Ogawa Ken-ichiro, Miyake Yoshihiro
Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, Yokohama, Kanagawa, Japan.
Biosystems. 2015 Jun;132-133:6-12. doi: 10.1016/j.biosystems.2015.04.004. Epub 2015 Apr 11.
Cell-to-cell communication in multicellular organisms is established through the transmission of various kinds of chemical substances such as proteins. It is well known that gene expression triggered by a chemical substance in individuals has stable spatial patterns despite the individual differences in concentration patterns of the chemical substance. This fact reveals an important property of multicellular organisms called "robustness", which allows the organisms to generate their forms while maintaining proportion. Robustness has been conventionally accounted for by the stability of solutions of dynamical equations that represent a specific interaction network of chemical substances. However, any biological system is composed of autonomous elements. In general, an autonomous element does not merely accept information on the chemical substance from the environment; instead, it accepts the information based on its own criteria for reaction. Therefore, this phenomenon needs to be considered from the viewpoint of cells. Such a viewpoint is expected to allow the consideration of the autonomy of cells in multicellular organisms. This study aims to explain theoretically the robust patterning of gene expression from the viewpoint of cells. For this purpose, we introduced a new operator for transforming a state variable of a chemical substance from an external coordinate system to an internal coordinate system of each cell, which describes the observation of the chemical substance by cells. We then applied this operator to the simplest reaction-diffusion model of the chemical substance to investigate observation effects by cells. Our mathematical analysis of this extended model indicates that the robust patterning of gene expression against individual differences in concentration pattern of the chemical substance can be explained from the viewpoint of cells if there is a regulation field that compensates for the difference between cells seen in the observation results. This result provides a new insight into the investigation of the mechanism of robust patterning in biological systems composed of individual elements.
多细胞生物中的细胞间通讯是通过蛋白质等各种化学物质的传递来建立的。众所周知，尽管化学物质的浓度模式存在个体差异，但个体中由化学物质触发的基因表达仍具有稳定的空间模式。这一事实揭示了多细胞生物的一个重要特性，即“稳健性”，它使生物体在保持比例的同时生成其形态。传统上，稳健性是通过代表化学物质特定相互作用网络的动力学方程解的稳定性来解释的。然而，任何生物系统都是由自主元件组成的。一般来说，一个自主元件不仅仅是从环境中接受关于化学物质的信息；相反，它是根据自身的反应标准来接受信息的。因此，需要从细胞的角度来考虑这种现象。这样的观点有望使我们能够考虑多细胞生物中细胞的自主性。本研究旨在从细胞的角度对基因表达的稳健模式进行理论解释。为此，我们引入了一个新的算子，用于将化学物质的状态变量从外部坐标系转换到每个细胞的内部坐标系，该坐标系描述了细胞对化学物质的观测。然后，我们将这个算子应用于化学物质最简单的反应扩散模型，以研究细胞的观测效应。我们对这个扩展模型的数学分析表明，如果存在一个调节场来补偿细胞观测结果中出现的差异，那么从细胞的角度就可以解释基因表达对化学物质浓度模式个体差异的稳健模式。这一结果为研究由个体元件组成的生物系统中稳健模式形成的机制提供了新的见解。
