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A Model for Selection of Eyespots on Butterfly Wings.

Sekimura T, Venkataraman C, Madzvamuse A - PLoS ONE (2015)

Bottom Line: A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not.We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface.The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell.

View Article: PubMed Central - PubMed

Affiliation: Department of Biological Chemistry, Graduate School of Bioscience and Biotechnology, Chubu University, Kasugai, Aichi 487-8501, Japan.

ABSTRACT

Unsolved problem: The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation.However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not.

Key idea and model: We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature.

Result: We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell.

No MeSH data available.


Incomplete vein development leaves two focus points with an eyespot covering two focus points.(a) Normal (left) and abnormal (right) eyespot patterns on the hind wing of the butterfly Ypthima arugus. (b) Sketch of the abnormal venation system and an arrow to show two distinct focus points. (c) Simulations of the abnormal case of incomplete vein development shown in (a) (right) by use of Eq (3.1). This incomplete vein development leads to two focus points forming close to both the incompletely developed vein’s end point. The eventual pattern observed on the butterfly wing is that of a single eyespot generated by two focus points that are in close proximity. The corresponding normal pattern is of two distinct eyespots with orally separated foci. Photos (a) and the sketch (b): courtesy of Mr.Toru Tokiwa.
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pone.0141434.g008: Incomplete vein development leaves two focus points with an eyespot covering two focus points.(a) Normal (left) and abnormal (right) eyespot patterns on the hind wing of the butterfly Ypthima arugus. (b) Sketch of the abnormal venation system and an arrow to show two distinct focus points. (c) Simulations of the abnormal case of incomplete vein development shown in (a) (right) by use of Eq (3.1). This incomplete vein development leads to two focus points forming close to both the incompletely developed vein’s end point. The eventual pattern observed on the butterfly wing is that of a single eyespot generated by two focus points that are in close proximity. The corresponding normal pattern is of two distinct eyespots with orally separated foci. Photos (a) and the sketch (b): courtesy of Mr.Toru Tokiwa.

Mentions: Fig 8 shows an abnormal eyespot pattern of the hind wing of the butterfly Ypthima arugus and for comparison the corresponding normal pattern. The left hand subfigure (a) shows two patterns: normal ventral hind wing pattern (left) and the corresponding abnormal pattern in which a vein did not fully develop. To illustrate the scenario during abnormal development of the vein, we include a sketch (right hand subfigure (b) of Fig 8) of the venation system and also an arrow in the picture where we see two distinct focus points and only one eyespot covering the two focus points.


A Model for Selection of Eyespots on Butterfly Wings.

Sekimura T, Venkataraman C, Madzvamuse A - PLoS ONE (2015)

Incomplete vein development leaves two focus points with an eyespot covering two focus points.(a) Normal (left) and abnormal (right) eyespot patterns on the hind wing of the butterfly Ypthima arugus. (b) Sketch of the abnormal venation system and an arrow to show two distinct focus points. (c) Simulations of the abnormal case of incomplete vein development shown in (a) (right) by use of Eq (3.1). This incomplete vein development leads to two focus points forming close to both the incompletely developed vein’s end point. The eventual pattern observed on the butterfly wing is that of a single eyespot generated by two focus points that are in close proximity. The corresponding normal pattern is of two distinct eyespots with orally separated foci. Photos (a) and the sketch (b): courtesy of Mr.Toru Tokiwa.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4633216&req=5

pone.0141434.g008: Incomplete vein development leaves two focus points with an eyespot covering two focus points.(a) Normal (left) and abnormal (right) eyespot patterns on the hind wing of the butterfly Ypthima arugus. (b) Sketch of the abnormal venation system and an arrow to show two distinct focus points. (c) Simulations of the abnormal case of incomplete vein development shown in (a) (right) by use of Eq (3.1). This incomplete vein development leads to two focus points forming close to both the incompletely developed vein’s end point. The eventual pattern observed on the butterfly wing is that of a single eyespot generated by two focus points that are in close proximity. The corresponding normal pattern is of two distinct eyespots with orally separated foci. Photos (a) and the sketch (b): courtesy of Mr.Toru Tokiwa.
Mentions: Fig 8 shows an abnormal eyespot pattern of the hind wing of the butterfly Ypthima arugus and for comparison the corresponding normal pattern. The left hand subfigure (a) shows two patterns: normal ventral hind wing pattern (left) and the corresponding abnormal pattern in which a vein did not fully develop. To illustrate the scenario during abnormal development of the vein, we include a sketch (right hand subfigure (b) of Fig 8) of the venation system and also an arrow in the picture where we see two distinct focus points and only one eyespot covering the two focus points.

Bottom Line: A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not.We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface.The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell.

View Article: PubMed Central - PubMed

Affiliation: Department of Biological Chemistry, Graduate School of Bioscience and Biotechnology, Chubu University, Kasugai, Aichi 487-8501, Japan.

ABSTRACT

Unsolved problem: The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation.However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not.

Key idea and model: We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature.

Result: We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell.

No MeSH data available.