| Pattern forming mechanism in 'traveling wave' patterned mice |  
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						August 20, 2003 — A well-characterized reaction that produces wave-like patterns in 
						chemical media provides an apt mathematical description for a pattern-forming phenomenon in 
						the skin of a mutant mouse, report researchers at the RIKEN Center for Developmental Biology 
						(CDB) in Kobe, Japan. These mice, which have defects in a gene responsible for hair follicle 
						development, develop bands of darkened skin that oscillate and traverse the body surface in 
						waves. In a paper published in the August 19 issue of the Proceedings of the National Academy 
						of Sciences, Shigeru 
						Kondo, in collaboration with researchers from the Medical School of Mie University, showed 
						that these traveling waves of skin coloration are strikingly similar to nonlinear waves produced 
						by the Belousov-Zhabotinskii (BZ) reaction in chemical systems, suggesting a shared underlying 
						principle.  
 
 
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| Stripes moving across the face of a single mouse in traveling waves. | 
 
 
 
 
The question of how complex patterns arise from seemingly disorganized or formless initial structures 
represents an intriguing challenge to mathematicians, physicists, chemists and biologists alike. Theoretical 
work indicates that the mechanisms underlying pattern formation are similar in both biological and non-biological 
systems, and a number of mathematical models capable of describing pattern generation in chemical media 
have been proposed, but the greater complexity of living systems has made it much more difficult to demonstrate 
a mathematical basis for biological patterns In 1952, Alan Turing proposed the reaction-diffusion model, 
which explained how patterns could self-organize in systems in which two chemical substances interact 
with each other and diffuse at different rates. This paper laid the groundwork for subsequent investigations 
into the mathematical underpinnings of living patterns. The research described in the PNAS article 
began when Kondo, whose research focuses on identifying the bases of biological pattern formation, was 
told about a mutant strain of mouse with an unusual striped phenotype. The mutation, a splicing defect 
in the Foxn1 (Whn or nude) gene, results causes hair follicle development to terminate just after skin 
pigments begin to accumulate. The immature follicles die off and are quickly replaced by a new hair cycle. 
The cyclical nature of this follicular attrition and re-activation by neighboring follicles produces a 
phenotype in which the mouse’s skin color at first uniformly oscillates between dark and light coloration, 
then begins to take on a remarkable striped appearance, with bands of pigmentation that originate from 
region under the forearms and travel across the body surface in all directions. These waves first appear 
at about three months after birth, and continue to arise and propagate throughout the life of the animal. 
 
 
By tracking the movements of traveling waves in the Foxn1 mouse skin pattern, Kondo et al ascertained 
that their formation was fundamentally similar to that of waves generated by the BZ reaction. Although 
this finding gives no indication of the specific molecular mechanism at work in the Foxn1 phenotype, an 
understanding of the nature of its mathematical basis does provide clues for investigators in their work 
to identify the molecules responsible for normal and aberrant follicle development. And, as many other 
species demonstrate similar striping mechanisms, the current report may help to provide biologists with 
a mathematical model to explain this skin patterning phenomenon. 
 
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