Mathematical Study on the Structure of Biological Systems and Its Organizational Specificity

在这项研究中，我们研究了组成元素之间的相互作用对生物系统结构形成的影响，范围从细胞种群到生物群落再到生态系统。通过对动力系统模型的数学分析，发现了以下特点。在生态系统层面，我们开发了一种理论方法，可以沿着营养水平“展开”食物网，即组成生物物种的能量和物质处理步骤。这种正在展开的食物网的转变揭示了拓朴过程的基本结构。此外，我们阐明了食物链中局部点的变化直接或间接地影响系统的其他部分，甚至可能改变整个结构的动态过程。在生物群落水平上，我们用fc…研究了物种间的相互作用，如竞争和捕食对群落中共存物种的数量和多样性的影响。我们更多地研究组成物种的特征性质，以推导出根据组成物种特征来确定群落的物种组成结构的规律。并对捕食者之间无直接相互作用的间接、正面或负面影响的机理和性质进行了理论上的解释。我们研究了细胞黏菌在迁移阶段的细胞分化模式的形成及其调控机制，表明典型的鼻塞模式是通过假设两种类型的细胞不同的密度依赖的动力学来解释的。此外，增加了依赖于局部细胞类型比率的细胞类型转换规则，使我们能够解释整个段塞两种细胞类型比率之间的调节。这也保证了块模式本身的维护。我们还分析了红细胞皱纹的形成，得到了支持细胞聚集机制的渗透应激假说的结果。较少

In this research we investigated the effects of interactions among constituent elements on the structure formation of a biological system, ranging from cell populations to biological community to ecosystem. By means of mathematical analysis of dynamical system models, the following specific features have been discovered.1. At the ecosystem level, we developed a theoretical means for "unfolding" a food web along trophic levels, i.e., steps of energy and matter processing by constituent biological species. This unfolding tranfomation of food webs reveals the essential strucuture of tophic process. Further, we elucidated the dynamic process by which a change at a local point within a food web directly and indirectly influences other parts of the system and even could modify the entire structure.2. At the biological community level, we investigated the effects of species interactions such as competion and predation on the number and diversity of coexisting species in a community , with foc … More us on characteristic properties of consituent species, to derive a law that determines species composition structure of a community in terms of constituent species characteristics. Also, a theoretical explanation was given for the mechanism and properties of the indirect, positive or negative, effects between predators with no direct interactions.3. We studied the formation of cell differentiation pattern and its regulation mechanism for the cellular slime molds at migrating stage, to show that a typical pattern of slug is explained by assuming different density-dependent dynamics of two types of cells. Further, the addition of a rule for cell type transition which depends on local cell type ratio allows us to explain the regulation of the ratio between the two types of cells for the whole slug. This also guarantees the maintenance of the slug pattern itself. We also analyzed the rouleaux pattern formation of red blood cells, and obtained the results which support the osmotic stress hypothesis for cell aggregation mechanism. Less