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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 eyespots with various levels of organising centre activity. Signals propagate according to the t-x curves depicted on the right side of the figure. By definition, the signalling process starts at t = 0 for all four eyespots shown in this figure. However, smaller eyespots were assumed to be associated with a lower v0 and shorter signal duration D. The signalling dynamics shown in Figure 6 are not shown here, but the single time point t = 10 is depicted as a snapshot. Signal durations are indicated by horizontal bars under the t axis. The front and rear of the signal for the same eyespot are depicted by arrows of the same colour. Organising centres are shown as red spots; the sizes of the spots reflect their signalling activities. Only half of an eyespot is drawn, with both the right and left sides deleted for simplicity. Note the differences in size and morphology among these four eyespots.
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Figure 7: Simulation of eyespots with various levels of organising centre activity. Signals propagate according to the t-x curves depicted on the right side of the figure. By definition, the signalling process starts at t = 0 for all four eyespots shown in this figure. However, smaller eyespots were assumed to be associated with a lower v0 and shorter signal duration D. The signalling dynamics shown in Figure 6 are not shown here, but the single time point t = 10 is depicted as a snapshot. Signal durations are indicated by horizontal bars under the t axis. The front and rear of the signal for the same eyespot are depicted by arrows of the same colour. Organising centres are shown as red spots; the sizes of the spots reflect their signalling activities. Only half of an eyespot is drawn, with both the right and left sides deleted for simplicity. Note the differences in size and morphology among these four eyespots.

Mentions: Here, four eyespots with different sizes were depicted at t = 10 (Figure 7). By definition, the prospective foci initiate the signalling step at t = 0 (which does not mean that they actually initiate the signalling step simultaneously on a wing), but their initial velocity v0 and signalling duration D are different from one another. Small eyespots are associated with a low initial velocity and a shorter duration of signalling. Furthermore, for small eyespots, there are a longer intervals before the beginning of the second signal. That is, the release of the second signal is delayed for smaller eyespots. Based on these reasonable conditions, the structural features of the small eyespots indicated in Figures 3 and 4 were successfully reproduced.


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

Otaki JM - BMC Syst Biol (2012)

Simulation of eyespots with various levels of organising centre activity. Signals propagate according to the t-x curves depicted on the right side of the figure. By definition, the signalling process starts at t = 0 for all four eyespots shown in this figure. However, smaller eyespots were assumed to be associated with a lower v0 and shorter signal duration D. The signalling dynamics shown in Figure 6 are not shown here, but the single time point t = 10 is depicted as a snapshot. Signal durations are indicated by horizontal bars under the t axis. The front and rear of the signal for the same eyespot are depicted by arrows of the same colour. Organising centres are shown as red spots; the sizes of the spots reflect their signalling activities. Only half of an eyespot is drawn, with both the right and left sides deleted for simplicity. Note the differences in size and morphology among these four eyespots.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 7: Simulation of eyespots with various levels of organising centre activity. Signals propagate according to the t-x curves depicted on the right side of the figure. By definition, the signalling process starts at t = 0 for all four eyespots shown in this figure. However, smaller eyespots were assumed to be associated with a lower v0 and shorter signal duration D. The signalling dynamics shown in Figure 6 are not shown here, but the single time point t = 10 is depicted as a snapshot. Signal durations are indicated by horizontal bars under the t axis. The front and rear of the signal for the same eyespot are depicted by arrows of the same colour. Organising centres are shown as red spots; the sizes of the spots reflect their signalling activities. Only half of an eyespot is drawn, with both the right and left sides deleted for simplicity. Note the differences in size and morphology among these four eyespots.
Mentions: Here, four eyespots with different sizes were depicted at t = 10 (Figure 7). By definition, the prospective foci initiate the signalling step at t = 0 (which does not mean that they actually initiate the signalling step simultaneously on a wing), but their initial velocity v0 and signalling duration D are different from one another. Small eyespots are associated with a low initial velocity and a shorter duration of signalling. Furthermore, for small eyespots, there are a longer intervals before the beginning of the second signal. That is, the release of the second signal is delayed for smaller eyespots. Based on these reasonable conditions, the structural features of the small eyespots indicated in Figures 3 and 4 were successfully reproduced.

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