Construction of theory for a link between microscopic and macroscopic models related to biological phenomena

2018 Fiscal Year Final Research Report

• Project/Area Number: 16KT0135
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 特設分野
• Research Field: Mathematical Sciences in Search of New Cooperation
• Research Institution: University of Miyazaki
• Principal Investigator: Izuhara Hirofumi 宮崎大学, 工学部, 准教授 (50515096)
• Project Period (FY): 2016-07-19 – 2019-03-31
• Keywords: 数理モデル / ミクロモデル / マクロモデル / パターン形成

Outline of Final Research Achievements

Many phenomena observed in nature have hierarchical structures. E.coli which is one of bacteria have a simple movement that each individual repeats straight motion and rotation motion alternately. However, when they are cultivated on a nutrient agar, it is well known that a very regular colony pattern is formed in a macroscopic level. From the viewpoint of experiments and numerical simulations of mathematical models, there are so many studies on E.coli motion in a microscopic level and colony patterns in a macroscopic level. But, a relation between a simple microscopic motion of each individual and a regular macroscopic colony pattern is not known. In this research, we revealed the microscopic and macroscopic relation from a mathematical point of view.

Free Research Field

応用数学

Academic Significance and Societal Importance of the Research Achievements

古くから複雑な物事でも、それを構成する要素に分解し、個別の要素を理解すれば、全体の性質や振る舞いを理解できると思われていたが、ミクロの情報だけでは、マクロの振る舞いを予想できない創発性が認識されるようになり、ミクロとマクロの橋渡しとなる新たな手法の確立が必要となっていた。そのため、本研究は階層を超えたミクロとマクロの関係性解明に挑戦した研究であり、これからの創発現象解明への一つのブレイクスルーとして意義があると考えている。