标题： 模拟振荡性微管聚合 显示英文标题

标题： Modeling oscillatory Microtubule--Polymerization

摘要： 微管的聚合在生物细胞中是普遍存在的，在某些条件下它会随时间产生振荡。 这里分析了简单的反应模型，这些模型能够捕捉到这种振荡以及微管的长度分布。 我们假设反应条件在多个振荡周期内是稳定的，并且在这些模型中，导致持续振荡的微管聚合的是一个霍普夫分支。 推导出了分岔阈值和振荡频率的解析表达式，以反应速率为依据，并给出了它们参数依赖性的典型趋势。 既包括一个依赖于{\it 三磷酸鸟苷} (GTP) 结合的微管蛋白二聚体密度的灾难率，也包括如缩回微管的解聚或寡聚物的衰变等延迟反应，都支持振荡。 当微管蛋白二聚体浓度低于阈值时，如模型方程的数值解所示，在达到稳定状态的路径上，振荡的微管聚合会暂时发生。 接近阈值时，推导出一个所谓的振幅方程，并表明微管振荡的分支是超临界。 显示英文摘要

摘要： Polymerization of microtubules is ubiquitous in biological cells and under certain conditions it becomes oscillatory in time. Here simple reaction models are analyzed that capture such oscillations as well as the length distribution of microtubules. We assume reaction conditions that are stationary over many oscillation periods, and it is a Hopf bifurcation that leads to a persistent oscillatory microtubule polymerization in these models. Analytical expressions are derived for the threshold of the bifurcation and the oscillation frequency in terms of reaction rates as well as typical trends of their parameter dependence are presented. Both, a catastrophe rate that depends on the density of {\it guanosine triphosphate} (GTP) liganded tubulin dimers and a delay reaction, such as the depolymerization of shrinking microtubules or the decay of oligomers, support oscillations. For a tubulin dimer concentration below the threshold oscillatory microtubule polymerization occurs transiently on the route to a stationary state, as shown by numerical solutions of the model equations. Close to threshold a so--called amplitude equation is derived and it is shown that the bifurcation to microtubule oscillations is supercritical.