max. I) Quantification of the area of the triangle obtained by a Delaunay triangulation over all the focal contacts for each siRNA condition at 0hr (dashed boxplot) and at 10hr (empty boxplot). The box plots represent the mean ± Min Max of all the triangles measured for each siRNAs. siCT, blue, n=23232, 7 fields of view, 0hr, n= 25140, 16 fields of view, 10hr; siCRB3, red, n= 12917, 4 fields of view, 0hr, n=37164, 18 fields of view, 10hr, siARP2/3, grey, n= 11737, n=4, 0hr, n= 13816, 6 fields of view, 10hr.
Nearest Neighbor Delaunay Triangulation, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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Mendeley Ltd delaunay triangulation
Unbiased Identification of i-niches in Multidimensional CODEX Data (A) On the left diagram explaining the terminology used for defining i-niche (a ring of first tier neighbors for central cell). On the right <t>Delaunay</t> <t>triangulation</t> graph used for identification of first tier of neighbors for every cell. (B) Heatmap depicting frequency of cell types in 100 types of i-niches identified by K-means (K = 100) clustering of all index cells in the dataset (each cell is an index cell for its i-niche) based on frequency of different cell types in the first tier of neighbors. The color indicates the average fraction of corresponding cell type in the the i-niche. (C) An example of marginal zone and follicular (B-zone) B cells defined by residence in distinct i-niches (e.g., marginal zone i-niche includes a marginal zone macrophage marked by letter H and green color). Positions of B cells in each i-niche is marked with red circles over the schematic of BALBc spleen. (D and E) Two heatmaps from top to bottom show average expression of selected surface markers measured in a central cell across 100 i-niches (same left to right order as in B) when central cell is B cells (D) or CD4 T cell (E) accordingly. The color indicates the relative level of surface-marker expression as measured across dataset. Gray columns indicate absence of cells in corresponding niches. Two orange rectangles over top heatmap indicates position of i-niches with high CD35 (containing FDCs and marginal zone macrophages). Cyan rectangle shows location of family of i-niches with high content of F4/80 macrophages and low B220 and CD19 in central B cells. Purple rectangle indicates family of i-niches enriched with ERTR-7 positive stroma. Below top heatmap, location of selected i-niches shown in (E) are indicated. Over bottom heatmap, yellow rectangle indicates the family of i-niches with dominating presence of B cells. Two green rectangles indicate family of niches with high levels of CD90 and CD27 in the index CD4 T cells. (F and G) Abundance of 100 i-niches in normal spleen (top bar graph) (F) and relative distribution of i-niches (G) between splenic histological subdivisions (PALS, red pulp, marginal zone, and B-zone) shown as a heatmap. To illustrate a variety of tissue distribution pattern by i-niches an overlay of selected i-niches over a schematic of normal spleen (BALBc-1) is shown. Heatmap color indicates fraction of corresponding i-niche per splenic anatomic subdivision. (H) Top right shows a biaxial plot of flow data for CD79b and B220 measured in isolated splenocytes. Top left shows levels of CD79b and B220 in central B cells as measured across all 100 i-niches. To illustrate i-niche-dependent variability of surface-marker expression, images of central cells (marked with red cross) with levels of surface marker indicated in pseudocolor palette are shown for selected exemplary i-niches in the bottom panels. See also K and S4L.
Delaunay Triangulation, supplied by Mendeley Ltd, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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MathWorks Inc delaunay triangulation
Unbiased Identification of i-niches in Multidimensional CODEX Data (A) On the left diagram explaining the terminology used for defining i-niche (a ring of first tier neighbors for central cell). On the right <t>Delaunay</t> <t>triangulation</t> graph used for identification of first tier of neighbors for every cell. (B) Heatmap depicting frequency of cell types in 100 types of i-niches identified by K-means (K = 100) clustering of all index cells in the dataset (each cell is an index cell for its i-niche) based on frequency of different cell types in the first tier of neighbors. The color indicates the average fraction of corresponding cell type in the the i-niche. (C) An example of marginal zone and follicular (B-zone) B cells defined by residence in distinct i-niches (e.g., marginal zone i-niche includes a marginal zone macrophage marked by letter H and green color). Positions of B cells in each i-niche is marked with red circles over the schematic of BALBc spleen. (D and E) Two heatmaps from top to bottom show average expression of selected surface markers measured in a central cell across 100 i-niches (same left to right order as in B) when central cell is B cells (D) or CD4 T cell (E) accordingly. The color indicates the relative level of surface-marker expression as measured across dataset. Gray columns indicate absence of cells in corresponding niches. Two orange rectangles over top heatmap indicates position of i-niches with high CD35 (containing FDCs and marginal zone macrophages). Cyan rectangle shows location of family of i-niches with high content of F4/80 macrophages and low B220 and CD19 in central B cells. Purple rectangle indicates family of i-niches enriched with ERTR-7 positive stroma. Below top heatmap, location of selected i-niches shown in (E) are indicated. Over bottom heatmap, yellow rectangle indicates the family of i-niches with dominating presence of B cells. Two green rectangles indicate family of niches with high levels of CD90 and CD27 in the index CD4 T cells. (F and G) Abundance of 100 i-niches in normal spleen (top bar graph) (F) and relative distribution of i-niches (G) between splenic histological subdivisions (PALS, red pulp, marginal zone, and B-zone) shown as a heatmap. To illustrate a variety of tissue distribution pattern by i-niches an overlay of selected i-niches over a schematic of normal spleen (BALBc-1) is shown. Heatmap color indicates fraction of corresponding i-niche per splenic anatomic subdivision. (H) Top right shows a biaxial plot of flow data for CD79b and B220 measured in isolated splenocytes. Top left shows levels of CD79b and B220 in central B cells as measured across all 100 i-niches. To illustrate i-niche-dependent variability of surface-marker expression, images of central cells (marked with red cross) with levels of surface marker indicated in pseudocolor palette are shown for selected exemplary i-niches in the bottom panels. See also K and S4L.
