二維細胞運動的相場模型：以盤基網柄菌趨熱行為為例

Abstract

細胞運動對生命而言是一個常見且不可或缺的機制，許多生物現象都以此為基礎，舉凡傷口癒合、免疫反應或是癌症轉移等。細胞運動主要由肌動蛋白(actin) 突出和肌球蛋白(myosin) 收縮引起，其中肌動蛋白聚集的位置由信號分子所決定。本研究提出了一個基於相場法的模型，並且聚焦在肌動蛋白、肌球蛋白以及信號分子對細胞運動的貢獻。本文的模型由若干方程式所構成，其中這幾個方程式分別描述這些物質在系統中的行為，分別是細胞位置ϕ、纖維狀肌動蛋白(F-actin) 密度ρf、肌球蛋白密度ρm 以及信號分子d 隨著時間迭代。ϕ 是細胞位置標記，其值介於0 到1 之間，其中0 被定義為細胞外部，相對地，1 被定義為細胞內部。在本研究的模型中，突出力以及收縮力的大小取決於纖維狀肌動蛋白以及肌球蛋白的密度，其中信號分子決定纖維狀肌動蛋白聚集的位置。 為了驗證模型，本研究選擇將盤基網柄菌(Dictyostelium discoideum) 這一模式生物(model organism) 的趨熱性作為研究對象，根據模式生物的科學研究結果，歸納出涵蓋諸多生物的模型，進而應用在各領域，為了確保孢子傳播的良好條件，該菌會根據環境而改變趨熱性。於本研究的模型中，細胞運動由趨熱性以及環境溫度梯度共同決定，透過定義細胞局部溫度與臨界溫度決定趨熱性是正或是負，當細胞局部溫度高於臨界溫度時，細胞呈現正趨熱性；反之，細胞則展示負趨熱性。同時，在一般情況下，環境溫度梯度越高，細胞的運動越快。本研究提出了 一個穩定的模型，並很好地實現了盤基網柄菌的細胞運動。期許能在未來加入隨機行走功能、趨食性或趨光性，使模型更加全面，從而更準確描述目標對象，進而應用於諸多領域中。

Cell motility is mainly caused by actin protrusion and myosin contraction. Here, we propose a model based on the phase-field method and focus on F-actin and myosin dynamic. We use several equations to describe each contribution of these proteins respectively. Cell location ϕ, density of F-actin ρf , density of myosin ρm and signal molecular d are evolve with time. ϕ is a position marker which value between 0 to 1, 0 is defined as the outside of a cell, similarly, 1 is defined as inside of a cell. The magnitude of the protrusion and contraction force depends on the concentration of F-actin and myosin, where, signal molecular determine the position F-actin polymerization. To test our model, we apply it to thermotaxis of Dictyostelium discoideum. They live and grow in the mulch on the forest floor and feed on bacteria. At daytime, the soil surface is warmer than the subsurface mulch, and hence the Dictyostelium discoideum is directed by positive thermotaxis towards the surface. At night, the soil surface is cooler than the subsurface mulch, they still move upwards, this time due to negative thermotaxis. They always tend to migrate towards the soil surface, thus ensuring good conditions for spore dispersal. To decide thermotaxis is positive or negative, we define a cell local temperature and critical temperature. When the cell local temperature is higher than the critical temperature, the cell displays positive thermotaxis. On the contrary, the cell shows negative thermotaxis. At the same time, our model is driven by temperature gradient, the higher the temperature gradient, the easier the polarization of F-actin. We propose a stable model and also well implement thermotaxis of Dictyostelium discoideum. Due to the stability, we could easily extend our model to more complex conditions in the future.