在細胞的眾多行為中，細胞的運動具有廣泛的影響，例如免疫反應過程，傷口治癒，腫瘤細胞的轉移與入侵組織，甚至胎胚形成等不同反應之中，細胞運動都扮演重要的角色，由此可知細胞運動對病理和生理現象的影響及其重要性。而博登量測器是經常被用於評估細胞運動特性的工具之一，能提供趨向因子穩定的梯度分佈，此特性有助於研究細胞對於不同化學物質的趨向性反應。本文研究人類胎盤源多功能幹細胞對於第一型膠原蛋白的反應，利用博登量測器評估此幹細胞對於第一型膠原蛋白的化學趨向性反應，以及分析細胞膜表面上的相關受體。同時，本研究也發展數學模型，考慮趨向因子在博登量測器中的輸送現象，利用Lapidus-Schiller 方程式模擬細胞的隨機漫步運動和化學趨向性反應，另外，也加入細胞在博登量測器上流體層的沈積現象，用以了解博登量測器實驗的過程。此外，更進一步採用受體反應方程式以探討細胞受體和趨向因子之間的反應，對於化學趨向運動的影響。本文結合實驗結果與數學模擬，以曲線擬合的方式得到細胞的運動係數以及對於第一型膠原蛋白相關的反應常數。利用無因次參數分析實驗的過程，以及探討各無因次參數對於博登量測器實驗的影響。本文發現考慮細胞的沈積現象時，因為沈積效應使得受體與趨向因子之間的反應產生延遲，Lapidus-Schiller 方程式所假設的細胞受體的準靜態會產生誤差，使用包含受體反應的完整數學模型，方能較準確的描述博登量測器的化學趨向實驗。Cell migration has various effects on the biological phenomena, such as wound healing, metastasis, and invasion. It is even involved in embryogenesis. Cell migration is one of the most important processes in physiology and pathology. The Boyden chamber can provide a stable gradient distribution and is commonly used to estimate cell motility. A Boyden chamber assay can be used to easily determine the chemotaxis of various chemicals.In this study, we examined the response of placenta-derived multipotent cells (PDMCs) on the collagen type I. We used a Boyden chamber to estimate the chemotactic responses of the cells to Type I collagen, and determined the integrins on the cell membrane using a flow cytometer. We concurrently developed a mathematical model to investige the process of the chemotaxis experiment that includes the chemoattractant transpont in the Boyden chamber assay. In addition, we used the Lapidus-Schiller equation to model cells’ random walk and chemotactic motility that combined with the cell sedimentation in the upper well of the Boyden chamber. Furthermore, we used a more detailed mathematical model to describe the chemotactic response. The response between the receptor and the chemoattratant was used to simulate chemotactic migration. Results show that once cell sedimentation is involved, the assumption of a quasi-steady receptor distribution by the Lapidus-Schiller equation may be invalid for the Boyden chamber assay. This is because the formation of the chemical-receptor complexes is profoundly delayed by the process of cell sedimentation in the upper well of the Boyden chamber.