Delaunay Triangulation, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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(A) Simulating chromatin-scanning trajectories for 1,000 steps: after one step of nucleoplasmic diffusion (green), the probability to diffuse again (P diffusion , green) or interact with chromatin (P interaction , red) is inferred from diffusion coefficients. If chromatin interaction occurs, the probability to interact with a site in low- (P compact , black) versus high-mobility (P open , orange) chromatin is inferred from radius of confinements and average displacements. (B–D) Representative scanning trajectories by a single molecule of FOXA1 (B), SOX2 (C), and HNF4A (D) exploring 1,000 chromatin sites. Each step of diffusion is set to occur in a random direction. Red dots: binding to low-mobility, compact chromatin. White dots: binding to high-mobility, open chromatin. (E and F) Total time of chromatin interaction (E) or nucleoplasmic diffusion (F) during the exploration of 1,000 sites. (G) Average areas (μm ) after <t>Delaunay</t> triangulation of low-mobility chromatin interaction spatial coordinates for 10,000 simulated scanning trajectories. For all panels, ***p < 0.0001, n.s., non-significant differences (p > 0.05) as determined by one-way ANOVA.
Delaunay Function, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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Determination of physical tissue volume from a convex hull spanned between nuclei reidentified over time. ( a ) Stable patterns of nuclei were reidentified over all timepoints and nucleus centre coordinates were sampled as fiducial markers throughout all stack dimensions. Two examples of reidentified nuclei are indicated by blue arrows. Maximum intensity Z-projection of 10 optical sections covering 20 µm. Scale bar = 20 µm. ( b ) Fiducial marker coordinates plotted inside single stack volume. Dot colours specify fiducials that could be reidentified reliably at all three time points. Grid lines spaced in 100 µm. ( c ) Three-dimensional <t>Delaunay</t> <t>triangulation</t> from fiducials create matching tetrahedra. All tetrahedra create a convex hull (entire volume in blue) whose subtle volume changes indicate shrinkage or expansion of the tissue within.
3d Delaunay Triangulation, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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Determination of physical tissue volume from a convex hull spanned between nuclei reidentified over time. ( a ) Stable patterns of nuclei were reidentified over all timepoints and nucleus centre coordinates were sampled as fiducial markers throughout all stack dimensions. Two examples of reidentified nuclei are indicated by blue arrows. Maximum intensity Z-projection of 10 optical sections covering 20 µm. Scale bar = 20 µm. ( b ) Fiducial marker coordinates plotted inside single stack volume. Dot colours specify fiducials that could be reidentified reliably at all three time points. Grid lines spaced in 100 µm. ( c ) Three-dimensional <t>Delaunay</t> <t>triangulation</t> from fiducials create matching tetrahedra. All tetrahedra create a convex hull (entire volume in blue) whose subtle volume changes indicate shrinkage or expansion of the tissue within.
Delaunay Interpolation In The Matlab Software, supplied by MathWorks Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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Determination of physical tissue volume from a convex hull spanned between nuclei reidentified over time. ( a ) Stable patterns of nuclei were reidentified over all timepoints and nucleus centre coordinates were sampled as fiducial markers throughout all stack dimensions. Two examples of reidentified nuclei are indicated by blue arrows. Maximum intensity Z-projection of 10 optical sections covering 20 µm. Scale bar = 20 µm. ( b ) Fiducial marker coordinates plotted inside single stack volume. Dot colours specify fiducials that could be reidentified reliably at all three time points. Grid lines spaced in 100 µm. ( c ) Three-dimensional <t>Delaunay</t> <t>triangulation</t> from fiducials create matching tetrahedra. All tetrahedra create a convex hull (entire volume in blue) whose subtle volume changes indicate shrinkage or expansion of the tissue within.
Delaunay Triangulation Method, supplied by COMSOL Inc, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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Determination of physical tissue volume from a convex hull spanned between nuclei reidentified over time. ( a ) Stable patterns of nuclei were reidentified over all timepoints and nucleus centre coordinates were sampled as fiducial markers throughout all stack dimensions. Two examples of reidentified nuclei are indicated by blue arrows. Maximum intensity Z-projection of 10 optical sections covering 20 µm. Scale bar = 20 µm. ( b ) Fiducial marker coordinates plotted inside single stack volume. Dot colours specify fiducials that could be reidentified reliably at all three time points. Grid lines spaced in 100 µm. ( c ) Three-dimensional <t>Delaunay</t> <t>triangulation</t> from fiducials create matching tetrahedra. All tetrahedra create a convex hull (entire volume in blue) whose subtle volume changes indicate shrinkage or expansion of the tissue within.
Delaunay Decomposition, supplied by Springborn Laboratories, used in various techniques. Bioz Stars score: 90/100, based on 1 PubMed citations. ZERO BIAS - scores, article reviews, protocol conditions and more
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Determination of physical tissue volume from a convex hull spanned between nuclei reidentified over time. ( a ) Stable patterns of nuclei were reidentified over all timepoints and nucleus centre coordinates were sampled as fiducial markers throughout all stack dimensions. Two examples of reidentified nuclei are indicated by blue arrows. Maximum intensity Z-projection of 10 optical sections covering 20 µm. Scale bar = 20 µm. ( b ) Fiducial marker coordinates plotted inside single stack volume. Dot colours specify fiducials that could be reidentified reliably at all three time points. Grid lines spaced in 100 µm. ( c ) Three-dimensional <t>Delaunay</t> <t>triangulation</t> from fiducials create matching tetrahedra. All tetrahedra create a convex hull (entire volume in blue) whose subtle volume changes indicate shrinkage or expansion of the tissue within.
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Image Search Results


