Power-law run length distributions obtained by superposing exponential distributions.

<p><b>A</b>): Nine exponential run length distributions for random walks with constant tumbling probabilities . The curves are plotted on double-logarithmic axes to demonstrate the power-law that results from their superposition. <b>B</b>): The superposition of the nine exponential distributions from A) leading to a power-law distribution (blue dots) with the exponent obtained by fitting (solid black line). The cumulative distribution of the same data is plotted in the inset. <b>C</b>): Combined run length distribution (blue dots) of the 9 bacteria from numerical simulations with constant CheR levels ( between 0.04 and 0.12, corresponding to the 9 values of from A)). The fitted exponent (solid black line) is again .</p

Run length distribution corresponding to different distributions of the CheR concentration level.

<p>Run length distribution corresponding to different distributions of the CheR concentration level.</p

Run length distributions from a numerical simulation of <i>E. coli</i> in nutrient free environment with deterministic and periodic (zigzag) CheR dynamics with uniform distribution on the interval .

<p>Both figures contain three panels. The upper left shows the CheR level variation , the lower left the correlation between consecutive run lengths and the right one the distribution of the run lengths . Signals with two different frequencies are compared: <b>A</b>) relatively high frequency and <b>B</b>) relatively low frequency. The power-law run length distributions extends over at least two decades in B) while it is confined to about one decade in A).</p

TGFβ enhances cell attraction to focal FGF sources.

<p>(A, B) Quantitative reverse transcription polymerase chain reaction (qRT-PCR) of E13.5 or E13.75 (with condensates) skins treated with transforming growth factor (TGF) β2, fibroblast growth factor (FGF) 9, or bone morphogenetic protein (BMP) 4 for 8 or 24 h, respectively, followed by assessment of transcript abundance. TGFβ2 upregulates expression of genes associated with cell movement and the extracellular matrix. Statistical significance from control was calculated using a Student <i>t</i> test (*<i>p</i> < 0.05, **<i>p</i> < 0.01, ***<i>p</i> < 0.001). Error bars represent SEM from at least 3 independent experiments. (C) Cell aggregation at FGF9 beads in E12.5 TCF/Lef::H2B-green fluorescent protein (GFP) skin explants. TGFβ2 (100 ng/ml) or LY2109761 (25 μM) is present in the culture medium as indicated. TGFβ2 enhances aggregation at FGF9 beads, while LY2109761 suppresses cell accumulation. (D) FGF9 presence in culture medium does not detectably increase cell recruitment to TGFβ2 beads. (E, F) Quantification of areas of high cell density around FGF9- or TGFβ2-coated beads under conditions as indicated. Statistical significance was calculated using Student <i>t</i> tests (*<i>p</i> < 0.05, **<i>p</i> < 0.01, ***<i>p</i> < 0.001). Error bars represent SEM of at least 3 independent experiments. Scale bars: 250 μm. The raw numerical values (for A, B, E, and F) can be found in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2002117#pbio.2002117.s016" target="_blank">S4 Data</a>.</p

BMP destabilises mesenchymal aggregates.

<p>(A) Epidermis and dermis isolated from E13.5 TCF/Lef::H2B-green fluorescent protein (GFP) skin explants cultured with LDN193189 (LDN) (10 μM) or fibroblast growth factor (FGF) 9 (1 μg/ml) for 27 h, counterstained with propidium iodide (PI) and imaged using confocal microscopy. Scale bar: 100 μm. (B) Number of condensates per square mm, (C) mean condensate area, and (D) intercondensate cell density measured in E13.5 TCF/Lef::H2B-GFP skin explants cultured with either LDN or FGF. Error bars represent SEM from 5 independent experiments. Significant difference was calculated using a Student paired <i>t</i> test (*<i>p</i> < 0.05, **<i>p</i> < 0.01, ***<i>p</i> < 0.001). (E) E13.75 TCF/Lef::H2B-GFP skin explants (with pre-existing dermal condensates) were treated with bone morphogenetic protein (BMP) 4 for 72 h. Skins were counterstained with 4’6-Diamidino-2-phenylindole dihydrochloride (DAPI) and confocal imaged for GFP at 72 h. Scale bars: 100 μm. (F) Quantification of individual condensate area following BMP supplementation. Error bars represent SEM from at least 3 independent experiments. Significant difference was tested using a paired Student <i>t</i> test (*<i>p</i> < 0.05, **<i>p</i> < 0.01, ***<i>p</i> < 0.001). The raw numerical values (for B, C, D, and F) can be found in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2002117#pbio.2002117.s015" target="_blank">S3 Data</a>.</p

