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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 PFE signal expansion. The initial velocity, deceleration rate, and signal duration are fixed at v0 = 10, a = -1, and D = 2, respectively. Signals are propagated according to the t-x plot shown on the right side of this figure. Signal durations are depicted by horizontal bars under the t axis. The front and rear of a signal for a single PFE are indicated by arrows of the same colour. As time progresses, the position and size of the PFEs change. Treatments that produced similar PFEs in Figure 4 are indicated above each simulated PFE.
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Figure 8: Simulation of PFE signal expansion. The initial velocity, deceleration rate, and signal duration are fixed at v0 = 10, a = -1, and D = 2, respectively. Signals are propagated according to the t-x plot shown on the right side of this figure. Signal durations are depicted by horizontal bars under the t axis. The front and rear of a signal for a single PFE are indicated by arrows of the same colour. As time progresses, the position and size of the PFEs change. Treatments that produced similar PFEs in Figure 4 are indicated above each simulated PFE.

Mentions: Similar to the results for the eyespots, PFE behaviour in response to tungstate and temperature treatments (Figure 4) was properly simulated (Figure 8). In the induction model, the PFE signal has already been released at the treatment time point. Therefore, the initial velocity is not affected by the treatment. In contrast, the propagation time (or speed) of the released signal is affected. Consistent with the experimental changes, PFEs located closer to the focus are wider in this simulation.


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

Otaki JM - BMC Syst Biol (2012)

Simulation of PFE signal expansion. The initial velocity, deceleration rate, and signal duration are fixed at v0 = 10, a = -1, and D = 2, respectively. Signals are propagated according to the t-x plot shown on the right side of this figure. Signal durations are depicted by horizontal bars under the t axis. The front and rear of a signal for a single PFE are indicated by arrows of the same colour. As time progresses, the position and size of the PFEs change. Treatments that produced similar PFEs in Figure 4 are indicated above each simulated PFE.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 8: Simulation of PFE signal expansion. The initial velocity, deceleration rate, and signal duration are fixed at v0 = 10, a = -1, and D = 2, respectively. Signals are propagated according to the t-x plot shown on the right side of this figure. Signal durations are depicted by horizontal bars under the t axis. The front and rear of a signal for a single PFE are indicated by arrows of the same colour. As time progresses, the position and size of the PFEs change. Treatments that produced similar PFEs in Figure 4 are indicated above each simulated PFE.
Mentions: Similar to the results for the eyespots, PFE behaviour in response to tungstate and temperature treatments (Figure 4) was properly simulated (Figure 8). In the induction model, the PFE signal has already been released at the treatment time point. Therefore, the initial velocity is not affected by the treatment. In contrast, the propagation time (or speed) of the released signal is affected. Consistent with the experimental changes, PFEs located closer to the focus are wider in this simulation.

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