Representative images of focal adhesions immunostained with paxillin (top) and paxillin/F- actin (bottom) for siCT(A), siCRB3 (B), siARP2/3 (C), at 0hr and siCT (A’), siCRB3 (B’), Arp2/3 (C’) at 10r.. Scale bars 10µm. Representative maps of the Delaunay Triangulation of paxillin for siCT (D), siCRB3 (E), siARP2/3 (F) at 0hr and siCT (D’), siCRB3 (E’), siARP2/3 (F’) at 10hr. Scale Bar 10µm. G) Quantification of the major length of the focal contacts is represented as dashed box plots (0hr) and empty box plot (10hr). Data are represented as mean ± Min Max. H) Quantification of the orientation of the focal contacts is represented as dashed box plots (0hr) and empty box plot (10hr). Data are represented as mean ± Min Max. The total number of focal contacts quantified for siCT, blue, n = 2530, 6 fields of view, 0hr, n= 6652, 15 fields of view, 10hr; siCRB3, red, n=2230, 4 fields of view, 0hr,n=7410, 17 fields, 10hr; siARP2/3, grey, n=1476, 4 fields of view, 0hr, n =5806, 13 fields of view, 10hr. Data are presented as mean ± Min Max. I) Quantification of the area of the triangle obtained by a Delaunay triangulation over all the focal contacts for each siRNA condition at 0hr (dashed boxplot) and at 10hr (empty boxplot). The box plots represent the mean ± Min Max of all the triangles measured for each siRNAs. siCT, blue, n=23232, 7 fields of view, 0hr, n= 25140, 16 fields of view, 10hr; siCRB3, red, n= 12917, 4 fields of view, 0hr, n=37164, 18 fields of view, 10hr, siARP2/3, grey, n= 11737, n=4, 0hr, n= 13816, 6 fields of view, 10hr.

