本計畫的第一部分探討配體引發的endocytosis。在這過程中，細胞外的配體首先吸附於細胞膜，然後在膜上聚集形成區塊，當區塊大小到達一臨界半徑時該區塊會形成液泡進入細胞內部。我們將考慮吸附、聚集、以及液泡脫附細胞膜等機制對每單位時間液泡進入細胞數量的影響。這部分研究的主要結果將可對此種細胞間訊息傳遞的模式提供許多量化的描述。計畫的第二部分探討與生物膜相連結的actin network 的運動。我們將考慮actin filaments 的polymerization 與depolymerization，actin monomors 的擴散，actin filaments 與細胞膜藉由Arp1 蛋白質連結而造成的mechanical coupling，細胞膜本身的運動，與細胞質的流場對此複雜系統的運動的影響。此系統的運動方程式是一組rection-advection-diffusion 方程式。藉由對此一方程式的解析與數值分析，我們將可瞭解在何種條件下細胞膜會形成手指狀，內含許多actin filaments 的 filopodium 突出，也可以瞭解這些filopodium 在各種條件下的寬度與前進速率。這部分的研究將可增進我們對細胞爬行的物理機制有更進一步的瞭解。 In part (i) we study the physics of ligand-induced endocytosis. Small ligand molecules on one side of a membrane reversibly bind to membrane surface, then aggregate, then form ligand-rich domains. Domains beyond some critical size bud, form vesicles and enter the cell. We plan to build a model that includes adsorption, aggregation, and vesicle formation. The goal is to find how does number of ligand-containing vesicles leaving membrane per unit time changes under different physical conditions. The result will shed light on quantitative prediction of some signaling processes in cells. In part (ii) we study the dynamics of a actin network in contact with a membrane. Actin filaments polymerize in the front and depolymerize in the rear, resulting a push on the membrane. When polymerization rate is sufficiently high, a flat membrane can become unstable, and membrane form many finger-like protrusions called filapodiums. We describe the complex dynamics of this system by a set of reaction-advection-diffusion equations that include actin filament polymerization, depolymerization, diffusion of actin monomers, dynamics of membrane and membrane associated proteins, and viscous flow of solvent. Our analytical study and numerical simulation will provide a 「phase diagram」 which indicates the region of parameter space that corresponds to different dynamic behavior related to cell motility. 研究期間：9608 ~ 9707
