Fig 1.
(A) Stolon bearing traps. Insert shows mature trap. Red line drawn from mouth (right) to the furthest point at the back of the trap. (B) OPT volume views of a trap in lateral view (top) or ventral view (bottom). (C) Volume view clipped in the sagittal plane. Coloured squares indicate landmarks: dorsal lip (red), ventral lip (magenta), and stalk indentation (green). Domains between these landmarks are colour-coded as red (dorsal midline), magenta (ventral midline), and green (stalk). Data https://doi.org/10.6084/m9.figshare.8966153.v1, Fig 1.7z archive. OPT, Optical Projection Tomography.
Fig 2.
Trap shape at mature and early stages.
(A) Volume view of a PI-stained mature U. gibba trap visualised by OPT. Three section planes are shown. PI fluorescence is red, and tissue autofluorescence is green (S1 Movie). (B–D) Green OPT channel clipped along the transverse (B), frontal (C), and sagittal (D) planes. Red channel is left in place to show region of the trap clipped away in E–G. (E–G) Shapes fitted to circumference in each plane: transverse, cyan (E); frontal, orange (F); sagittal, red (G). (H–J) Superimposed circumferences of six mature traps, colour-coded as in E–G, S1 Data. Ellipses were fitted to transverse and frontal circumferences (H, I). Sagittal circumference was drawn (J). (K) Volume view of young PI-stained U. gibba trap visualised by confocal microscopy. Three section planes colour-coded as in A, S2 Movie. (L–N) Dorsal (top) (L), ventral (front) (M), and lateral (side) (N) volume views. (O–Q) Ellipses fitted to circumference in each clipped plane colour-coded as in E–G. (R–T) Superimposed circumferences of seven young traps, colour-coded as in E–G, S1 Data. For H–J and R–T, circumferences were manually scaled and rotated to align with a common axis (shown as a line through the middle of each circumference). For both OPT and confocal data, lines were measured in the transverse plane from centre of mouth to back of trap, frontal plane at narrowest region between walls, sagittal plane from dorsal lip to back of trap, S2 Data. Scale bar refers to mean length of the common line. Data https://doi.org/10.6084/m9.figshare.8966153.v1, Fig 2.7z archive. OPT, Optical Projection Tomography; PI, propidium iodide.
Fig 3.
Developmental stages and growth rates.
(A–I) Clipped sagittal volume views of traps 4–11 DAI (in blue numbers above trap). Traps were stained with PI and visualised in three dimensions from confocal image stacks (A–F) and OPT reconstructions (G–I). Smaller traps within the circinate apex and traps with occluding stolon tissue were virtually dissected with VolViewer. Coloured squares indicate landmarks as described in Fig 1C. (J–K) Trap growth charts (S3 Data). (J) Natural log of trap length plotted against time for live imaging of traps at daily intervals. A best-fit line was extrapolated back to when the bladder was 10 μm long (dashed line), corresponding to 1–2 cells, which we took to be the initiation stage of the bladder. Mean growth rate was 1.8% h−1 ± 0.13 (R2 = 0.9607). Blue region shows developmental range of fixed traps analysed in (A–I) and (K, L). (K) Natural log of circumferences measured in VolViewer for transverse (cyan), frontal (orange), and sagittal (red) sections plotted against time (DAI, based on J). Growth rates: 1.52% h−1 ± 0.07 (R2 = 0.9757, n = 46), 1.39% h−1 ± 0.06 (R2 = 0.9772, n = 50), and 1 .65% h−1 ± 0.06 (R2 = 0.9832, n = 52), respectively. For mature traps, where it was not possible to image the entire depth of the trap by confocal microscopy, half the circumference was measured, and this value was doubled to obtain the total circumference. (L) Natural log lengths in sagittal sections for dorsal midline (brick red), ventral midline (magenta), and stalk (green) regions measured in VolViewer and plotted against time (DAI). Growth rates: 2.07% h−1 ± 0.09 (R2 = 0.9764, n = 51), 1.71% h−1 ± 0.09 (R2 = 0.9665, n = 51), and 0.77% h−1 ± 0.13 (R2 = 0.7527, n = 49). Mature traps showed 5.78% ± 0.45 shrinkage when prepared for OPT (S9 Data). To compensate for this shrinkage, trap-length measurements of all fixed traps were increased by 5.78% before calculating DAI. Data: https://doi.org/10.6084/m9.figshare.8966153.v1, Fig 3.7z archive. DAI, days after initiation; OPT, Optical Projection Tomography.