Journal: bioRxiv

Article Title: CRB3 and ARP2/3 regulate cell biomechanical properties to set epithelial monolayers for collective movement

doi: 10.1101/2023.04.18.537332

Figure Lengend Snippet: Representative images of focal adhesions immunostained with paxillin (top) and paxillin/F- actin (bottom) for siCT(A), siCRB3 (B), siARP2/3 (C), at 0hr and siCT (A’), siCRB3 (B’), Arp2/3 (C’) at 10r.. Scale bars 10µm. Representative maps of the Delaunay Triangulation of paxillin for siCT (D), siCRB3 (E), siARP2/3 (F) at 0hr and siCT (D’), siCRB3 (E’), siARP2/3 (F’) at 10hr. Scale Bar 10µm. G) Quantification of the major length of the focal contacts is represented as dashed box plots (0hr) and empty box plot (10hr). Data are represented as mean ± Min Max. H) Quantification of the orientation of the focal contacts is represented as dashed box plots (0hr) and empty box plot (10hr). Data are represented as mean ± Min Max. The total number of focal contacts quantified for siCT, blue, n = 2530, 6 fields of view, 0hr, n= 6652, 15 fields of view, 10hr; siCRB3, red, n=2230, 4 fields of view, 0hr,n=7410, 17 fields, 10hr; siARP2/3, grey, n=1476, 4 fields of view, 0hr, n =5806, 13 fields of view, 10hr. Data are presented as mean ± Min Max. I) Quantification of the area of the triangle obtained by a Delaunay triangulation over all the focal contacts for each siRNA condition at 0hr (dashed boxplot) and at 10hr (empty boxplot). The box plots represent the mean ± Min Max of all the triangles measured for each siRNAs. siCT, blue, n=23232, 7 fields of view, 0hr, n= 25140, 16 fields of view, 10hr; siCRB3, red, n= 12917, 4 fields of view, 0hr, n=37164, 18 fields of view, 10hr, siARP2/3, grey, n= 11737, n=4, 0hr, n= 13816, 6 fields of view, 10hr.

Article Snippet: XY position of all centroids were used to build triangles between the nearest neighbors with the Delaunay Triangulation Matlab script.

Techniques:

Unbiased Identification of i-niches in Multidimensional CODEX Data (A) On the left diagram explaining the terminology used for defining i-niche (a ring of first tier neighbors for central cell). On the right Delaunay triangulation graph used for identification of first tier of neighbors for every cell. (B) Heatmap depicting frequency of cell types in 100 types of i-niches identified by K-means (K = 100) clustering of all index cells in the dataset (each cell is an index cell for its i-niche) based on frequency of different cell types in the first tier of neighbors. The color indicates the average fraction of corresponding cell type in the the i-niche. (C) An example of marginal zone and follicular (B-zone) B cells defined by residence in distinct i-niches (e.g., marginal zone i-niche includes a marginal zone macrophage marked by letter H and green color). Positions of B cells in each i-niche is marked with red circles over the schematic of BALBc spleen. (D and E) Two heatmaps from top to bottom show average expression of selected surface markers measured in a central cell across 100 i-niches (same left to right order as in B) when central cell is B cells (D) or CD4 T cell (E) accordingly. The color indicates the relative level of surface-marker expression as measured across dataset. Gray columns indicate absence of cells in corresponding niches. Two orange rectangles over top heatmap indicates position of i-niches with high CD35 (containing FDCs and marginal zone macrophages). Cyan rectangle shows location of family of i-niches with high content of F4/80 macrophages and low B220 and CD19 in central B cells. Purple rectangle indicates family of i-niches enriched with ERTR-7 positive stroma. Below top heatmap, location of selected i-niches shown in (E) are indicated. Over bottom heatmap, yellow rectangle indicates the family of i-niches with dominating presence of B cells. Two green rectangles indicate family of niches with high levels of CD90 and CD27 in the index CD4 T cells. (F and G) Abundance of 100 i-niches in normal spleen (top bar graph) (F) and relative distribution of i-niches (G) between splenic histological subdivisions (PALS, red pulp, marginal zone, and B-zone) shown as a heatmap. To illustrate a variety of tissue distribution pattern by i-niches an overlay of selected i-niches over a schematic of normal spleen (BALBc-1) is shown. Heatmap color indicates fraction of corresponding i-niche per splenic anatomic subdivision. (H) Top right shows a biaxial plot of flow data for CD79b and B220 measured in isolated splenocytes. Top left shows levels of CD79b and B220 in central B cells as measured across all 100 i-niches. To illustrate i-niche-dependent variability of surface-marker expression, images of central cells (marked with red cross) with levels of surface marker indicated in pseudocolor palette are shown for selected exemplary i-niches in the bottom panels. See also K and S4L.

