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

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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