Fig 4.
Tissue-level modelling of trap development through areal conflict resolution.
Specified growth is isotropic in all cases. Initial spherical canvas is shown from side and front in the left two columns. Resultant shapes from side, front, and top are shown in right three columns, with experimentally observed circumferences (red, orange, cyan) superimposed in E, J, and N to allow comparison between model and data. (A–F) Growth promoted along sagittal circumference by MID, yielding oblate spheroid. (A) Initial canvas sphere clipped to show MID domain (red). Canvas wall thickness = 30 μm. (B) Initial canvas unclipped, showing MID domain. (C) Initial canvas showing specified areal growth rate promoted by MID (note darker orange in MID region). (D) Mature trap clipped views shown in Fig 2E–2G, with shapes fitted to circumference in each plane: sagittal, red; frontal, orange; and transverse, cyan. (E) Resultant canvas shape (oblate spheroid) showing MID domain, with mature trap shape outlines fitted. (F) Resultant canvas shape with major orientations of resultant growth shown as lines. Lines are oriented perpendicular to the MID (sagittal) circumference. (G–J) Growth promoted by MID and inhibited by STK. (G) Initial canvas showing STK domain (green) as well as MID. (H) Initial canvas showing specified areal growth rate promoted by MID and inhibited by STK (note white area at the ‘South Pole’). (I) Resultant canvas shape showing indentation in STK region. (J) Midsection clipped views of into resultant shape. (K–N) Growth promoted by MID and VEN and inhibited by STK. (K) Initial canvas showing VEN domain (magenta) as well as MID and STK. (L) Initial canvas showing specified areal growth rate promoted by MID and VEN and inhibited by STK (note darker orange in VEN domain). (M) Resultant canvas shape showing ventral bulge. (N) Midsections of resultant canvas, with bulge highlighted in the side view (sagittal section). Models: http://cmpdartsvr3.cmp.uea.ac.uk/wiki/BanghamLab/index.php/Software and https://doi.org/10.6084/m9.figshare.8966153.v1, Models.7z archive. MID, Midline factor; STK, Stalk factor; VEN, Ventral factor.
Fig 5.
All models have two basic parameters: bplanar = basic areal growth rate and bthickness = basic growth rate in thickness. The further parameters specific for each model are shown in the individual KRNs. Arrows indicate promotive effects, and blunt ends indicate inhibitory effects. (A) KRN for areal conflict model, with MID and VEN promoting specified areal growth rate and STK inhibiting specified areal growth rate. (B) KRN for directional conflict model, with MID and VEN promoting specified growth rate parallel to the polarity and STK inhibiting specified growth rate parallel to the polarity. Note that to maintain constant specified areal growth rate, an increase in Kpar has to be compensated for by a corresponding decrease in Kper (indicated by mutual inhibition). (C) Integrated model. Regulation of Kpar and Kper is separable. MID promotes Kpar. STK inhibits both Kpar and Kper, and VEN promotes Kpar and inhibits Kper. There is also a further parameter that influences the width of the VEN domain (tven) (not shown). (D) KRN for Arabidopsis leaf model for comparison. The MID factor for the Arabidopsis model is expressed in the midline region and has a higher level of expression in the proximal half of the primordium. The LAM factor is expressed in the presumptive lamina, which occupies most of the primordium except for its most proximal region. PGRAD has a graded distribution that decreases from proximal to distal positions. LATE is expressed uniformly and increases with time.
Fig 6.
Tissue-level modelling of trap development through directional conflict resolution.
