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Fig. 5 | Zoological Letters

Fig. 5

From: Polymorphism in the symmetries of gastric pouch arrangements in the sea anemone D. lineata

Fig. 5

Mathematical model for gastric pouch specification. a Schematic diagram of the irreversible specification stages after pedal laceration based on Atoda [28]. Temporal snapshots (denoted by t) framed with dotted lines at the bottom are simulated in our model (Fig. 2d). b Regulatory circuit (left) and spatial patterns (right) of an activator (a, dark blue) and two inhibitors (b, light blue; C, magenta). All morphogens are assumed to be diffused at the edge of the endoderm cell layer (light gray region inside) that extends to all oral surfaces but not in the ectoderm (dark gray region outside) or mesoglea (beige region at the center). PD, P1, and P2 are shown in dark blue, light blue, and magenta, respectively. The color of PD was matched with the color of the a morphogen, which is secreted only from PD. Colors P1 and P2 were matched up with the colors of the c and c morphogens, which inhibit the specification of P1 and P2, respectively. c Simulated conditions of activator and inhibitor concentrations (left) for the irreversible specification (right) to P1s (upper panel) and P2s (lower panel). Ta; activator threshold, Ti; inhibitor threshold. d–f Initial conditions (t = 0) with two gastric pouches positioned at two opposite sides. For initial condition 1, 20 pouches were arranged at an 18° interval and a radius of 5 (d). For initial conditions 2 and 3, 24 pouches were arranged at 15° intervals and a radius of 6 (e, f). Gastric pouch indexes were numbered from 1 onwards from the uppermost pouch in a clockwise rotation. PD, P1, and P2 denote directive, first, and second gastric pouches, respectively. g Bilaterally symmetrical arrangement for 10-striped individuals (20 pouches) initiated the condition (t = 0) of PD and P2 positioned oppositely (d). Temporal evolution (represented by t from upper to bottom panels) of the concentrations of a, b, and c (Eqs. 13) in a semilogarithmic plot (left panel) as a function of the gastric pouch index (d) and 2-D arrangement of specified and nonspecified pouches (right panel). At the top of the uppermost semilogarithmic plot, the arrangement of pouches in 1-D space with their corresponding colors is written in the line of gastric pouch indices in the plot. Dark blue circular, light blue rectangular, and pink triangular markers are used to demonstrate the concentrations of a, b, and c in gastric pouches, respectively. Bold fonts are used for the corresponding gastric pouch indexes that achieve irreversible specification conditions at a, b, and c concentrations. The activator threshold (Ta) and inhibitor threshold (Ti) are indicated as gray dashed and dotted lines, respectively. Following the rule of irreversible specification, pouches neighboring PD remain nonspecified pouches due to the suprathreshold of b and c (a > Ta, b,c > Ti) (t = 1, gastric pouch index = 10, 12). Adjacent pouches to these pouches, in which the suprathreshold of a was achieved, are specified as P2s due to subthreshold c (a > Ta, b > Ti, c < Ti) (t = 1, gastric pouch index = 9,13). B and C Secretion from P2s surrounding pouches as nonspecified pouches (a > Ta, b,c > Ti) (t = 2, gastric pouch index = 8, 14). Adjacent pouches to these pouches are irreversibly specified as first pouches (P1s) due to the subthreshold of b (a > Ta, b < Ti, c > Ti) (t = 2, gastric pouch index = 7, 15). Surrounding pouches are left as nonspecified pouches, and the adjacent pouches are irreversibly specified as P2s due to the subthreshold of c (a > Ta, b > Ti, c < Ti) (t = 3, gastric pouch index = 5, 17). Adjacent pouches to these pouches are irreversibly specified as first pouches (P1s) due to the subthreshold of b (a > Ta, b < Ti, c > Ti) (t = 4, gastric pouch index = 3, 19). Gray dotted lines indicate symmetry planes (right bottom panel)

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