Journal: Cell

Article Title: Deep Profiling of Mouse Splenic Architecture with CODEX Multiplexed Imaging

doi: 10.1016/j.cell.2018.07.010

Figure Lengend Snippet: Unbiased Identification of i-niches in Multidimensional CODEX Data (A) On the left diagram explaining the terminology used for defining i-niche (a ring of first tier neighbors for central cell). On the right Delaunay triangulation graph used for identification of first tier of neighbors for every cell. (B) Heatmap depicting frequency of cell types in 100 types of i-niches identified by K-means (K = 100) clustering of all index cells in the dataset (each cell is an index cell for its i-niche) based on frequency of different cell types in the first tier of neighbors. The color indicates the average fraction of corresponding cell type in the the i-niche. (C) An example of marginal zone and follicular (B-zone) B cells defined by residence in distinct i-niches (e.g., marginal zone i-niche includes a marginal zone macrophage marked by letter H and green color). Positions of B cells in each i-niche is marked with red circles over the schematic of BALBc spleen. (D and E) Two heatmaps from top to bottom show average expression of selected surface markers measured in a central cell across 100 i-niches (same left to right order as in B) when central cell is B cells (D) or CD4 T cell (E) accordingly. The color indicates the relative level of surface-marker expression as measured across dataset. Gray columns indicate absence of cells in corresponding niches. Two orange rectangles over top heatmap indicates position of i-niches with high CD35 (containing FDCs and marginal zone macrophages). Cyan rectangle shows location of family of i-niches with high content of F4/80 macrophages and low B220 and CD19 in central B cells. Purple rectangle indicates family of i-niches enriched with ERTR-7 positive stroma. Below top heatmap, location of selected i-niches shown in (E) are indicated. Over bottom heatmap, yellow rectangle indicates the family of i-niches with dominating presence of B cells. Two green rectangles indicate family of niches with high levels of CD90 and CD27 in the index CD4 T cells. (F and G) Abundance of 100 i-niches in normal spleen (top bar graph) (F) and relative distribution of i-niches (G) between splenic histological subdivisions (PALS, red pulp, marginal zone, and B-zone) shown as a heatmap. To illustrate a variety of tissue distribution pattern by i-niches an overlay of selected i-niches over a schematic of normal spleen (BALBc-1) is shown. Heatmap color indicates fraction of corresponding i-niche per splenic anatomic subdivision. (H) Top right shows a biaxial plot of flow data for CD79b and B220 measured in isolated splenocytes. Top left shows levels of CD79b and B220 in central B cells as measured across all 100 i-niches. To illustrate i-niche-dependent variability of surface-marker expression, images of central cells (marked with red cross) with levels of surface marker indicated in pseudocolor palette are shown for selected exemplary i-niches in the bottom panels. See also K and S4L.

Article Snippet: For each segmented object (i.e., cell) a marker expression profile, as well as the identities of the nearby neighbors were recorded using Delaunay triangulation ( https://data.mendeley.com/datasets/zjnpwh8m5b/1 ).