Specified areal growth rate is uniform in A–L (directional conflict model) but not in M–P (integrated model). Initial spherical canvas is shown from side and front in the left two columns. Resultant shapes from side, front, and top are shown in right three columns, with experimentally observed circumferences (red, orange, cyan as shown in Fig 4D) superimposed in C, H, L, and P to allow comparison between model and data. (A–D) Directional conflict resolution with anisotropy promoted by MID generating oblate spheroid. (A) Initial canvas showing MID domain (red), polarity (black arrows), and +/−ORGs. Polarity flows from +ORG (green) at the ‘South Pole’ towards −ORG (cyan) at the mouth. (B) Initial canvas showing specified anisotropy, defined as (Kpar − Kper)/(Kpar + Kper). Specified anisotropy is positive (red, Kpar > Kper) in MID domain. (C) Resultant canvas shape (oblate spheroid). (D) Resultant canvas with major orientations of growth shown as lines. Lines are oriented parallel to the MID (sagittal) circumference (in contrast to Fig 4F). (E–H) Directional conflict resolution with anisotropy modulated by MID and STK. (E) Initial canvas showing domains of STK (green) and MID. (F) Initial canvas showing specified anisotropy is positive (red, Kpar > Kper) in MID domain and negative (blue, Kpar < Kper) in STK domain. (G) Resultant shape with slight indentation at STK region. (H) Midsection through resultant shape. (I–L) Directional conflict resolution with anisotropy modulated by MID, VEN, and STK. (I) Initial canvas showing VEN domain (magenta) as well as MID and STK. (J) Initial canvas showing specified anisotropy is positive (red, Kpar > Kper) in MID domain, enhanced (deeper red) in VEN domain, and negative (blue, Kpar < Kper) in STK domain. (K) The resultant shape is an oblate spheroid with elongated ventral midline that does not bulge out (contrast with Fig 4M). (L) Midsection through resultant shape (contrast with Fig 4N). (M–P) Integrated areal and directional conflict resolution. (M) Areal growth rates of integrated model in the initial canvas. Growth rate is promoted by MID (deeper orange midline) and inhibited by STK (white ‘South Pole’). (N) Initial canvas showing specified anisotropy is slightly positive (Kpar > Kper) in MID domain and enhanced (red) in broadened VEN domain. (O) The resultant shape is an oblate spheroid with elongated ventral midline that does not bulge out. (P) Midsection through resultant shape. Colour scale (B, F, J, N) is specified anisotropy. Models: http://cmpdartsvr3.cmp.uea.ac.uk/wiki/BanghamLab/index.php/Software and https://doi.org/10.6084/m9.figshare.8966153.v1, Models.7z archive. MID, Midline factor; STK, Stalk factor; VEN, Ventral factor; −ORG, minus-organiser; +ORG, plus-organiser.
Fig 7.
Trap shape variation between species.
(A–C) Different traps from Utricularia species clipped in sagittal view. (A) U. bisquamata (terminal), (B) U. praelonga (basal), and (C) U. gibba (lateral). Dorsal midline (red), ventral midline (magenta), stalk (green), and threshold (yellow). (D–F) Illustrative modelling of different trap shapes, showing sagittal sections of resultant shapes. (D) Terminal type generated from integrated model by increased promotion of Kpar by VEN and reduced promotion by MID. (E) Basal type generated from integrated model by decreasing promotion of Kpar by VEN and increasing promotion by MID. (F) Lateral type, generated by integrated model as shown in Fig 6P. Scale = 500 μm. Data https://doi.org/10.6084/m9.figshare.8966153.v1, Fig 7.7z archive. Models: http://cmpdartsvr3.cmp.uea.ac.uk/wiki/BanghamLab/index.php/Software and https://doi.org/10.6084/m9.figshare.8966153.v1, Models.7z archive. MID, Midline factor; VEN, Ventral factor.
Fig 8.
Cell counts at different stages of trap development.
