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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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Signal dynamics according to Eq. (1). The signal position x changes as a function of time t. (A) t-x curves when a = -1 with various values of v0 according to Eq. (5). Blue dots indicate the maximum (final) positions for each value of v0. Blue lines indicate the constant positions after the blue dots. (B) t-x curves when v0 = 10 with various values of a according to Eq. (8). Orange dots indicate the maximum (final) positions for each a. Orange lines indicate the constant positions after the orange dots.
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Figure 5: Signal dynamics according to Eq. (1). The signal position x changes as a function of time t. (A) t-x curves when a = -1 with various values of v0 according to Eq. (5). Blue dots indicate the maximum (final) positions for each value of v0. Blue lines indicate the constant positions after the blue dots. (B) t-x curves when v0 = 10 with various values of a according to Eq. (8). Orange dots indicate the maximum (final) positions for each a. Orange lines indicate the constant positions after the orange dots.

Mentions: For example, consider Eq. (5) with v0 ranging from 9 to 12 for the sake of simplicity. Depending on v0, the position x varies as shown in the t-x plot (Figure 5A), indicating that the initial velocity v0 is an important factor for determination of eyespot size.


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

Otaki JM - BMC Syst Biol (2012)

Signal dynamics according to Eq. (1). The signal position x changes as a function of time t. (A) t-x curves when a = -1 with various values of v0 according to Eq. (5). Blue dots indicate the maximum (final) positions for each value of v0. Blue lines indicate the constant positions after the blue dots. (B) t-x curves when v0 = 10 with various values of a according to Eq. (8). Orange dots indicate the maximum (final) positions for each a. Orange lines indicate the constant positions after the orange dots.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Figure 5: Signal dynamics according to Eq. (1). The signal position x changes as a function of time t. (A) t-x curves when a = -1 with various values of v0 according to Eq. (5). Blue dots indicate the maximum (final) positions for each value of v0. Blue lines indicate the constant positions after the blue dots. (B) t-x curves when v0 = 10 with various values of a according to Eq. (8). Orange dots indicate the maximum (final) positions for each a. Orange lines indicate the constant positions after the orange dots.
Mentions: For example, consider Eq. (5) with v0 ranging from 9 to 12 for the sake of simplicity. Depending on v0, the position x varies as shown in the t-x plot (Figure 5A), indicating that the initial velocity v0 is an important factor for determination of eyespot size.

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