Development of mathematical tools for reaction pathway network

2014 Fiscal Year Final Research Report

• Project/Area Number: 24654023
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Osaka University
• Principal Investigator: SUZUKI TAKASHI 大阪大学, 基礎工学研究科, 教授 (40114516)
• Co-Investigator(Renkei-kenkyūsha): KAWASAKI Shuji 岩手大学, 人文社会科学部, 准教授 (10282922)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 細胞分子パスウェイ / MT1-MMP / 酸素反応 / 質量作用 / 質量保存 / 反応速度論 / グラフ理論 / 可積分系

Outline of Final Research Achievements

We studied the pathway network of cell molecules. First, we approached the activation of the degradation enzyme for basement membrane. The malignant tumor is provided with clonal growth, motility, and metastatis. Invasion arises at the early stage of metastatis, where tumor cell forms invadopodia to begin ECM degradation. MT1-MMP is the membrane protein with over expression inside the invadopodia. One of its main role is the activation of MMP2, the secretor degrdation enzyme of the basement membrane. This process is achieved under the presense of the third molecule, TIMP2. Based on this biological model, we constructed mathematical model using the law of mass action. In this modeling we applied the same reaction rates of the fundamental process to the polymerization. Mathematical analysis, however, revealed that the system is completely integrable by three fundamental equations. Generalization to the N-system and comparison to PySB is also done.

Free Research Field

非線形偏微分方程式