Dermal condensate formation occurs after epidermal patterning through local cell attraction.

<p>(A) Single frames from time-lapse sequences of E13.5 TCF/Lef::H2B-green fluorescent protein (GFP) skin explant culture captured by confocal microscopy. Dashed circles indicate ultimate condensate location. Scale bar: 50 μm. (B) Analysis of tracked cells showing the probability of joining the dermal condensate based upon initial location relative to its centre. Two hundred and forty individual cells were tracked across 8 condensates from 4 independent skins. (C) Protractor plot showing the distribution of Euclidean angles and Euclidean distances of individual cell movements in 6-h windows for cell tracks that start outside of, but ultimately terminate in, a follicle (condensate = red) and those that remain outside (intercondensate = blue). Tracking was halted on cell entry. (D) Plots showing the mean Euclidean angle (top) and mean level of persistence (bottom) of condensate-entering and intercondensate cells for 6-h windows relative to time of entry into the condensate. Error bars represent SEM (condensate cells <i>n</i> = 9, 14, and 20 and intercondensate <i>n</i> = 263, 245, and 197 for 12, 6, and 0 h before entry, respectively). Statistical significance was calculated using a Kruskal–Wallis test (<i>p</i> < 0.0001 and <i>p</i> < 0.001 for angle and persistence, respectively) followed by Mann–Whitney U tests with Bonferroni’s correction (**<i>p</i> < 0.01). The raw numerical tracking data (for B, C, and D) can be found in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2002117#pbio.2002117.s014" target="_blank">S2 Data</a>. (E) Detection of a molecular prepattern prior to dermal condensate formation. TCF/Lef::H2B-GFP skin explants were fixed at intermediate stages of pattern formation, imaged to detect GFP, and <i>Dkk4</i> expression determined in the same skin sample. Asterisk represents an area where <i>Dkk4</i>-positive foci are present but corresponding dermal condensates are absent. Scale bar: 500 μm. (F) Time-lapse images of E12.75 TCF/Lef::H2B-GFP dorsal skin explants cultured with recombinant fibroblast growth factor (FGF) 9- or bovine serum albumin (BSA)-loaded beads. Cells accumulate around FGF9-loaded beads. Scale bar: 250 μm.</p

Dependence of mesenchyme-only patterning on restricted TGFβ availability.

<p>(A) Western blot detection of phospho-SMAD2, total SMAD2 and γ-tubulin in E13.5 skin cultures treated with recombinant transforming growth factor (TGF) β2 (100 ng/ml), the TGFβ receptor inhibitor LY2109761 (25 μM,) or both agents for 8 h. (B) Effects of TGFβ2 supplementation and LY2109761 on normal and mesenchyme-only patterning. Condensates are slow to appear in LY2109761, and expression of the placode marker <i>Dkk4</i> expands through the epidermis. Mesenchyme-only patterning in FGF^HiBMP^Lo conditions is abolished upon either suppression or augmentation of TGFβ signalling. Scale bars: 250 μm. (C) Whole-mount in situ hybridisation (top panel) and corresponding transverse section (bottom panel) detecting spatial arrangement of <i>Tgfb2</i> expression in E14.5 mouse embryos. Expression is most intense at sites of dermal condensate formation. Scale bars: top panel = 1 mm, bottom panel = 50 μm. (D) At E13.5, phospho-SMAD2 immunofluorescence detects signal throughout the dermal mesenchyme (De.) and epidermis (Ep.), with this signal becoming intensified in the nascent dermal condensate at E14.5 (arrowhead). Epidermis is demarcated by dotted lines. Scale bar: 25 μm. (E) Dermal mesenchymal cell attraction (arrows) to sources of TGFβ2. Images of bovine serum albumin (BSA) control and TGFβ2 loaded beads placed on E12.5 TCF/Lef::H2B-green fluorescent protein (GFP) skin for 48 h. Scale bars: 250 μm.</p

