細胞在表面上爬行是藉由肌動蛋白細胞骨架、肌凝蛋白、細胞膜以及細胞和基板之間的鍵
結相互協調而成的運動。最近的實驗進展替理論建模提供了許多關於細胞爬行的資訊。
其中，有實驗量測了細胞爬行時施加在基板上的力，但是大多數前人的理論模型都著重於
細胞骨架的動力學。
在本論文中，我們使用一個簡單的一維模型，包含了細胞中的活性凝膠以及細胞和基
板間的鍵結，來模擬細胞爬行的基本物理。藉由這個模型，我們會先研究鍵結的性質對
鍵的分佈造成的影響。其中，肌凝蛋白的擴散對此亦會產生影響。接著，藉由改變細胞
的收縮能力、鍵結能力、肌動蛋白的聚合速率和細胞的極化程度來模擬細胞的爬行行為。
我們發現收縮能力、肌動蛋白的聚合速率和細胞的極化程度增加時將會增強細胞的移動
性。除了靜止與持續移動，我們也發現了週期性來回移動的細胞。類似的行為雖然在其
他細胞爬行的模型也被發現，但我們的模型裡不像其他模型，沒有包含肌動蛋白活化分子
的擴散反應行為。此外，在我們的模型中，週期性來回運動只出現在肌球蛋白擴散速率較
低的情形，並且發生在移動和靜止狀態之間。最後，牽引力的多極分析顯示了力四極在靜
止狀態下不會出現，並且在細胞移動時和細胞的方向呈現相反方向。而力偶極則是和細胞
的長度密切相關。

Cell crawling on
at substrates is a coordinated movement regulated by actin cytoskeleton,
myosin motors, cell membrane, and cell-substrate adhesion sites. Recent experimental advances
provided much information on cell crawling for theoretical modeling. However, most
of the theoretical models emphasized the roles played by the cytoskeleton, while experimental
probes reported force exerted on the substrate through the adhesion sites.
In this thesis, we use a simple one-dimensional active gel coupled to adhesion sites to
model the basic physics of cell crawling. In this model, we rst study the eect of myosin
diusion on the distribution of slip bonds and catch bonds between cell and substrate.
After that, various migratory behaviors for cells with catch bonds are simulated by varying
contractility, binding energy, polymerization rate, and degree of cell polarization induced
by cytosol
ow asymmetry. The result points out that the motility of a cell is enhanced
when polymerization rate, contractility, or cell polarizability increases. One of the migratory
behavior is periodic migration. In previous theoretical studies, such behavior has only been
found when cell motility is coupled to the dynamics of actin polymerization activators that
is not included in our model. In our model, this state arises only for a cell with slow myosin
diusion, and it occurs between moving and rest states. Dierent from the slow myosin
diusion case, when the cell motility increases, a cell with fast-diusing myosin motors
simply changes from rest to moving state. Finally, multipole expansion of traction force
shows that the force quadrupole vanishes in the rest state, and in the moving state has a
direction opposite to cell velocity. On the other hand, the force dipole is strongly correlated
to cell length.

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