运动细胞初始极化阶段胞内信号分子双向积聚的分子机制及动态数值模拟

真核细胞（Eukaryotes）,如盘基网柄菌细胞（Dictyo stelium）和白细胞（Leukocyte）等,受到前方传来的外信号刺激后,胞内物质发生两种方向相反的运动：胞质中与质膜结合的磷酸激酶PI3K及其在质膜上的生成物磷脂酰肌醇-3,4,5-三磷酸PI（3,4,5）P3以向前扩散的方式积聚到前沿;而胞质中与质膜结合的磷酸酶PTEN及其在质膜上的生成物磷脂酰肌醇-4,5-双磷酸PI（4,5）P2以向后扩散的方式积聚到质膜的后边.通过这种＂双向积聚＂,细胞形成头部和尾部,并在前沿生出伪足,完成初始极化.本文根据已知的实验,分析了＂双向积聚＂的分子机制,建立了相应的数学模型,通过数值模拟加以分析.以胞内被激活的小G蛋白（Rac）为触发信号,其梯度与外信号场的梯度一致;PI3K和PTEN作为调控因子,PI（3,4,5）P3和PI（4,5）P2作为标识细胞极化的信号分子,它们的浓度变化由一组耦合的非稳态二维反应-扩散方程描述.该反应-扩散体系源项中包含：PI（3,4,5）P3对PI3K,PI（4,5）P2对PTEN的识别和结合过程,是由蒙特-卡诺（Monte-Carlo）法处理;质膜结合态PI3K和PTEN对PI（3,4,5）P3和PI（4,5）P2施加的酶催化作用,由Michaelis-Menten动力学过程描述.反应-扩散方程组采用格子Boltzmann方法进行数值求解.数值试验显示,产生＂双向积聚＂的关键是受外信号梯度刺激后的胞内信号分子相互激发或抑制所形成的正反馈或负反馈回路：给细胞质膜头部一个较高的Rac激活率,Rac→PI3K？PI（3,4,5）P3将形成短程正反馈回路（亦即＂局部激励＂）,引起PI3K和PI（3,4,5）P3快速在细胞头部积聚;头部PI（3,4,5）P3增多,限制了PTEN与PI（4,5）P2结合,使得PI（3,4,5）P3？PTEN→PI（4,5）P2形成长程负反馈回路（亦即＂全局抑制＂）;引起PTEN和PI（4,5）P2慢慢在细胞尾部积聚.同时发现,PI3K和PTEN含量对细胞极化有明显的影响,并存在使细胞正确极化的最佳值.

Molecular mechanisms and dynamic simulations of bipolarization of chemotactic cells

Some eukaryotic cells, such as Dictyostelium and Leukocyte, are chemotactic. As a response of the cell to extracellular attractants that spread from the front, a bidirectional material movement occurs in the cell： an enzyme PI3K and its product PI（3,4,5）P3 （Phosphatidylinositol 3,4,5-trisphosphate） in plasma membrane diffuse forward and aggregate in the front edge, while PTEN （A degrading enzyme of PI（3,4,5）P3） and its product PI（4,5）P2 （Pho- sphatidylinositol 4,5-bisphosphate） run in the opposite way, which forms a bipolarization. To interpret this bipolarization phenomenon, a mathematic model was constructed based on the principle of ＂local excitation and global inhibitation＂ as well as the mechanism of positive/negative feedback in signal transduction. The activated Rac was employed as a trigger signal, and the evolution of PI（3,4,5）P3 and PI（4,5）P2 along with the activation and inhibitation of enzymes （i.e., PI3K, PTEN） was described by a set of coupled transient diffusion-reaction equations, being simulated by a lattice Boltzmann method. The source terms in the diffusion-reaction equations include the stochastic interactions between the intracellular signalation molecules （i.e., PI3K, PI（3,4,5）P3）, being simulated by a Monte-Carlo method according to the Michaelis-Menten catalytic kinetics. The simulation results show that the bipolarization is governed by a short-range positive feedback loop： Rac→PI3K←→ PI（3,4,5）P3, and a long-range negative feedback loop： PI（3,4,5）P3 → PTEN→PI（4,5）P2, which is a presentation of ＂local excitation and global inhabitation＂. In addition, it is found that the bipolarization rate is dependent on the total average concentration of PI3K or PTEN, and the optimum is 0.07 ktmol/L for the rapidest bipolarization.