Cell behaviours underlying mesenchymal self-organisation.

<p>(A) Time-lapse images showing dermal condensate formation in FGF^HiBMP^Lo conditions. Scale bar: 50 μm. (B) Protractor plot showing the distribution of Euclidean angles and Euclidean distances of individual cell movements in 6-h windows for cell tracks that start outside of, but ultimately terminate in, a follicle (condensate = red) and those that remain outside (intercondensate = blue) under FGF^HiBMP^Lo conditions. Tracking was halted on cell entry. Plots showing (C) the mean Euclidean angle and (D) the mean level of persistence of condensate and intercondensate cells for 360-minute windows relative to time of entry into the condensate. From 6 h before entry, the condensate-bound cells show oriented and persistent movement under FGF^HiBMP^Lo conditions. Error bars represent SEM (condensate cells <i>n</i> = 17, 21, and 25 and intercondensate <i>n</i> = 91, 104, and 108 for 12, 6, and 0 h before entry, respectively). Statistical significance was calculated using a Kruskal–Wallis test followed by Mann–Whitney U tests with Bonferroni’s correction (***<i>p</i> < 0.001). (E) Comparison between per track summaries of condensate (Cond.) and intercondensate (Int.) cells under control or FGF^HiBMP^Lo conditions for (top) accumulated velocity, (middle) Euclidian velocity, and (bottom) persistence. Statistical significance was calculated using a Kruskal–Wallis test followed by Mann–Whitney U tests with Bonferroni’s correction (*<i>p</i> < 0.05, ***<i>p</i> < 0.001). Error bars represent SEM (control intercondensate <i>n</i> = 292, control condensate <i>n</i> = 28, FGF^HiBMP^Lo intercondensate <i>n</i> = 137 and FGF^HiBMP^Lo condensate <i>n</i> = 33). Raw tracking data for (B–E) can be found in <a href="http://www.plosbiology.org/article/info:doi/10.1371/journal.pbio.2002117#pbio.2002117.s014" target="_blank">S2 Data</a>. (F) Particle image velocimetry analysis of normal and FGF^HiBMP^Lo condensate formation over 30 h. Coloured tracks show very local cell movement in control conditions but a much broader field of recruitment for the mesenchyme-only patterned condensates. Colour scale shows track length. Scale bar: 100 μm. (G) Simulation of boundary effects on patterning in chemotactic aggregation-driven patterning. (H) Experimental test of pattern behaviours. Distinct pattern behaviours at tissue edges. Under control conditions, primordia align along the edge. FGF^HiBMP^Lo condensates align with but form at a distance from boundaries introduced in skin explants prior to pattern formation. White dotted lines indicate the boundary. Magenta dotted lines indicate the extent of the patterned region where dermal condensates form. Scale bar: 250 μm.</p

Significant correlations between clinical symptoms and social cognition measures in SC.

<p>(A) Negative correlation between depression symptoms and intention to hurt ratings for intentional pain situations. (B) Negative correlation between depression symptoms and correctness ratings for intentional pain situations. (C) Negative correlation between depression symptoms and punishment ratings for intentional pain situations.</p

Emotional morphing accuracy and reaction times.

<p>RTs = Reaction Times.</p