(A–C) U. gibba traps between 3 and 11 DAI (live and PI-stained) were imaged with a confocal microscope and clipped in VolViewer. Circumference cell counts were obtained by manually placing points in (A) sagittal (red points), (B) frontal (orange), and (C) transverse (cyan) planes. In mature traps, where it was not possible to image the entire depth of the trap by confocal microscopy, half the circumference cells were counted in frontal and transverse views. This value was doubled to obtain estimated cell numbers. Trap shown was 139 μm long, 6.1 DAI. Scale bar = 50 μm. (D–F) Sagittal shown in (A) illustrating regional cell counts: (D) dorsal midline (red), (E) ventral midline (magenta), and (F) stalk diameter (green). (G–L) Natural log of cell number for the regions indicated above (A–F) plotted against time (DAI) and trend lines fitted during the early exponential period, S5 Data. Slopes (percent increase in cell number per hour) and twice the standard deviation of the slopes indicated. Note that this value may be less than the strain rate, in which case cell size increases as well as cell number. (G) Sagittal circumference, R2 = 0.8635, n = 13 traps. (H) Frontal circumference, R2 = 0.8908, n = 19 traps. (I) Transverse circumference R2 = 0.8602, n = 19 traps. (J) Dorsal midline, R2 = 0.8701, n = 14. (K) Ventral midline, R2 = 0.5496, n = 18. (L) Stalk cell number did not increase. Traps showed 5.78% ± 0.45 shrinkage when prepared for OPT (S9 Data). To compensate for this, trap-length measurements of all fixed traps were increased by 5.78% before time (DAI) calculation. Data https://doi.org/10.6084/m9.figshare.8966153.v1, Fig 8.7z archive. DAI, days after initiation; OPT, Optical Projection Tomography; PI, propidium iodide.
Fig 9.
Cellular-level area models and data.
(A) Growth snapshots of integrated areal and directional conflict model, side view from 4 DAI canvas start shape to resultant canvas shape at 10.5 DAI, coloured for cell area. Grey region shows approximate location of mouth. (B) Experimental data showing traps with cells segmented and coloured for cell area at time points corresponding to those shown for the integrated model shown in A, side view. Grey region shows approximate location of mouth where visible. (C–D) Experimental data. (C) Trap with cells segmented and coloured for cell area, front view; arrow highlights ventral midline cells. (D) Additional segmented data, arrow highlights ventral midline cells. (E–G) Zoomed-in resultant model front views. (E) Areal conflict model; arrow highlights larger ventral midline cells. (F) Directional conflict model; arrow highlights smaller ventral midline cells. (G) Integrated model; arrow highlights ventral midline cells. Magenta line shows ventral midline, and red line shows dorsal midline. In all images, colour scale shows cell area (μm2) on logarithmic scale. Data https://doi.org/10.6084/m9.figshare.8966153.v1, Figs 9, 10, S4 and S6.7z archive. Models: http://cmpdartsvr3.cmp.uea.ac.uk/wiki/BanghamLab/index.php/Software and https://doi.org/10.6084/m9.figshare.8966153.v1, Models.7z archive. DAI, days after initiation.
Fig 10.
Cellular-level anisotropy models and data.
(A) Integrated areal and directional conflict model side view from 4 DAI canvas start shape to resultant canvas shape at 10.5 DAI, coloured for cell anisotropy. Lines show orientation of the cell long axis and are shown where anisotropy exceeds 0.23. Grey region shows approximate location of mouth. (B) Experimental data showing traps with cells segmented and coloured for cell anisotropy at time points corresponding to those shown for the integrated model shown in (A), side view. Grey region shows approximate location of mouth where visible. (C–D) Experimental data; arrows highlight region of cell anisotropy parallel to the ventral midline. (C) Trap with cells segmented and coloured for cell anisotropy, front view. (D) Additional segmented data. (E–G) Zoomed-in resultant model front views. (E) Areal conflict model; arrow highlights region of cell anisotropy perpendicular to the ventral midline. (F) Directional conflict model; arrow highlights region of cell anisotropy parallel to the ventral midline. (G) Integrated model; arrow highlights wider region of cell anisotropy parallel to the ventral midline. Magenta line shows ventral midline; red line shows dorsal midline. Grey region shows mouth. Colour scale shows cell anisotropy. In all images, cell-shape anisotropy is defined by R − 1/R + 1, where R is the ratio of the long/short axis of an ellipsoid fitted to the cell. This equation evaluates to 0 for isometric cell shape and 0.333 when the long axis is twice the short axis. Data https://doi.org/10.6084/m9.figshare.8966153.v1, Figs 9, 10, S4 and S6.7z archive. Models: http://cmpdartsvr3.cmp.uea.ac.uk/wiki/BanghamLab/index.php/Software and https://doi.org/10.6084/m9.figshare.8966153.v1, Models.7z archive. DAI, days after initiation.
