Role of the boundary in feather bud formation on one-dimensional bioengineered skin.

Kentaro Ishida,Toshiyuki Mitsui

doi:10.1063/1.4989414

Abstract

The role of a boundary in pattern formation from a homogenous state in Turing's reaction–diffusion equations is important, particularly when the domain size is comparable to the pattern scale. Such experimental conditions may be achieved for in vitro regeneration of ectodermal appendages such as feathers, via reconstruction of embryonic single cells. This procedure can eliminate a predefined genetic map, such as the midline of chick feather bud formation, leaving uniformly distributed identical cells as a bioengineered skin. Here, the self-organizing nature of multiple feather bud formation was examined in bioengineered 1D-skin samples. Primal formation of feather buds occurred at a fixed length from the skin edge. This formation was numerically recapitulated by a standard two-component reaction-diffusion model, suggesting that the boundary effect caused this observation. The proper boundary conditions were nonstandard, either mixed Dirichlet–Neumann or partial-flux. In addition, the model implies imperfect or hindered bud formation as well as nearly equal distances between buds. In contrast, experimental observations indicated that the skin curvature, which was not included in our model, also strongly affected bud formation. Thus, bioengineered skin may provide an ideal template for modeling a self-organized process from a homogenous state. This study will examine the possible diffusion activities of activator or inhibitor molecular candidates and mechanical activities during cell aggregation, which will advance our understanding of skin appendage regeneration from pluripotent or embryonic stem cells.

Highlights

Turing’s model of two reaction–diffusion equations has been applied to a wide variety of patterns in living systems
We initially focused on morphological changes in the bioengineered skin samples
The results of our in vitro experiments indicate that the primal locations for feather bud formation were near the edges of 1D-like skins

Summary

Introduction

Turing’s model of two reaction–diffusion equations has been applied to a wide variety of patterns in living systems. Recent experimental studies of pattern formation have led to the identification of a number of molecular candidates for activator/inhibitor species and their underlying molecular mechanisms.3,4 This advance has led to the formulation of additional differential equations with nonhomogeneous initial conditions to generate the asymmetric order of multiple-structure formation in various complex patterns such as teeth, scales, feathers, hair, and other skin appendages during embryogenesis.. This advance has led to the formulation of additional differential equations with nonhomogeneous initial conditions to generate the asymmetric order of multiple-structure formation in various complex patterns such as teeth, scales, feathers, hair, and other skin appendages during embryogenesis.5–11 Such complexities are likely predefined genetically and allocated appropriately on the segmented skin of each animal species.

Methods

Results

Conclusion