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Shigeru KONDO, Ph. D. 
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,
the British mathematician Alan Turing proposed a simple mathematical equation
capable of generating a wide range of patterns commonly found in the natural
world, such as stripes, spots and reticulations. This model, known as
the reaction-diffusion model, demonstrates that the interaction between
a local activator and a long-range inhibitor can give rise to various
periodic structures in response to differences in their individual diffusion
rates.
Our
team is interested in demonstrating the mathematical basis of pattern
formation in development, and using mathematical models as predictive
tools to aid in the identification of genes and molecules involved in
the generation of spatial structures. The lab's research focuses
on skin surface and morphogenetic patterning, both of which feature prominent
examples of periodic structures that can be described in terms of standing
and moving waves. By studying the molecular genetic mechanisms underlying
pattern development in striped wild type and mutant organisms, including
zebrafish and mouse, we hope to provide biological evidence of the mathematically
explicable bases that underlie the formation of natural complex patterns.
