p226

反応拡散系に関して

鳥の羽の分布などのモデルとしてはうまくいく．

Lin et al., Spots and stripes: Pleomorphic patterning of stem cells via p-ERK-dependent cell chemotaxis shown by feather morphogenesis and mathematical simulation

DB  334 369 (2009)

*A continuum of feather patterns, ranging from stripes to spots, can be obtained when the

level of p-ERK activity is adjusted with chemical inhibitors. The patterns are dose-dependent, tissue stage dependent, and irreversibl

*A mathematical model based on short-range activation, long-range inhibition, and cell chemotaxis is developed and shown to simulate observed experimental results.

拡散とスイッチの組み合わせとしてショウジョウバエのGap遺伝子群の発現を論じた論文がある．　どのくらいrobustかあまり明確ではない．

9 Vakulenko et al., ``Size Regulation in the Segmentation of Drosophila: Interacting Interfaces between Localized Domains of Gene Expression Ensure Robust Spatial Patterning,’’

PRL  103 168102

*The proposed model of gap gene patterning is minimal involving only 4 genes and a morphogen gradient. \sigma = step function

* d u_i/dt = d_j\D u_i + R_i\sigma (T_{ij}u_j + m_i\mu + h_i)-\lambda_i u_i,

where u_i is the protein conc, d, R, m \lambda are constants; h_i = threshold

*That is, switch + diffusion.