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Structural analysis of eyespots: dynamics of morphogenic signals that govern elemental positions in butterfly wings.

Otaki JM - BMC Syst Biol (2012)

Bottom Line: However, a detailed structural analysis of eyespots that can serve as a foundation for future studies is still lacking.It appears that signals are wider near the focus of the eyespot and become narrower as they expand.Natural colour patterns and previous experimental findings that are not easily explained by the conventional gradient model were also explained reasonably well by the formal mathematical simulations performed in this study.

View Article: PubMed Central - HTML - PubMed

Affiliation: The BCPH Unit of Molecular Physiology, Department of Chemistry, Biology and Marine Science, Faculty of Science, University of the Ryukyus, Nishihara, Okinawa 903-0213, Japan. otaki@sci.u-ryukyu.ac.jp

ABSTRACT

Background: To explain eyespot colour-pattern determination in butterfly wings, the induction model has been discussed based on colour-pattern analyses of various butterfly eyespots. However, a detailed structural analysis of eyespots that can serve as a foundation for future studies is still lacking. In this study, fundamental structural rules related to butterfly eyespots are proposed, and the induction model is elaborated in terms of the possible dynamics of morphogenic signals involved in the development of eyespots and parafocal elements (PFEs) based on colour-pattern analysis of the nymphalid butterfly Junonia almana.

Results: In a well-developed eyespot, the inner black core ring is much wider than the outer black ring; this is termed the inside-wide rule. It appears that signals are wider near the focus of the eyespot and become narrower as they expand. Although fundamental signal dynamics are likely to be based on a reaction-diffusion mechanism, they were described well mathematically as a type of simple uniformly decelerated motion in which signals associated with the outer and inner black rings of eyespots and PFEs are released at different time points, durations, intervals, and initial velocities into a two-dimensional field of fundamentally uniform or graded resistance; this produces eyespots and PFEs that are diverse in size and structure. The inside-wide rule, eyespot distortion, structural differences between small and large eyespots, and structural changes in eyespots and PFEs in response to physiological treatments were explained well using mathematical simulations. Natural colour patterns and previous experimental findings that are not easily explained by the conventional gradient model were also explained reasonably well by the formal mathematical simulations performed in this study.

Conclusions: In a mode free from speculative molecular interactions, the present study clarifies fundamental structural rules related to butterfly eyespots, delineates a theoretical basis for the induction model, and proposes a mathematically simple mode of long-range signalling that may reflect developmental mechanisms associated with butterfly eyespots.

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Simulation of eyespot signal expansion with a fixed initial velocity v0. Two signals (n = 2) with the same initial velocity (v0 = 10) and signal duration (D = 3) were assumed. The signal interval I was set at 3. The released signals are distributed in a two-dimensional plane based on the t-x curve shown on the right side of each column. Signal durations are indicated by horizontal bars under the t axis. The signal front is indicated by a blue arrow and the signal rear by a blue-green arrow. Only half of an eyespot is drawn. Red focal dots indicate active organising centres releasing the signal, whereas blue dots indicate organising centres pausing during the signal intervals. As time progresses from t = 1 to t = 12, the widths of both black rings and light rings change dynamically. Under these conditions, typical eyespots probably lie within 8 ≤ t ≤ 10
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Figure 6: Simulation of eyespot signal expansion with a fixed initial velocity v0. Two signals (n = 2) with the same initial velocity (v0 = 10) and signal duration (D = 3) were assumed. The signal interval I was set at 3. The released signals are distributed in a two-dimensional plane based on the t-x curve shown on the right side of each column. Signal durations are indicated by horizontal bars under the t axis. The signal front is indicated by a blue arrow and the signal rear by a blue-green arrow. Only half of an eyespot is drawn. Red focal dots indicate active organising centres releasing the signal, whereas blue dots indicate organising centres pausing during the signal intervals. As time progresses from t = 1 to t = 12, the widths of both black rings and light rings change dynamically. Under these conditions, typical eyespots probably lie within 8 ≤ t ≤ 10

Mentions: This section discusses how the above mathematical and conceptual descriptions of signal dynamics can produce an eyespot. For simplicity, suppose that two signals are released from an identical organiser (n = 2) under the following conditions for both signals: a = -1; v0 = 10; D = 3 for both signals; and I = 3 (Figure 6). As a function of time, the signal distribution patterns produce various eyespots. Under these conditions, "typical" inside-wide eyespots were depicted at t = 9 and 10. The time-out mechanism or repulsive velocity-loss mechanism is necessary for these eyespots to be fixed in a typical shape.


