Bagci E Z, Vodovotz Y, Billiar T R, Ermentrout G B, Bahar I
Department of Computational Biology, School of Medicine, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA.
Biophys J. 2006 Mar 1;90(5):1546-59. doi: 10.1529/biophysj.105.068122. Epub 2005 Dec 9.
We propose a mathematical model for mitochondria-dependent apoptosis, in which kinetic cooperativity in formation of the apoptosome is a key element ensuring bistability. We examine the role of Bax and Bcl-2 synthesis and degradation rates, as well as the number of mitochondrial permeability transition pores (MPTPs), on the cell response to apoptotic stimuli. Our analysis suggests that cooperative apoptosome formation is a mechanism for inducing bistability, much more robust than that induced by other mechanisms, such as inhibition of caspase-3 by the inhibitor of apoptosis (IAP). Simulations predict a pathological state in which cells will exhibit a monostable cell survival if Bax degradation rate is above a threshold value, or if Bax expression rate is below a threshold value. Otherwise, cell death or survival occur depending on initial caspase-3 levels. We show that high expression rates of Bcl-2 can counteract the effects of Bax. Our simulations also demonstrate a monostable (pathological) apoptotic response if the number of MPTPs exceeds a threshold value. This study supports our contention, based on mathematical modeling, that cooperativity in apoptosome formation is critically important for determining the healthy responses to apoptotic stimuli, and helps define the roles of Bax, Bcl-2, and MPTP vis-à-vis apoptosome formation.
我们提出了一种线粒体依赖性细胞凋亡的数学模型，其中凋亡小体形成过程中的动力学协同作用是确保双稳态的关键因素。我们研究了Bax和Bcl-2的合成与降解速率以及线粒体通透性转换孔（MPTP）的数量对细胞凋亡刺激反应的作用。我们的分析表明，协同凋亡小体形成是诱导双稳态的一种机制，比其他机制（如凋亡抑制蛋白（IAP）对caspase-3的抑制）诱导的双稳态更稳健。模拟预测了一种病理状态，即如果Bax降解速率高于阈值或Bax表达速率低于阈值，细胞将表现出单稳态的细胞存活。否则，细胞死亡或存活取决于初始caspase-3水平。我们表明，Bcl-2的高表达率可以抵消Bax的作用。我们的模拟还表明，如果MPTP的数量超过阈值，会出现单稳态（病理）凋亡反应。这项研究支持了我们基于数学建模的观点，即凋亡小体形成中的协同作用对于确定对凋亡刺激的健康反应至关重要，并有助于定义Bax、Bcl-2和MPTP相对于凋亡小体形成的作用。
