Lohel Maiko, Ibrahim Bashar, Diekmann Stephan, Dittrich Peter
Bio Systems Analysis Group, Institute of Computer Science, Friedrich-Schiller-University, Jena, Germany.
Cell Cycle. 2009 Aug 15;8(16):2650-60. doi: 10.4161/cc.8.16.9383. Epub 2009 Aug 29.
The mitotic spindle assembly checkpoint (MSAC) is an important regulatory mechanism of the cell cycle, ensuring proper chromosome segregation in mitosis. It delays the transition to anaphase until all chromosomes are properly attached to the mitotic spindle by emitting a diffusible "wait anaphase"-signal from unattached kinetochores. Current models of the checkpoint disregard important spatial properties like localization, diffusion and realistic numbers of kinetochores. To allow for in silico studies of the dynamics of these models in a more realistic environment, we introduce a mathematical framework for quasi-spatial simulation of localized biochemical processes that are typically observed during checkpoint activation and maintenance. The "emitted inhibition" model of the MSAC by Doncic et al. (Proc Natl Acad Sci USA 2005; 102:6332-7) assumes instantaneous activation of the diffusible "wait anaphase"-signal upon kinetochore encounter. We modify this model to account for binding kinetics with finite rates and use the developed framework to determine the feasible range of the binding parameters. We find that for proper activation, the binding rate constant has to be fast and above a critical value. Furthermore, this critical value depends significantly on the amount of local binding sites at each kinetochore. The critical values lie in a physiological realistic regime (10(4)-10(6) M(-1)s(-1)). We also determine the feasible parameter range for fast checkpoint activation of the "Mad2 template" model, for which the kinetic parameters have recently been studied in vitro by Simonetta et al. (PLoS Biology 2009; 7:1000010). We find critical values for binding and catalysis rate constants, both significantly higher than the measured values. Our results suggest that yet unknown mechanisms at the kinetochores facilitate binding and catalysis in vivo. We conclude that quantitative models of the MSAC have to account for the limited availability of binding sites at kinetochores.
有丝分裂纺锤体组装检查点（MSAC）是细胞周期的一种重要调控机制，可确保有丝分裂过程中染色体的正确分离。它通过未附着的动粒发出可扩散的“等待后期”信号，延迟向后期的转变，直到所有染色体都正确附着到有丝分裂纺锤体上。当前的检查点模型忽略了诸如定位、扩散和实际动粒数量等重要的空间特性。为了在更真实的环境中对这些模型的动力学进行计算机模拟研究，我们引入了一个数学框架，用于对检查点激活和维持过程中通常观察到的局部生化过程进行准空间模拟。Doncic等人（《美国国家科学院院刊》2005年；102：6332 - 6337）提出的MSAC“发出抑制”模型假定动粒相遇时可扩散的“等待后期”信号会瞬间激活。我们对该模型进行修改，以考虑具有有限速率的结合动力学，并使用所开发的框架来确定结合参数的可行范围。我们发现，为实现正确激活，结合速率常数必须快速且高于临界值。此外，该临界值显著取决于每个动粒处局部结合位点的数量。临界值处于生理现实范围内（10⁴ - 10⁶ M⁻¹s⁻¹）。我们还确定了“Mad2模板”模型快速检查点激活的可行参数范围，最近Simonetta等人（《公共科学图书馆·生物学》2009年；7：e1000010）已在体外研究了该模型的动力学参数。我们找到了结合和催化速率常数的临界值，两者均显著高于测量值。我们的结果表明，动粒处尚未明确的机制在体内促进了结合和催化。我们得出结论，MSAC的定量模型必须考虑动粒处结合位点的有限可用性。
