Ishihara Shuji, Kaneko Kunihiko
Department of Pure and Applied Sciences, College of Arts and Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8902, Japan.
J Theor Biol. 2006 Feb 7;238(3):683-93. doi: 10.1016/j.jtbi.2005.06.016. Epub 2005 Aug 15.
Although Turing pattern is one of the most universal mechanisms for pattern formation, in its standard model the number of stripes changes with the system size, since the wavelength of the pattern is invariant. It fails to preserve the proportionality of the pattern, i.e. the ratio of the wavelength to the size, that is often required in biological morphogenesis. To get over this problem, we show that the Turing pattern can preserve proportionality by introducing a catalytic chemical whose concentration depends on the system size. Several plausible mechanisms for such size dependence of the concentration are discussed. Following this general discussion, two models are studied in which arising Turing patterns indeed preserve the proportionality. Relevance of the present mechanism to biological morphogenesis is discussed from the viewpoint of its generality, robustness, and evolutionary accessibility.
尽管图灵斑图是图案形成最普遍的机制之一，但在其标准模型中，条纹的数量会随系统大小而变化，因为图案的波长是不变的。它无法保持图案的比例关系，即波长与大小的比值，而这在生物形态发生中常常是需要的。为了解决这个问题，我们表明通过引入一种浓度依赖于系统大小的催化化学物质，图灵斑图可以保持比例关系。讨论了几种关于这种浓度大小依赖性的合理机制。在这一一般性讨论之后，研究了两个模型，其中产生的图灵斑图确实保持了比例关系。从其普遍性、稳健性和进化可达性的角度讨论了当前机制与生物形态发生的相关性。