Structural analysis of eyespots: dynamics of morphogenic signals that govern elemental positions in butterfly wings.

Otaki JM - BMC Syst Biol (2012)

Simulation of eyespot signal expansion with a fixed initial velocity v0. Two signals (n = 2) with the same initial velocity (v0 = 10) and signal duration (D = 3) were assumed. The signal interval I was set at 3. The released signals are distributed in a two-dimensional plane based on the t-x curve shown on the right side of each column. Signal durations are indicated by horizontal bars under the t axis. The signal front is indicated by a blue arrow and the signal rear by a blue-green arrow. Only half of an eyespot is drawn. Red focal dots indicate active organising centres releasing the signal, whereas blue dots indicate organising centres pausing during the signal intervals. As time progresses from t = 1 to t = 12, the widths of both black rings and light rings change dynamically. Under these conditions, typical eyespots probably lie within 8 ≤ t ≤ 10
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3368778&req=5

Figure 6: Simulation of eyespot signal expansion with a fixed initial velocity v0. Two signals (n = 2) with the same initial velocity (v0 = 10) and signal duration (D = 3) were assumed. The signal interval I was set at 3. The released signals are distributed in a two-dimensional plane based on the t-x curve shown on the right side of each column. Signal durations are indicated by horizontal bars under the t axis. The signal front is indicated by a blue arrow and the signal rear by a blue-green arrow. Only half of an eyespot is drawn. Red focal dots indicate active organising centres releasing the signal, whereas blue dots indicate organising centres pausing during the signal intervals. As time progresses from t = 1 to t = 12, the widths of both black rings and light rings change dynamically. Under these conditions, typical eyespots probably lie within 8 ≤ t ≤ 10
Mentions: This section discusses how the above mathematical and conceptual descriptions of signal dynamics can produce an eyespot. For simplicity, suppose that two signals are released from an identical organiser (n = 2) under the following conditions for both signals: a = -1; v0 = 10; D = 3 for both signals; and I = 3 (Figure 6). As a function of time, the signal distribution patterns produce various eyespots. Under these conditions, "typical" inside-wide eyespots were depicted at t = 9 and 10. The time-out mechanism or repulsive velocity-loss mechanism is necessary for these eyespots to be fixed in a typical shape.

Bottom Line: However, a detailed structural analysis of eyespots that can serve as a foundation for future studies is still lacking.It appears that signals are wider near the focus of the eyespot and become narrower as they expand.Natural colour patterns and previous experimental findings that are not easily explained by the conventional gradient model were also explained reasonably well by the formal mathematical simulations performed in this study.

View Article: PubMed Central - HTML - PubMed

Affiliation: The BCPH Unit of Molecular Physiology, Department of Chemistry, Biology and Marine Science, Faculty of Science, University of the Ryukyus, Nishihara, Okinawa 903-0213, Japan. otaki@sci.u-ryukyu.ac.jp

ABSTRACT

Background: To explain eyespot colour-pattern determination in butterfly wings, the induction model has been discussed based on colour-pattern analyses of various butterfly eyespots. However, a detailed structural analysis of eyespots that can serve as a foundation for future studies is still lacking. In this study, fundamental structural rules related to butterfly eyespots are proposed, and the induction model is elaborated in terms of the possible dynamics of morphogenic signals involved in the development of eyespots and parafocal elements (PFEs) based on colour-pattern analysis of the nymphalid butterfly Junonia almana.

Results: In a well-developed eyespot, the inner black core ring is much wider than the outer black ring; this is termed the inside-wide rule. It appears that signals are wider near the focus of the eyespot and become narrower as they expand. Although fundamental signal dynamics are likely to be based on a reaction-diffusion mechanism, they were described well mathematically as a type of simple uniformly decelerated motion in which signals associated with the outer and inner black rings of eyespots and PFEs are released at different time points, durations, intervals, and initial velocities into a two-dimensional field of fundamentally uniform or graded resistance; this produces eyespots and PFEs that are diverse in size and structure. The inside-wide rule, eyespot distortion, structural differences between small and large eyespots, and structural changes in eyespots and PFEs in response to physiological treatments were explained well using mathematical simulations. Natural colour patterns and previous experimental findings that are not easily explained by the conventional gradient model were also explained reasonably well by the formal mathematical simulations performed in this study.

Conclusions: In a mode free from speculative molecular interactions, the present study clarifies fundamental structural rules related to butterfly eyespots, delineates a theoretical basis for the induction model, and proposes a mathematically simple mode of long-range signalling that may reflect developmental mechanisms associated with butterfly eyespots.

Show MeSH
Related in: MedlinePlus