Ogawa Ken-ichiro, Miyake Yoshihiro
Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Nagatsuta-cho, Midori-ku, Yokohama, Japan.
Biosystems. 2011 Mar;103(3):400-9. doi: 10.1016/j.biosystems.2010.12.002. Epub 2010 Dec 16.
Many conventional models have used the positional information hypothesis to explain each elementary process of morphogenesis during the development of multicellular organisms. Their models assume that the steady concentration patterns of morphogens formed in an extracellular environment have an important property of positional information, so-called "robustness". However, recent experiments reported that a steady morphogen pattern, the concentration gradient of the Bicoid protein, during early Drosophila embryonic development is not robust for embryo-to-embryo variability. These reports encourage a reconsideration of a long-standing problem in systematic cell differentiation: what is the entity of positional information for cells? And, what is the origin of the robust boundary of gene expression? To address these problems at a cellular level, in this article we pay attention to the re-generative phenomena that show another important property of positional information, "size invariance". In view of regenerative phenomena, we propose a new mathematical model to describe the generation mechanism of a spatial pattern of positional values. In this model, the positional values are defined as the values into which differentiable cells transform a spatial pattern providing positional information. The model is mathematically described as an associative algebra composed of various terms, each of which is the multiplication of some fundamental operators under the assumption that the operators are derived from the remarkable properties of cell differentiation on an amputation surface in regenerative phenomena. We apply this model to the concentration pattern of the Bicoid protein during the anterior-posterior axis formation in Drosophila, and consider the conditions needed to establish the robust boundary of the expression of the hunchback gene.
许多传统模型利用位置信息假说解释多细胞生物发育过程中形态发生的每个基本过程。它们的模型假定，在细胞外环境中形成的形态发生素的稳定浓度模式具有一种重要的位置信息属性，即所谓的“稳健性”。然而，最近的实验报告称，果蝇胚胎早期发育过程中一种稳定的形态发生素模式，即双尾蛋白的浓度梯度，对于胚胎与胚胎之间的变异性并不稳健。这些报告促使人们重新思考系统细胞分化中一个长期存在的问题：细胞的位置信息实体是什么？以及，基因表达稳健边界的起源是什么？为了在细胞水平上解决这些问题，在本文中我们关注再生现象，这些现象展现了位置信息的另一个重要属性，即“大小不变性”。鉴于再生现象，我们提出了一个新的数学模型来描述位置值空间模式的生成机制。在这个模型中，位置值被定义为可分化细胞将提供位置信息的空间模式转化而成的值。该模型在数学上被描述为一个由各种项组成的结合代数，假设这些项是在再生现象中截肢表面细胞分化的显著特性推导出来的一些基本算子的乘积。我们将这个模型应用于果蝇前后轴形成过程中双尾蛋白的浓度模式，并考虑建立驼背基因表达稳健边界所需的条件。