Techniques: Expressing, Marker, Isolation

(A) Simulating chromatin-scanning trajectories for 1,000 steps: after one step of nucleoplasmic diffusion (green), the probability to diffuse again (P diffusion , green) or interact with chromatin (P interaction , red) is inferred from diffusion coefficients. If chromatin interaction occurs, the probability to interact with a site in low- (P compact , black) versus high-mobility (P open , orange) chromatin is inferred from radius of confinements and average displacements. (B–D) Representative scanning trajectories by a single molecule of FOXA1 (B), SOX2 (C), and HNF4A (D) exploring 1,000 chromatin sites. Each step of diffusion is set to occur in a random direction. Red dots: binding to low-mobility, compact chromatin. White dots: binding to high-mobility, open chromatin. (E and F) Total time of chromatin interaction (E) or nucleoplasmic diffusion (F) during the exploration of 1,000 sites. (G) Average areas (μm ) after Delaunay triangulation of low-mobility chromatin interaction spatial coordinates for 10,000 simulated scanning trajectories. For all panels, ***p < 0.0001, n.s., non-significant differences (p > 0.05) as determined by one-way ANOVA.

Journal: Cell reports

Article Title: Different chromatin-scanning modes lead to targeting of compacted chromatin by pioneer factors FOXA1 and SOX2

doi: 10.1016/j.celrep.2023.112748

Figure Lengend Snippet: (A) Simulating chromatin-scanning trajectories for 1,000 steps: after one step of nucleoplasmic diffusion (green), the probability to diffuse again (P diffusion , green) or interact with chromatin (P interaction , red) is inferred from diffusion coefficients. If chromatin interaction occurs, the probability to interact with a site in low- (P compact , black) versus high-mobility (P open , orange) chromatin is inferred from radius of confinements and average displacements. (B–D) Representative scanning trajectories by a single molecule of FOXA1 (B), SOX2 (C), and HNF4A (D) exploring 1,000 chromatin sites. Each step of diffusion is set to occur in a random direction. Red dots: binding to low-mobility, compact chromatin. White dots: binding to high-mobility, open chromatin. (E and F) Total time of chromatin interaction (E) or nucleoplasmic diffusion (F) during the exploration of 1,000 sites. (G) Average areas (μm ) after Delaunay triangulation of low-mobility chromatin interaction spatial coordinates for 10,000 simulated scanning trajectories. For all panels, ***p < 0.0001, n.s., non-significant differences (p > 0.05) as determined by one-way ANOVA.

Article Snippet: To measure the density of compact chromatin scanning in the 10,000 trajectories simulated by viz_tool3.m, the script uses the Delaunay function of MATLAB to triangulate the coordinates of compact chromatin scanning events (red dots in viz_tool2.m), and calculate the areas of the Delaunay territories (see ).

Techniques: Diffusion-based Assay, Binding Assay

(A) FOXA1-RRAA mutations in wing 2 target amino acids interacting with the DNA backbone and impair non-specific DNA binding. (B) FOXA1-NHAA mutations in alpha helix 3 target amino acids interacting with the DNA bases and impair specific DNA binding. (C) Representative scanning trajectories. (D) Average areas (μm 2 ) after Delaunay triangulation of low-mobility chromatin interaction spatial coordinates for 10,000 simulated scanning trajectories of FOXA1-WT, NHAA, and RRAA. ***p < 0.0001, n.s., non-significant differences (p > 0.05) as determined by one-way ANOVA.

Journal: Cell reports

Article Title: Different chromatin-scanning modes lead to targeting of compacted chromatin by pioneer factors FOXA1 and SOX2

doi: 10.1016/j.celrep.2023.112748

Figure Lengend Snippet: (A) FOXA1-RRAA mutations in wing 2 target amino acids interacting with the DNA backbone and impair non-specific DNA binding. (B) FOXA1-NHAA mutations in alpha helix 3 target amino acids interacting with the DNA bases and impair specific DNA binding. (C) Representative scanning trajectories. (D) Average areas (μm 2 ) after Delaunay triangulation of low-mobility chromatin interaction spatial coordinates for 10,000 simulated scanning trajectories of FOXA1-WT, NHAA, and RRAA. ***p < 0.0001, n.s., non-significant differences (p > 0.05) as determined by one-way ANOVA.

Article Snippet: To measure the density of compact chromatin scanning in the 10,000 trajectories simulated by viz_tool3.m, the script uses the Delaunay function of MATLAB to triangulate the coordinates of compact chromatin scanning events (red dots in viz_tool2.m), and calculate the areas of the Delaunay territories (see ).

