On applications of fatgraph techniques to the molecular biology via matrix models

2019 Fiscal Year Final Research Report

• Project/Area Number: 17K18781
• Research Category: Grant-in-Aid for Challenging Research (Exploratory)
• Allocation Type: Multi-year Fund
• Research Field: Particle-, Nuclear-, Astro-physics, and related fields
• Research Institution: Kagawa University
• Principal Investigator: Fuji Hiroyuki 香川大学, 教育学部, 准教授 (50391719)
• Co-Investigator(Kenkyū-buntansha): 樋上 和弘 九州大学, 数理学研究院, 准教授 (60262151) ; 村上 斉 東北大学, 情報科学研究科, 教授 (70192771) ; 佐竹 郁夫 香川大学, 教育学部, 教授 (80243161)
• Project Period (FY): 2017-06-30 – 2020-03-31
• Keywords: ファットグラフ / 行列模型 / 量子幾何学 / タンパク質 / メタ構造 / RNA / 量子曲線 / 位相的漸化式

Outline of Final Research Achievements

In this research project, various fatgraph techniques are applied to the study of the molecular biology. The basic concept of the fatgraph was introduced originally in the perturbative study of the quantum field theory, and such idea is found to be useful to represent the geometry and topology of moduli spaces in mathematics. In recent years, the fatgraph is applied to characterize the biomolecules such as RNAs and proteins, and it is found to be useful to improve the predictions of their secondary structures.
In our work, we focused mainly on the following two aspects of the fatgraph techniques: (1) propose a new model to predict the secondary structure of proteins, (2) develop the basic aspects of fatgraph techniques via matrix models.
On the aspect (1), we found a novel mathematical model to predict the reduced secondary structure referred to "meta-structure" of proteins. On the aspect (2), we have proposed novel fatgraph techniques in the mirror symmetry and two-color QCD.

Free Research Field

数理物理学

Academic Significance and Societal Importance of the Research Achievements

ファットグラフはこれまで，理論物理学や代数学・幾何学などの学際領域で主に用いられてきた手法であり，半世紀年近くの発展の中で素晴らしい結果をもたらしてきた．こうした純粋数理研究の応用先として，分子生物学におけるRNAやタンパク質の構造予測問題に取り組み，新たな学際研究の推進に役立てることが，本研究の意義の一つである．
本研究課題の期間中は，新たなタンパク質の構造予測モデルの構築に関する研究を，デンマークのオーフス大学QGM研究所と共同で取り組み，タンパク質の「メタ構造」と呼ぶ新たな構造予測問題を発見するに至った．
これらの結果は高分子化学などの新たな応用先を探る上で有用なものであると考えられる．