細胞はECMを形造り，ECMは細胞が働く場を形成する．本研究では，数理的・物理的な観点から「ECMの曲面形状や時間変動，フィラメント配向が細胞の運動にどのような変化を与えうるのか?」を問う．（1）曲面上のパターン形成と細胞運動（2）基質を介
して周期的な外力を受ける細胞・細胞集団系の運動 (3) ECMフィラメントの配向が細胞に誘起する運動について，数理的な枠組みを発展させる．さらにはこれらの効果-ECM表面形状とフィラメント配向，外力とフィラメント配向-を組み合わせることで，細胞層のパターニングや運動を解明し，さらにはその制御原理を与える．例えば，基質が一軸伸縮を受ける系には普遍的に細胞配向に非自明な角度が現れるが，その角度を説明し，また，それにより引き起こされるうる細胞パターニングを明らかにする．さらには，ECMフィラメントや細胞配向との相互作用を考えることで細胞制御手法を提案する．理論的観点から，さまざまな系に適用可能な汎用性の高い状況を考察し，ECMの形状や時間的変動が細胞層に与える効果について多くの実験の結果の解釈に資するような知見を得ることを目指す．

Cells shape the ECM through secretion, and the ECM forms the environment in which cells operate. Our study asks, from a mathematical and physical perspective, "How do the surface curvature, temporal variations, and filament orientation of the ECM affect cell movement?" Specifically, we aim to develop a mathematical framework for (1) pattern formation and cell　movement on curved surfaces, (2) the movement of cells and cell collectives subjected to cyclic external forces through the substrate, and (3) the interaction between ECM filament and cells in terms of their directionality. By combining these studies, we aim to elucidate the movement and patterning dynamics of cell layers and further provide principles for their control. For example, it is known that non-trivial angle of cell orientation generically appear in systems subjected to uniaxial stretching of the substrate. We will explain this angle and clarify the resulting cellular pattern. Furthermore, we will propose methods for cell control by considering the interactions between ECM filaments and cell orientation. We aim to obtain insights that can interpret the effects of ECM shape and temporal variations on cell layers in various systems from a theoretical perspective, contributing to the interpretation of numerous experimental results.