Fig 11.
(A–D) Virtual clones generated by areal conflict model. Clones were induced at 4 DAI. Resultant model outputs shown are 10.5 DAI. Magenta arrows highlight ventral midline clones. (A) Side view, (B) front view, (C) top view, (D) back view. Scale bar 500 μm. (E–H) Virtual clones generated by directional conflict model. Scale bar 500 μm. (I–L) Virtual clones generated by integrated areal and directional conflict model. Scale bar 500 μm. (M–P) HS-induced clones (green) imaged with a confocal microscope at 10–11 DAI. Scale bars 250 μm. (Q–T) Sector images were placed in their approximate location on the trap (dashed outlines). Ellipses were fitted to sectors, and major axes are shown (S17 Data). (U–V) Data histograms (S7 Data). (U) Clone anisotropy. Ratio of major/minor axis lengths for clones, ± SE. P-values of t tests are L to VM p = 0.0004 (***), VM to DM p = 0.0007 (***), DM to L p = 0.65. (V) Cell-number anisotropy. Ratio of cell numbers along major/minor axes of clones, ± SE. P-values of t tests are L to VM p = 0.053, VM to DM p = 0.046 (*), DM to L p = 0.73. (W) Cell-shape anisotropy. Ratio of clone anisotropy/cell-number anisotropy for individual clones, ± SE. P-values of t tests are L to VM p = 8.56 × 10−5 (***), VM to DM p = 0.0003 (***), DM to L p = 0.8; N = 59 clones in 36 traps. L = 25, VM = 15, DM = 19. Data https://doi.org/10.6084/m9.figshare.8966153.v1, Fig 11.7 archive. Models: http://cmpdartsvr3.cmp.uea.ac.uk/wiki/BanghamLab/index.php/Software and https://doi.org/10.6084/m9.figshare.8966153.v1, Models.7z archive. DAI, days after initiation; DM, dorsal midline; HS, heat shock; L, lamina; VM, ventral midline.
Fig 12.
Evidence for a polarity field in traps.
(A–D) Points at the quadrifid gland centre and at ends of each quadrifid gland arm were placed in VolViewer (red spots). Arrows (example shown in D) were oriented toward the greatest distance between arms with quadrifidScript software (DistArms). (E–G) Clipped sagittal view of OPT scan, looking into the trap at quadrifid glands on one side of the trap. (E) Arrows flow from stalk (St) to mouth (Mo). Lines with no arrow heads were allocated when the difference in distance between arms was less than a threshold value of 2 μm. Arrows were enlarged in Adobe Illustrator for clarity. (F) DistArms polarity arrow output from VolViewer shown in (E) displayed alone. 35/37 glands in proximodistal orientation, five unallocated (S8 Data). (G) Output of integrated model clipped sagittal view. Arrows indicate tissue polarity field from stalk to mouth. Stalk (green), mouth (cyan), dorsal midline (red), ventral midline (magenta). (H–J) Transverse clipped views of confocal scan looking into the ventral half of the trap. (H) Arrows diverge at stalk (St) and flow from stalk to mouth (Mo). (I) Polarity arrows shown in (H) displayed alone. 29/32 glands point away from stalk (S8 Data). (J) Output of integrated model, transverse clipped view into trap towards stalk. Shows diverging tissue polarity field from stalk to mouth. (K–M) Transverse clipped view of confocal scan looking into the dorsal half of the trap. (K) Polarity arrows shown in (K) displayed alone. 27/27 glands point to mouth (S8 Data). (L) Arrows point towards the mouth. (M) Output of integrated model, clipped view into top of trap. Arrows point towards mouth. Data https://doi.org/10.6084/m9.figshare.8966153.v1, Fig 12 and S8.7z archive. Models: http://cmpdartsvr3.cmp.uea.ac.uk/wiki/BanghamLab/index.php/Software and https://doi.org/10.6084/m9.figshare.8966153.v1, Models.7z archive. OPT, Optical Projection Tomography.