以數學模型解釋腫瘤壞死因子引起之細胞存活及細胞凋亡傳遞路徑之動態變化

Abstract

腫瘤壞死因子(TNFα)於決定細胞凋亡(apoptosis)或存活的命運中扮演著重要角色。經由腫瘤壞死因子受體的激活，可導致IIa族複合蛋白(Complex IIa)的形成，並進一步引起第八及第三凋亡蛋白酶(Caspase-8 / Caspase-3)的活化與伴隨而來的細胞凋亡。此外活化的腫瘤壞死因子受體可以增加I族複合蛋白(Complex I)的形成，並能導致與核因子活化B細胞κ輕鏈增強子(NF-κB) 相關或不相關的細胞存活訊息傳遞路徑的活化。因為腫瘤壞死因子能同時啟動細胞存活或凋亡的傳遞路徑，所以細胞如何在此刺激下決定細胞走向存活或凋亡是一個困難的問題。 我們使用常微分方程模型來闡明經由腫瘤壞死因子刺激引起的複雜訊息傳遞路徑。我們的數學模型可以模擬在腫瘤壞死因子刺激下不同細胞個存活概率、第八及第三凋亡蛋白酶活性變化及第三凋亡蛋白酶活性達到最高變化之一半值所需之時間的分佈。這個模型提供我們研究在不同環境下細胞凋亡如何被驅使或阻斷的定量分析基礎。參數敏感性試驗顯示，在低濃度的腫瘤壞死因子刺激下，與I族複合蛋白引起IκB kinase (IKK)活化及IKK引起之細胞質B淋巴细胞瘤-2 (Bcl-2c)活化相關之參數對於第三凋亡蛋白酶活化，扮演著重要的角色。我們引入治療指數來分析調整參數對於腫瘤壞死因子造成腫瘤細胞及正常組織細胞死亡的不同效應。這個模型能幫助我們更了解腫瘤壞死因子引起之細胞凋亡及細胞存活傳遞路徑，並且也可幫助我們挑選可應用於臨床治療之傳遞路徑目標。

TNFα plays an important role in determining the cell fate of apoptosis or survival. Activation of TNFR1 by TNFα can result in complex IIa proteins formation, and trigger the Caspase-8 and Caspase-3 activation with subsequent apoptosis. On the other hand, active TNFR1 induced via TNFα can increase the formation of complex I , and complex I can result in both pro-survival signals mediated by NF-κB-dependent or NF-κB-independent signals transduction pathways. Since TNFα mediated paathways can activate both survival and apoptosis pathways, it is difficult to see how the decision for apoptosis or survive is made. We constructed an ordinary differential equations (ODEs) based mathematical model to elucidate the complex signal transduction pathway induced via TNFα stimulation. Our model can reproduce the experimental observation of cell viability probability, Caspase-3 /Caspase-8 activity, and delay time distribution. The model provides us a quantitative base to study how apoptosis is initiated or blocked under different conditions. Parametric sensitivity test reveals that these parameters involving the complex I mediated IKK activation and IKK mediated cytoplasm Bcl-2 regulation play more important roles in Caspase-3 activity under lower TNFα stimulation. Inhibiting these pathways could lead to increased apoptosis of cells under lower TNFα stimulation. A therapeutic index was developed to analyze the likelihood to kill more malignant cells than normal cells in modifying parameters in the model. The current model enables us to better understand TNFα-mediated apoptosis and pro-survival pathway quantitatively and help to identify targets for therapeutic application.