Techniques: Binding Assay

(A and B) SOX2- (A) and FOXA1-HALO/V5 (B) constructs and corresponding DBD truncations. (C and D) ChIP-seq and DNase-seq signals for SOX2, SOX2-DBD (C), and FOXA1, FOXA1-DBD (D), at shared peaks (top panel) or peaks bound only by the full-length proteins. (E) SMT measurement of scanning of low-mobility, compact chromatin by HALO-tagged SOX2 and FOXA1 full-length and DBD truncations. (F) Representative scanning trajectories by a single molecule of SOX2-DBD and FOXA1-DBD. (G and H) Average areas (μm 2 ) after Delaunay triangulation of low-mobility, compact chromatin interactions spatial coordinates for 10,000 simulated scanning trajectories of full-length or DBD truncations of SOX2 (G) and FOXA1 (H). ***p < 0.0001, n.s., non-significant differences (p > 0.05) as determined by one-way ANOVA.

Journal: Cell reports

Article Title: Different chromatin-scanning modes lead to targeting of compacted chromatin by pioneer factors FOXA1 and SOX2

doi: 10.1016/j.celrep.2023.112748

Figure Lengend Snippet: (A and B) SOX2- (A) and FOXA1-HALO/V5 (B) constructs and corresponding DBD truncations. (C and D) ChIP-seq and DNase-seq signals for SOX2, SOX2-DBD (C), and FOXA1, FOXA1-DBD (D), at shared peaks (top panel) or peaks bound only by the full-length proteins. (E) SMT measurement of scanning of low-mobility, compact chromatin by HALO-tagged SOX2 and FOXA1 full-length and DBD truncations. (F) Representative scanning trajectories by a single molecule of SOX2-DBD and FOXA1-DBD. (G and H) Average areas (μm 2 ) after Delaunay triangulation of low-mobility, compact chromatin interactions spatial coordinates for 10,000 simulated scanning trajectories of full-length or DBD truncations of SOX2 (G) and FOXA1 (H). ***p < 0.0001, n.s., non-significant differences (p > 0.05) as determined by one-way ANOVA.

Article Snippet: To measure the density of compact chromatin scanning in the 10,000 trajectories simulated by viz_tool3.m, the script uses the Delaunay function of MATLAB to triangulate the coordinates of compact chromatin scanning events (red dots in viz_tool2.m), and calculate the areas of the Delaunay territories (see ).

Techniques: Construct, ChIP-sequencing

Determination of physical tissue volume from a convex hull spanned between nuclei reidentified over time. ( a ) Stable patterns of nuclei were reidentified over all timepoints and nucleus centre coordinates were sampled as fiducial markers throughout all stack dimensions. Two examples of reidentified nuclei are indicated by blue arrows. Maximum intensity Z-projection of 10 optical sections covering 20 µm. Scale bar = 20 µm. ( b ) Fiducial marker coordinates plotted inside single stack volume. Dot colours specify fiducials that could be reidentified reliably at all three time points. Grid lines spaced in 100 µm. ( c ) Three-dimensional Delaunay triangulation from fiducials create matching tetrahedra. All tetrahedra create a convex hull (entire volume in blue) whose subtle volume changes indicate shrinkage or expansion of the tissue within.

Journal: Scientific Reports

Article Title: Cellular correlates of gray matter volume changes in magnetic resonance morphometry identified by two-photon microscopy

doi: 10.1038/s41598-021-83491-8

Figure Lengend Snippet: Determination of physical tissue volume from a convex hull spanned between nuclei reidentified over time. ( a ) Stable patterns of nuclei were reidentified over all timepoints and nucleus centre coordinates were sampled as fiducial markers throughout all stack dimensions. Two examples of reidentified nuclei are indicated by blue arrows. Maximum intensity Z-projection of 10 optical sections covering 20 µm. Scale bar = 20 µm. ( b ) Fiducial marker coordinates plotted inside single stack volume. Dot colours specify fiducials that could be reidentified reliably at all three time points. Grid lines spaced in 100 µm. ( c ) Three-dimensional Delaunay triangulation from fiducials create matching tetrahedra. All tetrahedra create a convex hull (entire volume in blue) whose subtle volume changes indicate shrinkage or expansion of the tissue within.

Article Snippet: From these coordinates, we calculated a 3D Delaunay triangulation in MATLAB and determined the volume formed by the resulting convex hull (Fig. c).

Techniques: Marker