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標題: 以涂林模型模擬生物圖案
Turing model for generating biological patterns
作者: Liu, Ruey-Tarng
關鍵字: 生物圖案的形成
biological pattern formation
reaction diffusion
Turing mechanism
出版社: 物理學系所
摘要: In 1952, A. M. Turing[1] proposed that the reaction-diffusion system could explain the main phenomena of biological morphogenesis. Unfortunately, he died in 1954. However, Turing's intriguing ideas influenced the thinking of theoretical biologists and scientists of many fields. The Turing mechanism has been successfully used for generating patterns in mammals[2,3], fish[4-6], bacterial colonies[7-9], phyllotaxis[10,11] and many others. We simulate the patterns on the elytras of the lady beetles using a reaction-diffusion equation with two types of morphogens based on the Turing model[12]. A part of a half spherical surface is used to approximate the geometry of the hard wings.Various patterns common to lady beetles in Taiwan can be produced on this curved surface. A complex system like the leopard's skin marking still offers an optimal level of challenge for generating it, even though previous simulations using a one-stage Turing model[13-16] might have produced final rosette patterns similar the patterns of real leopards. Based on the results of phylogenetic analysis, which showed that flecks are the primitive pattern of the felid family and all other patterns including rosettes and blotches develop from it[17], we construct a two-stage Turing reaction-diffusion model[18] which generates spot patterns initially. In the first stage, spots are generated in a similar manner for both the leopard cub and the jaguar cub. In the second stage, we tune model paraments to generate, separately, the sequence of patterns transformation during the growth of the animals.
英國數學家涂林於1952年[1]提出「解釋生物形態發生的反應擴散模型」的創見,不幸卻於1954年早逝,但他的想法已經引起理論生物學家與許多領域的科學家的注意與興趣,開始從事於涂林機制的研究。至今在生物圖案形成的應用累積了許多豐碩的成果,例如成功模擬出哺乳動物毛皮圖案[2,3]、魚類的圖紋[4-6]、細菌群聚的圖樣[7-9]、與植物的葉序[10,11]…等等。 台灣特有的瓢蟲身上豔麗多樣的圖案吸引我們的注意,嘗試將部分的半球面視為瓢蟲的鞘翅(elytra),以兩種成形素(morphogens)的涂林方程,給予不同的初始濃度分佈與參數,成功製造出不同種類的瓢蟲花紋[12]。 此外對於複雜的豹紋花樣,過去一些以單階段涂林模型的研究,雖然曾經製造出與花豹相類似的玫瑰斑紋[13-16],但是斑紋隨年齡成長的變化過程的問題,仍然懸而未決。根據動植物種類史的分析(phylogenetic analysis),顯示貓科動物身上的不同種的斑紋─包括複雜的玫瑰紋(rosettes)與擴散狀的污斑(blotches)─是從點(flecks)演化而來的[17],我們提出了兩階段的涂林模型[18],成功的模擬出花豹(leopard)與美洲豹(jaguar)身上複雜的斑紋結構:第一階段首先利用涂林模型製造出點的圖案,對照於剛出生的幼豹的斑紋;第二階段以點為初始條件,調變模型中部分的參數,隨著參數的變化過程,圖案的改變呈現出真實豹紋在成長中的變化。
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