Mathematical modeling of a continuous system of cells growing on an elastic substrate

2022 Fiscal Year Final Research Report

• Project/Area Number: 19K03629
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Hokkaido University
• Principal Investigator: Kobayashi Yasuaki 北海道大学, 電子科学研究所, 准教授 (50455622)
• Project Period (FY): 2019-04-01 – 2023-03-31
• Keywords: パターン形成 / 形態形成 / 反応拡散系

Outline of Final Research Achievements

We have constructed mathematical models to analyze the pattern formation caused by cell systems proliferating on soft substrates like epidermal cells. We successfully incorporated cell division on the basement membrane indirectly as an adhesion strength field, and derived a mathematical model that can describe membrane deformation due to increased adhesion strength. Through the analysis of the model, we clarified that an upward protrusion is formed where the adhesion strength is large. We also extended the model and carried out numerical simulations of the basement membrane model describing plastic deformation and of the TJ expression layer in the epidermal granular layer. In both cases, we obtained results supporting the experimental findings.

Free Research Field

非線形動力学

Academic Significance and Societal Importance of the Research Achievements

本研究で提案する数理モデルは増殖細胞系の一般的な性質に基づくものであり，3次元の形態形成や多種の化学濃度場とのカップリングなど多くの系に拡張可能なモデルとなっている。従って様々な応用の可能性がある．また生命現象におけるパターン形成の一般的な原理の解明に寄与すると期待でき る。また皮膚科学の実験研究者に対して，数理モデルの予測に基づくフィードバックも与えており，生命科学や医学における学術的波及効果も期待できる。