定位螢光粒子分佈對三維細胞牽引力之研究與分析

Abstract

在細胞生物學領域中，細胞對外界牽引力在生理學上的眾多反應有顯著的影響，當細胞在移動或分化時，都會透過複雜的機制對外界產生連結並施加牽引力於外界，因此精確地量化細胞牽引力方向和大小能提供與生物學相關的有效資訊。而現今有許多量測分析細胞牽引力方法，從一開始將細胞培養在聚丙烯胺水膠（polyacrylamide gel，簡稱PA gel）上，觀察水膠輪廓變形來計算得到牽引力，到現今利用微陣列柱去計算細胞對微陣列柱造成的形變，或追蹤埋在水膠內螢光粒子的位移，利用三維包辛尼斯可-賽魯蒂方程式所化簡的格林函數作為基礎，以傅立葉轉換法做運算得其牽引力，然而和傅立葉轉換法相比，利用有限元素法推算牽引力，能夠更為有效的推廣至複雜的幾何形狀與材料性質，而不受包辛尼斯可-賽魯蒂方程式的假設限制。 本研究主要著重在計算方法，建立各種分析方法以及探討不同方法之差異，進而提供實驗設計的參考。實驗中是利用追蹤在水膠內受細胞牽引力而移動的螢光粒子位移，再利用有限元素模擬軟體計算細胞牽引力，為了驗證此系統的可靠度以及不同分析方法的影響，本研究建立一套細胞牽引力回復模擬，藉此來判斷系統回復的準確性，論文前段主要模擬螢光粒子的分布對分析造成的影響，歸納出螢光粒子集中於表面時能達到較為精確的分析結果，並且深入探討其背後原因，後段部分則利用模擬不同的資料點濃度，歸納出資料點分布在表面時能夠被回復的範圍，發現在資料點濃度較低時，會傾向於低估牽引力的大小值，並且回復的牽引力位置也更加不精確。最後，建立新的混合邊界條件系統，細胞牽引力為接觸力，只會發生在細胞接觸到PA膠的位置，藉由這項已知可將細胞內外分開施加不同的邊界條件，在細胞內施加實驗上量測的螢光小球位移，在細胞外則外力為零，用以更符合真實情況，並且和原有的分析方法做比較。

Many physiological processes can be affected by cellular traction force between cells and surroundings. Quantifying the magnitude and direction of cellular traction force can provide important information while cell migrating or in cell differentiation. Developments in three-dimensional (3D) traction force microscopy techniques with Finite Element Method, which measure the displacement of beads in whole substrate, make it accessible to measure traction force exerted by cell. However, the method is limited by the beads density and the technique of tracking beads in whole substrate. With special treatments, beads can be concentrated on the top surface of the polyacrylamide (PA) substrates. When the distribution of the beads is thin enough, it can be regarded as surface beads. In addition, it is easier to track the displacement and we can get higher resolution by using higher beads density. In the thesis, we get the displacements from the nodal solutions of simulated traction field, and put the x, y, and z component of displacements into three-dimensional regular grid. Then, we put the complete grid of displacement into finite element model to obtain traction field solution. Compared with the whole boundary condition, plane boundary condition can be readily applied to substrate and calculate better result. Following the same steps described above, we compare the two methods by solving traction field exerted by experimental cell data. In this thesis, we focus on the computational method, and develop a method to understand the influences of the beads density. We use simulations to find resolvable range for single focal adhesion and couple focal adhesion recovery under different beads density. We find that the lower beads density causes the recovered traction more dispersed and underestimated, and that also probably cause the deviation on the recovered position of tractions. We then construct mixed boundary method to calculated the cell traction force. For this condition, we applied displacement in the cell region and make traction free outside the cell region. For this case, we can obtain more accurate experimental result. In conclusion, we develop several analysis methods and compare their pros and cons, which provide helpful information for experimental conditions and a better understanding of the simulation results.