Hunding A, Sørensen P G
Panum Institute, Department of Chemistry, University of Copenhagen, Denmark.
J Math Biol. 1988;26(1):27-39. doi: 10.1007/BF00280170.
Spontaneous pattern formation may arise in biological systems as primary and secondary bifurcations to nonlinear parabolic partial differential equations describing chemical reaction-diffusion systems. Such Turing prepatterns have a specified geometry as long as D/R2 (the diffusion coefficient of the morphogen D divided by the square of a characteristic length) is confined to a (usually) limited interval. As real biochemical systems like cleaving eggs or early embryos vary considerably in size, Turing prepatterns are unable to maintain a specified prepattern-geometry, unless D/R2 is varied as well. We show, that actual biochemical control systems may vary Dapp/R2, where Dapp (kappa) is an apparent diffusion constant, dependent on enzyme regulated rate constants, and that such simple control systems allow Turing structures to adapt to size variations of at least a factor 10(3) (linearly), not only in large connected cell systems, but in single cells as well.
自发图案形成可能在生物系统中出现，作为描述化学反应 - 扩散系统的非线性抛物型偏微分方程的一级和二级分岔。只要D/R²（形态发生素D的扩散系数除以特征长度的平方）被限制在一个（通常）有限的区间内，这种图灵预图案就具有特定的几何形状。由于像正在分裂的卵子或早期胚胎这样的真实生化系统在大小上有很大差异，图灵预图案无法维持特定的预图案几何形状，除非D/R²也发生变化。我们表明，实际的生化控制系统可能会改变Dapp/R²，其中Dapp（κ）是一个表观扩散常数，取决于酶调节的速率常数，并且这样简单的控制系统允许图灵结构适应至少10³倍（线性）的大小变化，不仅在大型相连的细胞系统中，在单细胞中也是如此。
