Cummings F W
Physics Department, University of California, Riverside, CA 92521, USA.
J Theor Biol. 1996 Feb 7;178(3):229-38. doi: 10.1006/jtbi.1996.0022.
A model is given for the generation of pattern and form in living systems, based on the assumption of two types of a single adhesion molecule that form homotypic cell-cell contacts. The time dependence of the model is different from that of the Turing models, instead viewing the change in time as being driven by the change in time of the total area A, along with the sequential gene activation which is called into play at discrete times as the organism grows and changes shape. Two equations are derived on the assumption of an energy minimum equilibrium being achieved at all times on a scale that is short compared with the rate of change over time of the total area. The two equations derived from the simple assumptions of the model are the (nonlinear) Helmholtz equation and the Laplace equation. It is argued that a suitable "morphogen" should attempt to satisfy certain rather specific conditions.
基于单一黏附分子的两种类型形成同型细胞间接触的假设，给出了一个用于生成生物系统中模式和形态的模型。该模型的时间依赖性与图灵模型不同，它将时间变化视为由总面积A随时间的变化驱动，同时伴随着随着生物体生长和形状变化在离散时间发挥作用的顺序基因激活。在一个与总面积随时间变化率相比很短的尺度上，始终假设达到能量最小平衡的前提下，推导出了两个方程。从该模型的简单假设推导出来的两个方程是（非线性）亥姆霍兹方程和拉普拉斯方程。有人认为，合适的“形态发生素”应试图满足某些相当特定的条件。
